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Design of pipeline installation D-Geo Pipeline Verification Report D-G EO P IPELINE Design of pipeline installation Verification Report Version: 15.1 Revision: 00 13 April 2015 D-G EO P IPELINE, Verification Report 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 http://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 © 2015 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. Contents Contents Introduction 1 1 Group 1: Benchmarks from literature (exact solution) 1.1 Soil type and displacement at maximal friction (Micro-tunneling and Trenching) 1.1.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . 3 3 3 4 5 2 Group 2: Benchmarks from literature (approximate solution) 9 3 Group 3: Benchmarks from spreadsheets 11 3.1 HDD with 2D geometry – Steel pipe in two compressible undrained layers . . . 11 3.1.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 HDD with 2D geometry – Vertical bearing capacity in homogeneous compressible undrained layer with ϕ = 0 . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . 22 3.3 HDD with 2D geometry – Polyethylene (PE 80) pipe in two compressible undrained layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.3.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.3.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . 24 3.4 HDD with 2D geometry – Steel pipe in two incompressible drained layers . . . 26 3.4.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . 28 3.5 HDD with 2D geometry – Steel pipe in a sequence of a compressible undrained layer and a compressible drained layer . . . . . . . . . . . . . . . . . . . . 29 3.5.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.5.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.5.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . 30 3.6 HDD with 2D geometry – Steel pipe in a sequence of an incompressible undrained layer and an incompressible drained layer . . . . . . . . . . . . . 30 3.6.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.6.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.6.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . 31 3.7 HDD with 3D geometry – Steel pipe in 4 layers – Compressible border above drainage border . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.7.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.7.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.7.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . 36 3.8 Special strength analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.8.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.8.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.8.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . 38 3.9 HDD with 3D geometry – Bundled pipeline (3 steel pipes and 2 PE pipes) . . . 40 3.9.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.9.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.9.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . 45 3.10 HDD with 3D geometry – Bundled pipeline (2 PE pipes) . . . . . . . . . . . . 53 Deltares iii D-G EO P IPELINE, Verification Report 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 iv 3.10.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . HDD with 3D geometry – Bundled pipeline (3 steel pipes) . . . . . . . . . . 3.11.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . Micro tunneling with 3D geometry – Steel pipe . . . . . . . . . . . . . . . 3.12.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . Micro tunneling with 3D geometry – Synthetic pipe . . . . . . . . . . . . . 3.13.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.13.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.13.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . Micro tunneling with 3D geometry – Concrete pipe . . . . . . . . . . . . . 3.14.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.14.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.14.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . Trenching (3 sections) – 3D geometry in four layers – Compressible border above drainage border . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.15.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.15.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.15.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . Trenching (3 sections) – 3D geometry in four layers – Drainage border above compressible border . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.16.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.16.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.16.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . Bundled pipeline with Special Stress Analysis . . . . . . . . . . . . . . . . 3.17.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.17.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.17.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . HDD with 3D geometry – Pipeline configuration not ending at surface and with an angle between radii . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.18.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.18.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.18.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . HDD with 2D geometry – Stress Analysis per Vertical – Steel pipe . . . . . 