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3D modelling of single piles and pile groups

D-Pile Group

User Manual

D-P ILE G ROUP
3D modelling of single piles and pile groups

User Manual

Version: 16.1
Revision: 00
9 February 2016

D-P ILE G ROUP, User Manual

Published and printed by:
Deltares
Boussinesqweg 1
2629 HV Delft
P.O. 177
2600 MH Delft
The Netherlands

For sales contact:
telephone: +31 88 335 81 88
fax:
+31 88 335 81 11
e-mail:
sales@deltaressystems.nl
www:
http://www.deltaressystems.nl

telephone:
fax:
e-mail:
www:

+31 88 335 82 73
+31 88 335 85 82
info@deltares.nl
https://www.deltares.nl

For support contact:
telephone: +31 88 335 81 00
fax:
+31 88 335 81 11
e-mail:
support@deltaressystems.nl
www:
http://www.deltaressystems.nl

Copyright © 2016 Deltares
All rights reserved. No part of this document may be reproduced in any form by print, photo
print, photo copy, microfilm or any other means, without written permission from the publisher:
Deltares.

D-P ILE G ROUP, User Manual

ii

Deltares

Contents

Contents
1 General Information
1.1 Preface . . . . . . . . . . . . . . . . . . . . . . .
1.2 Features . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Calculation models and their advantages . .
1.2.2 Availability of options for the different models
1.2.3 When to use which model . . . . . . . . .
1.3 History . . . . . . . . . . . . . . . . . . . . . . .
1.4 Limitations . . . . . . . . . . . . . . . . . . . . .
1.5 Minimum System Requirements . . . . . . . . . .
1.6 Symbols, Units and Sign convention . . . . . . . .
1.7 Getting Help . . . . . . . . . . . . . . . . . . . .
1.8 Getting Support . . . . . . . . . . . . . . . . . . .
1.9 Deltares . . . . . . . . . . . . . . . . . . . . . .
1.10 Deltares Systems . . . . . . . . . . . . . . . . . .
1.11 On-line software (Citrix) . . . . . . . . . . . . . . .
2 Getting Started
2.1 Starting D-Pile Group . . . . . . . .
2.2 Main Window . . . . . . . . . . . .
2.2.1 The menu bar . . . . . . .
2.2.2 The icon bar . . . . . . . .
2.2.3 Top View Layout . . . . . .
2.2.4 Title panel . . . . . . . . .
2.2.5 Status bar . . . . . . . . .
2.3 Files . . . . . . . . . . . . . . . .
2.4 Tips and Tricks . . . . . . . . . . .
2.4.1 Keyboard shortcuts . . . . .
2.4.2 Exporting figures and reports
2.4.3 Copying part of a table . . .
3

General
3.1 File menu . . . . . . . . . . . . .
3.2 Tools menu . . . . . . . . . . . .
3.2.1 Program Options . . . . .
3.3 Help menu . . . . . . . . . . . .
3.3.1 Calculation Messages . .
3.3.2 Manual . . . . . . . . . .
3.3.3 Deltares Systems Website
3.3.4 Support . . . . . . . . . .
3.3.5 About D-Pile Group . . . .

4 Input
4.1 Project menu . . . . . . . .
4.1.1 Model . . . . . . .
4.1.2 Project Properties .
4.1.3 View Input File . . .
4.2 Soil menu . . . . . . . . . .
4.2.1 Soil Layers . . . . .
4.2.2 Soil Profiles . . . . .
4.2.3 Soil Interaction Model
4.3 Pile menu . . . . . . . . . .
4.3.1 Pile Types . . . . .
4.3.2 Pile Tip Curves . . .

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iii

D-P ILE G ROUP, User Manual

4.4

4.5

4.3.3 Pile Positions . . . . . . .
4.3.4 Pile Grid . . . . . . . . .
4.3.5 Pile Properties . . . . . .
4.3.6 Plasticity Factors . . . . .
4.3.7 Check Intersections . . . .
Cap menu . . . . . . . . . . . .
4.4.1 Cap Location . . . . . . .
4.4.2 Cap Mass . . . . . . . .
Loads menu . . . . . . . . . . .
4.5.1 Loads Cap . . . . . . . .
4.5.2 Loads Ship . . . . . . . .
4.5.3 Surface Loading Areas . .
4.5.4 Surface Loadings . . . . .
4.5.5 Soil Displacement Profiles
4.5.6 Soil Displacements . . . .

5 Calculation
5.1 Calculation Options . .
5.2 Start Calculation . . .
5.3 Calculation Messages
5.4 Batch Calculation . . .

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6 View Results
6.1 Report Selection . . . . . . .
6.2 Report . . . . . . . . . . . .
6.3 Calculation Messages . . . .
6.4 View Dump File . . . . . . . .
6.5 Top View . . . . . . . . . . .
6.6 Charts . . . . . . . . . . . .
6.7 Pile Force-Displacement Charts
6.8 Cap Plots . . . . . . . . . . .
6.9 PY Plots . . . . . . . . . . .
6.10 Ducbots . . . . . . . . . . .

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7 Tutorial 1: Laterally loaded single pile
7.1 Introduction . . . . . . . . . . . .
7.2 Project . . . . . . . . . . . . . .
7.2.1 Project Model . . . . . . .
7.2.2 Project Properties . . . .
7.3 Soil . . . . . . . . . . . . . . . .
7.3.1 Soil Layers . . . . . . . .
7.3.2 Soil Profiles . . . . . . . .
7.4 Pile . . . . . . . . . . . . . . . .
7.4.1 Pile Types . . . . . . . .
7.4.2 Pile Tip Curves . . . . . .
7.4.3 Pile Positions . . . . . . .
7.5 Cap . . . . . . . . . . . . . . . .
7.5.1 Cap Location . . . . . . .
7.6 Loads Cap . . . . . . . . . . . .
7.7 Calculation . . . . . . . . . . . .
7.7.1 Calculation Options . . . .
7.7.2 Start Calculation . . . . .
7.8 Results . . . . . . . . . . . . . .
7.8.1 Charts results . . . . . .

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7.9

7.8.2 P-Y curve plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

8 Tutorial 2: 4×4 pile group in homogeneous elastic soil
8.1 Introduction to the case . . . . . . . . . . . . . . .
8.2 Project Model and Properties . . . . . . . . . . . .
8.3 Soil Interaction Model . . . . . . . . . . . . . . . .
8.4 Pile . . . . . . . . . . . . . . . . . . . . . . . . .
8.4.1 Pile Types . . . . . . . . . . . . . . . . .
8.4.2 Pile Positions . . . . . . . . . . . . . . . .
8.4.3 Cap Location . . . . . . . . . . . . . . . .
8.5 Loads Cap . . . . . . . . . . . . . . . . . . . . .
8.6 Calculation and Results Top View Results . . . . . .
8.7 Conclusion . . . . . . . . . . . . . . . . . . . . .

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9 Tutorial 3: Pile plan analysis
9.1 Introduction to the case . .
9.2 Project . . . . . . . . . .
9.2.1 Project Model . . .
9.2.2 Project Properties
9.3 Soil . . . . . . . . . . . .
9.3.1 Soil Layers . . . .
9.3.2 Soil Profiles . . . .
9.4 Pile . . . . . . . . . . . .
9.4.1 Pile Types . . . .
9.4.2 Pile Tip Curves . .
9.4.3 Pile Positions . . .
9.5 Cap . . . . . . . . . . . .
9.5.1 Cap Location . . .
9.6 Loads Cap . . . . . . . .
9.7 Calculation and Results . .
9.7.1 Report Selection .
9.7.2 Report . . . . . .
9.7.3 Top View . . . . .
9.8 Conclusion . . . . . . . .

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10 Tutorial 4: Negative skin friction on single pile
111
10.1 Introduction to the case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
10.2 Loading on the pile head then development of negative skin friction . . . . . . 113
10.2.1 Project Model and Properties . . . . . . . . . . . . . . . . . . . . . 113
10.2.2 Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
10.2.3 Pile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
10.2.4 Cap Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
10.2.5 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
10.2.6 Calculation and Results . . . . . . . . . . . . . . . . . . . . . . . . 119
10.3 First development of negative skin friction followed by loading on the pile head 122
10.3.1 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
10.3.2 Calculation and Results . . . . . . . . . . . . . . . . . . . . . . . . 123
10.4 Mixed loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
10.4.1 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
10.4.2 Calculation and Results . . . . . . . . . . . . . . . . . . . . . . . . 127
10.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
11 Tutorial 5: Mono pile wind turbine foundation design, Dutch Standard
131
11.1 Introduction to the case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

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D-P ILE G ROUP, User Manual

11.2 Project Model and Properties . . . . . . . . . . . . . . . . .
11.3 Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.3.1 Soil Layers . . . . . . . . . . . . . . . . . . . . . .
11.3.2 Soil Profiles . . . . . . . . . . . . . . . . . . . . . .
11.4 Pile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.4.1 Pile Types . . . . . . . . . . . . . . . . . . . . . .
11.4.2 Pile Tip Curves . . . . . . . . . . . . . . . . . . . .
11.4.3 Pile Positions . . . . . . . . . . . . . . . . . . . . .
11.5 Cap Location . . . . . . . . . . . . . . . . . . . . . . . . .
11.6 Loads Cap . . . . . . . . . . . . . . . . . . . . . . . . . .
11.7 Calculation at Serviceability Limit State . . . . . . . . . . . .
11.7.1 Results at SLS for pile type 1 . . . . . . . . . . . . .
11.7.2 Results at SLS for pile type 2 . . . . . . . . . . . . .
11.8 Calculation at Ultimate Limit State . . . . . . . . . . . . . . .
11.8.1 Design values at ULS for material properties and loads
11.8.2 Results at ULS for pile type 1 . . . . . . . . . . . . .
11.8.3 Results at ULS for pile type 2 . . . . . . . . . . . . .
11.9 Verification of the horizontal bearing capacity . . . . . . . . .
11.10 Verification of the vertical bearing capacity . . . . . . . . . .
11.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . .

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12 Tutorial 6: Concept check of 6 piles offshore wind turbine foundation
12.1 Introduction to the case . . . . . . . . . . . . . . . . . . . . . . .
12.2 Project Model and Properties . . . . . . . . . . . . . . . . . . . .
12.3 Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.1 Soil Layers . . . . . . . . . . . . . . . . . . . . . . . . .
12.3.2 Soil Profiles . . . . . . . . . . . . . . . . . . . . . . . . .
12.4 Pile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4.1 Pile Types . . . . . . . . . . . . . . . . . . . . . . . . .
12.4.2 Pile Tip Curves . . . . . . . . . . . . . . . . . . . . . . .
12.4.3 Pile Positions . . . . . . . . . . . . . . . . . . . . . . . .
12.5 Cap Location . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.6 Loads Cap . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.7 Calculation and Results . . . . . . . . . . . . . . . . . . . . . . .
12.7.1 Top View Results . . . . . . . . . . . . . . . . . . . . . .
12.7.2 Charts Results . . . . . . . . . . . . . . . . . . . . . . .
12.7.3 Cap-plots Results . . . . . . . . . . . . . . . . . . . . . .
12.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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13 Tutorial 7: Collision of a ship against a pile
13.1 Introduction to the case . . . . . . . .
13.2 Project Model and Properties . . . . .
13.3 Soil . . . . . . . . . . . . . . . . . .
13.3.1 Soil Layers . . . . . . . . . .
13.3.2 Soil Profiles . . . . . . . . . .
13.4 Pile . . . . . . . . . . . . . . . . . .
13.4.1 Pile Types . . . . . . . . . .
13.4.2 Pile Tip Curves . . . . . . . .
13.4.3 Pile Positions . . . . . . . . .
13.5 Cap . . . . . . . . . . . . . . . . . .
13.5.1 Cap Location . . . . . . . . .
13.5.2 Cap Mass . . . . . . . . . .
13.6 Loading Parameters of Ship . . . . . .
13.7 Calculation and Results . . . . . . . .

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13.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
14 Tutorial 8: 3-piles group analysis using four different models
14.1 Introduction to the case . . . . . . . . . . . . . . . . . .
14.2 Calculation with the Cap model . . . . . . . . . . . . . .
14.2.1 Project Model . . . . . . . . . . . . . . . . . . .
14.2.2 Project Properties . . . . . . . . . . . . . . . .
14.2.3 Soil Layers . . . . . . . . . . . . . . . . . . . .
14.2.4 Soil Profiles . . . . . . . . . . . . . . . . . . . .
14.2.5 Pile Types . . . . . . . . . . . . . . . . . . . .
14.2.6 Pile Tip Curves . . . . . . . . . . . . . . . . . .
14.2.7 Pile Positions . . . . . . . . . . . . . . . . . . .
14.2.8 Cap Location . . . . . . . . . . . . . . . . . . .
14.2.9 Loads Cap . . . . . . . . . . . . . . . . . . . .
14.2.10 Calculation and Results . . . . . . . . . . . . . .
14.3 Calculation with the Plasti-Poulos model . . . . . . . . .
14.3.1 Project Model and Properties . . . . . . . . . . .
14.3.2 Soil Interaction Model . . . . . . . . . . . . . . .
14.3.3 Pile Positions . . . . . . . . . . . . . . . . . . .
14.3.4 Plasticity Factors . . . . . . . . . . . . . . . . .
14.3.5 Check of the calculated plasticity factors . . . . .
14.3.6 Calculation and Results . . . . . . . . . . . . . .
14.4 Calculation with the Cap soil interaction model . . . . . .
14.4.1 Project Model and Properties . . . . . . . . . . .
14.4.2 Soil Interaction Model . . . . . . . . . . . . . . .
14.4.3 Calculation and Results . . . . . . . . . . . . . .
14.5 Calculation with the Cap layered soil interaction model . .
14.5.1 Project Model and Properties . . . . . . . . . . .
14.5.2 Soil Interaction Model . . . . . . . . . . . . . . .
14.5.3 Calculation and Results . . . . . . . . . . . . . .
14.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . .

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188
190
192
192
193
193
194
194
194
195
196

15 Soil behavior
15.1 Lateral P-Y curves . . . . . . . . . . . . . . . . . . . . . . .
15.1.1 P-Y curves for clay and static lateral loads (API) . . . .
15.1.2 P-Y curves for clay and cyclic lateral loads (API cyclic) .
15.1.3 P-Y curves for sand and static lateral loads (API) . . . .
15.1.4 P-Y curves for sand and cyclic lateral loads (API Cyclic)
15.1.5 P-Y curves for undrained sand (API Undrained) . . . . .
15.2 Axial T-Z curves . . . . . . . . . . . . . . . . . . . . . . . . .
15.2.1 T-Z curves for sand and clay (API) . . . . . . . . . . .
15.2.2 T-Z curves for sand (Cone) . . . . . . . . . . . . . . .
15.2.3 T-Z curves for clay (Ratio) . . . . . . . . . . . . . . . .
15.3 Pile tip curves Pile Tip Curves . . . . . . . . . . . . . . . . .
15.3.1 Pile tip curve according to API . . . . . . . . . . . . .
15.3.2 Pile tip curves according to the Dutch Code NEN . . . .

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199
199
199
200
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204
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205
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207
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208
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16 Calculation models
16.1 Cap model . . . . . . . . . . . . . . . . . . . . .
16.2 Poulos model . . . . . . . . . . . . . . . . . . . .
16.3 Plasti-Poulos model . . . . . . . . . . . . . . . . .
16.3.1 Introduction . . . . . . . . . . . . . . . . .
16.3.2 Plasticity and single pile behavior . . . . . .
16.3.3 Introduction of plasticity in the Poulos model

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211
211
212
212
212
213
213

Deltares

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vii

D-P ILE G ROUP, User Manual

16.3.4 Implementation in D-Pile Group . . . . . . . . .
16.3.5 Special considerations when using Plasti-Poulos
16.4 Cap soil interaction model . . . . . . . . . . . . . . . .
16.5 Cap layered soil interaction model . . . . . . . . . . . .
16.6 Dynamic model . . . . . . . . . . . . . . . . . . . . .

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214
215
216
218
219

17 Benchmarks

221

Bibliography

223

viii

Deltares

List of Figures

List of Figures
1.1
1.2
1.3
1.4
1.5
1.6

Force-Displacement relation between pile and surrounding soil
Features in D-Pile Group . . . . . . . . . . . . . . . . . . .
Right-handed co-ordinate system . . . . . . . . . . . . . . .
Deltares Systems website (www.deltaressystems.com) . . . .
Support window, Problem Description tab . . . . . . . . . . .
Send Support E-Mail window . . . . . . . . . . . . . . . . .

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. 2
. 3
. 8
. 9
. 10
. 10

2.1
2.2
2.3
2.4
2.5
2.6
2.7

Modules window . . . . . . . . . . . . . . . . . . . . . .
D-Pile Group main window . . . . . . . . . . . . . . . . .
Menu bar . . . . . . . . . . . . . . . . . . . . . . . . . .
Icon bar . . . . . . . . . . . . . . . . . . . . . . . . . . .
Top View Layout window . . . . . . . . . . . . . . . . . .
Title panel and Status bar at the bottom of the main window
Selection of different parts of a table using the arrow cursor .

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13
14
14
15
16
17
19

3.1
3.2
3.3
3.4
3.5
3.6

Program Options window, View tab . .
Program Options window, General tab
Program Options window, Locations tab
Program Options window, Modules tab
Calculation Messages window . . . .
About window . . . . . . . . . . . .

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22
22
23
24
25
26

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
4.25
4.26
4.27
4.28
4.29
4.30
4.31

Model window . . . . . . . . . . . . . . . . . . . . . . . . . .
Project Properties window, Identification tab . . . . . . . . . . .
Identification bottom part when printing charts . . . . . . . . . .
Project Properties window, View Layout tab . . . . . . . . . . . .
Project Properties window, Graph Settings tab . . . . . . . . . .
Soil Layers window, Soil type sub-window . . . . . . . . . . . . .
Soil Layers window (Sand) . . . . . . . . . . . . . . . . . . . .
Soil Layers window (Clay) . . . . . . . . . . . . . . . . . . . . .
Soil Layers window (P-Y Soil) . . . . . . . . . . . . . . . . . . .
Soil Layers window (No Soil) . . . . . . . . . . . . . . . . . . .
Soil Profiles window . . . . . . . . . . . . . . . . . . . . . . .
Soil Profiles window, drop down list of available soil layers . . . . .
Soil Interaction Model window (Poulos model) . . . . . . . . . .
Soil Interaction Model window (Plasti-Poulos model) . . . . . . .
Soil Interaction Model window (Cap soil interaction model) . . . .
Soil Interaction Model window (Cap layered soil interaction model)
Pile Types window for Wood pile . . . . . . . . . . . . . . . . .
Pile Types window for Steel pile . . . . . . . . . . . . . . . . . .
Pile Types window for Concrete round pile . . . . . . . . . . . .
Pile Types window for Concrete square pile . . . . . . . . . . . .
Pile Types window for User specified pile . . . . . . . . . . . . .
Pile Tip Curves window . . . . . . . . . . . . . . . . . . . . . .
Pile Positions window . . . . . . . . . . . . . . . . . . . . . . .
Pile Grid window . . . . . . . . . . . . . . . . . . . . . . . . .
Properties of Pile 1 window . . . . . . . . . . . . . . . . . . . .
Plasticity Factors window . . . . . . . . . . . . . . . . . . . . .
Calculate Plasticity-Poulos Factor Curves window . . . . . . . . .
Check Intersections window . . . . . . . . . . . . . . . . . . . .
Cap Location window . . . . . . . . . . . . . . . . . . . . . . .
Cap Mass window . . . . . . . . . . . . . . . . . . . . . . . .
Loads Cap window . . . . . . . . . . . . . . . . . . . . . . . .

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27
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31
31
33
34
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35
35
36
37
37
38
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39
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40
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41
42
44
45
46
46
47
47
48
48

Deltares

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ix

D-P ILE G ROUP, User Manual

4.32
4.33
4.34
4.35
4.36

Loading Parameters of Ship window
Surface Loading Areas window . . .
Surface Loadings window . . . . . .
Soil Displacement Profiles window .
Soil Displacements window . . . . .

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49
50
50
51
52

5.1
5.2
5.3
5.4
5.5
5.6
5.7

Calculation Options window . . . . . . . . . . . . .
Calculation window . . . . . . . . . . . . . . . . .
Error window . . . . . . . . . . . . . . . . . . . .
Calculation Messages window . . . . . . . . . . .
Run window . . . . . . . . . . . . . . . . . . . .
Start Batch Calculation window . . . . . . . . . . .
Calculation progress window during batch calculation

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53
54
54
55
55
56
56

6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12

Report Selection window . . . . . . . . . . . . . .
Report window . . . . . . . . . . . . . . . . . . .
Calculation Messages window . . . . . . . . . . .
Dump File window . . . . . . . . . . . . . . . . .
Top View Results window . . . . . . . . . . . . . .
Displacement, force and moment results for pile 1 . .
Charts window in X and Y directions . . . . . . . .
Pile Force-Displacement Charts window . . . . . .
Cap-plots window . . . . . . . . . . . . . . . . . .
P-Y plots window . . . . . . . . . . . . . . . . . .
Ducbots window . . . . . . . . . . . . . . . . . .
Drop down list of charts available in Ducbots window

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57
58
59
60
61
61
62
63
64
65
65
66

7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.14
7.15
7.16
7.17
7.18
7.19

Soil profile and pile position (Tutorial 1) . . . . .
D-Pile Group main window . . . . . . . . . . .
Model window . . . . . . . . . . . . . . . . .
Functioning of the Cap model for Tutorial 1 . . .
Project Properties window, Identification tab . .
Soil Layers window . . . . . . . . . . . . . . .
Soil Profiles window . . . . . . . . . . . . . .
Pile Types window . . . . . . . . . . . . . . .
Pile Tip Curves window . . . . . . . . . . . . .
Pile Positions window . . . . . . . . . . . . . .
Cap Location window . . . . . . . . . . . . . .
Loads Cap window . . . . . . . . . . . . . . .
Calculation Options window . . . . . . . . . . .
Calculation window . . . . . . . . . . . . . . .
Save As window . . . . . . . . . . . . . . . .
Charts window in the X” direction . . . . . . . .
Chart Data window, Displacement tab . . . . . .
P-Y plots window in the X direction at top level .
Calculated and measured bending moment along
test . . . . . . . . . . . . . . . . . . . . . . .

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69
69
70
70
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8.2
8.3
8.4
8.5
8.6
8.7

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the
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4 × 4 pile group in a two-layered elastic soil. (Tutorial 2)
Functioning of the Poulos model for Tutorial 2 . . . . . .
Model window . . . . . . . . . . . . . . . . . . . . .
Soil Interaction Model window . . . . . . . . . . . . .
Pile Types window . . . . . . . . . . . . . . . . . . .
Pile Grid window . . . . . . . . . . . . . . . . . . . .
Pile Positions window . . . . . . . . . . . . . . . . . .

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81
82
83
83
84
85
85

Deltares

List of Figures

8.8
8.9
8.10
8.11
8.12
8.13

Top View Layout window . . . . . . .
Loads Cap window . . . . . . . . . .
Top View Results window, lateral force
Top View Results window, axial force .
Top View Results window, settlement .
Top View Results window, deflection .

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86
87
87
88
88
89

9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
9.11
9.12
9.13
9.14
9.15
9.16
9.17
9.18
9.19
9.20
9.21
9.22
9.23

3D view of the 16 piles connected to a cap (Tutorial 3) . . . . . . . .
Top view of the pile positions and the CPT location (Tutorial 3) . . . .
Soil profile and piles position (Tutorial 3) . . . . . . . . . . . . . . .
Functioning of the Cap model for Tutorial 3 . . . . . . . . . . . . . .
Model window . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Project Properties window, Identification tab . . . . . . . . . . . . .
Soil Layers window, properties of layer  . . . . . . . . . .
Soil Profiles window . . . . . . . . . . . . . . . . . . . . . . . . .
Top View Layout window after entering soil profile . . . . . . . . . . .
Pile Types window . . . . . . . . . . . . . . . . . . . . . . . . . .
Pile Tip Curves window . . . . . . . . . . . . . . . . . . . . . . . .
Pile Grid window . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pile Positions window after using the Pile Grid option . . . . . . . . .
Pile Positions window after corrections . . . . . . . . . . . . . . . .
Top View Layout window after entering the piles group . . . . . . . .
Cap Location window . . . . . . . . . . . . . . . . . . . . . . . . .
Loads Cap window . . . . . . . . . . . . . . . . . . . . . . . . . .
Report Selection window . . . . . . . . . . . . . . . . . . . . . . .
Report window, Pile top Results at Load step 10 section . . . . . . .
Pile 1 in the global (X, Y, Z) and local (X”, Y”, Z”) co-ordinates systems
Top View window, Lateral force in the Z direction at the pile head . . .
Top View window, Lateral force in the Y direction at the pile head . . .
Top View window, Bending moment around the Z direction . . . . . .

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108
109

10.1 Single pile under seaport crane on a quay composed of sand fill (Tutorial 4) . . 111
10.2 Functioning of the Cap model for Tutorial 4 . . . . . . . . . . . . . . . . . . 112
10.3 Soil Layers window, properties of Layer AW . . . . . . . . . . . . . . . . . . 114
10.4 Soil Profiles window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
10.5 Pile Types window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
10.6 Pile Tip Curves window . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
10.7 Pile Positions window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
10.8 Loads Cap window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
10.9 Soil Displacement Profiles window . . . . . . . . . . . . . . . . . . . . . . 118
10.10 Soil Displacements window . . . . . . . . . . . . . . . . . . . . . . . . . . 119
10.11 Cap-plots window, pile head load-settlement curve in the Y-direction (Tutorial-4a)120
10.12 Chart Data window, Displacement tab for the pile head load-settlement curve
in the Y-direction (Tutorial-4a) . . . . . . . . . . . . . . . . . . . . . . . . . 121
10.13 Charts window, Displacement-Axial Force-Reaction along the shaft pile in Ydirection for load step 20 (Tutorial-4a) . . . . . . . . . . . . . . . . . . . . . 121
10.14 Loads Cap window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
10.15 Soil Displacements window . . . . . . . . . . . . . . . . . . . . . . . . . . 123
10.16 Cap-plots window, pile head load-settlement curve in the Y-direction (Tutorial4b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
10.17 Charts window, Displacement-Axial Force-Reaction along the shaft pile in Ydirection for load step 20 (Tutorial-4b) . . . . . . . . . . . . . . . . . . . . . 125
10.18 Loading schedule (Tutorial 4c) . . . . . . . . . . . . . . . . . . . . . . . . 126
10.19 Loads Cap window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

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10.20 Soil Displacements window . . . . . . . . . . . . . . . . . . . . . . . . . . 127
10.21 Cap-plots window, pile head load-settlement curve in the Y-direction (Tutorial-4c)128
10.22 Charts window, Displacement-Axial Force-Reaction along the shaft pile in Ydirection for load step 590 (Tutorial-4c) . . . . . . . . . . . . . . . . . . . . 129

xii

11.1 Wind turbine on mono pile foundation (Tutorial 5) . . . . . . . . . . . . . .
11.2 Determination of the soil profile from the CPT results . . . . . . . . . . . .
11.3 Functioning of the Cap model for Tutorial 5 . . . . . . . . . . . . . . . . .
11.4 Soil Layers window . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5 Soil Profiles window . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.6 Pile Types window . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.7 Pile Tip Curves window . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.8 Pile Positions window for pile type 1 . . . . . . . . . . . . . . . . . . . . .
11.9 Loads Cap window, design loads for Serviceability Limit State . . . . . . . .
11.10 Charts window, results for Serviceability Limit State at load-step 10 for pile
type 1 (Tutorial-5a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.11 Cap-plots window, pile head load-displacement curve in the X-direction for
Serviceability Limit State for pile type 1 (Tutorial-5a) . . . . . . . . . . . . .
11.12 Charts window, results for Serviceability Limit State at load-step 10 for pile
type 2 (Tutorial-5b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.13 Cap-plots window, pile head load-displacement curve in the X-direction for
Serviceability Limit State for pile type 2 (Tutorial-5b) . . . . . . . . . . . . .
11.14 Charts window, results for Ultimate Limit State at load-step 10 for pile type 1
(Tutorial-5c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.15 Cap-plots window, pile head load-displacement curve in the X-direction for
Ultimate Limit State for pile type 1 (Tutorial-5c) . . . . . . . . . . . . . . .
11.16 Charts window, results for Ultimate Limit State at load-step 10 for pile type 2
(Tutorial-5d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.17 Cap-plots window, pile head load-displacement curve in the X-direction for
Ultimate Limit State for pile type 2 . . . . . . . . . . . . . . . . . . . . . .
11.18 Representation of the shaft friction and the tip resistance in case of nonplugging pile (a) and plugging pile (b) for a tubular pile . . . . . . . . . . .

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12.1 Offshore wind turbine on a 6 piles foundation (Tutorial 6) . . . . . . . . . .
12.2 Top view of the 6 piles position (Tutorial 6) . . . . . . . . . . . . . . . . .
12.3 Functioning of the Cap model for Tutorial 6 . . . . . . . . . . . . . . . . .
12.4 Soil Layers window . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.5 Soil Profiles window . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.6 Pile Types window . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.7 Pile Positions window . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.8 Loads Cap window . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.9 Top View Results window, calculated horizontal displacements at pile heads
12.10 Top View Results window, calculated vertical displacements at pile heads . .
12.11 Charts window, lateral displacements, bending moments and shear forces for
pile 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.12 Charts window, vertical displacement, axial force and soil resistance for pile 4
12.13 Cap-plots window, horizontal force versus horizontal cap-displacement . . .
12.14 Cap-plots window, vertical force versus vertical cap-displacement . . . . . .
12.15 Cap-plots window, moment versus cap-rotation . . . . . . . . . . . . . . .

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161
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163

13.1
13.2
13.3
13.4

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168
169

Collision of a ship against a pile (Tutorial 7) . .
Functioning of the Dynamic model for Tutorial 7
Model window . . . . . . . . . . . . . . . .
Soil Layers window, properties of the clay layer

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List of Figures

13.5 Soil Layers window, properties of the sand layer . . . . . . .
13.6 Soil Profiles window . . . . . . . . . . . . . . . . . . . .
13.7 Pile Types window . . . . . . . . . . . . . . . . . . . . .
13.8 Pile Positions window . . . . . . . . . . . . . . . . . . . .
13.9 Cap Mass window . . . . . . . . . . . . . . . . . . . . .
13.10 Loading Parameters of Ship window . . . . . . . . . . . .
13.11 Ducbots window, Displacement-Force curve with filtering . .
13.12 Chart Data window for the filtered DisplacementForce curve
13.13 Ducbots window, Displacement-Force curve without filtering
13.14 Ducbots window, Time-Displacement curve . . . . . . . . .
13.15 Ducbots window, Time-Force curve . . . . . . . . . . . . .

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172
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174
174
175
175

Soil profile and pile group position (Tutorial 8) . . . . . . . . . . . . . . . .
Functioning of the Cap model for Tutorial 8a . . . . . . . . . . . . . . . .
Functioning of the Plasti-Poulos model for Tutorial 8b . . . . . . . . . . . .
Functioning of the Cap soil interaction model for Tutorial 8c . . . . . . . . .
Functioning of the Cap layered soil interaction model for Tutorial 8d . . . . .
Pile Positions window . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Loads Cap window . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Cap-plots window, pile head load-displacement curve in the X direction (Tutorial 8a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.9 Charts window, axial force along pile 3 (Tutorial 8a) . . . . . . . . . . . . .
14.10 Charts window, bending moment along pile 3 (Tutorial 8a) . . . . . . . . .
14.11 Soil Interaction Model window (Plasti-Poulos model) . . . . . . . . . . . .
14.12 Calculate Plasti-Poulos Factor Curves window . . . . . . . . . . . . . . .
14.13 Plasticity Factors window, Force-Displacement curve in the X direction . . .
14.14 Calculate Plasti-Poulos Factor Curves window . . . . . . . . . . . . . . .
14.15 Plasticity Factors window, Force-Displacement curve in the X direction . . .
14.16 Load-displacement curve for plastic behavior . . . . . . . . . . . . . . . .
14.17 Report window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.18 Calculate Plasti-Poulos Factor Curves window . . . . . . . . . . . . . . .
14.19 Plasticity Factors window, Force-Displacement curve in the X direction . . .
14.20 Report window (Tutorial 8b) . . . . . . . . . . . . . . . . . . . . . . . . .
14.21 Cap-plots window, pile head load-displacement curve in the X-direction (Tutorial 8b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.22 Soil Interaction Model window (Cap soil interaction model) . . . . . . . . .
14.23 Cap-plots window, pile head load-displacement curve in the X-direction (Tutorial 8c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.24 Soil Interaction Model window (Cap layered soil interaction model) . . . . .
14.25 Cap-plots window, pile head load-displacement curve in the X-direction (Tutorial 8d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.26 Pile head load-displacement curve in the X-direction for the different models

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185
186
187
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188
189
189
190
190
191

14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8

15.1
15.2
15.3
15.4
15.5
15.6
15.7

Modeling of the P-Y curve (API) for clay and static loading . . . . . .
Modeling of the P-Y curve (API cyclic) for clay and cyclic loading . . .
Coefficients C1 , C2 and C3 as function of the angle of internal friction
Modeling of the P-Y curve (API) for sand . . . . . . . . . . . . . . .
T-Z curve (API) for clay and sand . . . . . . . . . . . . . . . . . . .
Pile tip curve according to API . . . . . . . . . . . . . . . . . . . .
Pile tip curve according to the Dutch Code . . . . . . . . . . . . . .

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16.1 Force-displacement relation of a laterally loaded single pile . . . . . . . . . . 213
16.2 Collision of a ship against a pile . . . . . . . . . . . . . . . . . . . . . . . . 219

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List of Tables

List of Tables
2.1

Keyboard shortcuts for D-Pile Group . . . . . . . . . . . . . . . . . . . . . 18

7.1

Soil properties for Tutorial 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 68

9.1
9.2

Soil properties for Tutorial 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Determination of ε50 as a function of the undrained sheart strength su . . . . 94

10.1 Soil properties for Tutorial 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 112
11.1
11.2
11.3
11.4
11.5
11.6

Magnitude of the loads in normal and extreme conditions . . . . . . . . . . .
Soil properties for Tutorial 5 . . . . . . . . . . . . . . . . . . . . . . . . . .
Name and description of the four D-Pile Group input files for Tutorial 5 . . . .
Design values of soil properties for Ultimate Limit State according to NEN 6740
Design values of loads for Ultimate Limit State according to NEN 6740 . . . .
Comparison of the calculated and required minimum rotational stiffness for
both pile type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.7 Results of the calculation of ultimate vertical bearing capacity . . . . . . . . .
11.8 Comparison of the applied vertical load and the ultimate vertical bearing capacity for different combinations . . . . . . . . . . . . . . . . . . . . . . . .

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143
147
149
150

12.1 Loading data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
12.2 Soil properties for Tutorial 6 . . . . . . . . . . . . . . . . . . . . . . . . . . 153
13.1 Loading parameters of the ship . . . . . . . . . . . . . . . . . . . . . . . . 165
13.2 Soil properties for Tutorial 7 . . . . . . . . . . . . . . . . . . . . . . . . . . 167
14.1 Soil properties for Tutorial 8 . . . . . . . . . . . . . . . . . . . . . . . . . . 178
14.2 Pile-soil-pile interaction properties for Tutorial 8 . . . . . . . . . . . . . . . . 179
15.1 Determination of ε50 as a function of the undrained shear strength su . . . .
15.2 Values of k as function of the angle of internal friction ϕ . . . . . . . . . . .
15.3 Values of C1 , C2 , C3 inputted in D-Pile Group as function of the angle of
internal friction ϕ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.4 Values of Wpunt /Deq as function of the percentage of mobilized end bearing
capacity for different pile types (NEN 6743) . . . . . . . . . . . . . . . . .

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1 General Information
1.1

Preface
D-P ILE G ROUP (formerly known as MPile) enables the analysis of the three-dimensional behavior of single piles and pile groups, interacting via the pile cap and the soil, as a function
of loading. D-P ILE G ROUP offers for this purpose a unique combination of the internationally
accepted design rules of the API (American Petroleum Institute) and special soil interaction
models. One of the great benefits of D-P ILE G ROUP is that it combines several computational
models into one program. Each of these models has its own advantages, and switching from
one model to another is easy to do. This flexibility gives the user the opportunity to choose
between a fast and simple calculation and a more complex but more accurate calculation, in
a way that best suits his or her particular needs.

1.2

Features
D-P ILE G ROUP offers the following functionality:


















analysis of all pile types, both pre-defined standard or user-defined special piles;
pile sections with different properties;
options for inclined piles;
pile head fixed or hinged in the pile cap (clamped or freely rotating);
sand and clay layers, drained or undrained, with common input properties;
influence of the pile tip resistance;
load on the cap by moments, horizontal and vertical forces, rotations and displacements;
load by horizontal and vertical soil displacements;
effect of surcharge;
monotonous increasing loads, load reversal and repeated (cyclic) loads;
dynamic load by ship collision (Dynamic model);
multiple models for the interaction between piles via the soil;
graphical output of displacements, shear forces and moments in top view
graphs of cap displacements and rotations versus loading;
graphs of internal forces and soil reactions along the piles;
automatic generation of a calculation report with tables and graphs in rich text format.

Soil springs
D-P ILE G ROUP describes the relation between pile and surrounding soil by the use of lateral
(mostly horizontal) and axial (mostly vertical) vertical soil springs along the piles. D-P ILE G ROUP
determines the non-linear relation between the force and displacement on basis of a design
rule which can be selected by the user (e.g. API or NEN Dutch standard). The relationship
can also be supplied via user defined force-displacement curves.

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Figure 1.1: Force-Displacement relation between pile and surrounding soil

The design rules require only standard soil parameters for each layer, which can be determined from CPT results. The design rules differentiate between soil type (sand and clay) and
load type (drained, undrained and cyclic).
As an important feature, D-P ILE G ROUP always includes hysteresis in the load-displacement
model, if plasticity is involved. This means a different behavior during virgin loading, unloading
and reloading.
Soil interaction models
In D-P ILE G ROUP, the interaction between piles is not limited to interaction via the cap, but also
three-dimensional interaction between piles via the soil can be taken into account. All these
interaction models are based on linear elasticity. They can be combined with the previously
mentioned non-linear relations between pile and soil. This way, D-P ILE G ROUP achieves an
optimal balance between the accuracy required and the efficiency desired.

 Poulos. The classic analytical Poulos model (Poulos, 1980; Poulos and Davis, 1974;
Randolph, 1981, 1996) assumes homogeneous elastic soil and vertical piles. It determines elastic interaction effects from between all piles at pile head level.
 Plasti-Poulos. The Plasti-Poulos model introduces non-linearity in the Poulos model,
which accounts for the decrease of interaction effects at higher load levels. It is in some
ways comparable with the approach of Focht and Koch Focht Jr. and Koch (1973).
 Cap soil interaction. The Cap soil interaction model based on the Mindlin theory
(Mindlin (1936) and Mindlin (1953)) determines the interaction along complete piles,
assuming homogeneous elastic soil with optionally inclined piles for the pile-soil-pile
interaction. It uses nonlinear lateral, axial and pile tip springs for the pile-soil stiffness
and plasticity.
 Cap layered soil interaction. The Cap layered soil interaction model uses the Finite
Element Method to determine the interaction along complete piles and has as extension
to the Mindlin model the possibility to determine interaction in a layered elastic half
space.

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General Information

Figure 1.2: Features in D-Pile Group

1.2.1

Calculation models and their advantages
Poulos model
The Poulos model is a simple elastic model which can be used for a quick analysis of very
large pile groups. It uses the Poulos theory for pile head-soil-pile head interaction.
Plasti-Poulos model
The Plasti-Poulos model is an extension of the Poulos model. It needs more input data to
generate the appropriate non-linear soil springs which it uses to determine the nonlinear pile
head load-displacement behavior. Main advantage is that it models the decrease of interaction
effects at higher load levels and is able to do that for large pile groups. Because of this nonlinearity it requires more calculation time than the Poulos model.
Cap model
The Cap model is a robust and fast calculation model. It represents the ‘classical’ analysis
of piles on basis of p-y, t-z and end bearing (tip) curves. While it does not take into account
pile-soil-pile interaction, it is an extension of many common programs that analyze piles on
basis of p-y and t-z curves since the interaction between the piles through the pile cap is
modeled. It allows for the analysis of lateral soil movements and negative skin friction by the
introduction of prescribed soil displacements.
Cap soil interaction model
The Cap soil interaction model is an extension of the Cap model that incorporates a more
sophisticated pile-soil-pile interaction than the Poulos and Plasti-Poulos models. It is not as
fast as the above mentioned models, but it allows for the use of surface loads. Furthermore, it
takes the interaction-effects in the cross direction (perpendicular to the main loading direction)
into account.

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Cap layered soil inter. model
The Cap layered soil interaction model is a powerful calculation model based on finite element method. Unfortunately, the results of this calculation model exhibit occasional instability
effects. Therefore the use of this model is at this moment disabled in the commercial versions
of D-P ILE G ROUP until these issues are fully resolved.
Dynamic model
The Dynamic model is a dedicated calculation model for dynamic analysis of a collision of a
ship against the pile cap. It can be used for both single-pile and multi-pile dolphins

Pile-Soil-Pile
interaction

Dynamics

Displacement load

Surface loads

Inclined piles

Max. nr. of piles

Model
Poulos
Plasti-Poulos
Cap
Cap soil
interaction
Cap layered
soil interaction
Dynamic

Layered soil

Availability of options for the different models

Soil plasticity

1.2.2

No
Yes
Yes
Yes

No
Yes
Yes
Yes

Yes (2 layers)*
Yes (2 layers)*
No
Yes (1 layer)

No
No
No
No

No
No
Yes
No

No
No
No
Yes

No
No
Yes
Yes

200
200
≈ 75
≈ 25

Yes

Yes

Yes (layered)

No

No

No

Yes

≈ 25

Yes

Yes

No

Yes

No

No

Yes

≈ 75

*: The soil system for pile-soil-pile interaction consists of 1 homogenous layer over the length
of the pile and one layer below the pile tip.
1.2.3

When to use which model
Dynamic loading
If inertia effects are dominant in the reaction of the pile-group only the Dynamic model can be
used. It accounts for the inertia effects due to the mass of the cap and the piles and its loading
is restricted to a mass (ship) impacting the cap at a point, in a direction and at a speed which
can be selected by the user. It also incorporates special soil reaction models that account for
undrained lateral loading in sand.
Static loading
In case of static loading, all models excepting the Dynamic model can be used. The choice
depends principally on the distance between piles:

 For single pile analysis or pile group with large centre distances (i.e. > 10 to 12 D behind each other or > 4 to 6 D next to each other in loading direction), the Cap model is
recommended, since no pile-soil-pile interaction is taken into account in this model.
 For pile group with small centre distances (i.e. < 6 to 8 D behind each other or < 3 to
4 D next to each other in loading direction), one of the four following models must be used

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depending on the desired accuracy:
Poulos model, for first analyses, when only a few data are available or when the loads
are small and completely in the elastic range;
Plasti-Poulos model, for more accurate analyses compared to the Poulos model, in
particular when larger loads are imposed and the system starts to show nonlinearity
effects and possibly even pile failure;
Cap soil interaction model, for more accurate analysis compared to the Poulos and
Plasti-Poulos models, as non-uniform piles can be inputted and the soil-pile interaction
is taken into account by means of lateral and axial rules. Also when detailed data
about forces and moments along the length of the piles need to be known the Cap soil
interaction model is the model to use.
Cap layered soil interaction, for more accurate analysis compared to the Cap soil interaction model, as a different pile-soil-pile interaction stiffness can be defined for each
layer.

Special cases
In case of surface loading, only the Cap soil interaction model can be used. In case of soil
displacement, only the Cap model can be used.
1.3

History
D-P ILE G ROUP is formerly known as MPile until version 4.2. The first working version of the
program (MPile version 1.0), contained only the Cap model was released for internal use
within GeoDelft in 1993.
MPile version 2.0 (October 1995) was the first external release of MPile, containing the full
set of originally anticipated calculation models.
MPile version 2.1 of December 1995 contained new features have to improve the userinterface and the graphical and numerical output.
MPile version 2.2 of June 1996 made it possible to vary the magnitude of the load in succeeding load steps and to situate the cap centre outside the origin.
MPile version 3.1 of November 2000 was the first Windows version of MPile.
MPile version 3.2 of July 2001 contained a new model: Plasti-Poulos.
MPile version 3.7 of February 2003 included an improved iteration process for the PlastiPoulos model, improved input and output and separately licensed modules.
MPile version 4.1 of April 2005 included an improved user interface with tables to give a
better overview of the input data and enabling copy and paste functions. The user manual
was extended, including several tutorials.
MPile version 4.2.1 (February 2008). The FEM calculation has been improved. The number
of decimals for soil displacements is larger (from 2 to 3) in the input table. The number of
decimals in the input tables of PY-tables, TZ-tables and Pile tip curves is also larger. In the
Soil Layers window, with Soil Type "PY-Soil", the PY-tables and TZ-tables can be edited.
MPile version 4.2.2 (March 2009). For the Plasti-Poulos model, the determination of PlastiPoulos factors (Mz-Thetaz) for projects with a critical pile which has a free pile top is done
assuming a fixed pile top. It is now possible to enter values into the PY-tables for “PY-Soil” in

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the Soil Layers window.
MPile version 4.2.3 (October 2009). In case raking (skew) piles are loaded by settlement,
the transformation of global axis to the local system of the pile has been corrected. Free top
condition is now real free and not with a very low rotation stiffness. Cap loadings can be
entered with a higher precision.
D-P ILE G ROUP version 5.1 (2011). The program has been renamed into D-P ILE G ROUP. Batch
processing has been implemented, see section 5.4. The benchmarks of the Verification section of this manual are described in a separate document. The plasticity factors for Tutorial 8b
(Plasti-Poulos model) have been re-calculated (section 14.3.4).
D-P ILE G ROUP version 5.2 (November 2011). This version has a new (32-bits) calculation
kernel. Note that the transition to a new calculation kernel will result in small differences in
the outcome of existing projects. An extensive test of the new kernel with the benchmark set
shows that only in the case of the model Dynamic significant differences are encountered with
the previous version of D-P ILE G ROUP. These differences however occur only in a less relevant
part of the results and were considered acceptable. The program now fully function in 64-bits
Windows. Projects up to 3000 piles can be defined, dependent of selected calculation model
and internal memory. A documentation about the practical limits of the different calculation
models has been added.
D-P ILE G ROUP version 14.1 (July 2014). This version implements only the improvements on
the changes in the new licensing scheme.
D-P ILE G ROUP version 15.1 (April 2015). This version implements some improvements:

 To be able to review the spring stiffness of piles, a new type of charts is made available
(Pile Force - Displacement Charts); as with all charts, the data on which these charts
are base can be viewed in a table. From this table, the data can be exported to p.e.
Excel.
 A toggle button is implemented in the Top View Layout (Figure 2.5), to switch between
same scale for X and Y-axis and not same scale for X and Y-axis.
 The Help file is no more available; clicking on the Help button will open the User Manual
in which a search by specific word can be performed.
D-P ILE G ROUP version 16.1 (January 2016). With this version, license(s) can be borrowed for
a certain period allowing working without connection to the licence server (see Figure 3.4 for
more information).
1.4

Limitations
When working with D-P ILE G ROUP the following restrictions apply:

 The unit weight of water can not be changed, but is set to 9.81 kN/m2 Unit weight of
water.

 A horizontal groundwater level is assumed within each soil profile.
 The program does not support a sloping ground surface, but piles may be combined
with soil-profiles with different surface levels. Pile-soil-pile interaction effects however
are based on piles in a half space with a horizontal surface.
 No excess pore pressures can be applied, except by manually defining p-y curves.
 K0 , the coefficient of horizontal effective stress over vertical effective stress, is constant
with depth within each soil layer.
 Loads are static, except the dynamic load in the Dynamic model.

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 The Plasti-Poulos model allows no load reversal (only increasing loads).
 Loads/displacements, moments/rotations can only be applied to the top of the pile
through the pile cap.

 The pile is modeled as a linear elastic beam with compression and bending (no shearing), but may be build-up in sections with different dimensions and siffnesses.

 Single piles have no torsion resistance (pile groups however, do!).
 The availability of different options for different models is summarized in section 1.2.2.
 The numerical restrictions for the various calculation data will be discussed with the
relevant help topics.
1.5

Minimum System Requirements
System RequirementsThe following minimum system requirements are needed in order to run
and install the D-P ILE G ROUP software, either from CD or by downloading from the Deltares
Systems website via MS Internet Explorer:

 Operating systems:

     

    

Windows 2003,
Windows Vista,
Windows 7 – 32 bits
Windows 7 – 64 bits
Windows 8
 Hardware specifications:
1 GHz Intel Pentium processor or equivalent
512 MB of RAM
400 MB free hard disk space
SVGA video card, 1024 × 768 pixels, High colors (16 bits)
CD-ROM drive
Microsoft Internet Explorer version 6.0 or newer (download from www.microsoft.com)
To display the D-P ILE G ROUP Help texts properly, the Symbol TrueType font must be installed
on the system.
1.6

Symbols, Units and Sign convention
The program uses a right-handed Cartesian co-ordinate system (see Figure 1.3). The direction of the positive Y-axis is opposite the gravity direction, pointing upwards. Positive translations and rotation signs correspond with positive load and moment signs.

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Figure 1.3: Right-handed co-ordinate system

The symbols used in the program are shown in the table below.
Symbols

X, Y, Z
g
Cu
t
j
F
P
M
u
q
qc
M

Unit
[m]
[kN/m3 ]
[kN/m2 ]
[kN/m2 ]
[◦ ]
[kN]
[kN/m2 ]
[kNm]
[m]
[◦ ]
[kN/m2 ]
[kg]

Description
Co-ordinate
Volumetric weight
Undrained shear strength
Shear strength
Friction angle
Force
Pressure
Moment
Displacement
Rotation
Cone resistance
Mass

Note: In the input rotations have to be specified in degrees, in the output however they are in
radians. Note also that the cone resistance is inputted in kN/m2 and not in MN/m2
1.7

Getting Help
From the Help menu, choose the Manual option to open the User Manual of D-P ILE G ROUP in
PDF format. Here help on a specific topic can be found by entering a specific word in the Find
field of the PDF reader.

1.8

Getting Support
Support D-P ILE G ROUP Deltares Systems tools are supported by Deltares. A group of 70
people in software development ensures continuous research and development. Support is
provided by the developers and if necessary by the appropriate Deltares experts. These
experts can provide consultancy backup as well.
If problems are encountered, the first step should be to consult the online Support at:
www.deltaressystems.com menu ‘Software’. Different information about the program can be

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found on the left-hand side of the window (Figure 1.4):

 In ‘Support - Frequently asked questions’ are listed the most frequently asked technical
questions and their answers.

 In ‘Support - Known issues’ are listed the bugs of the program.
 In ‘Release notes D-Pile Group’ are listed the differences between an old and a new
version.

Figure 1.4: Deltares Systems website (www.deltaressystems.com)

If the solution cannot be found there, then the problem description can be e-mailed (preferred)
or faxed to the Deltares Systems support team. When sending a problem description, please
add a full description of the working environment. To do this conveniently:

 Open the program.
 If possible, open a project that can illustrate the question.
 Choose the Support option in the Help menu. The System Info tab contains all relevant information about the system and the Deltares Systems software. The Problem
Description tab enables a description of the problem encountered to be added.

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Figure 1.5: Support window, Problem Description tab

 After clicking on the Send button, the Send Support E-Mail window opens, allowing sending
current file as an attachment. Marked or not the Attach current file to mail checkbox and
click OK to send it.

Figure 1.6: Send Support E-Mail window

The problem report can either be saved to a file or sent to a printer or PC fax. The document
can be emailed to support@deltaressystems.nl or alternatively faxed to +31(0)88 335 81 11.
1.9

Deltares
Since January 1st 2008, GeoDelft together with parts of Rijkswaterstaat /DWW, RIKZ and
RIZA, WL |Delft Hydraulics and a part of TNO Built Environment and Geosciences are forming the Deltares Institute, a new and independent institute for applied research and specialist
advice. Founded in 1934, GeoDelft was one of the oldest and most renowned geotechnical
engineering institutes of the world. As a Dutch national Grand Technological Institute (GTI),
Deltares’s role is to obtain, generate and disseminate geotechnical know-how. The institute
is an international leader in research and consultancy into the behavior of soft soils (sand
clay and peat) and management of the geo-ecological consequences which arise from these
activities. Again and again subsoil related uncertainties and risks appear to be the key factors
in civil engineering risk management. Having the processes to manage these uncertainties
makes Deltares the obvious Partner in risk management for all parties involved in the civil and

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environmental construction sector. Deltares teams are continually working on new mechanisms, applications and concepts to facilitate the risk management process, the most recent
of which is the launch of the concept "GeoQ" into the geotechnical sector. For more information on Deltares, visit the Deltares website: www.deltares.nl.
1.10

Deltares Systems
On a more practical level Deltares is active in disseminating and implementing geotechnical knowledge and experience into the civil engineering and construction sectors. It is recognized that ICT-based developments will be the basis of knowledge transfer in the next
decades. Deltares Systems hosts internet-facilitated tools, of which D-Foundations is part,
and experience databases and generally applicable geotechnical software for the calculation
of slope stability, settlement, groundwater flow and other phenomena.For more information
about geotechnical software, including download options, visit www.deltaressystems.com.

1.11

On-line software (Citrix)
Besides purchased software, Deltares Systems tools are available as an on-line service. The
input can be created over the internet. Heavy duty calculation servers at Deltares guarantee
quick analysis, while results are presented on-line. Users can view and print results as well
as locally store project files. Once connected, clients are charged by the hour. For more
information, please contact the Deltares Sales team: sales@deltaressystems.nl.

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2 Getting Started
This Getting Started section aims to familiarize the user with the structure and user interface of
D-P ILE G ROUP. The Tutorial section which follows uses a selection of case studies to introduce
the program’s functions. Getting Started
2.1

Starting D-Pile Group
Starting D-P ILE G ROUP To start D-P ILE G ROUP, click Start on the Windows menu bar and then
find it under Programs, or double-click an D-P ILE G ROUP input file that was generated during
a previous session.
For a D-P ILE G ROUP installation based on floating licenses, the Modules window may appear
at startup (Figure 2.1). Check that the correct modules are selected and click OK.

Figure 2.1: Modules window

When D-P ILE G ROUP is started from the Windows menu bar, the last project that was worked
on will open automatically, unless the program has been configured otherwise in the Program
Options window, reached from the Tools menu and D-P ILE G ROUP will display the main window
(section 2.2).
2.2

Main Window
When D-P ILE G ROUP is started, the main window is displayed (Figure 2.2). This window contains a menu bar (section 2.2.1), an icon bar (section 2.2.2), a top view layout (section 2.2.3)
providing a top view of the pile grid, a title panel (section 2.2.4) and a status bar (section 2.2.5).
The caption of the main window of D-P ILE G ROUP displays the program name, followed by the
model name and the project name. When a new file is created, the default model is Cap and
the default project name is Project1.

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Figure 2.2: D-Pile Group main window

2.2.1

The menu bar
To access the D-P ILE G ROUP menus, click the menu names on the menu bar.

Figure 2.3: Menu bar

The menus contain the following functions:
File

Project
Soil
Pile
Cap
Loads
Calculation
Results
Tools

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Standard Windows options for opening and saving files as well as several
D-P ILE G ROUP options for exporting and printing active windows and reports
(section 3.1).
Options for selecting the project model, project properties and viewing the
input file (section 4.1).
Options for defining the properties and profiles of the soil layers (section 4.2)
Options for defining the types and positions of the piles (section 4.3).
Options for defining the cap location and mass (section 4.4).
Options for defining loads cap, soil displacements, surface loading and
loading parameters of a ship (section 4.5).
Analysis of the following, based on input values: displacements, shear
forces, moments, rotations (chapter 5).
Options for displaying and creating reports and charts on displacements,
shear forces, moments, rotations in the X, Y and Z directions (chapter 6).
Options for editing D-P ILE G ROUP program defaults like setting the working
directory (section 3.2).

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Window
Help

Default Windows options for arranging the D-P ILE G ROUP windows and
choosing the active window.
Online Help options (section 1.7).

Detailed descriptions of these menu options can be found in the Reference section.
2.2.2

The icon bar
Use the buttons on the icon bar to quickly access frequently used functions (see below).

Figure 2.4: Icon bar

Buttons on icon bar Click on the following buttons to activate the corresponding functions:
Start a new D-P ILE G ROUP project.
Open the input file of an existing project.
Save the input file of the current project.
Print the contents of the currently active window.
Display a print preview of the contents of the currently active window.
Open the Project Properties window. Here the project title and other identification data can be entered, and the View Layout, View Results and Graph
Settings for the project can be determined.
Start the main calculation.
Display the contents of online Help.
Display the first page of the Deltares Systems website:
www.deltaressystems.com

2.2.3

Top View Layout
The Top View Layout window shows a graphic representation of the project data and provides
easy access to the main input windows, allowing editing and adding project data efficiently
and quickly by using the buttons which are available in the Edit and Tools panel.

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Figure 2.5: Top View Layout window

Select and Edit button
In this mode, click the left mouse button to graphically select a previously defined pile or soil profile in the Top View Layout window. Then the item can
be deleted or its properties can be modified by dragging or resizing it or by
choosing options from menu displayed when clicking the right mouse button.
Pan button
Click this button to change the visible part of the Top View Layout window by
clicking and dragging the mouse.
Add pile(s)
Click this button to add piles to the project by clicking on locations in the Top
View Layout window. Note that only the co-ordinates can be set by entering a
pile in this way. Double click the pile to set the other properties, such as pile
type and rake.
Add pile grid
Click this button to add piles to the project by dragging a rectangle in the Top
View Layout window. After the rectangle has been dragged, a properties dialog
opens to fill in the parameters of the piles.
Add soil profile(s)
Click this button to add profiles to the project by clicking on locations in the Top
View Layout window. Note that only the co-ordinates can be set by entering a
profile in this way. Double click the soil profile set the other properties, such as
water level and Y co-ordinate.
Add surface loading
Click this button to add profiles to the project by clicking on locations in the Top
View Layout window. If clicking four points, a quadrangle is entered. Double
click on this quadrangle to edit the properties. If clicking the third point exactly
on the first one, a triangle is entered.
Zoom in
Click this button to enlarge the drawing, then click on the part of the drawing
which is to be at the centre of the new image. Repeat if necessary.
Zoom out
Click this button, then click on the drawing to reduce the drawing. Repeat if
necessary.

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Zoom area
Click this button to click and drag a rectangle over the area to be enlarged. The
selected area will be enlarged to fit the window. Repeat if necessary.
Measure the distance between two points
Click this button, then click the first point on the Top View Layout window and
place the cross on the second point. The distance between the two points can
be read at the bottom of the Top View Layout window. To turn this option off,
click the escape key.
Undo zoom
Click this button to undo the zoom. If necessary, click several times to retrace
each consecutive zoom-in step that was made.
Zoom limits
Click this button to display the complete drawing.
Same scale for X and Y axis
Click this button to use the same scale for the horizontal and vertical directions.

2.2.4

Title panel
This panel situated below the Top View Layout window displays the project titles, as entered in
the Project Properties window (section 4.1.2). This panel is displayed only if the corresponding
checkbox in the View tab of the Program Options window (section 3.2.1) is selected.

Figure 2.6: Title panel and Status bar at the bottom of the main window

2.2.5

Status bar
This bar situated at the bottom of the main window displays a description of the selected icon
of the icon bar (section 2.2.2) or button of the current window. This bar is displayed only if
the corresponding checkbox in the View tab of the Program Options window (section 3.2.1) is
selected.

2.3

Files
*.pii

*.pis
*.dat
*.pio

*.pid
*.ppd
*.pip

Deltares

Input file (ASCII):
Contains the input with the problem definition. After interactive generation, this
file can be reused in subsequent D-P ILE G ROUP analyses.
Save file (ASCII):
Contains the preferences saved as default.
Data file (ASCII):
Contains the generated input for a FEM calculation.
Output file (ASCII):
After a calculation has been started, all output is written to this file. If there are
errors in the input, they are also described in this file.
Dump file (ASCII):
Contains the dump data.
Dump file (ASCII):
Contains the dump data for Poulos model.
Drawing file (Binary):
Working file containing plot data to display P-Y curves.

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*.grd

*.pib
*.mat

2.4
2.4.1

FEM graphical data file (ASCII):
Working file with plot data (Cap, Cap soil interaction, Cap layered soil interaction, Dynamic models).
Data file (ASCII):
Dynamic data file that can be used by the BOTS program.
FEM input file (ASCII):
Export file for a FEM analysis, containing the interaction matrix.

Tips and Tricks
Keyboard shortcuts
Keyboard shortcuts given in Table 2.1 are another way to reach the features of D-P ILE G ROUP
directly without selecting it from the bar menu. These shortcuts are also indicated in the
corresponding sub-menus.
Table 2.1: Keyboard shortcuts for D-Pile Group

Keyboard shortcut
Ctrl + N
Ctrl + O
Ctrl + S
F12
Shift + Ctrl + C
Ctrl + P
Ctrl + M
Ctrl + T
Ctrl + R
F9
2.4.2

Opened window
New
Open
Save
Save As
Copy Active Window to Clipboard
Print Report
Model
Pile Positions
Report
Start Calculation

Exporting figures and reports
All figures in D-P ILE G ROUP such as top view and graphical output can be exported in WMF
(Windows Meta Files) format. In the File menu, select the option Export Active Window to
save the figures in a file. This file can be later imported in a Word document for example or
added as annex in a report. The option Copy Active Window to Clipboard from the File menu
can also be used to copy directly the figure in a Word document.
The report can be entirely exported as PDF (Portable Document Format) or RTF (Rich Text
Format) file. To look at a PDF file Adobe Reader can be used. A RTF file can be opened
and edited with word processors like MS Word. Before exporting the report, a selection of the
relevant parts can be done with the option Report Selection (section 6.1).

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2.4.3

Copying part of a table
It is possible to select and then copy part of a table in another document (an Excel sheet
for example). If the cursor is placed on the left-hand side of a cell of the table, the cursor
changes in an arrow which points from bottom left to top right. Select a specific area by using
the mouse (see a) in Figure 2.7. Then, using the copy button (or ctrl+C) this area can be
copied.

(a)

(b)

(c)

(d)

Figure 2.7: Selection of different parts of a table using the arrow cursor

To select a row, click on the cell before the row number (see b) in Figure 2.7. To
select a column, click on the top cell of the column (see c) in Figure 2.7. To select the complete
table, click on the top left cell (see d) in Figure 2.7.
In some tables the buttons Cut, Copy, and Paste are also present at the left hand.

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3

General
This chapter contains a detailed description of the available menu options for inputting data
for a project, and for calculating and viewing the results.
The examples in the tutorial section provide a convenient starting point for familiarization with
the program.

3.1

File menu
Besides the familiar Windows options for opening and saving files, the File menu contains a
number of options specific to D-P ILE G ROUP:

 Copy Active Window to Clipboard








3.2
3.2.1

Use this option to copy the contents of the active window to the Windows clipboard so
that they can be pasted into another application. The contents will be pasted in either text
format or Windows Meta File format.
Export Active Window
Use this option to export the contents of the active window as a Windows Meta File (*.wmf)
or a Drawing Exchange File (*.dxf).
Export Report
This option allows the report to be exported in a different format, such as Adobe PDF file
(*.pdf), Richt Text Format file (*.rtf), HTML file (*.html) or ASCII Text file (*.txt).
Page Setup
This option allows definition of the way D-P ILE G ROUP plots and reports are to be printed.
The printer, paper size, orientation and margins can be defined as well as whether and
where axes are required for plots. Click Autofit
to get D-P ILE G ROUP to choose the
best fit for the page.
Print Preview Active Window
This option will display a print preview of the current contents of the Top View Layout or
Results window.
Print Active Window
This option prints the current contents of the Top View Layout or Results window.

Tools menu
Program Options
On the menu bar, click Tools and then choose Program Options to open the corresponding
input window. In this window, the user can optionally define their own preferences for some
of the program’s default values. When working with a network version of D-P ILE G ROUP using
Flex LM, this window allows the users to select the modules they wish to use for their current
session.

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Program Options – View

Figure 3.1: Program Options window, View tab

Toolbar & Status
bar
Title panel

Mark the relevant checkbox to display the toolbar and/or status bar
each time D-P ILE G ROUP is started.
Mark this checkbox to display the project titles, as entered on the
Identification tab in the Project Properties dialog, in a panel at the
bottom of the Top View Layout window.

Program Options – General

Figure 3.2: Program Options window, General tab

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Startup with

Save on
calculation

Use Enter key to

Click one of these toggle buttons to determine how a project should
be initiated each time D-P ILE G ROUP is started.
No project: Use the buttons in the toolbar or the options in the File
menu to open an existing project or to start a new one.
Last used project: The last project to be worked on is opened automatically.
New project: A new (empty) project is created containing no input
data at all.
Note that the Startup with option is ignored when D-P ILE G ROUP is
started by double-clicking on an input file.
The toggle buttons determine how input data is saved prior to calculation. It can either be saved automatically, using the same file
name each time, or a file name can be specified every time the data
is saved.
Use the toggle buttons to determine the way the Enter key is used in
D-P ILE G ROUP: either as an equivalent of pressing the default button
(Windows style) or to shift the focus to the next item in a window (for
users accustomed to the DOS version(s) of the program).

Program Options – Locations

Figure 3.3: Program Options window, Locations tab

Working directory

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Either mark the checkbox to automatically make the last used directory the working directory, or unmark the checkbox and specify a
default path for the working directory, which will be set automatically
when D-P ILE G ROUP is started.

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Program Options – Modules
This tab provides an overview of the modules for D-P ILE G ROUP. The functionality of this tab
depends on the type of license.

Figure 3.4: Program Options window, Modules tab

Dongle
(Single
User versions),
License Files
Flex LM (Network
versions)

Display only. Unavailable modules (modules for which the user does
not have a license) are shown grayed with the checkbox unchecked,
available modules are shown as regular text.
This tab can be used to select the available module(s) required for the
current session. Unavailable modules, modules for which the user
does not have a license or modules, for which all licenses are in use,
are shown grayed with the checkbox unchecked. Available modules
are shown as regular text with a selectable checkbox. By checking a
module, this module becomes available after the dialog window has
been closed and the module has been successfully checked out by
the license manager (Flex LM).
Click this button to see which modules are (at this moment) in used
and who (within the company) is using them.
Click this button to borrow the selected modules for a certain period.
The modules will be taken from the server pool and will be available
on this computer even if no connection to the license server is available. Set the date and time for the expiration of the borrowing and
press OK.
Click this button to end the borrow immediately.

The checkbox Show at start program can be used to cause the module selection window to
appear each time the program is started.
3.3

Help menu
The Help menu allows access to different options.

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3.3.1

Calculation Messages
Select the Calculation Messages option from the Help menu to open the Calculation Messages window displaying an overview of the input and the possible error(s) found in red (Figure 3.5).

Figure 3.5: Calculation Messages window

3.3.2

Manual
Select the Manual option from the Help menu to open the User Manual of D-P ILE G ROUP in
PDF format. Here help on a specific topic can be found by entering a specific word in the Find
field of the PDF reader.

3.3.3

Deltares Systems Website
Select Deltares Systems Website option from the Help menu to visit the Deltares Systems
website (www.deltaressystems.com) for the latest news.

3.3.4

Support
Use the Support option from the Help menu to open the Support window in which program
errors can be registered. Refer to section 1.8 for a detailed description of this window.

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3.3.5

About D-Pile Group
Use the About option from the Help menu to display the About D-P ILE G ROUP window which
provides software information (for example the version of the software).

Figure 3.6: About window

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Before analysis can be started, data for the piles, soil and loads need to be entered.
4.1

Project menu
Each project starts with the selection of an analysis model and the entry of general details
about the project.

4.1.1

Model
Choose Model from the Project menu to display the Model window. Here the calculation
model, used to generate the project results, can be selected.

Figure 4.1: Model window

Poulos

Plasti-Poulos
Cap

Cap soil interaction

Cap layered soil interaction

Dynamic

4.1.2

The classic analytical Poulos model which assumes homogeneous
elastic soil and vertical piles with pile-soil-pile interaction according to
Poulos/Randolph (Poulos, 1980; Randolph, 1981). See section 16.2
for background information.
The classical analytical Poulos model in combination with soil plasticity. See section 16.3 for background information.
Simple model without pile-soil-pile interaction but only cap-interaction
with elasto-plastic pile-soil interaction. See section 16.1 for background information.
The Cap soil interaction model assumes elastic pile-soil-pile interaction according to Mindlin theory (Mindlin, 1936, 1953) and elastoplastic pile-soil interaction. See section 16.4 for background information.
The Cap layered soil interaction model assumes elastic pile-soil-pile
interaction for a layered soil system and elasto-plastic pile-soil interaction using a Finite Element Method to determine the interaction
along complete piles. See section 16.5 for background information.
This model is dedicated for dynamic analysis of a collision of a ship
against the pile cap. See section 16.6 for background information.