3.19.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.19.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.19.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . HDD with 3D geometry – Stress Analysis per Vertical – PE pipe . . . . . . . 3.20.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.20.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.20.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . HDD – Determination of the minimum allowable radius . . . . . . . . . . . 3.21.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.21.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.21.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . HDD – PE pipe not filled with water on rollers . . . . . . . . . . . . . . . . 3.22.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.22.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . . . . 3.22.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 54 56 56 56 56 58 59 59 59 60 64 64 64 64 65 65 65 65 . . . . 68 68 69 70 . . . . . . . . 74 74 75 75 75 76 76 78 . . . . . . . . . . . . . . . . . . . . 79 79 79 81 82 82 82 83 88 88 88 89 94 94 97 99 101 101 101 102 Deltares Contents 3.23 HDD – PE pipe always filled (100%) – Implosion . . . . . . . . . . . 3.23.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . 3.23.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . 3.23.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . 3.24 HDD with 2D geometry – Effect of traffic loads . . . . . . . . . . . . 3.24.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . 3.24.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . 3.24.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . 3.25 HDD with safety factors from the European Standard CEN – Steel pipe 3.25.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . 3.25.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . 3.25.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . 3.26 HDD with safety factors from the European Standard CEN – PE pipe . 3.26.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . 3.26.2 Analytical results . . . . . . . . . . . . . . . . . . . . . . . 3.26.3 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 102 103 103 104 104 104 107 109 109 110 111 113 113 113 115 4 Group 4: Benchmarks generated by D-G EO P IPELINE 117 4.1 HDD with 3D geometry – Check of the pulling direction . . . . . . . . . . . . 117 4.1.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.1.2 D-G EO P IPELINE results . . . . . . . . . . . . . . . . . . . . . . . 117 5 Group 5: Benchmarks compared with other programs 5.1 Settlements according to Koppejan model . . . . . 5.1.1 Description . . . . . . . . . . . . . . . . 5.1.2 D-S ETTLEMENT results . . . . . . . . . . 5.1.3 D-G EO P IPELINE results . . . . . . . . . 5.2 Settlements according to Isotache model . . . . . 5.2.1 Description . . . . . . . . . . . . . . . . 5.2.2 D-S ETTLEMENT results . . . . . . . . . . 5.2.3 D-G EO P IPELINE results . . . . . . . . . Bibliography Deltares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 119 119 119 120 120 120 120 121 123 v D-G EO P IPELINE, Verification Report vi Deltares List of Figures List of Figures 1.1 Geometry of benchmark 1-1a (Construction in Trench) . . . . . . . . . . . . 3.1 2D Geometry of benchmark 3-1 (steel pipeline in two compressible undrained layers) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Locations of the characteristic points T1 to T6 . . . . . . . . . . . . . . . . 3D view of the pipeline configuration (benchmark 3-7) . . . . . . . . . . . . Lateral view of the 3 trench sections (benchmark 3-15) . . . . . . . . . . . Locations of the characteristic points T1 to T6 for case A (positive angle between radii) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Locations of the characteristic points T1 to T6 for case B (negative angle between radii) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Locations of the characteristic points (T1 to T6) and the 3 verticals . . . . . Geometry of benchmark 3-21a . . . . . . . . . . . . . . . . . . . . . . . Geometry of benchmark 3-21b . . . . . . . . . . . . . . . . . . . . . . . Warning message displayed for benchmark 3-21a . . . . . . . . . . . . . . Warning message displayed for benchmark 3-21b . . . . . . . . . . . . . . Geometry of benchmark 3-12 with 2 traffic loads . . . . . . . . . . . . . . Traffic load as a function of the depth, for different pipe diameters, according to NEN 3650-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 5.1 Deltares Geometry of benchmark 5-1 . . . . 4 12 14 33 69 . 80 . . . . . . . 81 82 95 97 99 100 104 . 105 . . . . . . . . . . . . . . . . . . . . . . . . . 119 vii D-G EO P IPELINE, Verification Report viii Deltares List of Tables List of Tables 1.1 1.2 1.3 1.4 1.5 1.6 Material properties of the different layers (benchmark 1-1) . . . . . . . . . . Displacement at maximal friction and classification of the soil type . . . . . Results of benchmark 1-1a, Global soil type for Construction in Trench . . . Results of benchmark 1-1a, Maximal displacement for Construction in Trench Results of benchmark 1-1b, Global soil type for Micro Tunneling . . . . . . . Results of benchmark 1-1b, Maximal displacement for Micro Tunneling . . . 