Project Properties
Setting the Project Properties determines the project information that is used on printout and
graphic plots.

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Project Properties – Identification
Use the Identification tab to specify the project identification data:

Figure 4.2: Project Properties window, Identification tab

Titles

Date

Drawn by
Project ID
Annex ID

Use Title 1 to give the project a unique, easily recognizable name. Title 2
and Title 3 can be added to indicate specific characteristics of the calculation. The three titles will be included on printed output.
The date entered here will be used on printouts and graphic plots for this
project. Either mark the Use current date checkbox to automatically use the
current date on each printout, or enter a specific date.
Enter the name of the user performing the calculation or generating the
printout.
Enter a project identification number.
Specify the annex number of the printout.

Enable the checkbox Save as default to use these settings every time D-P ILE G ROUP is started
or a new project is created.

Figure 4.3: Identification bottom part when printing charts

The logo and address information of the company can be entered or changed using the
program DGS Servicetool that is shipped with the Deltares Systems programs, and can be
launched from the Start menu.

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Project Properties – View Layout
Use the View Input tab to define the appearance of the Top View Layout window .

Figure 4.4: Project Properties window, View Layout tab

Layout
Grid
Snap to Grid
Rulers
Large Cursor
Info Bar
Global Axes
Local Axes
Legend
Same scale for X
and Y axis
Pile Positions
Soil Profiles
Surface Loading
Areas
Centre of Gravity
Piles in Perspective

Enable this checkbox to display the grid points.
Enable this checkbox to ensure that objects align to the grid automatically when they are moved or positioned in a graph.
Enable this checkbox to display the rulers.
Enable this checkbox to use the large cursor instead of the small one.
Enable this checkbox to display the information bar at the bottom of
the Outline View window.
Enable this checkbox to display.
Enable this checkbox to display.
Enable this checkbox to display the legend.
Enable this checkbox to display the x and y axis with the same scale.
Enable this checkbox to display the pile positions.
Enable this checkbox to display the soil profiles.
Enable this checkbox to display the surface loading areas.
Enable this checkbox to display the centre of gravity of the pile group.
Enable this checkbox to display the piles in perspective (useful in
case of raked or enlarged pile).

Numbering
Pile Positions
Profiles
Surface Loading
Areas

Enable this checkbox to display the pile numbering.
Enable this checkbox to display the soil profiles numbering.
Enable this checkbox to display the surface loading areas numbering.

Enable the Save as default checkbox to use the current settings every time D-P ILE G ROUP is
started.

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Project Properties – View Results
The View Results tab looks exactly the same as the View Layout tab, and allows customizing
the display settings for the Top View Results window.
Project Properties – Graph settings
The Graph Settings tab allows setting the distance between the grid points. This setting
applies to both the Top View Layout window and the View Results window.

Figure 4.5: Project Properties window, Graph Settings tab

Grid distance

Enter the distance between two grid points.

Enable the Save as default checkbox to use the current settings every time D-P ILE G ROUP is
started.
4.1.3

View Input File
On the menu bar, click Project and then choose View Input File to open the Input File
window where an overview of the input data is displayed. Click on the Print Active Window
icon to print this file.

4.2

Soil menu
For an D-P ILE G ROUP calculation, there are three different types of contribution of the soil.

 The first type of contribution is the upward force on the tip of the pile.
 The second type of contribution is the interaction between each pile and the soil by which
it is surrounded.

 The third type of contribution is the interaction between two piles via the soil between those
two piles.
For each type of interaction, different parameters are needed for the calculation.

 For the first type, the end bearing capacity is used (section 4.3.3).
 For the second type, the parameters in the Soil Layers window are used (section 4.2.1), in
combination with the profiles defined in the Soil Profiles window (section 4.2.2).

 For the third type, the parameters in the Soil Interaction Model window are used (sec30 of 226

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tion 4.2.3).
4.2.1

Soil Layers
All soil layers that will interact with the piles in the entire calculation must be defined here. To
add a soil layer, a name must be added to the list of soil layer names at the left-hand side
using the Add button. The soil layers entered here can be selected in the Soil Profiles input
window (section 4.2.2). The soil parameters will vary with the selected soil type (Figure 4.6).

Figure 4.6: Soil Layers window, Soil type sub-window

Soil Layers – Sand

Figure 4.7: Soil Layers window (Sand)

Dry unit weight
Wet unit weight
Phi
Cone resistance
Ko

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Volumetric mass of the soil above the water level.
Volumetric mass of the soil including water, under the water level.
The angle of internal friction.
The cone resistance qc as determined by a standard cone penetration test (CPT).
The coefficient of horizontal subgrade reaction.

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Lateral rule

Axial friction rule

Void ratio e_0
Void ratio e_min
Void ratio e_max
dz at 100 %
Friction at top
Friction at bottom

Factor alpha

Select the non-linear force-displacement relation (usually called P-Y
curve) that describes the soil resistance for a pile laterally loaded.
For the calculation of the lateral soil resistance, three relations according to API (1984) are available:
- API: the P-Y curve for static lateral loads. See section 15.1.3 for
background information.
- API Cyclic: the P-Y curve for cyclic lateral loads. See section 15.1.4
for background information. newline - API Undrained: the initial, minimum and maximum void ratio values must be entered. See section 15.1.5 for background information.
Select the non-linear force-displacement relation (usually called T-Z
curve) that describes the soil resistance for a pile axially loaded. For
the calculation of the axial soil resistance, two relations are available:
- API: the T-Z curve according to API. See section 15.2.1 for background information.
- Cone: the T-Z curve according to NEN 6743 using the cone resistance of the soil. See section 15.2.2 for background information.
Depending on the selected option, the required input fields will be
made accessible. The fields that irrelevant to a particular option will
appear as dimmed.
The initial, minimum and maximum void ratios respectively, only required with the API Undrained lateral P-Y curve.
The relative displacement between pile and soil at which the maximum value of the shaft friction is reached.
The maximum value of the shaft friction at the top and the bottom.
This option is available only if the API option in the Axial friction rule
sub-window is selected. See section 15.2.1 for background information.
The factor between the cone resistance and the shaft friction. This
option is available only if the Cone option in the Axial friction rule subwindow is selected. See section 15.2.2 for background information.

Soil Layers – Soft and Stiff Clay

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Figure 4.8: Soil Layers window (Clay)

Note: In the present version of D-P ILE G ROUP, stiff clay is treated in the same manner as soft
clay. This is not according to the API, but the reduction of strength described there can not be
modeled in the present Tilly version.
For clay soil type, some values that must be entered differ from the sand soil type:
Cu
Empirical constant
J
Strain at 50%
failure load
Lateral rule

Axial friction rule

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The undrained shear strength.
Dimensionless empirical constant.
The strain that occurs at one-half of the maximum stress on laboratory undrained compression tests of undisturbed soil samples.
Select the non-linear force-displacement relation (usually called P-Y
curve) that describes the soil resistance for a pile laterally loaded. For
the calculation of the lateral soil resistance, two relations according
to API (1984) are available:
- API: the P-Y curve for static lateral loads. See section 15.1.1 for
background information.
- API Cyclic: the P-Y curve for cyclic lateral loads. See section 15.1.2
for background information.
Select the non-linear force-displacement relation (usually called T-Z
curve) that describes the soil resistance for a pile axially loaded. For
the calculation of the axial soil resistance, two relations are available:
- API: the T-Z curve according to API. See section 15.2.1 for background information.
- Ratio: the T-Z curve according to API using a user-defined alpha
factor. See section 15.2.3 for background information.
Depending on the selected option, the required input fields will be
made accessible. The fields that irrelevant to a particular option will
appear as dimmed.

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Soil Layers (P-Y soil)
If the selected soil type is P-Y soil, user defined P-Y and T-Z curves can be inputted manually.
Therefore, it is possible to define the force-displacement relations of the soil according to
the wish of the user for both lateral and axial loading. For both curves, a certain number of
points have to be entered, the curve must be monotonously increasing and the first point must
always be (0, 0).

Figure 4.9: Soil Layers window (P-Y Soil)

P
Y

t
Z

The lateral soil resistance per unit length of the pile.
The lateral deflection at which the lateral resistance occurs.
The axial soil resistance per unit length of the pile.
The axial deflection at which the axial resistance occurs.

Soil Layers (No Soil)
If the selected soil type is No Soil, no further soil data need to be entered. With this option
the pile is unsupported in this layer. This can be used to model the freestanding part of a pile
above the surface level or a cavity in the soil.
Figure 4.10: Soil Layers window (No Soil)

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4.2.2

Soil Profiles
This option provides the means to add, delete, change and view the soil profiles. These
soil profiles are used for the pile-soil interaction and are therefore not present for the Poulos
model, which only has elastic pile-soil-pile interaction.Soil Profiles
To add a soil profile, click Add to add a number to the list of soil profile numbers at the lefthand side. The soil profile entered here can be selected with in the Pile Positions window
(section 4.3.3).
The data of the soil profile can be entered or changed in two ways:

 By using the tabular input at the right hand side of the window;
 By using the graphic representation of the profile at the middle of the window.
Tabular input of the soil profile
, Add row
Use the Insert row
remove layers in the profile.

and Delete row

buttons next to the table to add or

Figure 4.11: Soil Profiles window

Figure 4.12: Soil Profiles window, drop down list of available soil layers

Top Level

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The top level of the layer.

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Material

Materials can be selected from the drop down list of soil layers (see
Figure 4.12) that were entered in the Soil Layers window in section 4.2.1.
Enter the water level (relative to the reference level).
Enter the X and Z co-ordinates of the location of the profile in the X-Z
plane.

Water level
Location

Graphical input of the soil profile
Soil layers can be added to the profile by pressing the Add boundary
anywhere in the graphic representation of the profile.

button and clicking

Layer boundaries and the water level can be changed by mouse, dragging them upwards or
downwards. While dragging, the level is indicated in a panel below the button bar. Also, the
table and water level are updated continuously.
4.2.3

Soil Interaction Model
At this point, the profile that is to be used for pile-soil-pile interaction must be specified. Since
this interaction is elastic the data for this interaction profile differ from the “regular” soil profiles.
The input data will vary with the model used for the project.

 The Cap and Dynamic models include cap interaction only, therefore no interaction
profile is asked for when using those models.
 For the Poulos, Plasti-Poulos and Cap soil interaction models an interaction profile consisting of one layer is required.
 For the Cap layered soil interaction model the interaction profile can be composed of
several horizontal soil layers. The layer boundaries of this soil interaction profile do not
have to be consistent with the layer boundaries of the soil profile of each pile itself.
This means that the composition of the pile-soil-pile interaction profile is based on the
engineering judgment of the user.
Soil Interaction Model – Poulos model

Figure 4.13: Soil Interaction Model window (Poulos model)

Level at top
Poisson ratio
Young’s modulus at
surface level

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Level at the top of the interaction profile in relation to the reference
level.
The Poisson ratio of the soil layer.
The Young’s modulus of the soil layer at the surface level.

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Young’s modulus
below the pile tip

The Young’s modulus of the soil layer at pile tip.

Soil Interaction Model – Plasti-Poulos model

Figure 4.14: Soil Interaction Model window (Plasti-Poulos model)

Level at top
Poisson ratio
Young’s modulus
below the pile tip

Level at the top of the interaction profile in relation to the reference
level.
The Poisson ratio of the soil layer.
The Young’s modulus of the soil layer at pile tip.

Soil Interaction Model – Cap soil interaction model

Figure 4.15: Soil Interaction Model window (Cap soil interaction model)

Poisson ratio
Young’s modulus

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The Poisson ratio of the soil layer.
The Young’s modulus of the soil layer.

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Soil Interaction Model – Cap layered soil interaction model

Figure 4.16: Soil Interaction Model window (Cap layered soil interaction model)

Level at top
Young’s modulus
Poisson ratio

4.3

Pile menu

4.3.1

Pile Types

Level at the top of the interaction profile in relation to the reference
level.
The Young’s modulus of the soil layer.
The Poisson ratio of the soil layer.

All pile types used in the calculation must be defined here. To add a pile type, a name must
be added to the list of pile types at the left-hand side. The pile types entered here can be
selected with the Pile Positions window [section 4.3.3]. The parameters will vary with the pile
type selected.
Pile Types – Wood
If the selected material is wood, the following data must be entered for a calculation.

Figure 4.17: Pile Types window for Wood pile

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Pile Types – Steel
If the selected material is steel, the following data must be entered for a calculation. For a
steel pile, a pipe pile is assumed. This means that the cross section is always tubular.

Figure 4.18: Pile Types window for Steel pile

Pile Types – Concrete round
If the selected material is Concrete round, the following data must be entered for a calculation.
Note that regulations exist determining concrete quality.

Figure 4.19: Pile Types window for Concrete round pile

Pile Types – Concrete square
If the selected material is Concrete square, the following data must be entered for a calculation. Note that regulations exist, determining concrete quality.

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Figure 4.20: Pile Types window for Concrete square pile

Pile Types – User specified
This option allows defining multiple segments. For each segment used, a “tab” will be displayed where the required data must be entered. This offers the possibility of multiple sections
with a different diameter or stiffness for each section.

Figure 4.21: Pile Types window for User specified pile

Length
Diameter
Width
Mass
Wall thickness

E-Modulus

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The total length of the pile.
The diameter of the pile. For Steel pile, it is the outer diameter of the
pile. The value must range between 0.01 m and 10 m.
The width of the concrete pile. The value must range between 0.01 m
and 10 m (only available for Concrete square).
The volumetric mass of the pile material in kg per length of the pile
(only available with Dynamic model).
The thickness of the wall of the tubular pipe (only available for Steel).
The value must range between 0 m and half the diameter (massive
pile).
The Young’s modulus of the pile material. The value must range
between:
104 and 108 kN/m2 for Wood material
108 and 109 kN/m2 for Steel material
107 and 108 kN/m2 for Concrete material

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EI

EA

Number of
ments
Total length

seg-

The lateral stiffness of the pile. This value is calculated automatically by D-P ILE G ROUP for all the materials except the User specified
material.
The axial stiffness of the pile. This value is calculated automatically
by D-P ILE G ROUP for all the materials except the User specified material.
Select the number of segments the pile will consist of. For each
segment, a separate tab will be displayed.
The combined length of all segments that composed the pile.

Note: Although the lateral and axial stiffness can not be altered directly, the calculated values
are presented to offer a possibility to check whether these are the required stiffness and to
help the user to determine the stiffness for a User specified material. See paragraph 1.24 in
the Verification Report for detailed equations.
4.3.2

Pile Tip Curves
Pile tip behavior is determined by the ultimate tip resistance and by the load-displacement
behavior before reaching this ultimate resistance. In D-P ILE G ROUP the end bearing capacity
(ultimate tip resistance) is specified in the Pile Positions window (section 4.3.3) since this
value may vary with different positions. The pile tip curve specifies the load-displacement
behavior (in terms relative to the ultimate level) and is therefore more related to the pile type
(e.g. driven or bored). This allows for fast specification and/or change of the tip behavior of
multiple piles. The recommended pile tip curves according to API and the Dutch Code NEN
are given in section 15.3. To add a pile tip curve a number must be added to the list of curves
at the left-hand side. The pile tip curves entered here can be selected with the Pile Positions
window (section 4.3.3).

Figure 4.22: Pile Tip Curves window

Pile tip curve number
Rt
Zt

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The list of pile tip curves that have been defined for the project. Select
a curve to display the corresponding settings.
The percentage of the end bearing capacity (ultimate tip resistance).
The tip settlement at which Rt occurs.

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4.3.3

Pile Positions
The pile position in the 3-dimensional space can be specified here. In order to do this the
position of the pile head has to be specified as well as the rake and the angle in the horizontal
plane. From these data and the length of the pile the program calculates the position of the
pile tip (or the end of a segment).
Only for the Poulos and the Plasti-Poulos models a critical pile number is needed. For the
Plasti-Poulos model the pile type of the critical pile is used to determine the equivalent Young’s
modulus of the interaction profile. It is also used for the calculation of the Plasticity Factors.
The critical pile can be selected in the Pile Positions table by marking the desired pile.
Pile positions can also be entered in the pile position table. To allow fast input of regularly
spaced pile groups, a pile grid can be generated based on spacing in 2 directions.
In this input window, for each pile:

 a unique name can be given (only numbers are allowed),
 a soil profile, pile type and pile tip curve must be selected,
 the position of the pile head, the end bearing capacity and geometrical data must be
filled in.

Figure 4.23: Pile Positions window

Pile name
Soil profile

Pile type
Pile tip curve

Xtop
Ytop
Ztop

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The name of the pile (only numbers are allowed).
The soil profile can be selected from the drop down list of soil profiles
that were entered in the Soil Profiles window in section 4.2.2 (not
available for Poulos model).
The pile type can be selected from the drop down list of pile types
that were entered in the Pile Types window in section 4.3.1.
The pile tip curve can be selected from the drop down list of pile
tip curves that were entered in the Pile Tip curves window, see section 4.3.2 (not available for Poulos model).
The position of the pile head within the coordinate system.

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Critical pile

Top condition

End bearing

Angle in XZ-plane

Rake [hor/vert]

4.3.4

In the present version of the program a critical pile needs to be specified for the Poulos and the Plasti-Poulos model. In the Poulos model
this is not used. In the Plasti-Poulos model the pile number properties are used for the determination of the plasticity factors. These
properties include: the end bearing, the raking angle and the angle
in the XZ plane. So if pile 4 is the critical pile these data of pile 4 are
used for the determination of the plasticity factors. At present only
one critical pile can be specified, even if there are multiple pile types.
This means that in such a case selection of the appropriate critical
pile (a pile of the pile type for which the plasticity factors are going
to be calculated) is needed. This is not ideal since it implies that
for each new pile type switching between the plasticity factors input
screen and the pile position input screen is needed (and backwards)
before the plasticity factors can be calculated for the new pile type.
D-P ILE G ROUP deals with the calculation of pile groups of one or more
piles. In the model all piles are connected to a pile cap which is supposed to be of infinite stiffness. The connection between each pile
and the cap can either rotate freely (Free head pile) or be completely
fixed (Fixed head pile).
The end bearing capacity depends on both the pile type and the soil
resistance. It should therefore be connected with the position of the
pile head. Because the values may be greatly influenced by relatively
small variations in the soil properties they have not been connected
to a soil profile in order to avoid the need to specify a different soil
profile for each pile.
For these reasons the ultimate bearing capacity is specified in the
Pile Position window (not available for Poulos model).
Together with the pile head position and the rake, the angle in the
XZ-plane determines the position of the pile tip. The angle has to be
specified in degrees. The positive direction of the angle is from the
positive Z axis to the positive X axis (anti clockwise).
The rake is the angle of the pile in the vertical plane. It has to be
specified as a factor between the horizontal and vertical projected
length of the pile. So a rake of 5 means: 5 m horizontally for every
meter vertically.

Pile Grid
In the Pile Positions window, click the Pile Grid button to open the Pile Grid window in which
a grid of piles that gives a draft of the pile plan can be generated. This option can be used
even if the project does not have its piles exactly on a regular grid as modifications can be
performed latter.

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Figure 4.24: Pile Grid window

Click OK to generate the grid. The generated piles are now in the table of the Pile Positions
window.
Soil Profile
Pile Type
Pile tip curve
From X-coordinate Top
To X-coordinate Top
From Z-coordinate Top
To Z-coordinate Top
Number of piles in
X-direction
Number of piles in
Z-direction
Angle XZ plane
End bearing capacity
Rake
Level at top
Top condition

4.3.5

See section 4.3.3.
See section 4.3.3.
See section 4.3.3.
Range of the grid in the X-direction.
Range of the grid in the Z-direction.
The number of piles to generate in the X-direction.
The number of piles to generate in the Z-direction.
See section 4.3.3.
See section 4.3.3.
See section 4.3.3.
The level at the top of the interaction profile in relation to the
reference level.
See section 4.3.3.

Pile Properties
The properties of one single pile can be shown along with a graphical representation of that
pile in the soil where it is located. The graphical representation gives a good and quick insight
in the position of the pile in the soil layers. The graph may be printed using the Print button in
this dialog.

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Figure 4.25: Properties of Pile 1 window

See section 4.3.3 for the definition of the parameters.
4.3.6

Plasticity Factors
This option is available only for the Plasti-Poulos model. In the Plasticity Factors window (Figure 4.26), the plasticity factors used in the Plasti-Poulos model calculations are determined
automatically by D-P ILE G ROUP. The plasticity factors are used to reduce the elastic stiffness
of the classical Poulos model. They determine how much bigger the elasto-plastic displacement of a pile is compared to the elastic displacement. The Plasti-Poulos model assumes
that the displacement for a load of 2 kN including soil plasticity is about twice the one based
on the elastic stiffness. For a higher load level the difference becomes bigger: for 4 kN the
difference is about a factor 3.
Since this is dependent of the pile type, the pile type has to be specified at the top of the
window. Clicking the Calculate button will automatically generate plasticity factors for the
selected pile type. Five different charts are drawn at the right-hand side of the Plasticity
Factors window depending on the selected tab. For each chart, two curves are drawn:

 the blue curve (straight line) corresponds to an elastic stiffness (i.e. plasticity factor of
1);
 the red curve corresponds to a reduced stiffness with higher loading levels due to soil
plasticity.

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Figure 4.26: Plasticity Factors window

Pile Type

Select the pile type from the drop down list of pile types that were
defined in the Pile Types window in section 4.3.1.
The force in the X and Y directions.
The displacements in the X and Y directions.
The moment in the Z direction.
The rotation around Z direction.
The calculated plasticity factor.

Fx, Fy
ux, uy
Mz
Thetaz
Plasticity Factor

To generate the plasticity factors the ultimate loading level and the number of points on the
curve (steps) have to be inputted in the Calculate Plasticity-poulos Factor Curves window
(Figure 4.27).

Figure 4.27: Calculate Plasticity-Poulos Factor Curves window

Force X
Force Y Compression
Force Y Tension
Moment Z
Steps
Force

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The force in the X direction.
The force in compression in the Y direction.
The force in tension in the Y direction.
The moment in the Z direction.
The number of load steps that will be generated.
The ultimate loading level.

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Input

See section 16.3.3 for background information.
4.3.7

Check Intersections
With this option a check can be made whether the positioned piles intersect. The check is
performed for all piles and their combinations. For a large number of piles this may take
some time. Piles are considered to intersect when the sum of half the diameter of pile 1, half
the diameter of pile 2 and the intersection tolerance is smaller than or equals the distance
between the pile centers.Piles that fail the intersection criterion are marked by a connecting
line.

Figure 4.28: Check Intersections window

Intersection
tolerance

4.4
4.4.1

Minimum allowed distance between two piles not being considered
to intersect. Any value between 1 cm and 100 m can be used as the
tolerance.

Cap menu
Cap Location
No special data is needed for the pile cap itself, only the centre of gravity and loading can be
defined here by specifying X, Y and Z in the global co-ordinate system.Loading conditions are
always applied to a single point of the pile cap.

Figure 4.29: Cap Location window

X, Y, Z co-ordinate

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The X, Y and Z co-ordinates of the reference point (loading point) of
the cap.

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4.4.2

Cap Mass
This option is required for Dynamic model only.

Figure 4.30: Cap Mass window

Cap mass
Ix, Iy, Iz

4.5
4.5.1

The weight of the cap.
The mass moment of inertia must also be specified for the X, Y and Z
directions.

Loads menu
Loads Cap
This option is not required for the Dynamic model. Load conditions are always applied to a
single point of the pile cap. This point of application is the centre of gravity and loading of the
cap defined in the Cap Location window in section 4.4.1. For each direction a choice can be
made between:

 load controlled (forces and/or moments)
 displacement controlled (displacements and/or rotations)
 neither.
Depending on the load conditions, the magnitudes of the applied load or the prescribed displacements per load step and per direction have to be specified.

Figure 4.31: Loads Cap window

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Loadstep number

Translation/Forces

Rotation/Moments

X, Y, Z

4.5.2

The number of steps used to apply the specified load. Load-step
numbers must be increasing. If not, D-P ILE G ROUP skips all next loadsteps and a warning will be given in the output file. For example:
Load steps 1, 5, 10, 11 and 25: D-P ILE G ROUP interpolates the loading condition between 1 and 5, 5 and 10, 10 and 11, 11 and 25.
Load steps 1, 5, 10, 0 and 25: D-P ILE G ROUP stops applying loads
after step 10.
The applied type of load in the 3 directions can be selected from the
drop down list of 3 types of loads: Loads, Displacements or Neither.
The positive direction of Loads and Displacements is in the positive
axis direction. When Neither is selected, movements in this direction
are not prescribed and therefore dependent of the calculation result.
The applied type of moment in the 3 directions can be selected from
the drop down list of 3 types of moments: Moments, Rotations or
Neither. A positive value for Moments and Rotations means anticlockwise. When Neither is selected, rotations in this direction are
not prescribed and therefore dependent of the calculation result.
The 3 directions.

Loads Ship
This option is required for the Dynamic model only. In order to calculate the consequences of
the collision of a ship with a pile cap, the ship’s parameters must be entered.

Figure 4.32: Loading Parameters of Ship window

Mass
Velocity
Heading
Contact stiffness
Collision point
Time steps

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The weight of the ship.
The velocity of the ship at the time of collision.
The angle of collision.
The stiffness between the ship and the cap.
The point of the cap hit by the ship.
By dividing the collision in a number of time steps, the forces involved
and the consequences for the construction for each time step can be
determined.

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4.5.3

Surface Loading Areas
This option is required for the Cap soil interaction model only.The loads may consist of triangular or rectangular shapes with load values for the corners. Over the surface an interpolation
of the corner values is used. Loads can be applied in all 3 directions.To add a new area, a
new area number must be added to the list at the left-hand side.

Figure 4.33: Surface Loading Areas window

Item name
Triangle
Quadrangle
X, Z

Qx, Qy, Qz

4.5.4

The list of surface loading areas that have been defined for the
project. Select an area name to display the corresponding settings.
Select this option to define a load with triangular shape.
Select this option to define a load with rectangular shape.
The co-ordinates in the X and Z direction of the different corners of
the load (3 corners if Triangle is selected and 4 corners if Quadrangle
is selected).
The loads applied in the X, Y and Z directions, for the different corners.

Surface Loadings
This option is required for the Cap soil interaction model only. In this window the areas to be
used can be selected from the list of surface loading areas defined earlier in section 4.5.3.

Figure 4.34: Surface Loadings window

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Input

Surface Loading
Area Name
Factor

Start Step No.
End Step No.

4.5.5

The surface loading area can be selected from the drop down list of
surface loading areas that were defined in the Surface Loading Areas
window in section 4.5.3.
With this factor the size of the applied surface load is determined by
multiplying the surface load with this factor. This allows for gradual
increase/decrease of the various surface loads.
The load step from which point the surface load is applied.
The load step at which point which the surface load is fully applied.

Soil Displacement Profiles
This option is required for the Cap model only. The soil displacement profiles allow for soil
movements to be taken into account by specifying the soil displacements in all 3 directions at
levels chosen by the user. Since it is also possible to specify the load step from which point
these displacements will be taken into account, modeling the influence of down drag (negative
skin friction) can be done in this way by specifying the vertical displacements with depth that
are responsible for the negative skin friction.

Figure 4.35: Soil Displacement Profiles window

Profile number
Level
Ux, Uy, Uz

4.5.6

A list of soil displacement profiles that have been defined for the
project (only numbers are allowed).
Indicate the depth.
Indicate the size of the soil displacements in X, Y and Z directions.

Soil Displacements
This option is required for the Cap model only. In this window, the profiles to be used can
be selected from the list of soil displacement profiles defined earlier in the Soil Displacement
Profiles window in section 4.5.5.
For each pile one or more profiles can be selected with its applicable load factor. For example
it’s possible that pile nr. 1 has 1 time the displacements of soil displacement profile 1 whereas
pile nr. 2 has 0.5 times the displacements of soil displacement profile 1 plus 0.5 times those
of soil displacement profile 2.
Here also the load steps have to be specified in which the soil displacements are to be applied.
For example for negative skin friction this can be done after the cap loads have been applied.

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Figure 4.36: Soil Displacements window

Pile Number

Displacement Profile Nr.

Factor

Start Step No.
End Step No.

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The number of the pile to which the selected soil displacement profile apply. The pile number can be selected from the drop down list
of pile numbers that were entered in the Pile Positions window in
section 4.3.3.
The number of the soil displacement profile selected for this calculation. The soil displacement profile number can be selected from
the drop down list of profile numbers that were entered in the Soil
Displacement Profiles window in section 4.5.5.
With this factor the size of the soil displacement is determined by
multiplying the displacement with this factor. This allows for stepwise
increase/decrease of the various displacements.
The load step from which point the soil displacement is applied.
The load step at which point which the soil displacement is fully applied.

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5 Calculation
5.1

Calculation Options
Before a calculation is made, the calculation options should be set in the appropriate input
window. The only exception to this is the Poulos model that does not need any options to be
set.The calculation options are needed for the Tilly program that performs calculations in the
background.

Figure 5.1: Calculation Options window

Minimum number
of pile modes

Accuracy
Maximum number
of iterations

Info on screen
Print in output file
Dump in graphic
file
Required accuracy
Maximum number
of iterations
Relaxation factor

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During the calculation, each pile is divided into parts, each of which
is represented by a node. The minimum number of nodes influences
both the accuracy of the calculation and the time needed to perform
the calculation. The default value of 20 normally gives a good tradeof between those two parameters.
The accuracy of each load step.
If the total available number of iterations has been reached, calculated data may be inaccurate. The results of such a calculation
should therefore be closely examined. A good solution is to repeat
the calculation with more loading steps. More information is given in
the Tilly user’s manual.
The interval between the calculation steps to be dumped on the
screen. When set at 1 all steps are given.
The interval between the calculation steps to be dumped in the output
file. When set at 1 all steps are given.
The interval between the calculation steps to be dumped on the
graphic file. When set at 1 all steps are given.
The required accuracy for the iteration process used for the PlastiPoulos model.
The maximum number of iterations used for the Plasti-Poulos model.
The relaxation factor for the iteration process used for the PlastiPoulos model. A small value of the relaxation factor will increase
the number of iterations and make the calculation more stable but
also more time consuming.

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5.2

Start Calculation
To start the calculation, choose the Start option in the Calculation menu or press the function
key F9.

Figure 5.2: Calculation window

Create P-Y Curve
dumpfile

Calculation
progress

5.3

Click this button to check the data files without calculating the project.
The data are stored in a project file with extension *.dat.
This option is not available for Poulos and Plasti-Poulos models.
Mark this checkbox to create a dump file in which the P-Y curves are
calculated. The PY Plots option from the Results menu [section 6.9]
will be available after performing the calculation only if this checkbox
is marked.
The different calculation sequences are described.

Calculation Messages
If errors are found in the input (Figure 5.3), no calculation can be performed and D-P ILE G ROUP
opens the Calculations Messages window displaying the error(s) in red (Figure 5.4). Those
errors must be corrected before performing a new calculation.

Figure 5.3: Error window

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Figure 5.4: Calculation Messages window

Note: The following warning message can be issued when performing a calculation with
Poulos or Plasti-Poulos model:
*** This project contains raking/rotated piles*** The Poulos method made some simplifications
to be able to proces this
This warning means that raking piles may result in an a-symmetric system matrix for Poulos.
D-P ILE G ROUP uses a symmetric solver. To be able to solve the system , the matrix is made
symmetric. This is done by replacing the a-symmetric elements with their calculated average.
5.4

Batch Calculation
D-P ILE G ROUP offers the possibility to perform calculations in batch which means successive
calculations for different input files. This can be useful for time consuming calculations (probabilistic calculations for example). To do so, D-P ILE G ROUP program must be started from the
Run window by specifying its location followed by ‘/b’, as shown in Figure 5.5.

Figure 5.5: Run window

Then the Start Batch Calculation window opens where the location of the files must be specified (Figure 5.6).

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Figure 5.6: Start Batch Calculation window

D-P ILE G ROUP will run the specified files successively. The calculation progress can be viewed
in the Calculation progress window (Figure 5.7).

Figure 5.7: Calculation progress window during batch calculation

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6 View Results
The options in the Results menu can be used to view the results of the performed calculations
6.1

Report Selection
In the Report Selection window, the user can select the chapters and paragraphs that will be
displayed in the report that D-P ILE G ROUP generates from the calculation results.
In the tree view that opens when clicking the Report Selection item in the Results menu
(Figure 6.1, each chapter and paragraph that may be included in the report can be checked
or unchecked.
The visibility of the items is indicated with the symbols in the tree, as follows.
The chapter or paragraph is included in the report.
The chapter or paragraph is not included in the report.
Some of the paragraphs in this chapter are included in the report,
and some of them are not.

By checking or unchecking a box before a chapter name, all of the paragraphs in this chapter
are included at once.
To select or unselect all chapters and paragraphs in the complete report, press the Select All
and Deselect All buttons on the bottom left side of the window.

Figure 6.1: Report Selection window

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6.2

Report
On the menu bar, click Results and then choose Report to view a window displaying an
overview of the most recent analysis results (Figure 6.2). This window displays the chapters
and paragraphs that were selected with the Report Selection option (section 6.1).The report
can be printed, and a preview can be made by selecting the appropriate items in the File
menu or the buttons on the tool bar.
Use the Export Report option from the File menu in order to export the report in RTF, PDF,
HTML or ASCII text format.

Figure 6.2: Report window

The report has its own toolbar:
Those four buttons enable the user to zoom in, to zoom out, to zoom
the full page or to zoom the page width.
Those four buttons enable the user to browse through the report by
respectively moving to first page, moving to previous page, moving
to next page or moving to last page.
Another way of quickly browsing through the report is by entering a
page number in the input field on the toolbar and pressing the Enter
key.

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6.3

Calculation Messages
The Calculation Messages window appears automatically at the end of the calculation. However, it can also be opened by clicking Results on the menu bar and then choosing Calculation
Messages (Figure 6.3). This window displays an overview of the input data adding error messages in red if the calculation failed.

Figure 6.3: Calculation Messages window

6.4

View Dump File
On the menu bar, click Results and then choose View Dump file to open the Dump File window
which displays an overview of the input data and analysis results.

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Figure 6.4: Dump File window

6.5

Top View
This window shows the graph of the chosen parameter (e.g. displacement, bending moment
or shear force) in the chosen direction (X, Y or Z) for all piles. It is possible to select 1, 2 or 3 of
these parameters on the screen simultaneously. Data are presented in the global co-ordinate
system.

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Figure 6.5: Top View Results window

Step
Direction

Select the cap loading step for which the chart will be displayed.
Select the direction for which the chart will be displayed.
If the Show displacement button is down, the result graph displays the
displacements of the pile tops, indicated with a black arrow for each pile
and a number showing the displacement of the pile top in meters (see Figure 6.6a).
If the Show force button is down, the result graph displays the forces on the
piles, indicated with a red arrow for each pile and a number showing the
force of the pile top in kN (see Figure 6.6b).
If the Show moment button is down, the result graph displays the moments
on the piles, indicated with a blue arrow for each pile and a number showing
the force of the pile top in kNm (see Figure 6.6c).

Figure 6.6: Displacement, force and moment results for pile 1

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The three buttons of the Display sub-window can be up or down independently from each
other.
The definitions of the other icons of the Edit and Tools sub-windows in the left-hand side panel
can be found in section 2.2.3.
6.6

Charts
On the menu bar, click Results and then choose Charts to open the Charts window which
shows the graph of the chosen parameter:

 Displacement, bending moment and/or shear force against depth, in the X and Z direction;

 Displacement, axial force and/or reaction against depth, in the Y direction.
It is possible to have 1, 2 or 3 of these charts on the screen simultaneously.

Figure 6.7: Charts window in X and Y directions

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Pile
Step
Direction

Select the pile number for which the chart will be displayed.
Select the cap loading step for which the chart will be displayed.
Select the direction for which the chart will be displayed.
Show or hide the chart that displays the displacements of the selected pile.
Show or hide the chart that displays the moments on the selected pile,
around the X or Z axis.
Show or hide the chart that displays the shear forces of the selected pile,
around the X or Z axis.
Show or hide the chart that displays the axial force on the selected pile, in
the Y direction.
Show or hide the chart that displays the reaction on the selected pile, in the
Y direction.

Data are presented in the local co-ordinate system. The definitions of the other icons of the
Edit and Tools sub-windows in the left-hand side panel can be found in section 2.2.3.
6.7

Pile Force-Displacement Charts
This option is available for all models. On the menu bar, click Results and then choose Pile
Force-Displacement Charts to open the Pile Force-Displacement Charts window which shows
the spring stiffness of piles.

Figure 6.8: Pile Force-Displacement Charts window

Pile
Direction

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Select the pile number for which the chart will be displayed.
Select the direction for which the chart will be displayed.

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6.8

Cap Plots
On the menu bar, click Results and then choose Cap Plots to open the Cap-plots window
which shows the graph for the pile cap behavior: a bending moment against rotation or force
against displacement. It is possible to have the two graphs on the screen simultaneously.

Figure 6.9: Cap-plots window

Direction

Select the direction for which the chart will be displayed.
Show or hide the chart that displays the displacements of the selected pile.
Show or hide the chart that displays the rotations on the selected pile.

The definitions of the other icons of the Edit and Tools sub-windows in the left-hand side panel
can be found in section 2.2.3.
6.9

PY Plots
This result is available only if the checkbox Create P-Y Curve dumpfile was marked in the
Calculation window (see section 5.2). On the menu bar, click Results and then choose PY
Plots to open the P-Y plots window which displays the results.The definitions of the icons of
the Edit and Tools sub-windows in the left-hand side panel can be found in section 2.2.3.

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Figure 6.10: P-Y plots window

Pile
Direction
Level

6.10

Select the pile number for which the chart will be displayed.
Select the direction for which the chart will be displayed.
Select the level for which the chart will be displayed.

Ducbots
This result is available for Dynamic model only.On the menu bar, click Results and then
choose Ducbots to open the Ducbots window which displays the results for a dynamic calculation. Four different charts can be displayed depending on the selection made from the
drop down list (Figure 6.12) located at the top of the Ducbots window.

Figure 6.11: Ducbots window

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Figure 6.12: Drop down list of charts available in Ducbots window

Displacement –
Force (Filtered)
Displacement –
Force
Time –
Displacement
Time – Force

Select it to display the chart of force versus displacement with filtering
of data.
Select it to display the chart of force versus displacement without
filtering of data.
Select it to display the chart of displacement versus time.
Select it to display the chart of force versus time.

The definitions of the icons of the Edit and Tools sub-windows in the left-hand side panel can
be found in section 2.2.3.

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7 Tutorial 1: Laterally loaded single pile
This first tutorial describes a single steel pile laterally loaded in a clay layer. The soil and pile
properties are the ones used for the Lake Austin test which is one of the tests that from the
basis of the American Petroleum Institute (API) rules. Indeed, the results of this test were used
to analytically model the non-linear force-displacement relation (usually called P-Y curve) that
describes the soil resistance for a laterally loaded pile.
The objectives of this exercise are:

 To choose the appropriate model for the given project.
 To learn the steps needed to enter the project geometry, the layer and pile properties
and the lateral load.

 To analyze the calculation results by inspecting the plots and tables that result from this
calculation.
For this tutorial the following modules are needed:

 D-P ILE G ROUP Standard module (Poulos model)
 Cap module
This tutorial is presented in the file Tutorial-1.pii.
7.1

Introduction
For this tutorial, a single steel pile is loaded with a lateral load of 80.9 kN.

Figure 7.1: Soil profile and pile position (Tutorial 1)

Pile data
The pile has a length of 12.8 m, a diameter of 0.319 m and a wall thickness of 12.7 mm. The
Young’s modulus of steel is set equal to 2.1 × 108 kN/m2 . The pile head is fixed to the cap
and is situated at level 0 m.

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Soil data
The soil is composed of Lake Austin clay which properties are given in Table 7.1. The soil is
completely saturated as the water level coincides with the soil surface.
Table 7.1: Soil properties for Tutorial 1

Soil type
Saturated unit weight
Unsaturated unit weight
Undrained shear strength su
Lateral rule from API:

J
ε50

[kN/m3 ]
[kN/m3 ]
[kN/m2 ]

Lake Austin clay
Soft clay
20
20
38.3

[-]
[-]

0.25
0.012

Lateral rule
The force-displacement relation (usually called P-Y curve) that describes the soil resistance
for the laterally loaded pile is taken according to the API rule which is an internationally accepted Design Code. Two parameters are needed for the determination of the P-Y curve:
the empirical constant J which can range between 0.25 to 0.5 and the strain which occurs
at one-half the maximum stress, noted ε50 . Both are determined from field testing and the
resulting values are given in Table 7.1.
7.2

Project
In the project menu, the project model is chosen and the project properties are described.

7.2.1

Project Model
To create a new project, follow the steps described below:
1. Start D-P ILE G ROUP from the Windows taskbar (Start/Programs/Deltares/D-P ILE G ROUP).
2. Click File and choose New on the menu bar to start a new project. This will result in a
screen similar to Figure 7.2. In the main window opened, the caption of the main window
of D-P ILE G ROUP displays the program name, followed by the default model, Cap, and the
default project name: Project1.

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Figure 7.2: D-Pile Group main window

3. In the Project menu, select Model to get an overview of all available models (Figure 7.3).

Figure 7.3: Model window

4. Select the Cap model as it is the more appropriate model for this tutorial.
5. Click OK to confirm.
Six different models are available in D-P ILE G ROUP. For the Poulos and Plasti-Poulos models,
the pile-soil interaction model doesn’t use springs; the pile is considered as an elastic body
in a homogeneous elastic soil. As this tutorial uses the soil-pile spring relation (P-Y curve)
according to the API, those two models are not relevant here. The Dynamic model is dedicated for dynamic analysis of a collision of a ship against a pile which is not the case in this
tutorial. The Cap soil interaction, Cap layered soil interaction and Cap models use a soil-pile
spring relation. The Cap soil interaction and Cap layered soil interaction models also take into
account the interaction between piles via the soil between. However, this tutorial models a
single pile therefore no pile-soil-pile interaction model is needed in this case. Consequently,
the Cap model is the more appropriate model for this problem as it is less time consuming
(no need to input a pile-soil-pile interaction model and faster calculation) compared to the Cap
soil interaction and Cap layered soil interaction models.

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Figure 7.4: Functioning of the Cap model for Tutorial 1

Figure 7.4 schematizes the functioning of the Cap model for this tutorial: the pile is laterally
loaded by means of the cap which transmits the load to the pile. Only the lateral soil springs
will be active to transmit the lateral load from the pile to the soil. For the Cap model, axial
springs along and at the tip of the pile exist but they are not active in this case, that’s why they
are not represented.
See section 4.1.1 for a detailed description.
7.2.2

Project Properties
To give the project a meaningful description, follow the steps described below:
6. Open the Project Properties window by selecting Properties in the Project menu.
7. Fill in  and  for Title 1 and
Title 2 respectively in the Identification tab.
8. Click OK to confirm.

Figure 7.5: Project Properties window, Identification tab

See section 4.1.2 for a detailed description.

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7.3

Soil
In the Soil menu all information about the geometry and the soil layers that are present at the
site where the pile is to be located can be specified.

7.3.1

Soil Layers
The properties of the clay layer need to be defined before the location of the layer itself is
specified. Input of the soil profile is described in the next paragraph.
9.
10.
11.
12.
13.
14.

In the Soil menu, select Layers.
In the window displayed, click Add to enter the material data of the first layer.
Change the default soil layer name  to .
In the Soil type sub window, select .
In the Layer data sub window, enter the required soil properties as indicated in section 7.1.
In the Lateral rule sub window, the force-pile displacement relation (usually called PY
curve) must be selected. For clay layer, two relations according to the API design rules are
available: API and API Cyclic, which correspond to a static and a cyclic loading respectively. As this tutorial described a static loading, the API Lateral rule must be selected.
15. The Axial friction rule and Axial friction data sub windows are not relevant in this tutorial
as no axial load is applied on the pile. The Axial friction rule is left to the default API rule
and the dz at 100% is set equal to <0.002 m> as a value different of 0 must be entered
to avoid error during the calculation process.
16. Click OK to confirm the input data for the layer properties.

Figure 7.6: Soil Layers window

See section 4.2.1 for a detailed description.
7.3.2

Soil Profiles
Once the layer properties have been entered, one or more soil profiles can be entered to
reflect the available site investigation data. To do this, the top level of each layer is input and
one of the previously defined soils is selected.

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17. Select Profiles from the Soil menu to open the Soil Profiles window.

Figure 7.7: Soil Profiles window

18. Click Add to create a soil profile with number <1>.
button in the table
19. Compose the profile composed of one layer by clicking the Add row
at the right side of the window.
20. In the first column, enter a top level of <0 m> and in the second column select the  from the drop down list.
21. Set the water level for this profile equal to <0 m>.
22. The X and Z co-ordinates of this profile correspond to the location of the boring that have
been performed in situ. This information is relevant when several soil profiles are defined
which is not the case in this tutorial. Therefore the X and Z co-ordinates are set equal to
their default values <0 m>.
23. Click OK to confirm.
See section 4.2.2 for a detailed description.
7.4

Pile
Now that the geometry has been described, the pile location must be defined. First, the pile
characteristics of the pile type that shall be used must be specified.

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7.4.1

Pile Types
24.
25.
26.
27.
28.
29.

Click Types in the Pile menu to open the Pile Types window.
Click Add to create a new pile type.
Change the default pile type name  to .
In the Material sub-window, choose Steel.
In the Parameters sub-window, enter the properties given in section 7.1.
Click OK to confirm.

Figure 7.8: Pile Types window

See section 4.3.1 for a detailed description.
7.4.2

Pile Tip Curves
The pile tip curve specifies the axial load-displacement relation of the pile tip. In this tutorial,
only a lateral load is applied therefore no pile tip curve is needed in the calculation as it
describes the axial behavior. However, at least one pile tip curve is needed as input in the Pile
Positions window in section 7.4.3. Therefore, a simple linear tip curve must be defined.The
pile tip curve is different from the axial T-Z curve as the first one concerns the spring at the
pile tip whereas the second one concerns the springs along the pile.The simple linear pile tip
curve must be defined in terms relative to the end bearing capacity which will be entered in
the Pile Positions window, in the next paragraph, section 7.4.3.
30. Click Pile Tip Curves in the Pile menu to open the Pile Tip Curves window.
31. Click Add to create a pile tip curve.
32. Enter two points, with co-ordinates (0 %, 0 m) and (100 %, 0.01 m) as shown in Figure 7.9.

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Figure 7.9: Pile Tip Curves window

In the table at the right hand side of the window, the points that composed the pile tip curve
must be entered. Two points are required as a minimum. Rt corresponds to the axial load
relative to the end bearing capacity and Zt corresponds to the tip settlement at which Rt
occurs.
33. Click OK to confirm the input.
See section 4.3.2 for a detailed description.
7.4.3

Pile Positions
Now that the geometry, the pile type and the pile tip curve are defined, the pile position can be
specified. According to Figure 7.1, the pile is positioned vertically with its top at co-ordinates
(0, 0, 0). The pile types, soil profiles and pile tip curves defined in the previous paragraphs can
be associated to each inputted pile. In this tutorial, only one pile is considered and associated
to the unique pile type, soil profile and pile tip curve previously inputted.
34. Open the Pile Positions window from the Pile menu.
35. Define pile <1> with Soil profile <1>, Pile type  and Pile tip
curve <1>.
36. Enter the Xtop, Ytop and Ztop co-ordinates given above with a  Top condition as
the pile is not fixed to the cap.
37. The End bearing capacity is <500 kN> as specified in section 7.1. This value is only
used to determine the pile tip axial load-displacement relation (called pile tip curve, see
section 7.4.2). Since in this tutorial only a lateral load is applied on the pile the End bearing
value will not be used.The Rake [hor/vert] and the Angle in XZ plane are used to define the
pile inclination and orientation in the XZ plane when the pile is not vertical. When the pile
is vertical they are set to <0> (see “Tutorial 3: Pile plan analysis” for more explanation on
these parameters).
38. Click OK to confirm the input.

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Figure 7.10: Pile Positions window

See section 4.3.3 for a detailed description.
7.5
7.5.1

Cap
Cap Location
Before entering the loads that apply to the cap, the reference coordinates (and point of load
application) of the cap needs to be specified. In this tutorial it coincides with the position of
the pile head as shown in Figure 7.1.
39. Click Location in the Cap menu to open the Cap Location window.
40. Fill in the X, Y and Z co-ordinates as (0, 0, 0).
41. Click OK to confirm.
Note: In a D-P ILE G ROUP calculation all forces apply to one single point of the cap.

Figure 7.11: Cap Location window

See section 4.4.1 for a detailed description.
7.6

Loads Cap
Now that the location where the lateral force applies to the cap has been specified, the lateral
load itself can be entered. Loads can be applied by defining either a translation or a force,
and by defining a rotation or a moment, in all three directions of our co-ordinate system. In
this tutorial, the lateral load is defined by entering a force in the X-direction. In order to see
the development of plasticity during the loading of the pile, the load must be applied in several
steps called load-steps. A number of 10 steps is considered to be enough for most loading
conditions. The load-step number will have little or no influence on the calculation results but
permits to see the plasticity effect in the resulting charts at the intermediate loading stages.
For very large loads, far into the plastic region and close to pile failure, it may be wise to
increase the number of load steps in order to impose the load in a more gradual way.

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42. Click Cap in the Loads menu to open the Loads Cap window.

Figure 7.12: Loads Cap window

43. Select Load from the drop down list for Translation/Forces in the X direction and enter a
force of <80.9 kN>.
44. Enter a Loadstep number of <10>.
45. Click OK to confirm.
See section 4.5.1 for a detailed description.
7.7
7.7.1

Calculation
Calculation Options
Experimental results of this tutorial exist in literature Matlock (1970). In order to compare them
to the D-P ILE G ROUP predictions, the calculation must be performed with a maximum number
of nodes to get the more accurate results.
46. Click Options from the Calculation menu to open the Calculation Options window.
47. Change the default Minimum number of pile nodes into <200> which is the maximum
allowable number.
48. Click OK to confirm.

Figure 7.13: Calculation Options window

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See section 5.1 for a detailed description.
7.7.2

Start Calculation
Now that all input has been entered, the calculation can be executed. But before doing this,
the project must be saved, giving it a name.
49. Click Start from the Calculation menu to open the Calculation window.
50. In the window displayed, mark the checkbox Create PY Curve dumpfile in order to view
the P-Y curve plot after calculation (Figure 7.14).

Figure 7.14: Calculation window

51. Click OK to calculate the results.
Because this project was not saved before, the Save As window opens and prompts to give
this project a name.

Figure 7.15: Save As window

52. Browse to a folder where the file can be saved and type in the file name 
for example and click Save.
During the calculation, the current activity is shown in the Calculation window. After the calculation has finished, the Calculation Messages window opens and gives an echo of the input
file. As the calculation was executed successfully, no error messages appear in red color in

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this window.
See Start Calculation [section 5.2] for a detailed description.
7.8
7.8.1

Results
Charts results
To see the charts of the displacement, force and bending moment along the pile in X”, Y” and
Z” directions:
53. Select Charts from the Results menu.
The window displayed (Figure 7.16) shows the lateral displacement, the shear force and the
bending moment around the lateral axis X”, along the pile, at load-step 10 which corresponds
to the end of loading. As expected, the lateral deflection of the pile is maximal at the pile head
where the load is applied.

Figure 7.16: Charts window in the X” direction

More accurate results can be obtained by doing the following.
54. Click the right side mouse button and select View Data to open a Chart Data window.
The Displacement tab of the window displayed (Figure 7.17) shows that the pile head deflection is 34.66 mm.

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Figure 7.17: Chart Data window, Displacement tab

It can be checked that no movements occur in the Y” and Z” directions as no loads were
applied by selecting Direction . In the window displayed, the settlement, axial force and
friction along the pile are nil. The same observation can be done by selecting Direction .
See section 6.6 for a detailed description.
7.8.2

P-Y curve plots
To see the plot of the lateral P-Y curve:
55. Select PY Plots from the Results menu.

Figure 7.18: P-Y plots window in the X direction at top level

The window displayed (Figure 7.18) shows the relation between the lateral force called P
and the lateral displacement called X” for the elasto-plastic spring located at depth 0.02 m
below the surface level. By selecting a different depth at the left hand side of the window, a
different curve corresponding to a different spring will be displayed because the P-Y relation

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depends on the depth (see Equation 15.3 and Equation 15.6 in the Background section for
more details).
It can also be noticed that the P-Y curve is not a continuous non-linear curve but is modeled
with five linear branches. See section 15.1.1 for background information. This approximation
is however quite exact, as demonstrate in the Verification Report (see paragraph 1.25).
See section 6.9 for a detailed description.
7.9

Conclusion
This tutorial models a laterally loaded single pile. The results of this test were used by the
API to determine their analytical non-linear force-displacement relation (P-Y curve) that describes the soil resistance for a pile laterally loaded. Experimental results for this test exist in
Matlock (1970) and are compared to the D-P ILE G ROUP calculations in Figure 7.19 below. The
agreement between test and D-P ILE G ROUP predictions is very good. Moreover, the measured
pile head lateral displacement is 34.78 mm which is very close to the calculated displacement
(34.66 mm).

Figure 7.19: Calculated and measured bending moment along the pile for the Lake Austin
test

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8 Tutorial 2: 4×4 pile group in homogeneous elastic soil
This tutorial describes the design of a 4×4 pile group under general loading (combination of
axial and lateral loads with a moment load). The soil is two-layered with a constant stiffness
from the surface to the level of the pile tip and another (higher) stiffness from the pile tip
downwards. For this project, the analytical and fast Poulos model is used which assumes an
elastic soil interaction model.
The objective of this exercise is:

 To perform a calculation with the Poulos model by inputting a soil interaction model.
For this tutorial the following module is needed:

 D-P ILE G ROUP Standard module (Poulos model)
This tutorial is presented in the file Tutorial-2.pii.
8.1

Introduction to the case
This tutorial describes the design of a 4×4 pile group subjected to a combination of an axial force of 5600 kN, a lateral force of 420 kN and a moment of 2200 kNm. The piles are
embedded into stiff clay.

Figure 8.1: 4 × 4 pile group in a two-layered elastic soil. (Tutorial 2)

Pile data
The round concrete piles are 18 m long, 0.6 m in diameter with centre-to-centre spacing of
three pile diameters. All pile heads are fixed to a stiff concrete foundation plate and have a
Young’s modulus of 25 GPa.

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Soil data
The Young’s modulus of the soil 20 MPa over the length of the pile and 85 MPa below the pile
tip. The Poisson ratio is set to 0.5.
Model
For this example, no detailed soil properties and profile data are available, only the soil stiffness is known. Moreover piles are very close to each other as the centre spacing is only
three diameters. This leads to use the Poulos model for the calculation as this model take into
account the pile-soil-pile interaction using few data.
Figure 8.2 schematizes the functioning of the Poulos model: the soil system for pile-soil-pile
interaction consists of one homogeneous layer over the length of the pile and one layer at the
pile tip. Each pile interacts with all the other piles through the cap and also through the elastic
soil. In this tutorial, the cap corresponds to a stiff concrete foundation plate.

Figure 8.2: Functioning of the Poulos model for Tutorial 2

8.2

Project Model and Properties
For this tutorial, the simple and fast Poulos model is used as explained in section 8.1.
1. Before inputting the data, create a new project by selecting New in the File menu and save
it as  in the Save As window.
2. Open the Model window from the Project menu.
3. Select the Poulos model and click OK to confirm.

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Figure 8.3: Model window

4. Open the Project Properties window by selecting Properties in the Project menu to give
the project a meaningful description.
5. Fill in ,  and  for Title 1, Title 2 and Title 3 in the Identification tab.
See section 4.1.1 and section 4.1.2 for a detailed description.
8.3

Soil Interaction Model
6. Enter a Poisson ratio of <0.4999> as a value equal or more than 0.5 is not allowed.
7. In the Soil Interaction Model window from the Soil menu, enter the Young’s modulus
of the two layers according to Figure 8.2 with a Young’s modulus at surface level of
<20 000 kPa> and a Young’s modulus below the pile tip of <85 000 kPa>.

Figure 8.4: Soil Interaction Model window

See section 4.2.3 for a detailed description.
8.4

Pile
Now that the soil interaction model has been inputted, the pile plan must be defined.

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8.4.1

Pile Types
8. In the Pile Types window from the Pile menu, click Add to create a new pile type.
9. Change the default pile type name  to  and define it as a Concrete round
pile material.
10. Enter the pile characteristics described in section 8.1 and given in Figure 8.5 below.

Figure 8.5: Pile Types window

See section 4.3.1 for a detailed description.
8.4.2

Pile Positions
To enter the pile plan, the Pile Grid option can be used as this tutorial have its piles exactly
on a regular grid as shown in Figure 8.1.
11. Click Positions Table in the Pile menu to open the Pile Positions Table window.
12. Click Pile Grid to generate automatically the actual pile plan.
13. Generate 4 piles in the X direction with co-ordinates ranging From X-coordinate Top <2.70 m> To X-coordinate Top <2.70 m>, and 4 piles ranging From Z-coordinate Top
<-2.70 m> To Z-coordinate Top <2.70 m>, as indicated in Figure 8.1.
14. Fill in all properties that are common for all piles (Figure 8.6): Pile type is , Level at
top is <0 m> and the Top condition is . Leave the Angle XZ plane and the Rake
to their default nil values as the piles are vertical.

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Figure 8.6: Pile Grid window

15. Click OK to confirm and automatically generate the 16 piles in the Pile Positions window
(Figure 8.7).

Figure 8.7: Pile Positions window

16. Click OK to confirm this pile plan and review the graphical representation of the piles in
the Top View Layout window.

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Figure 8.8: Top View Layout window

See section 4.3.4 and section 4.3.3 for a detailed description.
8.4.3

Cap Location
The loads apply to the center of gravity of the stiff concrete foundation plate which corresponds
to the cap.
17. Click Location in the Cap menu.
18. In the window displayed, fill in <0 m> for the X, Y and Z co-ordinates.
19. Click OK to confirm.
See section 4.4.1 for a detailed description.

8.5

Loads Cap
Now that the location where forces apply to the cap has been specified, the axial, lateral and
moment loads can be entered.
20. Click Cap in the Loads menu to open the Loads Cap window.
21. Select Load from the drop down list for Translation/Forces in the X direction and enter a
force of <420 kN> which corresponds to the lateral load.
22. Select Load from the drop down list for Translation/Forces in the Y direction and enter a
force of <-5600 kN> which corresponds to the axial load.
23. Select Moment from the drop down list for Rotation/Moments in the Z direction and enter
a bending moment of <-2200 kNm>.
24. Enter a Loadstep number of <1> to apply the loads in only one step as the Poulos model
assumes an elastic behavior.
25. Click OK to confirm.

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Figure 8.9: Loads Cap window

See section 4.5.1 for a detailed description.
8.6

Calculation and Results Top View Results
26. Select Start from the Calculation menu and click OK to start the calculation.
27. Select Top View from the Results menu to see the values of the displacement, force and
bending moment at the top of each pile.
button of the Edit panel to optimize the top view. The window
28. Use the Zoom rectangle
displayed (Figure 8.10) gives the lateral force (in the X direction) at the top of each pile.
The lateral force is 46.1 kN at the top of the corner piles 1, 4, 13 and 16.

Figure 8.10: Top View Results window, lateral force

29. Select the  direction to view the axial forces. In the window displayed (Figure 8.11),
the axial force at the top of corner piles of the trailing row (piles 1 and 4) are 435.2 kN and
671.9 kN for the leading row (piles 13 and 16).

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Figure 8.11: Top View Results window, axial force

30. Click the Show force button at the left of the window to deselect this option and click the
button at the left of the window to view the settlement (vertical disShow displacement
placement) results at the pile head. In the window displayed (Figure 8.12), the settlements
of the trailing row (piles 1 to 4) are equal to 6 mm whereas the settlements of the leading
row (piles 13 to 16) are equal to 8 mm.

Figure 8.12: Top View Results window, settlement

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Figure 8.13: Top View Results window, deflection

In the window displayed (Figure 8.13), the deflection is the same for all piles (3 mm).
See section 6.5 for a detailed description.
8.7

Conclusion
The displacements, forces and bending moments at the top of a 4 × 4 pile group have been
calculated using a simple and fast model (Poulos model) which only takes into account the
interaction between the soil and the piles. No soil profile is needed.
Results show that the cap settlement is about 7 mm and the cap deflection only 3 mm, which
is acceptable.

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9 Tutorial 3: Pile plan analysis
This tutorial describes the analysis of a more complex set of 16 piles that are connected by a
cap which is loaded by a prescribed displacement.
The objectives of this exercise are:

 To learn the steps needed to enter the project geometry and properties, in particular
inclined piles.

 To input a prescribed displacement.
 To analyze the calculation results by inspecting the plots and tables that result from this
calculation.
For this tutorial the following modules are needed:

 D-P ILE G ROUP Standard module (Poulos model)
 Cap module
This tutorial is presented in the file Tutorial-3.pii.
9.1

Introduction to the case
This tutorial deals with the analysis of a 16 piles group (Figure 9.1) connected with a cap
loaded by a prescribed displacement of 10 mm in the Z direction (see Figure 9.2).

Figure 9.1: 3D view of the 16 piles connected to a cap (Tutorial 3)

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Pile data
All piles consist of a concrete square pile with a width of 400 mm and a length of 25 m. They
are fixed to the cap and their top level is at 2.91 m. Their position in the XZ plane is given in
Figure 9.2.

Figure 9.2: Top view of the pile positions and the CPT location (Tutorial 3)

Soil data
The analysis of a cone penetration test (CPT) located at X = 2 m and Z = 2 m allowed to
define the soil profile of Figure 9.3 composed of four clay/peat layers surrounded with two
sand layers. Their properties were determined from laboratory tests performed on a borehole
and are given in Table 9.1. For the pile-soil interaction, soil behavior according to the American
Petroleum Institute (API) is used.

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Figure 9.3: Soil profile and piles position (Tutorial 3)

Table 9.1: Soil properties for Tutorial 3

Soil type
Unsat. unit weight [kN/m3 ]
Sat. unit weight [kN/m3 ]
Friction angle ϕ [◦ ]
Delta friction angle δ [◦ ]
su [kN/m2 ]
Cone resistance [kN/m2 ]
K0 [-]
Lateral rule
Axial rule
J [-]

ε50
dz at 100 % [m]

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Clay
humeus
Stiff
clay
14
14

Clayey
peat
Soft
clay
11.1
11.1

Silty
clay
Stiff
clay
15.6
15.6

10

10

10

API
API
0.25
0.02
0.004

API
API
0.25
0.02
0.004

API
API
0.25
0.02
0.004

Sand
fill
Sand

Deep
sand
Sand

17
19
32.5
21

17
20
32.5
21

Peat
Soft
clay
11
11

10
5000
0.5
API
API

5000
0.5
API
API

0.0025

0.0025

API
API
0.25
0.02
0.004

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Lateral and axial rules
The lateral and axial force-displacement relations (called P-Y and T-Z curves respectively) that
describe the soil resistance are taken according to the internationally accepted Code API.
For the lateral rule, two specific parameters J and e50 are needed for clay and peat layers
(see Equation 15.3 in section 15.1.1). They should normally be determined from field testing.
However, those specific tests are generally not performed in situ (which is the case in this
tutorial) and estimated values are used:

 The empirical constant J can range from 0.25 until 0.5 according to the API; therefore the
conservative value of 0.25 is used.

 The strain ε50 is determined from Table 9.2 as a function of the undrained shear strength.
For the axial rule, parameter “dz at 100%” is needed and corresponds to the relative displacement between pile and soil at which the maximum value of the skin friction is reached. The
API prescribed a value of 0.1 inches (2.54 mm) for sand and 0.01 D for clay, where D is the
pile diameter equal to 0.4 m in this tutorial. Therefore, values of 0.0025 m and 0.004 m are
used for sand and clay layers respectively.
Table 9.2: Determination of ε50 as a function of the undrained sheart strength su

su
[kN/m2 ]
5-25
25-50
50-100
100-200
200-400

ε50
[-]
0.020
0.010
0.007
0.005
0.004

Model
For this tutorial, the Cap model is used as it is the only model for which a prescribed displacement can be inputted. Figure 9.4 schematizes the functioning of the Cap model in this
case: piles move axially and laterally by means of the cap which transmits the prescribed
displacement to the piles. The springs transmit the piles displacement to the soil.

Figure 9.4: Functioning of the Cap model for Tutorial 3

9.2

Project
To create a new project, follow the steps described below:

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1. Click File and choose New on the menu bar to start a new project.
2. In the Save As window from the File menu, save it as .
3. Click OK to confirm.
9.2.1

Project Model
To get an overview of all available models in D-P ILE G ROUP:
4. Select Model from the Project menu (Figure 9.5).
5. Select the Cap model for this tutorial as it is the only model for which a prescribed displacement can be inputted.
6. Click OK to confirm.

Figure 9.5: Model window

See section 4.1.1 for a detailed description.
9.2.2

Project Properties
To give the project a meaningful description, follow the steps described below:
7. Open the Project Properties window by selecting Properties in the Project menu.
8. Fill in  and  for Title 1 and Title 2 in
the Identification tab.

Figure 9.6: Project Properties window, Identification tab

9. Click OK to confirm.
See section 4.1.2 for a detailed description.

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9.3

Soil
In the Soil menu all information about the geometry and the soil layers that are present at
the site where the pile plan is to be located can be specified. In this tutorial, this information
is known from the analysis of a cone penetration test and laboratory tests performed on a
borehole.

9.3.1

Soil Layers
The properties of each soil layer need to be defined before the location of the layer itself is
specified. Input of the soil profile is described in the next paragraph.
10.
11.
12.
13.

In the Soil menu, select Layers.
In the window displayed, click Add to enter the material data of the first layer.
Change the default soil layer name  to .
Enter the required soil properties for the first layer  as indicated in Figure 9.7.

Figure 9.7: Soil Layers window, properties of layer 

14. Repeat this process for the five other soil layers by adding five additional layers, , , ,  and , and entering the
lateral and axial rules according to API and the soil properties given in Table 9.1.
15. Click OK to confirm the input data for the layer properties.
See section 4.2.1 for a detailed description.
9.3.2

Soil Profiles
Once the layer properties have been entered, one or more soil profiles from experimental
results can be specified. To do this, the top level of each layer is input and one of the previously
defined soils is selected.
16. Select Profiles from the Soil menu.
17. In the window displayed, click Add to create a soil profile with number <1>.
18. Compose the profile according to Figure 9.1 by clicking the Add row
button in the table

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at the right side of the window. In the first column, the top levels of the layers may be
entered. In the second column, the available materials may be selected from a drop down
list. Finally, the table as indicated in Figure 9.8 must be entered.

Figure 9.8: Soil Profiles window

19. Set the water level for this profile equal to <0 m>.
20. The X and Z co-ordinates of this profile are set equal to <2 m>, which corresponds to the
location of the boring that have been performed in situ (see Figure 9.3).
21. Click OK when all these data are entered.
In the Top View Layout window displayed (Figure 9.9), a green triangle with co-ordinates (2, 2)
appears with number 1 beside. It corresponds to the soil profile number <1> just defined.

Figure 9.9: Top View Layout window after entering soil profile

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See section 4.2.2 for a detailed description.
9.4

Pile
Now that the geometry has been described, the pile plan must be defined. First, the pile
characteristics of the pile type that shall be used must be specified. Then, the locations and
rake of all piles present must be specified.

9.4.1

Pile Types
22. Click Types in the Pile menu to open the Pile Types window.
23. Click Add to create a new pile type.
24. Change the default pile type name  to <400_25>. The name of this pile type is
chosen after the dimensions: a  pile with a width of <400 mm> and
a length of <25 m>.
25. In the Material sub-window, choose Concrete square.
26. In the Parameters sub-window, enter the above mentioned dimensions. For Young’s modulus, enter <107 kN/m2 >.

Figure 9.10: Pile Types window

27. Click OK to close the Pile Types window.
See section 4.3.1 for a detailed description.
9.4.2

Pile Tip Curves
The pile tip curve specifies the load-displacement behavior of the pile tip in terms relative
to the end bearing capacity which will be entered in the Pile Positions window, in the next
paragraph (section 9.4.3). In this tutorial, the pile tip curve is taken from line 1 in figure 6 in
NEN 6743 NEN (1991). We consider this line to be described accurately enough with four
points: (0, 0), (50, 0.01), (75, 0.02) and (100, 0.04).
Define this pile tip curve by following these steps:
28. Click Pile Tip Curves in the Pile menu to open the Pile Tip Curves window.
29. Create a pile tip curve by clicking Add.
30. Enter the points given above. The table displayed in Figure 9.11 should be obtained.

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Figure 9.11: Pile Tip Curves window

See section 4.3.2 for a detailed description.
9.4.3

Pile Positions
Now that the geometry, the pile types and their pile tip curves are defined, the pile plan can
be entered. To do this, the Pile Grid option is used as it gives a powerful means to generate
a great part of the input. Pile Grid
31. Click Positions Table in the Pile menu to open the Pile Positions Table window.
32. In the window displayed, click Pile Grid to generate a grid of piles that gives us a draft of
the actual pile plan.The problem analyzed in this tutorial does not have its piles exactly
on a regular grid as shown in Figure 9.1 and Figure 9.3. This does not mean that the
generation of a pile grid cannot be used.
33. Fill in all properties that are common for all piles in the Pile Grid window: Soil profile is
<1>, Pile type is <400_25>, Pile tip curve is <1>, End bearing capacity is <500 kN>,
Level at top is <2.91 m> and the Top condition is .Furthermore, most of the piles
are not positioned straight, but have a rake of 0.2. This means that over a length of 1 m,
the distance between the pile tip and the pile top, projected in the XZ plane, is 20 cm.
34. Fill in a Rake of <0.2>. This rake does not apply to all piles, but to the majority of them.
This will be corrected later on.The direction of the pile is specified with the angle of the pile
in the XZ plane regarding to the positive X axis. A positive angle means anti-clockwise.
35. Fill in an Angle XZ plane of <0◦ >. This angle does not apply to all piles, but only for piles
11, 12, 14 and 15 of Figure 9.3. This will be corrected later on. All piles are located in
two rows that have the same X co-ordinate. Only the Z co-ordinates are not distributed
regularly. The Z co-ordinates will be corrected later on.
36. Generate 2 piles in the X direction with co-ordinates ranging From X-coordinate Top <0.03 m>
To X-coordinate Top <1.03 m>, and 9 piles ranging From Z-coordinate Top <-8 m> To
Z-coordinate Top <8 m>, as indicated in Figure 9.12.

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Figure 9.12: Pile Grid window

37. Click OK to generate the grid of 18 piles. All generated piles are now given in the Pile
Positions table, as indicated in Figure 9.13.

Figure 9.13: Pile Positions window after using the Pile Grid option

The number, co-ordinates, angles and rakes of the different piles defined in the table of the
figure above are not exactly those defined in Figure 9.2. Therefore, some modifications must
be performed:
38. Delete piles 12 and 16 by selecting them and clicking the Delete row
button.
39. Rename piles 13, 14, 15, 17 and 18 into respectively 12, 13, 14, 15 and 16 in the Pile
name column.
40. Correct the Z co-ordinates of all piles (except piles 5 and 13) in the Z top column by
changing -8 m, -6 m, -4 m, -2 m, 2 m, 4 m, 6 m and 8 m into respectively -6.5 m, -4.5 m,
-2.5 m, -0.8 m, 0.8 m, 2.5 m, 4.5 m and 6.5 m.
41. Fill in the correct Angle in XZ plane for all piles: for piles 1 and 10, an angle of <90◦ >; for
piles 9 and 16, an angle of <270◦ >; for piles 2, 4, 6 and 8, an angle of <180◦ >; for all
other piles, an angle of <0◦ >.
42. The piles 3, 5, 7 and 13 stand straight, so their rake should be set to 0.
Note: When deleting a pile, the other piles are not renumbered automatically.

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Figure 9.14: Pile Positions window after corrections

43. Click OK to close the input window, and review the graphical representation of the piles in
the Top View Layout window.

Figure 9.15: Top View Layout window after entering the piles group

See Pile Positions [section 4.3.3] and Pile Grid [section 4.3.4] for a detailed description.

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9.5
9.5.1

Cap
Cap Location
Before entering the loads that apply to the cap, the location of the cap needs to be specified.
We suppose that the loads apply to the center of gravity of the pile plan. The pile plan is line
symmetric in the X axis, so the value of the Z co-ordinate is 0 m. All piles have a Y co-ordinate
of 2.91 m. The X co-ordinate is the weighted mean of 9 piles with a co-ordinate of 0.03 m and
7 piles with a co-ordinate of 1.03 m, which lead to (9 × 0.03 + 7 × 1.03) /(9 + 7) = 0.4675 m.
To enter this point:
44. Click Location in the Cap menu.
45. In the window displayed, fill in the X, Y and Z co-ordinates as calculated above. The same
window as Figure 9.16 should be obtained.
46. Click OK to confirm.
Note: In a D-P ILE G ROUP calculation all forces apply to one single point of the cap.

Figure 9.16: Cap Location window

See section 4.4.1 for a detailed description.
9.6

Loads Cap
Now that the location where the forces apply to the cap have been specified, the loads themselves can be entered. Loads can be applied by defining either a translation or a force, and
by defining a rotation or a moment, in all three directions of our co-ordinate system. In this
tutorial, the load is defined by giving up a displacement of 10 mm of the cap in the Z-direction
that is being applied in 10 steps. Furthermore, there is no rotation around the X-axis. In order to see the development of plasticity in the resulting charts during the loading, the load is
applied in 10 steps.
47. Click Cap in the Loads menu to open the Loads Cap window.
48. Select Displ. from the drop down list for Translation/Forces in the Z direction and enter a
displacement of <-0.01 m>.
49. Select Rotation from the drop down list for Rotation/Moments in the X direction and enter
a rotation of <0◦ >.
50. Enter a Loadstep number of <10>.
51. Click OK to confirm.

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Figure 9.17: Loads Cap window

See section 4.5.1 for a detailed description.
9.7

Calculation and Results
Now that all input has been entered, the calculation can be executed.
52. Click Start from the Calculation menu.
53. In the window displayed, click OK to calculate the results.

9.7.1

Report Selection
This window allows selection of the report content for viewing, exporting and printing, by
marking the checkboxes in the tree view (Figure 9.18).
54. To open this window, select Report Selection from the Results menu.
55. Click OK to generate a report with the selected content.

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Figure 9.18: Report Selection window

See section 6.1 for a detailed description.
9.7.2

Report
The total report content contains a top view layout of the project, graphical and tabular results.
56. Click Report in the Result menu to view the report with the selected content.
button to view the different pages of the report.
57. Use the Move to next page
Page 5 of the report (Figure 9.19) displays the tabular results of the global and local forces
and the displacements at the pile top, at the end of the loading (load step 10), for all 16 piles.

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Figure 9.19: Report window, Pile top Results at Load step 10 section

The global forces are the values of the forces in the global Cartesian co-ordinate system
(X, Y, Z) where the direction of the positive Y-axis is opposite the gravity direction (see section 1.6). The local forces are the values of the forces in the local Cartesian co-ordinate
system (X”, Y”, Z”) of a given pile, where the direction of the positive Y”-axis corresponds
with the pile direction pointing upwards and the rotation angle of the X”-axis compared to the
X-axis is equal to the Angle in XZ plane inputted in the Pile Positions window (section 9.4.3).
This is illustrated in Figure 9.20.

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Figure 9.20: Pile 1 in the global (X, Y, Z) and local (X”, Y”, Z”) co-ordinates systems

If the pile is vertical with a nil Angle in XZ plane, then the local axis coincide with the global
axis. This can be checked with pile number 3 for which the global and local forces, displacements and moments calculated in the Report window are the same (see Figure 9.19).
If the pile is inclined, then the global and local forces, displacements and moments are different. This can be checked with pile number 1 for which, according to Figure 9.20, the local
forces are related to the global forces by the following relations:
FX00 = FY ×sin(θ)−FZ ×cos(θ) =-148.208 sin(11.537◦ ) + 159.045 cos(11.537◦ ) = 126.2 kN
FY00 = FY × cos(θ) + FZ × sin(θ) =-148.208 cos(11.537◦ ) – 159.045 sin(11.537◦ ) = 176.5 kN
FZ00 = FX =0.017 kN
Those values are the same as the local forces calculated in the Report window (see Figure 9.19). See section 6.2 for a detailed description.
9.7.3

Top View
The pile top results from the Report window [section 9.7.2] can also be found in the Top View
window.
58. Select Top View from the Results menu.
59. In the window displayed, select the  direction to view the horizontal forces (in the Z
direction) at the pile head (Figure 9.21).
It can be checked that the values of the lateral forces in the Z direction in Figure 9.21 coincide
with the global forces in the Z direction (Fz) given in Figure 9.19 of the Report window.

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Figure 9.21: Top View window, Lateral force in the Z direction at the pile head

60. Select the  direction to view the horizontal forces (in the Y direction) at the pile head
(Figure 9.22).
It can be checked that the values of the lateral forces in the Y direction in Figure 9.22 coincide
with the global forces in the Y direction (Fy) given in Figure 9.19 of the Report window

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Figure 9.22: Top View window, Lateral force in the Y direction at the pile head

button at the left of the window to deselect this option.
61. Click the Show force
62. Click the Show moment
button at the left of the window to view the bending moment
results at the pile head (Figure 9.23).

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Figure 9.23: Top View window, Bending moment around the Z direction

It can be checked that the values of the bending moment around the Z direction (Mxx) in
Figure 9.23 coincides with the (global) bending moment Mxx given in Figure 9.19 (paragraph
2.5.1) of the Report window.
See section 6.5 for a detailed description.
9.8

Conclusion
A complex 16 piles group fixed to a cap has been modeled. A lateral displacement of the
cap of 10 mm along the Z-axis will result in lateral forces (in the same direction) with values
between 128.5 and 159.0 kN and vertical forces (in the Y-direction) with values between 146.8
and 148.2 kN for the four inclined piles at the cap extremity.

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10 Tutorial 4: Negative skin friction on single pile
This tutorial describes the analysis of a pile which supports a seaport crane on a sea quay. A
cap load allows modeling whatever the unloading or the loading of a ship by the crane. The
development of negative skin friction due to the loading of the quay with containers is modeled
using the Soil Displacement Profile option.
Three sequence loading are studied in this tutorial depending on whatever negative skin friction takes place before, after or at the same time that loading/unloading of a chip by the
seaport crane.
The objectives of this exercise are:

 To model the negative skin friction due to drag down along the pile using the Soil Displacements option.

 To model different sequences of loading for negative skin friction and load cap using the
appropriate load step intervals.
For this tutorial the following modules are needed:

 D-P ILE G ROUP Standard module (Poulos model)
 Cap module
This tutorial is presented in the files Tutorial-4a.pii, Tutorial-4b.pii and Tutorial-4c.pii.
10.1

Introduction to the case
This example considered piles which are supporting the seaport crane rails. The distance
between the piles is large enough to consider the piles as separate piles. Therefore only a
single pile is considered.

Figure 10.1: Single pile under seaport crane on a quay composed of sand fill (Tutorial 4)

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Figure 10.2: Functioning of the Cap model for Tutorial 4

Soil data
The crane is situated close to the quay side, where the soil consists of a layer of 31 m of sand
fill on top of the existing soil (sand with shells + glauconite). The sand fill is deposited in layers
under water (UW) and above water (AW) as shown in Figure 10.1. The properties of all layers
are given in the table below. For the pile-soil interaction, the soil behavior according to the
Dutch design code NEN 6743 is used.
Table 10.1: Soil properties for Tutorial 4

Soil type
Dry unit weight [kN/m3 ]
Wet unit weight [kN/m3 ]
Phi [◦ ]
Cone resistance [kN/m2 ]
Lateral rule
Axial rule
Ko [-]
dz at 100 % [m]
Factor α [-]

Layer AW

Layer UW

Sand
18
20
35
12000
API
Cone
0.5
0.01
0.01

Sand
17
20
32.5
7000
API
Cone
0.5
0.01
0.01

Sand with
shells
Sand
18
20
37.5
15000
API
Cone
0.5
0.01
0.01

Glauconite
Sand
18
20
35
15000
API
Cone
0.5
0.01
0.01

Lateral and axial rules
The lateral P-Y curve is taken according to API for static loading. For the axial T-Z curve in
sand layers, D-P ILE G ROUP offers the choice between two design codes: the API or the Dutch
design code NEN 6743. For this tutorial, the second one is chosen which means that the
inputted cone resistance qc values is used to determine the maximum skin friction along the
pile (see Equation 15.14 in section 15.2.2) with a factor α of 0.01 and a value of “dz at 100%”
(relative displacement between pile and soil at which the maximum value of the skin friction is
reached) equal to 0.01 m.

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Pile data
The foundation piles are prefabricated concrete piles with a cross section of 0.5 × 0.5 m, a
length of 33 m and a Young’s modulus of 3.6 × 107 kN/m? The ultimate bearing capacity of
the pile is 3750 kN and the pile head is fixed.
Loads data
Under its own weight and under the surface loading by containers, the sand fill will settle
and cause negative skin friction on the pile. Due to the large thickness of the sand fill layer
the negative skin friction may becomes very high so a more thorough examination than using standard design approaches is justified. Negative skin friction That’s why three loading
sequences are modeled in three different D-P ILE G ROUP files:

 Tutorial-4a: First a load on top of the pile and then development of negative skin friction
(the crane unloads a ship and fills the quay with containers).

 Tutorial-4b: First development of negative skin friction and then a load on top of the pile
(the crane loads a ship with containers from a full quay).

 Tutorial-4c: Development of negative skin friction in time with alternating loads on top of
the pile.
Model
For this tutorial, the Cap model is used as only one pile is modeled therefore no pile-soilpile interaction model is needed. Moreover, a prescribed vertical soil displacement must be
inputted to model the negative skin friction and the Cap model is the only model for which this
option is available. Figure 10.2 schematizes the functioning of the Cap model for this tutorial:
the pile is laterally loaded by means of the cap which transmits the load to the pile. Only the
lateral soil springs will be active to transmit the lateral load from the pile to the soil. For the
Cap model, axial springs along and at the tip of the pile exist but they are not active in this
case, that’s why they are not represented.
10.2
10.2.1

Loading on the pile head then development of negative skin friction
Project Model and Properties
For this tutorial, the Cap model is used as only one pile is modeled therefore no pile-soilpile interaction model is needed. Moreover, a prescribed vertical soil displacement must be
inputted to model the negative skin friction and the Cap model is the only model for which this
option is available.
1. Before inputting the data, create a new project by selecting New in the File menu and save
it as  in the Save As window.
2. Open the Model window from the Project menu.
3. Select the Cap model and click OK to confirm.
4. Open the Project Properties window by selecting Properties in the Project menu to give
the project a meaningful description.
5. Fill in ,  and  for respectively Title 1, Title 2 and Title 3 in the
Identification tab.

10.2.2

Soil

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Soil Layers
6.
7.
8.
9.

Open the Soil Layers window from the Soil menu.
In the window displayed, click Add to enter the material data of the first layer.
Change the default soil layer name  to .
Enter the required soil properties for this first top layer as given in section 10.1, subparagraph “Soil data” with the table with the soil properties for layers and subparagraph
“Lateral and axial rules”.
10. Repeat this process for the four other sand layers by adding the four additional layers given
in the table with the soil properties for layers (section 10.1).
In order to achieve the correct interface strength between soil and pile, it is needed to put
the soil stresses at the correct magnitude: when the surface load is present (containers on
the quay) the vertical effective stress at surface level is obviously not zero but is estimated to
60 kN/m2 . So a stress increase of 60 kN/m2 has to be used.
This is done by adding a “surcharge layer” with a thickness of 0.10 m and an effective unit
weight of 600 kN/m3 . The thickness is chosen very small in order to avoid friction effect of this
“surcharge layer” on the pile. If this “surcharge layer” is not added the negative skin friction
that is calculated would be considerably too low.
11. Click Add and change the default soil layer name to .
12. Enter a dry and wet unit weight of <600 kN/m2 >. For the other properties, used the same
as layer .
13. Click OK to confirm the input data for the layer properties.

Figure 10.3: Soil Layers window, properties of Layer AW

Soil Profiles
Once the layer properties have been entered, the soil profile can be specified and the “surcharge layer” just defined above must also be added at the top of this profile.
14. Open the Soil Profiles window from the Soil menu.
15. Click Add at the bottom left side of the window to create soil profile number <1>.

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16. Click on the Add row button to insert the “surcharge layer” by selecting 
as Material and enter a Top Level of <7.10 m> to get a thickness of 0.1 m as desired.
17. Define the position of each sand layer by specifying there name and their top level, as
indicated in Figure 10.1.
18. Define the Water level at <-2.0 m> and the location of the soil profile at (0, 0).
19. Click OK to confirm.

Figure 10.4: Soil Profiles window

10.2.3

Pile
Pile Types
20. Open the Pile Types window from the Pile menu.
21. Click Add to create a new pile type and give it the name <500>.
22. Select the Concrete square pile with a width of <500 mm>, a length of <33 m> and a
Young’s modulus of 3.6 × 107 kN/m? as described in section 10.1.

Figure 10.5: Pile Types window

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Pile Tip Curves
The pile tip curve specifies the load-displacement behavior of the pile tip in terms relative to
the end bearing capacity. In this tutorial, the pile tip curve is described using three points:
(0 %, 0 m), (50 %, 0.006 m) and (100 %, 0.050 m).
23. In the Pile Tip Curves window from the Pile menu, create a pile tip curve by clicking the
Add button.
24. Enter the three points given above (Figure 10.6) and click OK to confirm.

Figure 10.6: Pile Tip Curves window

Pile Positions
According to Figure 10.1, the pile is positioned vertically with its top at co-ordinates (0, 7, 0).
25.
26.
27.
28.
29.

Open the Pile Positions window from the Pile menu.
Define pile <1> with Soil profile <1>, Pile type <500> and Pile tip curve <1>.
Enter the Xtop, Ytop and Ztop co-ordinates given above with a  Top condition.
The End bearing capacity is <3750 kN> as specified in section 10.1.
The Angle in XZ plane and the Rake [hor/vert] are set to <0> as the pile is vertical.

Figure 10.7: Pile Positions window

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10.2.4

Cap Location
30. Open the Cap Location window from the Cap menu.
31. In the window displayed, fill in the X, Y, Z-coordinates as (0, 7, 0) which corresponds to the
application point of the crane load.
32. Click OK to close the window.

10.2.5

Loads
Because of the surface loading of 60 kN/m2 (containers on the quay) a settlement of the sand
fill is expected up to 50 mm. The maximum loading of the pile caused by the crane loads is
2000 kN. Those two kinds of loads have to be inputted.
Loads Cap
As the location where the crane load apply to the cap have been specified in the previous
paragraph, the crane load themselves can be entered.
33. Open the Loads Cap window from the Loads menu.
34. Enter a load in the Y direction of <-2000 kN> due to the seaport crane. The Rotation in
the Z direction is set to <0◦ >.

Figure 10.8: Loads Cap window

See section 4.5.1 for a detailed description.
Soil Displacement Profiles
As the Cap model is used, a soil displacement profile can be entered to take into account the
vertical soil movements due to down drag (negative skin friction). Negative skin frictionFor
this tutorial, it is assumed that the surface settlements were calculated and estimated to be
approximately 50 mm for the surface load of 60 kN/m2 . These displacements are imposed on
the pile in a simplified way: from the maximum value at the quay surface (50 mm settlement at
level 7 m) linear decreasing to zero settlement at the original seabed level (-24 m). Therefore,
the vertical soil displacements in the Y-direction must be specified at two levels.
35. Select Soil Displacement Profiles from the Loads menu.
36. In the window displayed, specify a vertical displacement Uy of <-0.05 m> at Level <7 m>

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and <0 m> at Level <-24 m>. The displacements in X and Z directions are nil, as shown
in Figure 10.9 below.

Figure 10.9: Soil Displacement Profiles window

37. Click OK to confirm.
See section 4.5.5 for a detailed description.
Soil Displacements
The soil displacement profile just defined in must now be related to the pile defined in section 10.2.3.
38. Open the Soil Displacements window from the Loads menu.
39. In the Pile Number column, select pile <1> and in the Displacement Profile Nr column,
select profile <1>.
40. Enter a Factor of <1>, which means that pile 1 has 1 time the displacements of soil
displacement profile 1.
The load steps must also be specified in which the soil displacements have to be applied.
In this tutorial, it is assumed that negative skin friction modeled by Soil Displacement Profile
number 1occurs after the loads cap. As the load cap is applied at load step number 10, the
Soil Displacements must be applied after this load step. Therefore, an interval between step
10 and 20 is chosen.
41. Enter a Start Step Nr of <10> and an End Step Nr of <20>.
42. Click OK to confirm.

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Figure 10.10: Soil Displacements window

See section 4.5.6 for a detailed description.
Another important factor is the pile-soil displacement that is needed to reach the maximum
skin friction value. In the example here a value of 0.01 m is used. This is a generally accepted
value in the Netherlands, however the API advises the use of a value of about 0.003. The
reader is invited to study the effect of this different value.
10.2.6

Calculation and Results
43. In the Calculation Options window from the Calculation menu, enter a Minimum number of
pile nodes of <50> in order to get more accurate results than using the default value of
20.
44. Select the Start option from the Calculation menu to open the Calculation window and click
OK.
Cap Plots
To see the chart of the pile head load-settlement curve:
45. Select Cap-plots from the Results menu.
46. Select Direction .
In the window displayed (Figure 10.11), it can be seen that due to the pile head loading of
2000 kN a settlement of almost 5 mm occurs. Due to the settlement of the soil and the
negative skin friction that is thereby generated the pile head settlement increases to more
than 30 mm.

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Figure 10.11: Cap-plots window, pile head load-settlement curve in the Y-direction
(Tutorial-4a)

More accurate results can be obtained by doing the following.
47. Click the right side mouse button and select View Data to open a Chart Data window.
The Displacement tab of the window displayed (Figure 10.12) shows that the load cap of
2000 kN is applied in 10 load steps, as inputted in section 10.2.5, with a settlement of 4.79 mm
at the end of the load application (point number 11). Between points 11 and 21, which correspond to load steps 10 to 20, the soil displacement as inputted in section 10.2.5 occurs and
leads to a pile head settlement of 30.89 mm.

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Figure 10.12: Chart Data window, Displacement tab for the pile head load-settlement
curve in the Y-direction (Tutorial-4a)

Charts
To see the charts of the displacement, the axial force and the reaction along the pile in X, Y
and Z directions:
48. Select Charts from the Results menu.
49. Select Direction  and Step <20>. Figure 10.13 displays the Charts window for the
Y direction and for load step 20, after all loads are applied.

Figure 10.13: Charts window, Displacement-Axial Force-Reaction along the shaft pile in
Y-direction for load step 20 (Tutorial-4a)

The friction between pile and soil is presented at the right hand side of the window (chart
Depth vs. Reaction Y ). By comparing this chart to the chart Depth vs. Axial force Y (at the
middle of the window), it can be noticed that the depth of friction sign reversal occurs at the
same depth than maximum axial force in the pile. By using the View data option as previously,

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this depth is estimated at about 16.1 m below the pile head, which corresponds to level Y = 7 –
16.1 = -9.1 m. This means that negative skin friction occurs until this level. Below this level
the pile displacement (caused by compression of the pile shaft and settlement of the pile tip)
exceeds the settlement of the soil and this results in positive skin friction.
10.3

First development of negative skin friction followed by loading on the pile head
The same input file as Tutorial 4a is used and adapted to get a new loading sequence: the
seaport crane is now loading a ship from a full quay. This will result in first development of
negative skin friction and then application of a load on top of the pile. To do this, start with the
following steps:
50. Save the current project into  using the Save As window from the File
menu.
51. In the Project Properties window of the Project menu, change the Identification into ,  and  for respectively Title 1, Title 2 and Title 3.

10.3.1

Loads
The order of applying the crane load (in Loads Cap window) and the development of negative
skin friction (in Soil Displacements window) have to be reversed.
Loads Cap
52. Open the Loads Cap window from the Loads menu.
53. For the <10> first Loadstep number, no load is applied, so enter <0> in the Y direction. Between Loadstep number <10> and <20>, enter a load of <-2000 kN> in the Y
direction.

Figure 10.14: Loads Cap window

labelfig:10-14

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Soil Displacements
54. Open the Soil Displacements window from the Loads menu.
55. Change the Start Step Nr into <1> and the End Step Nr into <10>.

Figure 10.15: Soil Displacements window

10.3.2

Calculation and Results
Select the Start option from the Calculation menu to open the Calculation window and click
OK to perform a calculation.
Cap Plots
To see the chart of the pile head load-settlement curve:
56. Select Cap-plots from the Results menu.
57. Select Direction .

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Figure 10.16: Cap-plots window, pile head load-settlement curve in the Y-direction
(Tutorial-4b)

In the window displayed (Figure 10.16) it can be seen that due to the negative skin friction that
is generated a pile head settlement occurs of about 20 mm. Due to the pile head loading this
settlement increases to about 25 mm. This is about 5 mm less than in the previous sequence
loading (section 10.2.6). The difference is caused by the fact that now the pile head load
generates a reduction of the negative skin friction at the top of the pile.
Charts results
To see the charts of the displacement, the axial force and the reaction along the pile in X, Y
and Z directions:
58. Select Charts from the Results menu.
59. Select Direction  and Step <20>.

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Figure 10.17: Charts window, Displacement-Axial Force-Reaction along the shaft pile in
Y-direction for load step 20 (Tutorial-4b)

Figure 10.17 displays the Charts window obtained for the Y direction and for load step 20,
which means after all loads are applied. As in the previous sequence loading (section 10.2.6),
the depth of friction sign reversal occurs at the same depth than maximum axial force in the
pile. By using the View data option as previously, this depth is estimated at about 20 m below
the pile head, which corresponds to level Y = 7 - 20 = -13 m.
By comparison with the Charts results of the previous sequence loading (section 10.2.6), the
negative skin friction occurs on a larger surface reducing the pile displacement.
In the previous sequence loading, the settlement was so big that the maximum negative skin
friction value was reached for the soil at the top of the pile shaft regardless of the fact that
there was, initially, a positive friction present due to the pile head loading.
10.4

Mixed loading
The same input file as Tutorial 4a is used and adapted to get a new loading sequence: development of negative skin friction in time with alternating application of a load on top of the
pile.
The negative skin friction is applied between load steps 10 and 500. The pile head load
alternates every 20 steps: starts at 0, 10 steps later peaks at 2000 kN and is 0 again another
10 steps later. After the maximum negative skin friction has been reached 5 load cycles are
still applied for the pile head force. The loading schedule is shown in Figure 10.18 below.

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Figure 10.18: Loading schedule (Tutorial 4c)

To do this, start with the following steps:
60. Save the current project into  using the Save As window from the File
menu.
61. In the Project Properties window of the Project menu, change the Identification into ,  and  for respectively Title 1, Title 2 and Title 3.
10.4.1

Loads
The loading schedule of Figure 10.18 has to be entered.
Loads Cap
62. Open the Loads Cap window from the Loads menu.
63. Every 10 Loadstep number, enter alternatively a vertical load of <-2000 kN> and <0 kN>
until Loadstep number <600> (see Figure 10.19 below).

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Figure 10.19: Loads Cap window

Soil Displacements
64. Open the Soil Displacements window from the Loads menu.
65. Change the Start Step Nr into <10> and the End Step Nr into <500>.

Figure 10.20: Soil Displacements window

10.4.2

Calculation and Results
66. Select the Start option from the Calculation menu to open the Calculation window and click
OK to perform a calculation.
Cap Plots
To see the chart of the pile head load-settlement curve:
67. Select Cap-plots from the Results menu.

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68. Select Direction .

Figure 10.21: Cap-plots window, pile head load-settlement curve in the Y-direction
(Tutorial-4c)

In the window displayed (Figure 10.21), it can be seen that the pile head load-settlement
behavior now shows an increase with each load cycle until the maximum negative skin friction
has been reached. Since no soil strength degradation is present in the model the pile head
displacement for each of the last 5 cycles, where the maximum negative skin friction is already
present, remains the same. This can not be seen clearly in Figure 10.21 since the lines are
on top of each other but can easily be checked by viewing the data of this plot using the View
data option.
It can also be seen that the pile head settlement is reduced compared to the two previous
loading sequences. This is caused by the fact that in the top layers alternatively maximum
positive and negative skin friction values are reached

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Charts results
To see the charts of the displacement, the axial force and the reaction along the pile in X, Y
and Z directions:
69. Select Charts from the Results menu.
70. Select Direction  and Step <590>.

Figure 10.22: Charts window, Displacement-Axial Force-Reaction along the shaft pile in
Y-direction for load step 590 (Tutorial-4c)

In the window displayed (Figure 10.22), it can be seen that the maximum axial load is lower
than in the two previous loading sequences. This means that the safety factor of the pile is
higher.
10.5

Conclusion
A seaport crane loading and unloading a ship with containers has been modeled. The weight
due to containers on the quay has been modeled with a fictive layer. Three different loading
sequences have been taken into account. Results show that the pile head settlement depends
on the loading sequence: this settlement is lowest for the realistic loading sequence (case
c). Moreover, the safety factor of the pile is higher for this realistic loading sequence as the
maximum axial load is lower.

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11 Tutorial 5: Mono pile wind turbine foundation design, Dutch
Standard
This tutorial describes the design of a mono pile foundation for a small to medium sized
windmill at an onshore location. Although dynamic aspects, such as the resonance frequency
of the wind turbine/pile foundation, are important factors for the design for a certified mast
type a static approach is quite common for small structures. This is treated in this example.
The objectives of this exercise are:

 To model a steel pile.
 To check the vertical and the horizontal bearing capacity according to the Dutch design
codes NEN 6740 NEN (2006) and NEN 6743 NEN (1991).
For this tutorial the following modules are needed:

 D-P ILE G ROUP Standard module (Poulos model)
 Cap module
This tutorial is presented in the files Tutorial-5a.pii, Tutorial-5b.pii, Tutorial-5c.pii and Tutorial5d.pii.
11.1

Introduction to the case
This tutorial describes the design of a mono pile foundation for windmill at an onshore location.
Two different pile dimensions are investigated. The wind turbine mast has a length of 39 m
above soil surface and a diameter of 1.71 m as shown in Figure 11.1. Although dynamic
aspects, such as the resonance frequency of the wind turbine/pile foundation, are important
factors for the design for a certified mast type a static approach is quite common. This is
treated in this tutorial.

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Figure 11.1: Wind turbine on mono pile foundation (Tutorial 5)

Loads data
The values given in Table 11.1 are the ones used for certification of the mast. The corresponding required minimum rotational stiffness of the foundation is 550 000 kNm/rad.
Table 11.1: Magnitude of the loads in normal and extreme conditions

Horizontal load Fh
Vertical load Fv
Moment load Mz

[kN]
[kN]
[kNm]

Normal conditions
23.2
-158
-605

Extreme conditions
110.4
-158
-2592

Pile data
For the mono pile foundation a steel pipe pile is used (without driving shoe) with the same
diameter as the mast and a Young’s modulus of 2.1 × 108 kN/m2 . Two different pile types are
investigated:

 Pile type 1: Mono pile with a length of 15 m below the surface level and a wall thickness
of 12 mm;

 Pile type 2: Mono pile with a length of 10 m below the surface level and a wall thickness
of 10 mm.
For pile type 2, the pile tip is situated in the “Sand medium dense” layer. So the tip resistance
is estimated to 3 900 kN/m2 . For pile type 1, the pile tip is situated in the “Slightly sandy clay

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medium stiff” layer, so the tip resistance is reduced to 3 150 kN/m2 . The tip resistance of the
pile has to be translated a bearing capacity of the pile tip by multiplication with the pile tip
area. One has to verify that the end bearing capacity is governed by the tip resistance and
not by the friction over the inside of the pile.
Note: The input bearing capacity (called End bearing capacity in D-P ILE G ROUP) must be
entered in kN. Here the End bearing is equal to:
3150 × p × 1.712 / 4 = 7234.24 kN for pile type 1
3900 × p × 1.712 / 4 = 8956.67 kN for pile type 2.
Soil data
The soil investigation for this location consists of a bore hole and a CPT performed at location
(0, 0, 0). The borehole identifies the top layer as clay, medium stiff followed by loose sand.
Based on the CPT and the boring the soil conditions are schematized according to Dutch
design code NEN 6740 NEN (2006). The result is given in Table 12.2.

Figure 11.2: Determination of the soil profile from the CPT results

Table 11.2: Soil properties for Tutorial 5

Soil type
Dry weight [kN/m3 ]
Wet weight [kN/m3 ]
Cu [kN/m2 ]
Phi [◦ ]
Friction angle [◦ ]
Cone resistance [kN/m2 ]

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Clay,
medium
stiff

Sand, loose

Sand,
medium
dense

Soft clay
17
17
30
-

Sand
17
19
30
20
3000

Sand
18
20
32.5
21.66
10000

Slightly
sandy clay,
medium
stiff
Soft clay
18
18
90
-

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Ko [-]
Lateral rule
Axial rule
J [-]
e50 [-]
dz at 100 %

API Cyclic
API
0.25
0.010
0.0171

0.5
API Cyclic
API
0.0025

0.5
API Cyclic
API
0.0025

API Cyclic
API
0.25
0.007
0.0171

The water level is situated 1.6 m below the surface level.
Lateral and axial rules
For all layers The lateral P-Y and axial T-Z curves are taken according to the internationally
accepted Code API with a cyclic loading due to the wind. Parameters J, e50 and “dz at 100%”
are determined as explained in the sub-paragraph “Lateral and axial rules” in section 9.1.

Figure 11.3: Functioning of the Cap model for Tutorial 5

Model
For this tutorial, the Cap model is used as no pile-soil-pile interaction model is needed when
modeling a single pile. Figure 11.3 schematizes the functioning of the Cap model in this case:
the pile is laterally and axially loaded by means of the cap which transmits the loads to the
pile. The lateral and axial springs transmit the loads from the pile to the soil.
Check of horizontal and vertical bearing capacity according to NEN 6743
The horizontal and vertical bearing capacities will be checked in this example according to the
Dutch design code NEN 6743 NEN (1991) which includes two limit state checks: the Ultimate
Limit State (ULS) and the Serviceability Limit State (SLS). Moreover the verification will also
be made for both pile types. Therefore, four D-P ILE G ROUP input files need to be created, as
shown in Table 11.3.
Table 11.3: Name and description of the four D-Pile Group input files for Tutorial 5

Pile type 1
Pile type 2

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Serviceability Limit State
Tutorial-5a
Tutorial-5b

Ultimate Limit State
Tutorial-5c
Tutorial-5d

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11.2

Project Model and Properties
For this tutorial, the Cap model is used as no pile-soil-pile interaction model is needed when
modeling a single pile.
1. Create a new project by selecting New in the File menu and save it as 
in the Save As window.
2. Open the Model window from the Project menu.
3. Select the Cap model and click OK to confirm.
4. Open the Project Properties window by selecting Properties in the Project menu to give
the project a meaningful description.
5. Fill in ,  and  for Title 1, Title 2 and Title
3 in the Identification tab.

11.3
11.3.1

Soil
Soil Layers
6. In the Soil Layers window from the Soil menu, click Add to enter the different four soil
layers properties as indicated in Table 11.2.
7. Click OK to confirm the input data for the layer properties.

Figure 11.4: Soil Layers window

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11.3.2

Soil Profiles
8. In the Soil Profiles window from the Soil menu, click Add to create a soil profile with
number <1>.
button and fill in
9. Compose the profile according to Figure 11.1 by clicking the Add row
the table at the right side of the window.
10. Enter the Water level at <-1.6 m> and the location of the CPT (X = 0 m; Z = 0 m) as given
in the sub-paragraph “Soil data” of section 11.1.

Figure 11.5: Soil Profiles window

11.4
11.4.1

Pile
Pile Types
11. In the Pile Types window from the Pile menu, click Add to create two pile types with names
 and  corresponding to both pile types that are investigated in this
tutorial.
12. Select the Steel material and fill in the different dimensions of the Parameters sub-window
as given in the sub-paragraph “Pile data” of [section 11.1].

Figure 11.6: Pile Types window

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11.4.2

Pile Tip Curves
The pile tip curve specifies the load-displacement behavior of the pile tip in terms relative
to the end bearing capacity (inputted in the Pile Positions window in section 11.4.3). In this
tutorial, the pile tip curve is described using two points: (0 %, 0 m) and (100 %, 0.01 m).
13. In the Pile Tip Curves window from the Pile menu, create a pile tip curve by clicking the
Add button.
14. Enter the two points given above (Figure 11.7).

Figure 11.7: Pile Tip Curves window

11.4.3

Pile Positions
According to Figure 11.1, the pile is positioned vertically with his top at co-ordinates (0, 0, 0).
15. In the Pile Positions window from the Pile menu, define pile <1> with Soil profile <1>,
Pile type  and Pile tip curve <1>.
16. Enter the Xtop, Ytop and Ztop co-ordinates given above with a  Top condition.
17. For pile type 1, the End bearing capacity is <7234.24 kN>.
18. The Angle in XZ plane and the Rake [hor/vert] are set to <0> as the pile is vertical.

Figure 11.8: Pile Positions window for pile type 1

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11.5

Cap Location
19. In the Cap Location window from the Cap menu, fill in the X, Y, Z-coordinates as (0, 0, 0)
which corresponds to the tip of the wind turbine (see Figure 11.1).
20. Click OK to close the window.

11.6

Loads Cap
According to NEN 6470 NEN (2006), all partial factors for Serviceability Limit State (SLS) are
equal to 1. Therefore, the values of the loads and moment as given in Table 11.1 for normal
conditions must be inputted in the Loads Cap window from the Loads menu. Special care
must be taken on the sign of the loads and the moment to be in accordance with Figure 11.1.
21. In the Loads Cap window from the Loads menu, enter a  of <23.20 kN> in
the X direction, a  of <-158 kN> in the Y direction and a  of <605.00 kNm> in the Z direction, during the first <10> load steps.
22. In order to model unloading, enter values of <0.00> for the same loads between load step
<10> and <20>, as shown in Figure 11.9.

Figure 11.9: Loads Cap window, design loads for Serviceability Limit State

11.7

Calculation at Serviceability Limit State
23. In the Calculation Options window from the Calculation menu, enter a Minimum number
of pile nodes of <30>, an Accuracy of <10−9 > and a Maximum number of iterations of
<100> in order to get more accurate results than using the default values. Click OK to
confirm.
24. Select the Start option of the Calculation menu and click OK to start the calculation.

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11.7.1

Results at SLS for pile type 1
25. Open the Charts window (Figure 11.10), from the Results menu and select Step <10>
which corresponds to the end of loading.

Figure 11.10: Charts window, results for Serviceability Limit State at load-step 10 for pile
type 1 (Tutorial-5a)

26. Open the Chart Data window by clicking the right-hand mouse button and selecting View
data.
The Moment tab provides a calculated maximum bending moment of 617.19 kNm and the Displacement tab a calculated deflection of the pile head (at soil surface level) of 2.693 mm. The
rotational stiffness can be determined using the rotation of the pile head. According to the Displacement tab, the displacement at depth -0.367 m (which corresponds to the node just below
the pile head) is 2.406 mm. Therefore, the rotation of the pile head is estimated to be:(2.693 –
2.406) × 10−3 / [0 – (-0.367)] = 7.820 × 10−4 radian, for a moment of 617.19 kNm.So the
rotational stiffness is equal to: 617.19 / (7.820 × 10−4 ) = 789 229 kNm/rad.
The displacement chart of Figure 11.10 also shows that the pile tip does not move under the
given loading.
27. Select Direction . The window displayed shows that the maximum axial force appears
at the pile head and is equal to the applied vertical load of -158 kN.
28. Reselect Direction  and select Step <20> which corresponds to the end of unloading. In the window displayed, it can be noticed that after unloading no stresses and
deformations remain present in the pile. This means that no gap can be expected to form
which could lead to progressive deformations for continuing loading cycles. To confirm this,
the load-displacement chart can be used.
29. Select the Cap-plots option from the Results menu. The window displayed (Figure 11.11)
shows that the deformations are completely elastic: the represented line looks like a single
line from 0 to 2.693 mm, but is in fact a double line going from zero to 2.693 mm and back
to 0 again for unloading. This can be checked using the Chart Data window.

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Figure 11.11: Cap-plots window, pile head load-displacement curve in the X-direction for
Serviceability Limit State for pile type 1 (Tutorial-5a)

11.7.2

Results at SLS for pile type 2
To obtain the results at Serviceability Limit State for pile type 2, the pile properties in the input
file must be changed compared to Tutorial-5a:
30. Save the current file into  using the Save As window from the File menu.
31. Modify Title 1 and Title 3 of the Project Properties window into respectively  and  in the
Identification tab.
32. In the Pile Positions window, select  as Pile type and enter an End bearing
capacity of <8956.67 kN>.
33. Select the Start option of the Calculation menu and click OK to start the calculation.
34. Open the Charts window from the Results menu and select Step <10> which corresponds
to the end of loading.
35. In the window displayed (Figure 11.12), open the Chart Data window by clicking the righthand mouse button and selecting View data.
The Moment tab provides a calculated maximum bending moment of 615.32 kNm and the
Displacement tab a calculated deflection of the pile head (at soil surface level) of 3.147 mm.
The rotational stiffness can be determined using the rotation of the pile head. According
to the Chart Data window, the displacement at depth -0.275 m (which corresponds to the
node just below the pile head) is 2.892 mm. Therefore, the rotation of the pile head is esti-

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mated to be:(3.147 – 2.892) × 10−3 / [0 – (-0.275)] = 9.273 × 10−4 radian, for a moment of
615.32 kNm.So the rotational stiffness is equal to: 615.32 / (9.273 × 10−4 ) = 663 580 kNm/rad.

Figure 11.12: Charts window, results for Serviceability Limit State at load-step 10 for pile
type 2 (Tutorial-5b)

The displacement chart of Figure 11.12 also shows that the pile tip moves under the given
loading (0.379 mm).
36. Select Direction . The window displayed shows that the maximum axial force appears
at the pile head and is equal to the applied vertical load of -158 kN.
37. Reselect Direction  and select Step <20> which corresponds to the end of unloading. The window displayed shows that after unloading no stresses and deformations
remain present in the pile. This means that no gap can be expected to form which could
lead to progressive deformations for continuing loading cycles. To confirm this, the loaddisplacement chart can be used.
38. Select the Cap-plots option from the Results menu.The window displayed (Figure 11.13)
shows that the deformations are completely elastic: the represented line looks like a single
line from 0 to 3.147 mm, but is in fact a double line going from zero to 3.147 mm and back
to 0 again for unloading.

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Figure 11.13: Cap-plots window, pile head load-displacement curve in the X-direction for
Serviceability Limit State for pile type 2 (Tutorial-5b)

11.8
11.8.1

Calculation at Ultimate Limit State
Design values at ULS for material properties and loads
The calculations at the Ultimate Limit State are for verification of the stability of the construction only; the actual deformations will be smaller than those calculated for the Ultimate Limit
State.
According to NEN 6740, the following partial factors have to be used for design at Ultimate
Limit State:






for the volumetric weight of the soil: γm;g = 1.1
for the tangent of the angle of internal friction: γm;ϕ0 = 1.2
for the undrained shear strength: γm;su = 1.5
for the loads: γload = 1.2

The design values of the soil properties are obtained by dividing the representative values of
Table 11.2 with the corresponding partial factors given above. Resulting design values are
given in Table 11.4 below.
Table 11.4: Design values of soil properties for Ultimate Limit State according to
NEN 6740

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Dry weight [kN/m3 ]
Wet weight [kN/m3 ]
Cu [kN/m2 ]
Friction angle [◦ ]

Clay, medium
stiff

Sand, loose

15.45
15.45
20
-

15.45
17.27
25.69

Sand,
medium
dense
16.36
18.18
27.96

Slightly sandy
clay, medium
stiff
16.36
16.36
60
-

The design values of loads are obtained by multiplying the representative values of loads at
extreme conditions (see Table 11.1) with partial factor 1.2. Resulting design values are given
in Table 11.5 below.
Table 11.5: Design values of loads for Ultimate Limit State according to NEN 6740

Horizontal load
Vertical load
Moment load

11.8.2

Fh
Fv
Mz

[kN]
[kN]
[kNm]

132.48
-189.60
-3110.40

Results at ULS for pile type 1
The soil properties and the loads magnitude must be adapted compared to the Serviceability
Limit State calculation. To do this:
39. Open  and save it as  in the Save As window of the File
menu.
40. Modify Title 1 and Title 2 of the Project Properties window into respectively  and < Check of mono pile wind turbine foundation at ULS> in the
Identification tab.
41. In the Soil Layers window from the Soil menu, change the Dry unit weight, Wet unit weight,
Cu and Phi according to Table 11.4 for the four layers.
42. In the Loads Cap window from the Loads menu, change the forces and moment magnitude
into the values of Table 11.5.
43. Select the Start option from the Calculation menu and click OK to perform the calculation.
44. In the Charts window of the Results menu, select Step <10> which corresponds to the
end of loading.
45. In the window displayed (Figure 11.14), open the Chart Data window by clicking the righthand mouse button and selecting View data.

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Figure 11.14: Charts window, results for Ultimate Limit State at load-step 10 for pile type
1 (Tutorial-5c)

The Moment tab provides a calculated maximum bending moment of 3277.01 kNm and the
Displacement tab a calculated deflection of the pile head (at soil surface level) of 27.70 mm.
The rotational stiffness can be determined using the rotation of the pile head. According
to the Chart Data window, the displacement at depth -0.367 m (which corresponds to the
node just below the pile head) is 25.55 mm. Therefore, the rotation of the pile head is estimated to be:(27.70 – 25.55) × 10−3 / [0 – (-0.367)] = 5.858 × 10−3 radian, for a moment of 3277.01 kNm. So the rotational stiffness is equal to: 3277.01 / (5.858 × 10−3 ) =
559 378 kNm/rad.
46. Select Direction . The window displayed shows that the maximum axial force appears
at the pile head and is equal to the applied vertical load of -189.60 kN.
47. Reselect Direction  and select Step <20> which corresponds to the end of unloading.In the window displayed, it can be noticed that after unloading, stresses and deformations remain present in the pile. This means that progressive deformations for continuing
loading cycles will be formed. To confirm this, the load-displacement chart can be used.
48. Select the Cap-plots option from the Results menu.

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Figure 11.15: Cap-plots window, pile head load-displacement curve in the X-direction for
Ultimate Limit State for pile type 1 (Tutorial-5c)

The window displayed (Figure 11.15) shows that the deformations are not elastic: a residual
displacement of 2.07 mm remains present after unloading.
11.8.3

Results at ULS for pile type 2
To obtain the results at Ultimate Limit State for pile type 2, the pile properties in the input file
must be changed compared to Tutorial-5c:
49. Save the current file as  using the Save As window of the File menu.
50. Modify Title 1 and Title 3 of the Project Properties window into respectively  and  in the
Identification tab.
51. In the Pile positions window from the Pile menu, select  as Pile type and enter
an End bearing capacity of <8956.67 kN>.
52. Select the Start option from the Calculation menu and click OK to perform the calculation.
53. In the Charts window of the Results menu, select Step <10> which corresponds to the
end of loading.
54. In the window displayed (Figure 11.16), open the Chart Data window by clicking the righthand mouse button and selecting View data.

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Figure 11.16: Charts window, results for Ultimate Limit State at load-step 10 for pile type
2 (Tutorial-5d)

The Moment tab provides a calculated maximum bending moment of 3244.53 kNm and the
Displacement tab a calculated deflection of the pile head (at soil surface level) of 51.92 mm.
The rotational stiffness can be determined using the rotation of the pile head. According
to the Chart Data window, the displacement at depth -0.275 m (which corresponds to the
node just below the pile head) is 49.15 mm. Therefore, the rotation of the pile head is estimated to be:(51.92 – 49.15) × 10−3 / [0 – (-0.275)] = 10.073 × 10−3 radian, for a moment of
3244.53 kNm. So the rotational stiffness is equal to: 3244.53 / (10.073 × 10−3 ) = 322 110 kNm/rad.
55. Select Direction . The window displayed shows that the maximum axial force appears
at the pile head and is equal to the applied vertical load of -189.60 kN.
56. Reselect Direction  and select Step <20> which corresponds to the end of unloading.In the window displayed, it can be noticed that after unloading, stresses and deformations remain present in the pile. This means that progressive deformations for continuing
loading cycles will be formed. To confirm this, the load-displacement chart can be used.
57. Select the Cap-plots option from the Results menu. The window displayed (Figure 11.17)
shows that the deformations are not elastic: a residual displacement of 7.77 mm remains
present after unloading.

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Figure 11.17: Cap-plots window, pile head load-displacement curve in the X-direction for
Ultimate Limit State for pile type 2

11.9

Verification of the horizontal bearing capacity
The horizontal bearing capacity is checked by means of the rotational stiffness. Table 11.6
below gives an overview of the calculated rotational stiffness for both pile types and both
limit states (see section 11.7.1, section 11.7.2, section 11.8.2 and section 11.8.3) and compares those values to the required minimum rotational stiffness of 550 000 kNm/rad given in
section 11.1.
Table 11.6: Comparison of the calculated and required minimum rotational stiffness for
both pile type

Pile type

Limit state

Type 1 (15 m)

SLS
ULS
SLS
ULS

Type 2 (10 m)

Calculated rotational
stiffness
[kNm/rad]
789 229
559 378
663 580
322 110

Required minimum
rotational stiffness
[kNm/rad]
550 000
550 000
550 000
550 000

Checked

Yes
Yes
Yes
No

Based on these results, pile type 2 (length of 10 m and wall thickness of 10 mm) is not suitable
as the required minimum rotational stiffness is not reached at Ultimate Limit State.

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11.10

Verification of the vertical bearing capacity
In addition to the horizontal bearing capacity the vertical bearing capacity of the pile needs to
be checked as well. For this check 2 ultimate cases must be considered:

 non-plugging pile: shaft friction at both the outer and inner side of the tube. Point resistance of the annulus of the pipe only.

 plugging pile: shaft friction at the outer side of the tube only. Point resistance of the whole
cross section of the pipe (including soil plug).

Figure 11.18: Representation of the shaft friction and the tip resistance in case of nonplugging pile (a) and plugging pile (b) for a tubular pile

The minimum of these two is to be taken. Therefore, only the case with a plugging pile
should be considered as the friction section is less than for the case with a non-plugging
pile. According to the Dutch design code NEN 6743, the design value of the ultimate vertical
bearing capacity of a mono pile F max;d is:

Fmax;d =

ξ
γm;b

Fmax;rep and Fmax;rep = Fmax;tip + Fmax;shaft

(11.1)

where:

ξ
γm;b
Fmax;rep
Fmax;tip
Fmax;shaft
Atip
Ashaft

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is a factor depending on the number M of piles and the number N of sondering. According to table 1 of NEN 6743, for a single pile and one CPT (M = 1
and N = 1), ξ = 0.75
is the material factor. According to table 3 of NEN 6740, γm;b = 1.25
is the representative value of the ultimate vertical bearing capacity, in kN;
is the end bearing capacity, in kN: Fmax;tip = Atip × pmax;tip
is the shaft capacity, in kN: Fmax;shaft = Ashaft × pmax;shaft
is the pile tip section, in m2 :
Atip = π × D2 / 4 for plugging pile
Atip = π × d × (D − d) for unplugging pile
is the shaft section, in m2 :
Ashaft = π × D × L for plugging pile
Ashaft = π × (2D − d) × L for unplugging pile
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D
D
L
pmax;tip
pmax;shaft

is the pile diameter, in m;
is the wall thickness of the pile, in m;
is the length of the pile, in m;
is the maximum tip resistance, in kN;
is the maximum skin friction, in kN.

The skin friction in clay layers is never taking into account. Therefore, only the skin friction
in “Sand loose” and “Sand medium dense” layers is taken into account.According to Table 3
of the Dutch design code NEN 6743, in sand a maximum skin friction of 0.75 % of the cone
resistance can be used:

pmax;shaft = 0.0075 qc

(11.2)

where qc corresponds to the average cone resistance of the sand layers along the pile:
n

qc =

1X
qc,i × hi
L i=1

(11.3)

where:

qc,i
hi
N

is the cone resistance of sand layer i, in kN/m2 ;
is the thickness of layer i crossed by the pile, in m;
is the number of sand layers along the pile.

According to Figure 11.1, the average cone resistance along the mono pile is equal to:
qc = (3000 × 2.8 + 10000 × 10.7) / 15 = 7693.33 kN/m2 for pile type 1
qc = (3000 × 2.8 + 10000 × 6.1) / 10 = 6940.00 kN/m2 for pile type 2
The calculated design values for the ultimate vertical bearing capacity for both piles combined
with both tip conditions (plugged or unplugged) are given in Table 11.7.
Table 11.7: Results of the calculation of ultimate vertical bearing capacity

Atip
Ashaf t
qc
Pmax;tip
Pmax;shaf t
Fmax;tip
Fmax;shaf t
Fmax;rep
Fmax;d

2

[m ]
[m2 ]
[kN/m2 ]
[kN/m2 ]
[kN/m2 ]
[kN]
[kN]
[kN]
[kN]

Pile type 1
(15 m)
plugged
2.297
80.582
7693.33
3150
57.70
7234.24
4649.57
11883.81
7130.29

unplugged
0.064
160.598
7693.33
3150
57.70
201.64
9266.52
9468.16
5680.89

Pile type 2
(10 m)
plugged
2.297
53.721
6940.00
3900
52.05
8956.67
2796.19
11752.86
7051.72

unplugged
0.053
107.128
6940.00
3900
52.05
208.29
5576.03
5784.32
3470.59

Those values are compared in Table 11.8 to the maximum calculated axial forces, which
correspond to the design applied vertical load, for both pile types and both limit states (see
section 11.7.1, section 11.7.2, section 11.8.2 and section 11.8.3).

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Table 11.8: Comparison of the applied vertical load and the ultimate vertical bearing capacity for different combinations

Pile type

Tip
condition

Limit
state

Type 1
(15 m)

Plugged

SLS
ULS
SLS
ULS
SLS
ULS
SLS
ULS

Unplugged
Type 2
(10 m)

Plugged
Unplugged

Applied vertical
load
[kN]
158
158 × 1.2 = 189.6
158
158 × 1.2 = 189.6
158
158 × 1.2 = 189.6
158
158 × 1.2 = 189.6

Ultimate vertical
bearing capacity
[kN]
7130.29
7130.29
5680.89
5680.89
7051.72
7051.72
3470.59
3470.59

Checked

Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

For all pile combinations the ultimate vertical bearing capacity is not reached as the applied
vertical load is quite small. Therefore, for the determination of the pile tip level the horizontal
bearing capacity is the governing factor.
11.11

Conclusion
Two pile types were investigated. Only the smooth open ended steel pipe pile with a diameter
of 1.71 m, a wall thickness of 12 mm and a pile tip level of 15 m below the soil surface satisfies
the required minimal rotational stiffness and the ultimate vertical bearing capacity of the Dutch
design code NEN 6740 at both Serviceability and Ultimate Limit States.

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foundation
This tutorial checks the design of a 6 pile offshore wind turbine foundation.
The objectives of this exercise are:

 To input a circular pile plan
 To model a tubular steel pile composed of two different sections
 To input the combination loads due to wind turbine.
For this tutorial the following modules are needed:

 D-P ILE G ROUP Standard module (Poulos model)
 Cap module
This tutorial is presented in the file Tutorial-6.pii.
12.1

Introduction to the case
This tutorial describes the check of the concept of a 6 pile foundation for a large wind turbine
at an offshore location. Since this is a check of the concept in the early stage of the design
no exact data were available for both the turbine loadings as well as the seabed conditions.
Loading data were not provided by the client. Only quasi-static wind loading of the turbine is
considered here, based on extrapolation of available dynamic loading data, for a 25 m/s wind
speed, for a slightly smaller turbine. Other loadings such as wave forces or ice loading are not
included.

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Figure 12.1: Offshore wind turbine on a 6 piles foundation (Tutorial 6)

Loads data
The direction of the three applied loads is given in Figure 12.1.
Table 12.1: Loading data

Vertical load
Horizontal load
Moment

Fv [kN]
Fh [kN]
Mz [kNm]

125
550
61000

Pile data
For the foundation steel pipe piles are used (without driving shoe). The foundation consists
of 6 piles evenly spaced at 60◦ intervals along a 25 m diameter footing. Piles are driven
through a 4 m long casing connected to the mast foundation. Piles are therefore made up of
2 sections:

 top section: diameter 1.1 m, wall thickness 50 mm and length 4 m,;
 bottom section: diameter 1.0 m, wall thickness 30 mm and length 15 m.
For both sections, the Young’s modulus is 2.1 × 108 kN/m2 (steel material). For the top
section, the values of EA and EI are equal to: EI = 2.1 × 108 × π × [(1.1/2)4 – (1.1/2 – 0.03 –
0.05)4 ] / 4 = 7044222 kNm2 EA = 2.1 × 108 × π × (0.03 + 0.05) × [1.1 – (0.03 + 0.05)] = 53834332 kN

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And for the bottom section: EI = 2.1 × 108 × π × [(1/2)4 – (1/2 – 0.03 )4 ] / 4 = 2260117 kNm2
EA = 2.1 × 108 × π × 0.03 × (1 – 0.03) = 19198273 kN
The pile end bearing is considered to be 7800 kN (plugging) while the pile tip curve is taken
as bi-linear (sufficient at this stage of the design). All pile heads are fixed.

Figure 12.2: Top view of the 6 piles position (Tutorial 6)

Soil data
Both the stratification present at the site as well as the properties of the soil layers themselves
are unknown. In this case a 2-layers system is adopted consisting of a top layer of clay, with
a thickness of 7 m, overlying a sandy soil. The seabed is assumed to be horizontal and no
scour or plate bearing of the foundation itself is taken into account. For the pile soil interaction,
soil behavior according to the API has been used.The soil data used are given in Table 12.2,
cyclic effects have not been considered.
Table 12.2: Soil properties for Tutorial 6

Soil type
Dry weight [kN/m3 ]
Wet weight [kN/m3 ]
Cu [kN/m2 ]
Phi [◦ ]
Friction angle [◦ ]
Cone resistance [kN/m2 ]
Ko [-]
Lateral rule
Axial rule
J [-]
e50 [-]
dz at 100 % [m]

Clay
Soft clay
17
17
20
API Cyclic
API
0.25
0.020
0.011

Sand
Sand
18
20
30
20
10000
0.5
API Cyclic
API
0.0025

The water level coincides with the surface level.

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Lateral and axial rules
The lateral P-Y and axial T-Z curves are taken according to the internationally accepted Code
API for all layers, using the cyclic loading for the lateral curve due to the wind. Parameters
J, e50 and “dz at 100%” are determined as explained in the sub-paragraph “Lateral and axial
rules” in section 9.1.

Figure 12.3: Functioning of the Cap model for Tutorial 6

Model
Due to the uncertainty of the input values and the relatively large pile distances no pile-soil-pile
interaction is taken into account which means the Cap model can be used.
Figure 12.3 schematizes the functioning of the Cap model for this tutorial: the pile is laterally
loaded by means of the cap which transmits the load to the pile. Only the lateral soil springs
will be active to transmit the lateral load from the pile to the soil. For the Cap model, axial
springs along and at the tip of the pile exist but they are not active in this case, that’s why they
are not represented.
12.2

Project Model and Properties
Before inputted the data’s, a new project must be created where the Cap model is used as
explained in section 12.1.
1.
2.
3.
4.
5.

12.3

Select New in the File menu and save it as  in the Save As window.
Open the Model window from the Project menu.
Select the Cap model and click OK to confirm.
Open the Project Properties window by selecting Properties in the Project menu.
Fill in ,  and  for respectively Title 1, Title 2 and Title 3 in the Identification tab.

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12.3.1

Soil Layers
6. In the Soil Layers window from the Soil menu, click Add to enter the two soil layers properties as indicated in Table 12.2.

Figure 12.4: Soil Layers window

7. Click OK to confirm the input data for the layer properties.
12.3.2

Soil Profiles
8. In the Soil Profiles window from the Soil menu, click Add to create a soil profile with
number <1>.
9. Compose the profile according to Figure 11.1 by clicking the Add row button and fill in the
table at the right side of the window.
10. Enter the Water level at <0 m> and the location of the CPT at X = 0 m and Z = 0 m as
given in section 12.1. CPT

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Figure 12.5: Soil Profiles window

12.4
12.4.1

Pile
Pile Types
11. In the Pile Types window from the Pile menu, click Add to create a pile types with name
<1M>.

Figure 12.6: Pile Types window

12. Select the User specified material and a Number of segments of <2> corresponding to
both upper and lower sections of the pile.
13. For the two tabs called #1 and #2, fill in the different dimensions of the Parameters subwindow as given in the sub-paragraph “Pile data” of [section 12.1].

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12.4.2

Pile Tip Curves
The pile tip curve specifies the load-displacement behavior of the pile tip in terms relative
to the end bearing capacity. In this tutorial, the pile tip curve is described using two points:
(0 %, 0 m) and (100 %, 0.02 m).
14. In the Pile Tip Curves window from the Pile menu, create a pile tip curve by clicking the
Add button.
15. Enter the two points given above.

12.4.3

Pile Positions
The 6 piles position must be entered according to Figure 12.2.
16. In the Pile Positions window from the Pile menu, create 6 piles all with Soil profile <1>,
Pile type <1> and Pile tip curve <1>.
17. Enter the Xtop, Ytop and Ztop co-ordinates according to Figure 12.2 with a  Top
condition.
18. The End bearing capacity is <7800 kN> for all piles.
19. The Angle in XZ plane and the Rake [hor/vert] are set to <0> as all piles are vertical.

Figure 12.7: Pile Positions window

12.5

Cap Location
20. In the Cap Location window from the Cap menu, fill in the X, Y, Z-coordinates as (0, 0, 0)
which corresponds to the centre of the 6 piles group (see Figure 12.2).
21. Click OK to close the window.

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12.6

Loads Cap
Special care must be taken on the sign of the loads and the moment to be in accordance with
Figure 12.1.
22. Open the Loads Cap window from the Loads menu.
23. Enter the values shown in Figure 12.8 below.

Figure 12.8: Loads Cap window

12.7

Calculation and Results
Select the Start option of the Calculation menu and click OK to perform a calculation.

12.7.1

Top View Results
24. Select the Top View option from the Results menu to display the Top View Results window.
25. Click the Show force button at the left of the window to deselect this option.
26. Click the Show displacement button
at the left of the window to view the horizontal displacement results at the pile head (Figure 12.9). The horizontal calculated displacements
at seabed level are about 7 mm.

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Figure 12.9: Top View Results window, calculated horizontal displacements at pile heads

27. Select the Y-direction to view the vertical displacement results at the pile head (Figure 12.10).
The vertical calculated displacements at seabed level are 21 mm upwards at one side of the
foundation and 8 mm downward at the other side, causing tilt of the mast.

Figure 12.10: Top View Results window, calculated vertical displacements at pile heads

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12.7.2

Charts Results
28. Select the Charts options from the Results menu.
29. In the window displayed, select Direction  and Pile <4> to view the charts of lateral
displacement, bending moment and shear force along the pile shaft for pile 4 for lateral
loading (Figure 12.11).

Figure 12.11: Charts window, lateral displacements, bending moments and shear forces
for pile 4

30. Select Direction  and Pile <4> to view the charts of vertical displacement, axial force
and soil resistance along the pile shaft for pile 4 for vertical loading (Figure 12.12).

Figure 12.12: Charts window, vertical displacement, axial force and soil resistance for
pile 4

The bending moments in Figure 12.11 show that the stronger upper section of the pile is
relatively short. Bending moments are decreased significantly only after 6 or 7 meters below
the pile head. It is therefore probably economically attractive to use a pile with a stronger and

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stiffer top section of 7 m long and a lighter deeper section.
12.7.3

Cap-plots Results
31. Select the Cap Plots options from the Results menu.
32. In the window displayed, select Direction  to view the horizontal force versus horizontal cap-displacement (Figure 12.13).

Figure 12.13: Cap-plots window, horizontal force versus horizontal cap-displacement

Horizontal displacements of the foundation increase almost linearly until a loading level of
about 385 kN. After that displacements increase at a higher rate, especially for horizontal
loads higher than 500 kN (see Figure 12.13).
33. Select Direction  to view the vertical force versus vertical cap-displacement (Figure 12.14).

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Figure 12.14: Cap-plots window, vertical force versus vertical cap-displacement

Vertical displacements increase almost linearly until a loading level of about 87 kN. After that
displacements increase at a higher rate (see Figure 12.14).
34. Select Direction  to view the moment versus cap-rotation (Figure 12.15).

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Figure 12.15: Cap-plots window, moment versus cap-rotation

A similar behavior is shown in Figure 12.15 were the relationship between rotations and the
moment load is presented. All this shows that the last 10 % of loading is responsible for
almost 50 % of the displacements. This implies that optimization of the foundation design, for
this location, is possible.
12.8

Conclusion
For the chosen location properties, loading conditions and pile configuration, the results of the
calculation are:

 The difference in vertical displacements at seabed level between both sides of the foundation causes tilt of the mast.

 The top section of the pile is relatively short. Using piles with a stronger and a stiffer top
section of 7 m instead of 4 m and a lighter bottom section will probably be economically
more attractive.
 The last 10 % of loading is responsible for almost 50 % of the displacements. This implies
that the foundation design could be optimized.

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13 Tutorial 7: Collision of a ship against a pile
This tutorial models the collision of a ship against a pile.
The objectives of this exercise are:

 To model the collision of a ship against a pile using the Dynamic model.
 To model a pile composed of different sections.
For this tutorial the following modules are needed:

 D-P ILE G ROUP Standard module (Poulos model)
 Cap module
 Dynamic module
This tutorial is presented in the file Tutorial-7.pii.
13.1

Introduction to the case
This tutorial models the collision of a ship against a pile using the Dynamic model which is the
only model in D-P ILE G ROUP assuming dynamic loading. The collision against the pile occurs
horizontally at level 0.95 m.

Figure 13.1: Collision of a ship against a pile (Tutorial 7)

Ship data
The loading parameters of the ship are given in Table 13.1 below.
Table 13.1: Loading parameters of the ship

Mass

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[kg]

562 000

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Velocity
Contact stiffness

[m/s]
[kN/m]

0.56
10 000

Pile data
The tubular steel pile has a diameter of 1.2 m and is composed of three sections filled with
sand:

 Top section: length 8 m and wall thickness 13 mm;
 Middle section: length 11.5 m and wall thickness 18 mm;
 Bottom section: length 2 m and wall thickness 13 mm.
The steel and sand materials which compose the pile have a unit weight of 7500 and 2000 kg/m3
respectively. This leads to a mass of:

 For the top and bottom sections:
π × 0.013 × (1.2 – 0.013) × 7500 + π /4 × (1.2 – 2 × 0.013)2 × 2000 = 2529 kg/m
 For the middle section:
π × 0.018 × (1.2 – 0.018) × 7500 + π /4 × (1.2 – 2 × 0.018)2 × 2000 = 2630 kg/m
The Young’s modulus of steel is set to 2.1 × 108 kN/m2 . Therefore:

 For the top and bottom sections:
EI = 2.1 × 108 × π × [(1.2/2)4 – (1.2/2 – 0.013)4 ] / 4 = 1 793 192 kNm2
EA = 2.1 × 108 × π × 0.013 × (1.2 – 0.013) = 10 180 362 kN
 For the middle section:
EI = 2.1 × 108 × π × [(1.2/2)4 – (1.2/2 – 0.013)4 ] / 4 = 2 451 912 kNm2
EA = 2.1 × 108 × π × 0.018 × (1.2 – 0.018) = 14 036 510 kN
Soil data
The soil properties are given in Table 13.2.

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Table 13.2: Soil properties for Tutorial 7

Soil type
Dry weight [kN/m3 ]
Wet weight [kN/m3 ]
Cu [kN/m2 ]
Friction angle [◦ ]
Delta friction [◦ ]
Cone resistance [kN/m2 ]
Ko [-]
Lateral rule
Axial rule
J [-]
e50 [-]
dz at 100 % [m]
Void ratio [-]

Top
Bottom

Initial
Minimum
Maximum

Clay
Soft clay
15
15
10
API
API
0.25
0.020
0.012
-

Sand
Sand
18
20
35
20
5000
10000
0.5
API Undrained
API
0.0025
0.54
0.54
0.89

Lateral and axial rules
The lateral P-Y and axial T-Z curves are taken according to the internationally accepted Code
API for all layers. Parameters J, e50 and “dz at 100%” are determined as explained in the subparagraph “Lateral and axial rules” in section 9.1. For the sand layer, the lateral P-Y curve
used is for undrained conditions. This curve is especially dedicated to the Dynamic model and
corresponds to the standard API P-Y curve for drained sand multiplied by a factor depending
on the void ratio. See section 15.1.5 for background information.

Figure 13.2: Functioning of the Dynamic model for Tutorial 7

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Figure 13.2 schematizes the functioning of the Dynamic model for this tutorial: the pile is
laterally loaded by means of the cap which transmits the load to the pile. Only the lateral soil
springs will be active to transmit the lateral load from the pile to the soil. Axial springs along
and at the tip of the pile are also present but they are not active in this case, that’s why they
are not represented. The top part of the pile situated above the collision point is modeled in
D-P ILE G ROUP as the cap. Therefore, the input length of the top pile section is 5.95 m instead
of 8 m.
13.2

Project Model and Properties
For this tutorial, the Dynamic model is used to model the dynamic collision.
1. Before inputting the data, create a new project by selecting New in the File menu and save
it as  in the Save As window.
2. Open the Model window from the Project menu.
3. Select the Dynamic model and click OK to confirm.
4. Open the Project Properties window by selecting Properties in the Project menu to give
the project a meaningful description.
5. Fill in  and  for Title 1
and Title 2 respectively in the Identification tab.

Figure 13.3: Model window

13.3
13.3.1

Soil
Soil Layers
6. In the Soil Layers window from the Soil menu, click Add to enter the two soil layers properties as indicated in Table 13.2.

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Figure 13.4: Soil Layers window, properties of the clay layer

Figure 13.5: Soil Layers window, properties of the sand layer

7. Click OK to confirm the input data for the layer properties.

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13.3.2

Soil Profiles
8. In the Soil Profiles window from the Soil menu, click Add to create a soil profile with
number <1>.
9. Compose the profile according to Figure 13.1 by clicking the Add row button and fill in the
table at the right side of the window.
10. Enter the Water level at <0 m>.

Figure 13.6: Soil Profiles window

13.4
13.4.1

Pile
Pile Types
The pile is composed of three sections, therefore a user specified pile as to be inputted.
11. In the Pile Types window from the Pile menu, click Add to create a new pile type.
12. Change the default pile type name  to  and define it as a User specified
pile material with a Number of segments of <3>.
13. Enter the pile characteristics of each section as described in section 13.1 and illustrated in
Figure 13.2: the pile top section has a length of only 8 – 2.05 = 5.95 m because the top
part of the pile situated above the collision point is modeled with the cap.

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Figure 13.7: Pile Types window

13.4.2

Pile Tip Curves
The pile tip curve specifies the load-displacement behavior of the pile tip in terms relative
to the end bearing capacity. In this tutorial, the pile tip curve is described using two points:
(0 %, 0 m) and (100 %, 0.03 m).
14. In the Pile Tip Curves window from the Pile menu, create a pile tip curve by clicking the
Add button and enter the co-ordinates of the two points given above.

13.4.3

Pile Positions
According to Figure 13.2, the pile top corresponds with the collision point situated at coordinates (0, 0.95, 0).
15. In the Pile Positions window from the Pile menu, define pile <1> with Soil profile <1>,
Pile type  and Pile tip curve <1>.
16. Enter the Xtop, Ytop and Ztop co-ordinates given above with a  Top condition
and an End bearing capacity of <500 kN>.
17. The Angle in XZ plane and the Rake [hor/vert] are set to <0> as the pile is vertical.

Figure 13.8: Pile Positions window

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13.5

Cap
In this tutorial, the cap represents the pile part above the collision point which has a height of
3 – 0.95 = 2.05 m. As the pile top section has a mass per length of 2529 kg/m, this leads to a
total mass of 2.05 × 2529 = 5184.45 kg.
The mass moments of inertia of the cap must also be inputted. In this tutorial, the cap is solid
cylinder of radius R = 0.6 m, height h = 2.05 m and mass m = 5184.45 kg, which leads to:
Ix = Iz = m × (3R2 + h2 ) /12 = 5184.45 × (3 × 0.62 + 2.052 ) /12 = 27386.86 kg.m2
Iy = m × R2 /2 = 5184.45 × 0.62 /2 = 933.20 kg.m2

13.5.1

Cap Location
18. In the Cap Location window from the Cap menu, fill in the X, Y, Z-coordinates as (0, 0.95, 0)
which corresponds to the collision point (see Figure 11.1).
19. Click OK to close the window.

13.5.2

Cap Mass
20. In the Cap Mass window from the Cap menu, enter the Cap mass and the mass moments
of inertia Ix , Iy and Iz calculated above.
21. Click OK to close the window.

Figure 13.9: Cap Mass window

13.6

Loading Parameters of Ship
22. In the Loads menu, select the Ship option to open the Loading Parameters of Ship window.
23. Enter the values as given in Table 13.1: Mass of <562 000 kg> for the weight of the ship,
Velocity of <0.56 m/s> which corresponds to the speed of the ship at the time of collision,
Heading of <0 degree> which corresponds to the angle of collision with the horizontal
axis and Contact stiffness of <10 000 kN/m> for the stiffness between the ship and the
pile. The co-ordinates of the Collision point are given in Figure 13.1.
24. In order to determine the forces involved during the collision, the collision time is divided in
a number of steps of <500> having each one a duration of <0.005 s>. This corresponds
to a collision time of 500 × 0.005 = 2.5 s which is realistic.
25. Click OK to close the window.

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Figure 13.10: Loading Parameters of Ship window

13.7

Calculation and Results
26. In the Calculation Options window from the Calculation menu, change the default Minimum
number of pile nodes into <100> in order to get more accurate results and click OK to
confirm.
27. Select the Start option of the Calculation menu and click OK to start the calculation.
28. Choose the Ducbots option from the Results menu.
29. An informative window appears which tell that the raw data were cut off after point 144 due
to continuously decreasing force. Click OK to continue.
30. A second informative window appears to inform that the input file for the BOTS program
is written as Tutorial-7.pib. This means that this project can be calculated with an other
program called BOTS developed by Rijkwaterstaat.
31. Click OK to continue.
The window displayed (Figure 13.11) shows the filtered displacement-force curve.

Figure 13.11: Ducbots window, Displacement-Force curve with filtering

32. Open the Chart Data window by clicking the right-hand mouse button and selecting View
data. In the table displayed (Figure 13.12) it can be seen that the force applied on the pile
at the end of the collision is 730 kN and the displacement of the pile is 27.57 cm.

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Figure 13.12: Chart Data window for the filtered DisplacementForce curve

33. Click Close to close the window.
34. Select Displacement – Force from the drop down list at the top left hand side of the Ducbots
window to display the same chart as previously but without filtering.

Figure 13.13: Ducbots window, Displacement-Force curve without filtering

35. Select Time-Displacement from the drop down list at the top left hand side of the Ducbots
window to display the curve of pile displacement against time.
In the window displayed (Figure 13.14), the collision ends after 2.5 seconds which corresponds to the input values of the Loading Parameters of Ship window (section 13.6) as 500
time steps of 0.005 seconds were inputted. Between 1.3 and 2.5 seconds the curve is linearly
decreasing which means that the ship is moving back at constant speed.

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Figure 13.14: Ducbots window, Time-Displacement curve

36. Select Time-Force from the drop down list at the top left hand side of the Ducbots window
to display the curve of force applied to the pile against time.

Figure 13.15: Ducbots window, Time-Force curve

In the window displayed (Figure 13.15) it can be noticed that the collision force is completely
absorbed by the pile after 1.5 seconds.
13.8

Conclusion
During the collision of the ship with the pile the maximum force calculated by D-P ILE G ROUP
is 733 kN for a contact stiffness (also called fender stiffness) of 10 000 kN/m. Therefore the
fender compression is equal to 730 /10000 = 0.0730 m. As the maximum calculated displacement is 0.2757 m, the real pile displacement is estimated to be: 0.2757 – 0.0730 = 0.2020 m.

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14 Tutorial 8: 3-piles group analysis using four different models
This tutorial analyses a 3-piles group in a 2-layers system using four different models that
differ on the pile-soil-pile interaction modeling. Results of the different models are compared
and discussed.
The objectives of this exercise are:

 To input the pile-soil-pile interaction data for the Cap soil interaction, Cap layered soil
interaction and Plasti-Poulos models.

 To calculate the plasticity factors needed for the Plasti-Poulos model.
For this tutorial the following modules are needed:







D-P ILE G ROUP Standard module (Poulos model)
Cap module
Plasti-Poulos module
Cap Soil Interaction module
Cap Layered Soil Interaction module

This tutorial is presented in the files Tutorial-8a.pii until Tutorial-8d.pii.
14.1

Introduction to the case
This tutorial deals with the analysis of a simple pile group composed of 3 piles connected with
a cap loaded by a vertical load of 320 kN and a lateral load of 80 kN.

Figure 14.1: Soil profile and pile group position (Tutorial 8)

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Table 14.1: Soil properties for Tutorial 8

3

Unsaturated unit weight [kN/m ]
Saturated unit weight [kN/m3 ]
Undrained shear strength su [kN/m2 ]
Friction angle [◦ ]
Delta friction [◦ ]
Cone resistance [kN/m2 ]
K0 [-]
Lateral rule
Axial rule
J [-]
ε50 [-]
dz at 100 % [m]

Soft clay
15
15
10
API
API
0.25
0.020
0.0030

Sand
18
20
35
20
10000
0.5
API
API
0.0025

Pile data
All piles consist of an open ended steel pipe with a length of 15 m, a diameter of 0.3 m, a wall
thickness of 15 mm and a modulus of 2.1 × 108 kN/m2 . Their heads are fixed to the cap and
their top level is at 0 m. Their position in the global co-ordinate system (X, Y, Z) is given in the
top view of Figure 14.1.
Soil data
The soil profile is composed of a soft clay and a sand layers. Their properties are given in
Table 14.1.
Lateral and axial rules
The lateral P-Y and axial T-Z curves are taken according to the internationally accepted Code
API for all layers. Parameters J , ε50 and “dz at 100%” are determined as explained in the
sub-paragraph “Lateral and axial rules” in section 9.1.
Model
For this project, the results of four different models using a different pile-soil-pile interaction
model are compared:

 In Tutorial-8a, the Cap model is used which assumes no pile-soil-pile interaction model
between piles (see Figure 14.2);

 In Tutorial-8b, the Plasti-Poulos model is used which assumes two homogeneous elastoplastic soil layers, one along the pile and one below the pile tip (see Figure 14.3);
 In Tutorial-8c, the Cap soil interaction model which assumes a unique homogeneous elastic soil (see Figure 14.4);
 In Tutorial-8d, the Cap layered soil interaction model is used which assumes a layered
elastic soil (see Figure 14.5).
The elastic properties used for the different interaction models are given in Table 14.2.

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Table 14.2: Pile-soil-pile interaction properties for Tutorial 8

2

Young’s modulus [kN/m ]
Poisson ratio [-]

Soft clay
5 000
0.3

Sand
100 000
0.2

Figure 14.2: Functioning of the Cap model for Tutorial 8a

Figure 14.3: Functioning of the Plasti-Poulos model for Tutorial 8b

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Figure 14.4: Functioning of the Cap soil interaction model for Tutorial 8c

Figure 14.5: Functioning of the Cap layered soil interaction model for Tutorial 8d

14.2
14.2.1

Calculation with the Cap model
Project Model
1. Before inputting the data, create a new project by selecting New in the File menu and save
it as  in the Save As window.
2. In the Project menu, select Model to get an overview of all available models.
3. The Cap model is chosen for the first calculation.
4. Click OK to confirm.

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14.2.2

Project Properties
To give the project a meaningful description, follow the steps described below:
5. Open the Project Properties window by selecting Properties in the Project menu.
6. Fill in , <3-piles group analysis using four different models>
and  for Title 1, Title 2 and Title 3 in the Identification tab.
7. Click OK to confirm.

14.2.3

Soil Layers
8. In the Soil Layers window from the Soil menu, click Add to enter both soil layers properties
as indicated in Table 14.1.
9. Click OK to confirm.

14.2.4

Soil Profiles
10. In the Soil Profiles window from the Soil menu, click Add to create a soil profile with
number <1>.
11. Compose the profile according to Figure 14.1 by clicking the Add row button and fill in the
table at the right side of the window.
12. Enter the Water level at <-1 m>.
13. Click OK to confirm.

14.2.5

Pile Types
14. In the Pile Types window from the Pile menu, click Add to create a pile type with name
.
15. Select the Steel material and fill in the different dimensions of the Parameters sub-window
as given in section 14.1.
16. Click OK to confirm.

14.2.6

Pile Tip Curves
The pile tip curve specifies the load-displacement behavior of the pile tip. In this tutorial, the
pile tip curve is described using two points: (0 %, 0 m) and (100 %, 0.03 m).
17. In the Pile Tip Curves window from the Pile menu, create a pile tip curve by clicking the
Add button.
18. Enter the two points given above and click OK to confirm.

14.2.7

Pile Positions
19. In the Pile Positions window from the Pile menu, define 3 piles with Soil profile <1>, Pile
type  and Pile tip curve <1>.
20. Enter the Xtop, Ytop and Ztop co-ordinates given in Figure 14.1 with a  Top
condition and an End bearing capacity of <500 kN>.
21. The Angle in XZ plane and the Rake [hor/vert] are set to <0> as the pile is vertical.
22. Click OK to confirm.

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Figure 14.6: Pile Positions window

14.2.8

Cap Location
According to Figure 14.1, the co-ordinates of the center of gravity of the cap is the weighted
mean of the 3 piles which leads to (2 × 0.5 - 1) / 3 = 0 m in the X direction and (0.5 0.5 + 0) / 3 = 0 m in the Y direction.
23. In the Cap Location window from the Cap menu, fill in the X, Y, Z-coordinates as (0, 0, 0).
24. Click OK to confirm.

14.2.9

Loads Cap
25. In the Loads Cap window from the Loads menu, enter a  of <80 kN> in the X
direction during the first <10> load steps and then a  of <-320 kN> in the Y
direction during between load-steps <10> and <20>.
26. Click OK to confirm.

Figure 14.7: Loads Cap window

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14.2.10

Calculation and Results
27. Select the Start option of the Calculation menu and click OK to start the calculation.
28. When the calculation is finished, select the Cap Plots option from the Results menu to view
the pile head load-displacement curve in the X direction (Figure 14.8).

Figure 14.8: Cap-plots window, pile head load-displacement curve in the X direction (Tutorial 8a)

In the window displayed, open the Chart Data window by clicking the right-hand mouse button
and selecting View data. The lateral deflection is 15.59 mm at the end of the lateral loading
of 80 kN and increase up to 15.73 mm during the axial loading of 320 kN.
29. Select the Charts option from the Results menu.
30. Select Pile <3> and Direction  to view the axial force along the right pile (Figure 14.9).

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Figure 14.9: Charts window, axial force along pile 3 (Tutorial 8a)

31. Select Direction  to view the bending moment around Z axis along the pile (Figure 14.10).

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Figure 14.10: Charts window, bending moment along pile 3 (Tutorial 8a)

14.3

Calculation with the Plasti-Poulos model
Different data must be inputted for the Plasti-Poulos model compare to the Cap model.

14.3.1

Project Model and Properties
32. Save the current file as  using the Save As window of the File menu.
33. In the Model window from the Project menu, select the Plasti-Poulos model and click OK
to confirm.
34. Modify Title 1 and Title 3 of the Project Properties window into respectively  and  in the Identification tab and click OK to
confirm.

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14.3.2

Soil Interaction Model
The parameters needed for the pile-soil-pile interaction model must be inputted in this window.
According to Poulos theory, two layers are considered: one along the pile and one below the
pile tip level, with a different Young’s modulus. For the layer above the pile tip, the properties
of the “Soft clay” layer are used as it is the thickest layer in this area. For the layer below the
pile tip, the properties of the “Sand” layer are used according to Figure 14.1.
35.
36.
37.
38.

Open the Soil Interaction Model window from the Soil menu.
Enter a Level at top of <0 m> to coincide with the ground level.
Enter a Poisson ratio of <0.3> corresponding to the “Soft clay” layer of Table 14.2.
Enter a Young’s modulus below the pile tip of <100 000 kN/m2 > corresponding to the
“Sand” layer of Table 14.2.
39. Click OK to confirm.

Figure 14.11: Soil Interaction Model window (Plasti-Poulos model)

14.3.3

Pile Positions
40. In the Pile Positions window from the Pile menu, select pile 1 as critical pile.
41. Click OK to confirm.

14.3.4

Plasticity Factors
In the Plasticity Factors window, the plasticity factors used in the Plasti-Poulos model calculations are determined automatically by D-P ILE G ROUP. The plasticity factors are used to reduce
the elastic stiffness of the classical Poulos model. They determine how much bigger the
elasto-plastic displacement of a pile is compared to the elastic displacement. For background
information on their determination, see section 16.3.3.
42. Select the Plasticity Factors option from the Pile menu.
43. In the window displayed, click the Calculate button to open the Calculate Plasti-Poulos
Factor Curves window (Figure 14.12).This window allows generating automatically plasticity factors by specifying the number of load-steps of the curve and the maximum values for
the forces in the X and Y directions and for the moment around the Z axis.

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Figure 14.12: Calculate Plasti-Poulos Factor Curves window

44. Leave the Steps and Force values to their default values and click OK to generate the
plasticity factors.
Five different charts (in the five different tabs) used in the calculation are drawn at the righthand side of the Plasticity Factors window (Figure 14.13). For each chart, two curves are
drawn:

 the blue curve (straight line) corresponds to an elastic stiffness (i.e. plasticity factor of 1);
 the red curve corresponds to a reduced stiffness with higher loading levels due to soil
plasticity.

Figure 14.13: Plasticity Factors window, Force-Displacement curve in the X direction

The values of the plasticity factors are given in the table at the left-hand side. For the Fx-ux
tab which corresponds to the force-displacement curve in the X direction, it can be noticed
that only the two first points of the curve have a plasticity factor of 1.
This is not good enough to describe correctly the soil stiffness. At least three points with a
plasticity factor of 1 are needed at the beginning of the curve. The same remark can be done
for the other charts. In order to increase this number, the number of steps in the Calculate
Plasti-Poulos Factor Curves window has to be increased. A number of 100 steps should be
enough.

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45. Click the Calculate button to open again the Calculate Plasti-Poulos Factor Curves window
and enter a number of Steps of <100> for all loads (Figure 14.14).
46. Click OK to generate the plasticity factors. In the Plasticity Factors window displayed
(Figure 14.15), it can be checked that at least the three first points of each curve have a
plasticity factor of 1 as desired.
47. Click OK to confirm.

Figure 14.14: Calculate Plasti-Poulos Factor Curves window

Figure 14.15: Plasticity Factors window, Force-Displacement curve in the X direction

Note: This tutorial uses only one pile type. In case of several pile types, the plasticity factors
must be calculated for each pile type by selecting it in the drop down list at the top of the
Plasticity Factors window and by repeating the process described above.
See Plasticity Factors (section 4.3.6) for a detailed description.
14.3.5

Check of the calculated plasticity factors
All the new input data needed for the Plasti-Poulos model has been entered and a calculation
can be performed.
48. Select Start from the Calculation menu.
49. In the Calculation window displayed, click OK to execute the calculation.

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Before inspecting the plots that result from this calculation, it must be checked that the calculated loads and moments are lower than the ultimate loads and moments used for the
determination of the plasticity curves. If not, D-P ILE G ROUP assumes a constant force equal to
the ultimate load as illustrated by Figure 14.16.

Figure 14.16: Load-displacement curve for plastic behavior

According to Figure 14.14, the ultimate loads are 100 kN in both X and Y directions and the
ultimate moment is 100 kNm around the Z axis.
Those values must be compared to the calculated loads and moments.
50. Open the Report window from the Results menu.
51. Select the pile top results at load steps 10 and 20 which correspond to the end of application of the lateral and axial loads respectively (Figure 14.17).

Figure 14.17: Report window

The maximum pile head force in the X direction is 27.657 kN which is lower than 100 kN.
The maximum pile head moment is 17.797 kNm which is also lower than 100 kNm. On

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the other hand, the maximum pile head compressive and tensile forces in the Y direction
are 134.201 kN and 51.813 kN. Therefore, new plasticity factors must be determined using
appropriate ultimate loads. The ultimate force X and moment Z can be lower to 30 kN and
20 kNm respectively whereas the ultimate force Y must be higher to 160 kN in compression
and 60 kN in tension. Values much larger than the calculated one are used for force Y because
the first calculation was performed with lower plasticity factors. So, the calculated forces in
the Y direction were under-estimated.
52. Select the Plasticity Factors option from the Pile menu.
53. In the window displayed, click the Calculate button to open the Calculate Plasti-Poulos
Factor Curves window.
54. Enter ultimate forces and moment higher than the calculated one: for Force X enter
<30 kN>, for Force Y in Compression and Tension enter <-160 kN> and <60 kN>
respectively and for Moment Z enter <20 kNm> (Figure 14.18).
55. Click OK to generate the plasticity factors. In the window displayed (Figure 14.19), the
force-displacement curve Fx-ux ends for a force of 30 kN as inputted previously. The
same check can be performed for the other curves.

Figure 14.18: Calculate Plasti-Poulos Factor Curves window

Figure 14.19: Plasticity Factors window, Force-Displacement curve in the X direction

14.3.6

Calculation and Results
A new calculation can be performed with new plasticity factors.

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56. Select Start from the Calculation menu.
57. In the Calculation window displayed, click OK to execute the calculation.
58. In the Calculation Messages window displayed it can be noticed that the Calculated soil
Young modulus for model with plasticity is approximately 2562 kN/m2 .
59. In the Report window from the Results menu, select the pile top results at load steps 10
and 20 as previously to check that the ultimate loads and moments used for the plasticity
factors determination are lower than the calculated values (Figure 14.20).

Figure 14.20: Report window (Tutorial 8b)

The maximum pile head force in the X direction is 27.629 kN which is lower than 30 kN. The
maximum pile head moment is 18.108 kNm which is also lower than 20 kNm. The maximum
pile head compressive and tensile forces in the Y direction are 157.937 kN and 51.948 kN
respectively which is lower than 160 kN and 60 kN respectively. Therefore, calculations were
performed with correct plasticity factors.
60. Open the Cap-plots window from the Results menu to view the pile head load-displacement
curve in the lateral direction (Figure 14.21). In the window displayed, open the Chart
Data window by clicking the right-hand mouse button and selecting View data. The lateral
deflection is 15.67 mm at the end of the lateral loading of 80 kN and decrease up to
15.65 mm during the axial loading of 320 kN.
Note: For the calculation of the plasticity factors, take care that:

 In the plasticity factor tables, the first three (or more) values are equal to 1;
 The specified ultimate load is higher than the calculated load;
 New plasticity factors must be calculated each time input data change.

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Figure 14.21: Cap-plots window, pile head load-displacement curve in the X-direction (Tutorial 8b)

14.4
14.4.1

Calculation with the Cap soil interaction model
Project Model and Properties
61. Save the current file as  using the Save As window of the File menu.
62. In the Model window from the Project menu, select the Cap soil interaction model and click
OK to confirm.
63. Modify Title 1 and Title 3 of the Project Properties window into respectively  and  in the Identification tab.

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14.4.2

Soil Interaction Model
The Soil Interaction Model window has to be adapted compare to the Plasti-Poulos model as
only one layer is modeled for the Cap soil interaction model instead of two. As the “Soft clay”
layer is the thickest layer, its properties are used for the soil interaction model.
64. Open the Soil Interaction Model window from the Soil menu.

Figure 14.22: Soil Interaction Model window (Cap soil interaction model)

65. Enter a Poisson ratio of <0.3> and a Young’s modulus of <5 000 kN/m2 > as given in
Table 14.2 for “Soft clay”.
66. Click OK to confirm.
14.4.3

Calculation and Results
Now that all input is entered, the calculation can be performed.
67. Select Start from the Calculation menu.
68. In the Calculation window displayed, click OK to execute the calculation.
69. When the calculation is finished, open the Cap-plots window from the Results menu.

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Figure 14.23: Cap-plots window, pile head load-displacement curve in the X-direction (Tutorial 8c)

In the window displayed, open the Chart Data window by clicking the right-hand mouse button
and selecting View data. The lateral deflection is 21.14 mm at the end of the lateral loading
of 80 kN and increase up to 22.10 mm during the axial loading of 320 kN.
14.5
14.5.1

Calculation with the Cap layered soil interaction model
Project Model and Properties
70. Save the current file as  using the Save As window of the File menu.
71. In the Model window from the Project menu, select the Cap layered soil interaction model
and click OK to confirm.
72. Modify Title 1 and Title 3 of the Project Properties window into respectively  and  in the Identification tab.

14.5.2

Soil Interaction Model
In the Soil Interaction Model window, the Cap layered soil interaction model allows to input a
different pile-soil-pile behavior for each layer (“Soft clay” and “Sand” layers, in this tutorial).
73. Open the Soil Interaction Model window from the Soil menu.

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74. Click Add to create a new soil interaction model corresponding to the “Soft clay” layer and
give it the name .
75. Enter a Level at top of <0 m> as indicated in Figure 14.1, a Young’s modulus of <5 000 kN/m2>
and a Poisson ratio of <0.3> as given in Table 14.2.
76. Repeat this process for the  interaction model of the “Sand” layer by entering a
Level at top of <-12 m>, a Young’s modulus of <100 000 kN/m2 > and a Poisson ratio of
<0.2> (Figure 14.24).
77. Click OK to confirm.

Figure 14.24: Soil Interaction Model window (Cap layered soil interaction model)

See section 4.2.3 for a detailed description.
14.5.3

Calculation and Results
78. Select Start from the Calculation menu.
79. In the Calculation window displayed, click OK to execute the calculation.
80. When the calculation is finished, open the Cap-plots window from the Results menu to see
the pile head force-displacement curve in the X-direction (Figure 14.25).
In the window displayed, open the Chart Data window by clicking the right-hand mouse button
and selecting View data. The lateral deflection is 18.78 mm at the end of the lateral loading
of 80 kN and increase up to 19.24 mm during the axial loading of 320 kN.

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Figure 14.25: Cap-plots window, pile head load-displacement curve in the X-direction (Tutorial 8d)

14.6

Conclusion
Figure 14.26 below shows the pile head load-displacement curve in the lateral direction for
the different models.

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Figure 14.26: Pile head load-displacement curve in the X-direction for the different models

The Cap model gives the stiffest force-displacement curve as it doesn’t take into account
the pile-soil-pile interaction but considers the soil + piles as a block.The Cap soil interaction and Cap layered soil interaction models give a less stiff behavior compare to the Cap
model as they take into account the pile-soil-pile interaction. The Cap layered soil interaction
model is a little stiffer compare to the Cap soil interaction model due to the layered interaction
(E = 5000 kN/m2 for Cap soil interaction model whereas E = 5000 kN/m2 above depth 12 m
and E = 100 000 kN/m2 below depth 12 m for Cap layered soil interaction model).
The final pile head displacements calculated with the Plasti-Poulos and Cap models are very
close.

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15 Soil behavior
For lateral loads the method described by Matlock Matlock (1970) is used. This method
describes the soil resistance for a single pile by a so-called "P-Y curve" approach. A "P-Y
curve" is a non-linear force (P) - displacement (Y) relation. The method is accepted by the
API (1984) and DNV (1977).
For vertical loads a comparable method can be used (T-Z curves) and besides the "negative
skin friction" option is introduced.
Note: In the following sections the internationally accepted notation is used: a lateral soil
resistance curve is called a P-Y curve. The Y in this curve is however not related to the axis
system that is being used by D-P ILE G ROUP where the Y-axis is in the vertical direction. In
the D-P ILE G ROUP axis system a P-Y curve will be in the X-Z plane, so it is a P-X or a P-Z
curve (in the local pile axis system). A similar thing applies to the T-Z curves that are in the
D-P ILE G ROUP Y direction; so it is a T-Y curve in the local pile axis system.
15.1
15.1.1

Lateral P-Y curves
P-Y curves for clay and static lateral loads (API)
According to the API, the ultimate resistance depends upon the failure mechanism of the
clay which differs for shallow (pus ) and deep depths (pud ). The API presents the following
formulas:

pus = 3 su + γ 0 × H + J × su

H
D

pud = 9 su

(15.1)

(15.2)

where:
is the ultimate lateral soil resistance at shallow depth, in kN/m2 ;
is the ultimate lateral soil resistance at deep depth, in kN/m2 ;
is the undrained shear strength, in kN/m2 ;
is the effective unit weight of the soil, in kN/m3 ;
is the depth below soil surface, in m;
is a dimensionless empirical constant. A value ranging from 0.25 to 0.5 is recommended;
is the pile diameter, in m.

pus
pud
su
γ0
H
j
D

In the API the shape of the API curve for soft clay is not given as a continuous curve, but is
defined by a small table. The points in this table are part of the continuous curve given by the
formula:


p=

1

0.5pu (y/y50 ) 3 for y < 8 y50
pu
for y ≥ 8 y50

(15.3)

where:

p
pu

is the actual lateral soil resistance at depth H , in kN/m2 ;
is the ultimate lateral soil resistance at depth H , in kN/m2 :

pu = min (pus ; pud )
y
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y50
ε50
D

is the displacement which occurs at one-half the maximum stress on laboratory
undrained compression tests of undisturbed soil samples, in m:
y50 = 2.5 × ε50 × D;
is the strain which occurs at one-half the maximum stress on laboratory undrained
compression tests of undisturbed soil samples;
is the pile diameter, in m.

Figure 15.1: Modeling of the P-Y curve (API) for clay and static loading

In D-P ILE G ROUP the P-Y curve for clay is modeled by five parallel elasto-plastic springs. The
springs are chosen such that the resulting multi-linear spring characteristic is correct at displacements 0.1 y50 , 0.3 y50 , y50 , 3 y50 and 8 y50 (Figure 15.1). These values have been
chosen because the initial stiffness of the curve is relatively high compared to the stiffness at
larger strains, and a correct description of the stiffness at small strains greatly influences the
overall results of the calculation.
For the determination of the value ε50 , Table 15.1 can be used.
Table 15.1: Determination of ε50 as a function of the undrained shear strength su

su
[kN/m2 ]
5-25
25-50
50-100
100-200
200-400

15.1.2

ε50
[-]
0.020
0.010
0.007
0.005
0.004

P-Y curves for clay and cyclic lateral loads (API cyclic)
Lateral P-Y curves:for clay (API Cyclic) According to the API, the ultimate lateral soil resistance for clay and cyclic loads is the same as for static loads (see Equation 15.1 and Equation 15.2 in section 15.1.1).

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The API curve for soft clay and cyclic loading is not given as a continuous curve, but is defined
by two small tables. The points in those tables are part of the continuous curves given by the
formulas:

p
=
pu



1

0.5 (y/y50 ) 3 for y < 3 y50
0.72
for y ≥ 3 y50

for H > HR

(15.4)


1

0.5 (y/y50 ) 3  


 for y < 3 y50
p
y
H
=
0.06 y50 + 0.54
− 1 for 15 y50 ≥ y ≥ 3 y50 forH ≤ HR
HR
pu 

0.72 (H/HR )
for y > 15 y50
(15.5)
where HR is the depth below soil surface to bottom of reduced resistance zone:

HR =

γ0

6D
× D/c + J

The definition of the other parameters is the same as for section 15.1.1.
Note: In the current version of D-P ILE G ROUP, only the case with H > HR is implemented
as the case with H < HR considers a decreasing stiffness (for 15 y50 > y > 3 y50 ) which is
not currently possible to implement in D-P ILE G ROUP.
In D-P ILE G ROUP the P-Y curve for clay and cyclic loading is modeled by four parallel elastoplastic springs The springs are chosen such that the resulting multi-linear spring characteristic
is correct at displacements 0.1 y50 , 0.3 y50 , y50 and 3 y50 (Figure 15.2).

Figure 15.2: Modeling of the P-Y curve (API cyclic) for clay and cyclic loading

15.1.3

P-Y curves for sand and static lateral loads (API)
According to the API, the P-Y curve for sand can be defined as:


P = A × pu × tanh

kH
×Y
A pu


(15.6)

where:

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P
A

is the actual lateral soil resistance at depth H , in kN/m;
is a factor to account for loading conditions. For static loads:
≥ 0.9;
A = 3 − 0.8 H
D
is the ultimate lateral soil resistance at depth H , in kN/m:
pu = min (pus ; pud ), see Equation 15.7 and Equation 15.8 below;
is the initial modulus of subgrade reaction, in kN/m3 , determined by figure 6.8.7-1
of the API (1984). D-P ILE G ROUP determines this parameter by linear interpolation
of the values given in Table 15.2;
is the depth below soil surface, in m;
is the pile diameter, in m;
is the actual lateral deflection, in m.

pu
k
H
D
Y

Table 15.2: Values of k as function of the angle of internal friction ϕ

Angle of internal friction ϕ
[◦ ]
29
29.5
30
33
36
38
40

k (dry condition)
[kN/m3 ]
2715
6109
11199
25453
42761
59051
75341

k (wet condition)
[kN/m3 ]
2715
5090
8145
16303
25453
32580
41743

Note: The definition of pu as given by the API differs for clay and sand: for clay the dimension
of pu is kN/m2 whereas for sand pu is in kN/m!
As with clay the ultimate resistance pu at depth H is the smallest of the values of pus and
pud . These values are defined by:

pus = (C1 × H + C2 × DH ) × γ 0 × H
pud = C3 × DH × γ 0 × H
with:



C1 = tan α tan β

(15.7)
(15.8)




tan β
cot (β − ϕ)
− K0 + K0 sin β tan ϕ
+ tan β
tan (β − ϕ)
cos α

tan β
− Ka
tan (β − ϕ)
C3 = Ka (tan8 β − 1) + K0 tan ϕ tan4 β
Ka = tan2 (45◦ − ϕ/2)
K0 = 0.4
β = 45◦ + ϕ/2
α = ϕ/2

C2 =

where:

pus
pud
C1 , C2 , C3

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is the ultimate lateral soil resistance at shallow depth, in kN/m;
is the ultimate lateral soil resistance at deep depth, in kN/m;
are the coefficients determined by figure 6.8.6-1 of the API (1984) or using
the equations given in Reese et al. (1979) and presented in Figure 15.3. In
D-P ILE G ROUP, those three constants are determined by linear interpolation
of the values given in Table 15.3;

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is the angle of internal friction, in ◦ ;
is the depth below soil surface, in m;
is the average pile diameter from surface to depth H , in m;
is the effective unit weight of the soil, in kN/m3 .

ϕ
H
DH
γ0

Figure 15.3: Coefficients C1 , C2 and C3 as function of the angle of internal friction

Table 15.3: Values of C1 , C2 , C3 inputted in D-Pile Group as function of the angle of
internal friction ϕ

ϕ
[◦ ]
20
25
30
35
40

C1
[-]
0.77
1.22
1.90
3.00
4.67

C2
[-]
1.58
2.03
2.67
3.45
4.35

C3
[-]
9.00
15.50
28.50
54.25
100.00

In D-P ILE G ROUP the P-Y curve for sand is modeled by five parallel elasto-plastic springs.
The springs are chosen such that the resulting multi-linear spring characteristic is correct at
displacements 0.25 ymax , 0.5 ymax , ymax , 1.5 ymax and 2.5 ymax (Figure 15.4) with:

ymax =

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A pu
kH

(15.9)

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Figure 15.4: Modeling of the P-Y curve (API) for sand

15.1.4

P-Y curves for sand and cyclic lateral loads (API Cyclic)
For cyclic lateral loads, the same equations that for static lateral loads [section 15.1.3] apply
except for factor A which is constant and equal to 0.9 in Equation 15.6.

15.1.5

P-Y curves for undrained sand (API Undrained)
This special API-rule may only be used when the Dynamic model has been selected.The P-Y
curve for undrained sand is obtained by multiplying the P-Y curve for drained sand and static
loading with a factor α = α(y):

Puu (y) = α (y) × Pu (y)

(15.10)

with:

Puu (y) is the actual lateral soil resistance at depth H , in kN/m, for undrained sand;
α(y) is a factor, see Equation 15.11 below;
Pu (y) is the actual lateral soil resistance at depth H , in kN/m, for drained sand. See
Equation 15.6;
is the actual lateral deflection, in m.

y

The factor α is equal to:


ur3

1
−
0.185
if |ur3 | < |ueven |


"p1
#

0.226
α (y) =
ueven
ueven


1 − 0.815
if |ur3 | ≥ |ueven |
 1− p
ur3
1

(15.11)

where:

ur3

2
is the excess pore water
 pressure, in kN/m
 :0 

ur3 =

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kunload × c1
1 + e0

e0 − c4 − c5 ln

σv
p0

6y
;
D

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Soil behavior

ueven

is the maximum excess pore water pressure, in kN/m2 , limited in one hand by
the cavity stress and inthe other 
hand by the effective stress:

ueven = σv0 − p0 exp
ucav
pa
gw
H
Hw
kunload
qc
s0v
p0
c1 , c4 , c5

e0
emin
emax
y
D

e 0 − c4
, with: ucav < ueven < σv0 ;
c5

is the cavitation stress, in kN/m2 :
ucav = −pa − γw (H − Hw ) with H − Hw ≥ 0;
is the atmospheric pressure (100 kN/m2 );
is the unit weight of water (9.81 kN/m3 );
is the actual depth, in m;
is the depth of water level, in m;
is the stiffness for unloading, in kN/m2 :
kunload = 4 qc ;
is the cone resistance, in kN/m2 ;
is the initial effective stress, in kN/m2 ;
is the reference pressure:
p0 = 100 kN/m2 ;
are constant terms:
c1 = 13.86;
c4 = 0.61 emax + 39 emin ;
c5 = 0.13 (emin − emax );
is the initial void ratio;
is the minimum void ratio;
is the maximum void ratio;
is the actual lateral deflection, in m;
is the pile diameter, in m.

In D-P ILE G ROUP the P-Y curve for undrained sand is modeled the same way as for drained
sand (see Figure 15.4).
15.2
15.2.1

Axial T-Z curves
T-Z curves for sand and clay (API)
For vertical loads the calculation method is comparable to the one used in horizontal direction.
An elaborate description of this method is given by Coyle and Reese (1966).
D-P ILE G ROUP offers the possibility to determine the ultimate skin friction in vertical direction
according to the API. It should be noted that this option applies to open-ended steel tubes.
Skin friction on the inside of the pile is therefore not included.
In order to obtain the correct ultimate bearing capacity of the pile the pile-tip resistance has to
be determined according to the API; minimum of annular resistance + inner friction or full tip
area resistance (plugging).
For materials other than steel “user specified friction curves” can be used.
In D-P ILE G ROUP the spring stiffness can be specified by entering the displacement (dz at
100 %) corresponding with the ultimate resistance (Rs).
A correct determination of the value of this spring stiffness is not trivial. In design codes
usually only the overall pile-friction behavior is described. That is the development of the
pile-shaft friction related to the settlement of the pile tip.

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For example the Dutch code NEN 6743 gives 3 curves for the development of the pile friction
for soil displacement piles, augured piles and bored piles. However, for the local pile-soil
displacement at the pile shaft surface the influence of compression/extension of the pile itself
needs to be included. Furthermore the behavior of soft, compressible, soil layers and that of
stiffer granular layers will be different.
To obtain accurate load-deformation behavior these matters have to be included in the analysis. As a rule of thump values of 2 mm for sand and 5 mm for clay are often used as values
where the maximum friction is reached. It should be noted that these values include the elastic deformation of the soil around the pile. In case of an analysis that includes pile-soil-pile
interaction this elastic deformation will automatically be included in the analysis and should
therefore not be included in the spring stiffness. In that case a very stiff soil spring is recommended (maximum friction at a displacement of 1 mm).
Skin friction for clay (cohesive soil)
For the skin friction in cohesive soil the API gives:

f = α × su

(15.12)

where:
is the skin friction, in kN/m2 ;
is a dimensionless
factor:


F
A

0.5 ψ −0.5 if ψ ≤ 1.0
0.5 ψ −0.25 if ψ > 1.0
with the constraint that α ≤ 1.0 and with ψ = su /p00 ;

α=
p00
su

is the effective overburden pressure at the point in question, in kN/m2 ;
is the undrained shear strength, in kN/m2 .

Skin friction for sand (cohesionless soil)
For the skin friction in cohesionless soil the API gives:

f = K × p00 × tan δ

(15.13)

where:

F
k
p00
δ

is the skin friction, in kN/m2 ;
is the coefficient of lateral earth pressure (ratio of horizontal to vertical normal effective stress), in kN/m3 ;
is the effective overburden pressure at the point in question, in kN/m2 ;
is the friction angle between soil and pile wall, in ◦ .

T-Z curves for clay and sand
The linear elastic part of the T-Z curve can be specified in D-P ILE G ROUP by entering the
displacement (dz at 100 %) corresponding with the ultimate resistance as illustrated in Figure 15.5, where:

t
Tmax
F
As

is the mobilized total skin friction, in kN;
is the maximum total skin friction, in kN:Tmax = f × As ;
is the maximum skin friction, in kN/m2 . See Equation 15.12 and Equation 15.13;
is the side surface area of pile, in m2 .

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Figure 15.5: T-Z curve (API) for clay and sand

Note: For “dz at 100 %”, API recommends a value of 0.1 inches (= 2.54 mm) for sand and
0.01 D for clay, where D is the pile diameter.
15.2.2

T-Z curves for sand (Cone)
An alternative method used in the Netherlands to determine the maximum skin friction is
based on the cone resistance, according to the Dutch code NEN 6743:

f = α qc

(15.14)

where:
is the skin friction in kN/m2 ;
is a dimensionless factor, usually between 0.005 - 0.014 for cohesionless soil depending on the pile type used;
is the cone resistance of the soil in kN/m2 .

F
α
qc
15.2.3

T-Z curves for clay (Ratio)
An alternative method for the API in cohesive soil to determine the maximum skin friction is a
user-defined factor:

f = α × su

(15.15)

where:

F
a
su

is the skin friction in kN/m2 ;
is a dimensionless factor;
is the undrained shear strength in kN/m2 .

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15.3

Pile tip curves Pile Tip Curves
The pile tip curve specifies the axial load-displacement behavior of the pile tip and must be
inputted in the Pile Tip Curves window (section 4.3.2).To help the user defining this curve,
prescribed curves from the API and the NEN Design Codes are given in section 15.3.1 and
section 15.3.2 respectively.

15.3.1

Pile tip curve according to API
According to the API, the recommended pile tip load-displacement curve Q-Z for both sand
and clays is shown in Figure 15.6 where:

q
Qp
Z
D

is the mobilized end bearing capacity, in kN;
is the total end bearing capacity, in kN;
is the axial tip displacement, in m;
is the pile diameter, in m.

Figure 15.6: Pile tip curve according to API

Note: In D-P ILE G ROUP, the total end bearing Qp must be inputted in the Pile Positions
window under the name End bearing (section 4.3.3).
15.3.2

Pile tip curves according to the Dutch Code NEN
According to Figure 6 of NEN 6743 NEN (1991), the pile tip load-displacement curve depends
on the pile type as shown in Figure 15.7 where:

Fr;punt
Fr;max;punt
Wpunt
Deq

is the mobilized end bearing capacity, in kN;
is the total end bearing capacity, in kN;
is the axial tip displacement, in m;
is the equivalent pilep
diameter, in m:

Deq = 1.13 × a ×

b/a

where:
a is the smallest side of the larger cross section of the pile;
b is the largest side of the larger cross section of the pile.

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Figure 15.7: Pile tip curve according to the Dutch Code

The pile tip load-displacement curve recommended by NEN 6743 can be inputted in the Pile
Tip Curves window (section 4.3.2) using the co-ordinates of the four points given in Table 15.4
below.
Table 15.4: Values of Wpunt /Deq as function of the percentage of mobilized end bearing
capacity for different pile types (NEN 6743)

Fr;punt /Fr;max;punt
[%]
0
25
50
75
100

Wpunt /Deq
Driven piles
0
0.004
0.015
0.042
0.100

CFA piles
0
0.010
0.029
0.073
0.200

Bored piles
0
0.019
0.045
0.095
0.200

NOTE: In D-P ILE G ROUP, the total end bearing Fr;max;punt must be entered in the Pile Positions
window under the name End bearing (section 4.3.3).

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16 Calculation models
ModelIn D-P ILE G ROUP there are several different methods to calculate the behavior of a pile
group. Each pile however, except for the Poulos and Plasti-Poulos models, is modelled by
a series of springs representing the compression stiffness and the bending stiffness in both
directions perpendicular to the pile. The pile is connected to the soil by sets of springs representing the lateral and axial pile-soil interaction (P-Y and T-Z curves respectively).
In the present version of D-P ILE G ROUP the following calculation models are available:

 Cap model (section 16.1)










With this choice a calculation is performed with cap-interaction only. Pile-soil interaction
is elasto-plastic, but pile-soil-pile interaction is not included. The calculation is performed
using the Tilly program, pre- and post-processing is done by D-P ILE G ROUP.
Poulos model (section 16.2)
In this case a fully elastic calculation with pile-soil-pile interaction according to Poulos/Randolph
is performed. The calculation is performed by a special module of D-P ILE G ROUP, so the
Tilly program is not used for this model.
Plasti-Poulos model (section 16.3)
In this case plasticity effects are included in the classical Poulos model in order to obtain
more realistic pile-group interaction effects.
Cap soil interaction model (section 16.4)
In this case a calculation with elastic pile-soil-pile interaction according to Mindlin (constant Young’s modulus with depth) is performed. Pile-soil interaction may be elasto-plastic.
The calculation is performed using the Tilly program, pre- and post-processing is done by
D-P ILE G ROUP.
Cap layered soil interaction model (section 16.5)
In this case a calculation with elastic pile-soil-pile interaction for a layered soil system is
performed. Pile-soil interaction may be elasto-plastic. The calculation is performed using
both a built in Finite Element Method and the Tilly program, pre- and post-processing is
done by D-P ILE G ROUP.
Dynamic model (section 16.6)
This model can be used to analyze the effects of a collision of a ship against a pile/pile
group. The calculation is a dynamic analysis based on the Cap model. The calculation
is performed using the Tilly program, pre- and post-processing is done by D-P ILE G ROUP.
An interface for a special computer program for ship-dolphin interaction (BOTS) exists, so
input for this program can be generated.

Note: The parameters needed to perform a valid calculation depend on the choice of model.
Changing the model means a careful check of all other input data is needed. The program
automatically checks whether all necessary data are available, but it is recommended to check
whether the actual values still apply. For the Poulos and Plasti-Poulos models, the present
version of D-P ILE G ROUP supports uniform piles only.
16.1

Cap model
In this model the piles are connected to the pile cap, but there is no pile-soil-pile interaction.
Only the soil resistance for each pile is considered, and the pile-head to pile-head interaction
through the pile cap. The pile-soil interaction is elasto-plastic. The calculation is performed
using the Tilly program.

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16.2

Poulos model
In this case an elastic calculation with pile-soil-pile interaction according to Poulos is performed. For an introduction of the technical background of the method, see Poulos (1980).
The Poulos model is the simplest model using a fully elastic approach, in which the soil is considered to be a homogeneous elastic half space. Interaction factors between pile heads are
derived from relatively simple analytical formulas. Furthermore only interaction in the loading
direction is taken into account. Interaction normal to the loading direction is considered to be
zero.
In the Poulos model, soil properties are considered to be constant for the pile length, and
results are given for pile top positions only.
In D-P ILE G ROUP the equations derived by Randolph (1981) are used to determine the interaction coefficients for horizontal loading. This method is based on the concept of "critical depth",
and therefore correct for flexible piles only. Flexible in this case stands for "piles for which the
horizontal load-deformation behavior of the pile head does not depend on the length of the
pile".
In Poulos’s theory interaction between piles is based on equal pile dimensions, interaction between piles of different dimensions is not described. In D-P ILE G ROUP the interaction between
two piles is determined based on the pile properties of the “second” pile. The determination
of which is the first and which the second pile is based on the line number in the pile position
table.
So for “normal” pile numbering for the interaction between pile 1 and pile 2 the properties of
pile 2 are used. In case the first pile in the pile position table has nr 10, the second nr 9 etc,
for the interaction between pile 9 and 10 the properties of pile 9 are used.
This method does not use the Tilly program, but consists of a separate module that generates
and solves the applying equations according to Poulos’ theory.
The user will have to specify a Young’s modulus (E ) and a Poisson ratio (ν ) which he considers appropriate for the profile.

16.3
16.3.1

Plasti-Poulos model
Introduction
A commonly used method to determine pile group efficiency and the distribution of loading in
a pile group is the method described by Poulos (1980). In this method pile-soil-pile interaction
is purely elastic.
For small groups with a low loading level this method provides acceptable answers. However
when loading levels are high the calculated pile-soil-pile interaction is too high resulting in low
group efficiency.
In the Plasti-Poulos model plasticity effects are included in order to obtain more realistic pilegroup interaction effects.

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16.3.2

Plasticity and single pile behavior
Single pile load-deflection curves usually have a shape as the one shown in Figure 16.1 below.

Figure 16.1: Force-displacement relation of a laterally loaded single pile

This curve implies that:

 Initial (elastic) stiffness is high
 Stiffness reduces with higher loading levels due to soil plasticity.
16.3.3

Introduction of plasticity in the Poulos model
As can be seen from Figure 16.1 above, the displacement for a load of 2 kN including soil
plasticity is about twice the one based on the initial (elastic) stiffness. For a higher load level
the difference becomes bigger: for 4 kN the difference is about a factor 3.
From the load displacement curve of Figure 16.1 such a “plasticity-factor” can be determined
for each load level. Since this factor determines how much bigger the displacement of a pile
is compared to the elastic displacement it can be used to reduce the (elastic) stiffness in a
Poulos model calculation.
In the Poulos model a pile group interaction matrix is formed that contains both individual pile
stiffness components as well as components that describe the effect of (elastic) interaction.
For most commonly used pile spacings and moderate loading levels soil plasticity is localized
around each pile and therefore does not really influence the interaction between the piles.
The effect of plasticity can therefore be introduced rather easily by reducing the stiffness
component of each pile (according to the load level of the pile). The matrix components
describing the pile-soil-pile interaction remains in this case unaltered.
For very small pile spacings and high loading levels plastic soil regions of the individual piles
may overlap and therefore influence each other. The approach used here will not be valid for
that case.

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16.3.4

Implementation in D-Pile Group
In D-P ILE G ROUP the Plasti-Poulos model as described in the section above is almost completely automated. Since plasticity will be included in the calculation, soil data have to be
provided concerning this behavior.
In the Plasti-Poulos model therefore not only a soil interaction profile has to be specified (as
for the Poulos model) but also soil layers and a soil profile (like in case of the Cap model
calculation).
In the Soil Interaction Model window (section 4.2.3), the default option for determination of the
equivalent Young’s modulus is to calculate it automatically as the checkbox Calculate Young’s
modulus is marked. In that case an estimation of the Young’s modulus is made in such a way
that the elastic stiffness of a pile in the Poulos model is almost the same as for a Cap model
calculation. For the estimation the following formula is used:
1

(Ep /Gc ) 7
u=
ρc Gc

"

 −1
 −2 #
lc
lc
0.27 Fh
− 0.3 M
2
2

(16.1)

where:

u
Ep

is the lateral displacement of the pile top, in m;
is the equivalent Young’s modulus of the pile, in kN/m2 :

Ep =
r0
Gc

4 (EI)p
π r04

is the radius of the pile, in m;
2
is the shear modulus 
of the soil at depth
 of half the critical length, in kN/m :

Gc = (1 + 0.75 ν)
ν
G0
M

G0 +

m × lc
2

is the Poisson’s ratio;
is the shear modulus at soil surface, in kN/m2 ;
Factor describing the linear increase of g with depth y :

G = G0 + m × y
g

Shear modulus of the soil at depth y , in kN/m2 :

G=
y
lc

E
2 (1 + ν)

is the depth below soil surface, in m;
is the critical length of the pile, in m:


lc = 2 r0

Ep
Gc

2/7

ρc

is a factor denoting the degree of homogeneity of the soil:

Fh
M

is the lateral force acting at the pile top, in kN;
is the bending moment acting at the pile top, in kNm.

G∗0 + m × lc /4
ρc =
with G∗0 = G0 (1 + 0.75 ν)
Gc

Since there is no exact formula available the result is only “almost the same”. In most cases
the difference is less then 10 %. If this is not accurate enough then it is always possible to determine the correct value of the Young’s modulus by manually performing Poulos calculations.
For the Plasti-Poulos model, an additional option called Plasticity Factors is present in the Pile
menu of D-P ILE G ROUP (section 4.3.6). In the window displayed, the plasticity factors as de-

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scribed above are calculated automatically for a selected pile type. The plasticity factors that
have been determined are used in the final part of the calculation. As a start a “conventional”
Poulos calculation is performed. With the resulting pile loads, a plasticity factor is determined
for each individual pile, the stiffness matrix is adapted to include these factors and a new
calculation is performed. This results in a different load distribution and therefore in different
plasticity factors and therefore in a loop of calculations.
The program shows the progress of the calculation loop and the achieved accuracy. After
the specified maximum number of steps or the required accuracy has been reached, the
calculation stops. The results are presented in the same way as for the “conventional” Poulos
model.
16.3.5

Special considerations when using Plasti-Poulos
Since the Plasti-Poulos model is a new model most users will not be familiar with it. Furthermore the implementation in the present version of D-P ILE G ROUP is somewhat basic. Some
special considerations therefore apply when using this model:

 The determination of the Plasti-Poulos factors may not be possible due to incorrect
or incomplete input for the cap-model calculations that are automatically generated by
D-P ILE G ROUP. In that case only the message is shown that such is the case. If a
fast check of the input does not show the incorrect item, the procedure that has to be
followed is to manually perform a single pile analysis with the cap model. Any incorrect
or incomplete item will then be marked in the corresponding report so easy correction
is possible. With those same corrections the Plasti-Poulos calculation can than also be
made.

 It should be checked if the load-displacement curve used for the determination of the
Plasti-Poulos factors has a linear initial part. That means in this case, since (0, 0) is
also represented, that at least 3 values should have a factor of 1.000. If that is not the
case, smaller load steps should be used for the cap-calculations.

 To determine the plasticity factors, an ultimate load level and the load steps have to be
specified. The calculated plasticity factors are then used in the Plasti-Poulos calculation for each applicable load level. If the actual pile load is higher than the previously
specified ultimate load level, the value of the highest calculated plasticity factor is used.
In effect this means that the plasticity factor is kept at a constant value for load levels
higher than the specified ultimate load level. Since this will result in a too stiff behavior
for such load levels it is recommended to always check if the specified ultimate load
level is not exceeded.

 If the “Calculate Young’s modulus” option is used, a best estimate is made of the equivalent Young’s modulus using the formula mentioned above. Most of the time this is
a good estimate, however sometimes the value is not correct. It is therefore recommended to always check the calculated results. A superficial check is to compare the
calculated displacements of a certain pile with the displacements given in the PlastiPoulos factors table. Since the Plasti-Poulos model includes pile-soil-pile interaction
the displacements in the Plasti-Poulos factors table should be smaller. A more thorough approach is to use the estimated Young’s modulus value in a separate Poulos
calculation and check the calculated displacements with those of the initial (linear) part
of the displacements given in the Plasti-Poulos factors table. These should be equal. If
that is not the case a different value has to be tried until the differences are acceptable.

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16.4

Cap soil interaction model
The Cap soil interaction model accounts for pile-soil plasticity by using P-Y and T-Z curves
and is based on the Mindlin analytical solution of the stresses and displacements in a homogeneous, elastic half space, caused by a point loading, see Mindlin (1953). Influence of point
loads is integrated to determine pile-load influence and to form an elastic interaction matrix.
Although this method is the basis of Poulos model, and should therefore yield comparable
results, additional features such as plasticity, interaction between piles of different sizes, and
raking piles can be used. Interaction normal to the loading direction is also included.The
method can therefore also be used for interaction between vertical and raked piles of different dimensions and shape. The interaction effect is restricted to one soil interaction profile
consisting of only one soil layer. This method generates a Tilly model with numerous cross
connections.
Original Mindlin’s Formulas for Large Distances
Mindlin (1953) has derived analytical solutions for both a vertical and a horizontal point load
acting beneath the surface of a semi-infinite mass.
For a vertical point load P , the Mindlin’s formulas are:


σx =


−P

8π (1 − ν) 

(1−2ν)(y−c)
+ (1−2ν)[3(y−c)−4ν(y+c)]
R13
R23
3x2 (y−c)
3(3−4ν)x2 (y−c)−6(y+c)[(1−2ν)y−2νc]
− R5 −
R25
1


30cx2 y(y+c)
4(1−ν)(1−2ν)
x2
x2
−
1
−
−
−
R2 (R2 +y+c)
R2 (R2 +y+c)
R27
R22





(16.2)



− (1−2ν)(y−c)
+
R3

 3(y−c)13
−P
 − 5 −
σy =
R1
8π (1 − ν)  30cy(y+c)
3
− R7

(1−2ν)(y−c)
R23
3(3−4ν)y(y+c)2 −3c(y+c)(5y−c)
R25






(16.3)

2


σz =


−P

8π (1 − ν) 

(1−2ν)(y−c)
+ (1−2ν)[3(y−c)−4ν(y+c)]
R13
R23
3z 2 (y−c)
3(3−4ν)z 2 (y−c)−6(y+c)[(1−2ν)y−2νc]
− R5 −
R25
1

2
30cz 2 y(y+c)
4(1−ν)(1−2ν)
−
− R2 (R2 +y+c) 1 − R2 (R2z+y+c)
R27



−



 
2

z
R22

(16.4)

P x
ux =
16πG (1 − ν)



(y − c) (3 − 4ν) (y − c) 4 (1 − ν) (1 − 2ν) 6cy (y + c)
+
−
+
R13
R23
R2 (R2 + y + c)
R25



(16.5)



8(1−ν)2 −(3−4ν)
(y−c)2
3−4ν
+
+
3
P
R2
R1
 R1

uy =
2
2
(3−4ν)(y+c)
−2cy
6cy(y+c)
16πG (1 − ν)
+
+
3
5
R
R
2

P z
uz =
16πG (1 − ν)



(16.6)

2

(y − c) (3 − 4ν) (y − c) 4 (1 − ν) (1 − 2ν) 6cy (y + c)
+
−
+
R13
R23
R2 (R2 + y + c)
R25
(16.7)

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Calculation models

For a horizontal point load q , the Mindlin’s formulas are:


σx =

−Q x 

8π (1 − ν) 



σy =

−Q x 
8π (1 − ν)


σz =

−Q x 

8π (1 − ν) 

2
(1−2ν)(5−4ν)
− 3x R(y−c)
3
R
1
2

 15 2
2
4(1−ν)(1−2ν)
x (3R2 +y+c)
− 3(3−4ν)x
−
3
−
R25
R22 (R2 +y+c)
R2 (R2 +y+c)2

5x2 y
6c
+ R5 3c − (3 − 2ν) (y + c) + R2
2
2

− (1−2ν)
+
R3

(1−2ν)
(1−2ν)
3(y−c)2
−
−
3
3
R1 
R2
R15
− R6c5 c + (1 − 2ν) (y +
2

2
3(3−4ν)z 2
(1−2ν)
+ (1−2ν)(3−4ν)
− 3z
3
5 −
R13
R
R
1
 R25
2
2
2 +y+c)
− 4(1−ν)(1−2ν)
1 − zR2(3R
R2 (R2 +y+c)
2 (R2 +y+c)


2
+ R6c5 c − (1 − 2ν) (y + c) + 5yz
R22
2


ux =

Q

16πG (1 − ν)

Qx
uy =
16πG (1 − ν)

2
− 3(3−4ν)(y−c)
5
R2

5y(y+c)2
c) + R2
2



2
2
(3−4ν)
+ 2cy
+ R12 + Rx 3 + (3−4ν)x
3
3
R1
R
1
2

R2
2
4(1−ν)(1−2ν)
+ (R2 +y+c) 1 − R2 (Rx2 +y+c)






(16.8)


(16.9)










1−

(16.10)

3x2
R22

 
 (16.11)

y − c (3 − 4ν) (y − c) 6cy (y + c) 4 (1 − ν) (1 − 2ν)
+
−
+
R13
R23
R25
R2 (R2 + y + c)
(16.12)

Qxz
uz =
16πG (1 − ν)
with: q

R1 =

R2 =

q



1
(3 − 4ν) 6cy 4 (1 − ν) (1 − 2ν)
+
− 5 −
3
R1
R23
R2
R2 (R2 + y + c)2


(16.13)

x2 + (y − c)2 + z 2
x2 + (y + c)2 + z 2

where:

x, y , z
sx , sy , sz
ux , uy , uz
P
q
E
n
g
c>0

Deltares

are the co-ordinates of the calculated point, in m;
are the stresses at the calculated point, in kN/m2 ;
are the displacements at the calculated point, in m;
is the vertical point load, in kN;
is the horizontal point load, in kN;
is the Young’s modulus of the soil, in kN/m2 ;
is the Poisson ratio of the soil;
is the shear modulus of the soil, in kN/m2 ;
is the depth beneath the surface where the load is acting, in m.

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Mindlin Interaction at Short Distances
The displacements for the point of application of both the vertical and the horizontal force
according to original Mindlin’s formulas given above however, are of infinite value. Since in
the D-P ILE G ROUP program the formulas are to be used to determine the interaction between
piles the displacements should not be known at the point of loading, but at a certain distance
of this point (that is: at the position of the other pile(s)). These displacements are used to
determine the interaction matrix.
In case of relatively large distances Mindlin’s formula’s can be used without adaptation. For
a relatively short distance between the point of loading and the point where the displacement needs to be determined the original Mindlin’s formulas will result in unrealistically high
displacement values. To achieve a realistic displacement several strategies can be adopted:

 The original Mindlin’s formulas can be adapted to those that describe a pressure applied

 

to a rigid area instead of a point load. A derivation for the plane of loading of a horizontal
load is given by Douglas and Davis (1964). Basic assumptions are:
the pile section is inflexible (rigid)
the plate has negligible thickness

 Both assumptions are not correct when a pile is concerned. However if a pile is divided
into multiple small sections the error of considering each segment to be rigid is relatively
small if sufficiently small segments are used. Furthermore, the shape of the pile will only
be of influence in the region near the pile.

 Instead of using only 1 point load at the centre of the pile segment multiple loads at
the pile segment boundary can be used. Although the displacement at each point of
loading is infinite, the resulting displacement at the pile segment centre will be of a finite
value.
16.5

Cap layered soil interaction model
The Cap layered soil interaction model (which is an extension of the Cap soil interaction
model) is the most sophisticated model of pile interaction included in the program. The model
allows the use of a multi-layered soil profile. To determine the interaction between the piles an
axi-symmetric linear elastic finite element program for non-symmetric loading (FEM) is used.
The model is based on Fourier series.
A more elaborate description of the theoretical background of the model is presented by
Zienkiewicz and Taylor (1991). This model generates a Tilly input file similar to the one created by the Cap soil interaction model. The difference lies in the interaction matrices. With
the Cap layered soil interaction model a layered elastic half space is used resulting in different
flexibility factors.
For the width and depth of the finite element mesh the following criteria are used in D-P ILE G ROUP:
Depth:

 at least two times the maximum driving-depth of all piles;
 at least the maximum driving-depth beneath the bottom layer of the soil-interaction profile.

218 of 226

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Calculation models

Width:

 at least two times the maximum distance of all piles;
 width must always be larger than the depth (special criteria for single pile).
If possible the average element height is 1 meter. The element width of the first column is the
radius of the pile and increases quadratically with each column.
16.6

Dynamic model
A dynamic analysis of a collision of a ship against the pile cap (Figure 16.2) is described with
this model.
The Dynamic model is based on the BOTS model which is a program specially made by
Delft Hydraulics for Rijkwaterstaat to calculate the response of a ship that has a collision (in
Dutch “botsing”) with a mooring dolphin. The Dynamic model implemented in D-P ILE G ROUP
has been adapted compared to the model used in the BOTS program in order to model the
collision of a ship with a pile. See Bijnagte (1990) for a detail description of the Dynamic
model implemented in D-P ILE G ROUP.

Figure 16.2: Collision of a ship against a pile

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17

Benchmarks
With the recently growing attention for quality control and quality assurance, the need arose
to develop a more formal and extensive procedure to verify the correct working of a program.
The procedure described in the above paragraph is still very useful, but has been extended
to provide a better verification of the program at hand. The new procedure requires that
all benchmark calculations in this verification report are made, and the results verified. The
benchmarks are subdivided into four separate groups as follows:

 Group 1 - Benchmarks from literature (exact solution)
Simple benchmarks for which an exact analytical result is available from literature.

 Group 2 - Benchmarks from literature (approximate solution)
More complex benchmarks described in literature for which an approximate solution is
known.

 Group 3 - Benchmarks from spread sheets
Benchmarks which test program features specific to D-P ILE G ROUP.

 Group 4 – Benchmarks generated by D-P ILE G ROUP
Benchmarks for which the reference results are generated using D-P ILE G ROUP.

 Group 5 - Benchmarks compared with other programs
Benchmarks for which the results of D-P ILE G ROUP are compared with the results of
other programs.

The number of benchmarks in group 1 will probably remain the same in the future. The reason
for this is that they are very simple, using only the most basic features of the program.
The number of benchmarks in group 2 may grow in the future. The benchmarks in this chapter
are well documented in literature. There are no exact solutions for these problems available;
however in the literature estimated results are available. When verifying the program, the
results should be close to the results found in the literature.
Groups 3 and 4 of benchmarks will grow as new versions of the program are released. These
benchmarks are designed in such a way that (new) features specific to the program can be
verified. The benchmarks are kept as simple as possible so that, per benchmark, only one
specific feature is verified.
As much as software developers would wish they could, it is impossible to prove the correctness of any non-trivial program. Re-calculating all the benchmarks in this report, and making
sure the results are as they should be, will prove to some degree that the program works as it
should.
Nevertheless there will always be combinations of input values that will cause the program to
crash or produce wrong results. Hopefully by using the verification procedure the number of
times this occurs will be limited.
The benchmarks are all described in details in the Verification Report available in the installation directory of the program. The benchmarks are all described to such detail that reproduction is possible at any time. The results are presented in text format with each benchmark
description.

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Bibliography
API, 1984. “Recommended practice for planning, designing, and constructing fixed offshore
platforms.” Washington D.C.
Bijnagte, J. L., 1990. Ducbots dynamisch modelleren van ducdalven.
294782/27, GeoDelft.

Tech. Rep. CO-

Coyle, H. M. and L. C. Reese, 1966. “Load transfer for axially loaded piles in clay.” Journal of
the Soil Mechanics and Foundation, Division ASCE 92 pages 1-26.
DNV, 1977. Rules for the design construction and inspection of offshore structures. Det
Norske Veritas (Norway).
Douglas, D. J. and E. H. Davis, 1964. “The movement of buried footings due to moment and
horizontal load and the movement of anchor plates.” Geotechnique 2 14: 115-132.
Focht Jr., J. A. and K. J. Koch, 1973. “Rational analysis of the lateral performance of offshore
pile groups.” In Proc. of the V offshore technology Conference, Houston, Texas, pages
701-708.
Matlock, H., 1970. “2nd Offsh. Techn. Conf., Texas.” In Correlations for design of laterally
loaded piles in soft clay, OTC 1204.
Mindlin, R. D., 1936. “Force at a point in the interior of a semi-infinite solid.” Applied Physics
7 (5): 195-202.
Mindlin, R. D., 1953. “1st Mid-west. Conf. Solid Mech., University of Illinois, Illinois.” In Force
at a point in the interior of a semi-infinite solid, pages 56-59.
NEN, 1991. NEN 6743:1991. Geotechniek - Berekeningsmethode voor funderingen op palen
- Drukpalen (Geotechnics - Calculation method for bearing capacity of pile foundation Compression piles), in Dutch.
NEN, 2006. NEN 6740:2006. Geotechniek - TGB 1990 - Basiseisen en belastingen (Geotechnics - TGB 1990 - Basic requirements and loads), in Dutch.
Poulos, E. H., H. G. Davis, 1980. Pile foundation analysis and design. Wiley, New York.
Poulos, H. G. and E. H. Davis, 1974. Elastic Solutions for Soil and Rock Mechanics. New
York.
Randolph, M. F., 1981. “The response of flexible piles to lateral loading.” Geotechnique 2 31:
247-259.
Randolph, M. F., 1996. PIGLET, Analysis and Design of pile groups. University of Western
Australia.
Reese, L. C., W. R. Cox and F. D. Koop, 1979. “Offshore Technology Conference Dallas.” In
Analysis of Laterally Loaded Piles in Sand, Paper number OTC 2080.
Sullivan, W. R., L. C. Reese and C. W. Fenske, 1980. “Unified method for analysis of laterally loaded piles in clay, Numerical Methods in Offshore Piling.” The Institution of Civil
Engineers, London pages 135-146.
Xu, H. G., K. J. Poulos, 2000. “General elastic analysis of pile groups.” Int. J. Numer. Anal.
Meth. Geomechs. 24: 1109-1138.
Zienkiewicz, O. C. and R. L. Taylor, 1991. The finite element method : solid and fluid mechanics, dynamics and non-linearity, vol. 2. McGraw-Hill, London, UK, 4 ed.

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Photo’s by: Elsam A/S and BeeldbankVenW.nl, Rijkswaterstaat.

PO Box 177
2600 MH Delft
Rotterdamseweg 185
2629 HD Delft
The Netherlands

+31 (0)88 335 81 88
sales@deltaressystems.nl
www.deltaressystems.nl



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