3.1 3.2 3.3 3.4 3.6 3.7 3.8 3.9 3.10 3.11 Soil material properties (bm3-1) . . . . . . . . . . . . . . . . . . . . . . . . Pipe material data (bm3-1) . . . . . . . . . . . . . . . . . . . . . . . . . . Analytical results for the calculation of dp/dz for the three stages . . . . . . . Analytical results for the calculation of the maximum drilling fluid pressures . . Results of benchmark 3-01, Pulling forces in the pipeline . . . . . . . . . . . Set for calculation of the maximum stresses for load combination 1A . . . . . Set for calculation of the maximum stresses for load combination 1B . . . . . Set for calculation of the maximum stresses for load combination 3 . . . . . . Set for calculation of the maximum stresses for load combination 4 . . . . . . Results of benchmark 3-01, Maximum allowable drilling fluid pressure (plastic zone related to deformation bore hole) . . . . . . . . . . . . . . . . . . . . Results of benchmark 3-01, Maximum allowable drilling fluid pressure (plastic zone related to soil cover) . . . . . . . . . . . . . . . . . . . . . . . . . . . Results of benchmark 3-01, Minimum required drilling fluid pressure (from left to right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results of benchmark 3-01, Minimum required drilling fluid pressure (from right to left) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results of benchmark 3-01, Equilibrium between drilling fluid pressure and pore pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results of benchmark 3-01, Vertical soil stresses . . . . . . . . . . . . . . . Results of benchmark 3-01, Neutral horizontal soil stress and bearing capacities Results of benchmark 3-01, Vertical and horizontal moduli of subgrade reaction Results of benchmark 3-01, Maximal axial friction and displacements . . . . . Results of benchmark 3-01, Buoyancy control . . . . . . . . . . . . . . . . . Results of benchmark 3-01, Pulling forces in the pipeline . . . . . . . . . . . Results of benchmark 3-01, Strength calculation for Combination 1A . . . . . Results of benchmark 3-01, Strength calculation for Combination 1B . . . . . Results of benchmark 3-01, Strength calculation for Combination 2 . . . . . . Results of benchmark 3-01, Strength calculation for Combination 3 . . . . . . Results of benchmark 3-01, Strength calculation for Combination 4 . . . . . . Results of benchmark 3-01, Maximum allowable stresses . . . . . . . . . . . Results of benchmark 3-01, Deflection of the pipeline . . . . . . . . . . . . . Results of benchmark 3-01, Implosion . . . . . . . . . . . . . . . . . . . . Analytical results for the calculation of the vertical bearing capacity . . . . . . Results of benchmark 3-02, Ultimate vertical bearing capacity . . . . . . . . . Pipe material data (benchmark 3-3) . . . . . . . . . . . . . . . . . . . . . . Analytical results for the calculation of the five components of the pulling force for the six characteristic points . . . . . . . . . . . . . . . . . . . . . . . . Results of benchmark 3-03, Buoyancy control . . . . . . . . . . . . . . . . . Results of benchmark 3-03, Pulling forces in the pipeline . . . . . . . . . . . Results of benchmark 3-03, Strength calculation for Combination 1A . . . . . Results of benchmark 3-03, Strength calculation for Combination 1B . . . . . Results of benchmark 3-03, Strength calculation for Combination 2 . . . . . . Results of benchmark 3-03, Strength calculation for Combination 3 . . . . . . Results of benchmark 3-03, Strength calculation for Combination 4 . . . . . . 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29 3.30 3.31 3.32 3.34 3.35 3.36 3.37 3.38 3.39 3.40 3.41 Deltares . . . . . . 3 4 5 6 7 8 11 12 13 13 15 15 16 16 16 17 17 17 18 18 18 19 19 19 19 20 20 20 20 20 21 21 21 21 22 22 23 24 24 25 25 25 25 25 26 ix D-G EO P IPELINE, Verification Report 3.42 3.43 3.44 3.45 3.46 3.47 3.48 3.49 3.50 3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.59 3.60 3.61 3.62 3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71 3.72 3.73 3.74 3.75 3.76 3.77 3.78 3.79 3.80 3.81 3.82 3.83 x Results of benchmark 3-03, Maximum allowable stresses . . . . . . . . . . . Results of benchmark 3-03, Deflection of the pipeline . . . . . . . . . . . . . Results of benchmark 3-03, Implosion . . . . . . . . . . . . . . . . . . . . Analytical results – General data’s . . . . . . . . . . . . . . . . . . . . . . Analytical results for the calculation of the neutral reduced vertical stress . . . Analytical results for the calculation of the maximum drilling fluid pressures . . Results of benchmark 3-04, Vertical soil stresses . . . . . . . . . . . . . . . Results of benchmark 3-04, Maximum allowable drilling fluid pressure (plastic zone related to deformation bore hole) . . . . . . . . . . . . . . . . . . . . Results of benchmark 3-04, Maximum allowable drilling fluid pressure (plastic zone related to soil cover) . . . . . . . . . . . . . . . . . . . . . . . . . . . Analytical results for the calculation of the maximum drilling fluid pressures . . Results of benchmark 3-05, Maximum allowable drilling fluid pressure (plastic zone related to deformation bore hole) . . . . . . . . . . . . . . . . . . . . Results of benchmark 3-05, Maximum allowable drilling fluid pressure (plastic zone related to soil cover) . . . . . . . . . . . . . . . . . . . . . . . . . . . Results of benchmark 3-06, Vertical soil stresses . . . . . . . . . . . . . . . Soil material properties (benchmark 3-07) . . . . . . . . . . . . . . . . . . . Pipe material data (benchmark 3-07) . . . . . . . . . . . . . . . . . . . . . Position of the characteristic points (benchmark 3-07a) . . . . . . . . . . . . Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points for case a . . . . . . . . . . . . . . . . . . . Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points for case b . . . . . . . . . . . . . . . . . . . Results of benchmark 3-07a, Vertical soil stresses . . . . . . . . . . . . . . Results of benchmark 3-07a, Neutral horizontal soil stress and bearing capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results of benchmark 3-07a, Vertical and horizontal moduli of subgrade reaction Results of benchmark 3-07a, Maximal axial friction and displacements . . . . Results of benchmark 3-07a, Pulling forces in the pipeline . . . . . . . . . . . Results of benchmark 3-07b, Pulling forces in the pipeline . . . . . . . . . . . Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-08) . . . . . . . . . . . . . . . . . . . Results of benchmark 3-08, Buoyancy Control . . . . . . . . . . . . . . . . Results of benchmark 3-08, Pulling forces in the pipeline . . . . . . . . . . . Results of benchmark 3-08, Strength calculation for Combination 1A . . . . . Results of benchmark 3-08, Strength calculation for Combination 1B . . . . . Results of benchmark 3-08, Strength calculation for Combination 2 . . . . . . Results of benchmark 3-08, Strength calculation for Combination 3 . . . . . . Results of benchmark 3-08, Strength calculation for Combination 4 . . . . . . Results of benchmark 3-08, Maximum allowable stresses . . . . . . . . . . . Results of benchmark 3-08, Deflection of the pipeline . . . . . . . . . . . . . Results of benchmark 3-08, Implosion . . . . . . . . . . . . . . . . . . . . Pipe material data (benchmark 3-09) . . . . . . . . . . . . . . . . . . . . . Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-09) . . . . . . . . . . . . . . . . . . . Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-09) . . . . . . . . . . . . . . . . . . . Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-09) . . . . . . . . . . . . . . . . . . . Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-09) . . . . . . . . . . . . . . . . . . . Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-09) . . . . . . . . . . . . . . . . . . . 26 26 26 27 27 28 28 28 29 29 30 30 31 32 32 33 35 35 36 36 36 37 37 37 38 38 38 39 39 39 39 40 40 40 40 41 42 43 43 43 44 Deltares List of Tables 3.84 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-09) . . . . . . . . . . . . . . . . . . . 3.85 Maximal pulling forces without partial factors (bm3-09) . . . . . . . . . . . . 3.86 Results of benchmark 3-09, Buoyancy control . . . . . . . . . . . . . . . . . 3.87 Results of benchmark 3-09, Pulling forces in the pipeline . . . . . . . . . . . 3.88 Results of benchmark 3-09 for pipe nr. 1, Strength calculation for Combination 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.89 Results of benchmark 3-09 for pipe nr. 1, Strength calculation for Combination 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.90 Results of benchmark 3-09 for pipe nr. 1, Strength calculation for Combination 2 3.91 Results of benchmark 3-09 for pipe nr. 1, Strength calculation for Combination 3 3.92 Results of benchmark 3-09 for pipe nr. 1, Strength calculation for Combination 4 3.93 Results of benchmark 3-09 for pipe nr. 1, Maximum allowable stresses . . . . 3.94 Results of benchmark 3-09 for pipe nr. 1, Deflection of the pipeline . . . . . . 3.95 Results of benchmark 3-09 for pipe nr. 1, Implosion . . . . . . . . . . . . . . 3.96 Results of benchmark 3-09 for pipe nr. 2, Strength calculation for Combination 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.97 Results of benchmark 3-09 for pipe nr. 2, Strength calculation for Combination 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.98 Results of benchmark 3-09 for pipe nr. 2, Strength calculation for Combination 2 3.99 Results of benchmark 3-09 for pipe nr. 2, Strength calculation for Combination 3 3.100 Results of benchmark 3-09 for pipe nr. 2, Strength calculation for Combination 4 3.101 Results of benchmark 3-09 for pipe nr. 2, Maximum allowable stresses . . . . 3.102 Results of benchmark 3-09 for pipe nr. 2, Deflection of the pipeline . . . . . . 3.103 Results of benchmark 3-09 for pipe nr. 2, Implosion . . . . . . . . . . . . . . 3.104 Results of benchmark 3-09 for pipe nr. 3, Strength calculation for Combination 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.105 Results of benchmark 3-09 for pipe nr. 3, Strength calculation for Combination 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.106 Results of benchmark 3-09 for pipe nr. 3, Strength calculation for Combination 2 3.107 Results of benchmark 3-09 for pipe nr. 3, Strength calculation for Combination 3 3.108 Results of benchmark 3-09 for pipe nr. 3, Strength calculation for Combination 4 3.109 Results of benchmark 3-09 for pipe nr. 3, Maximum allowable stresses . . . . 3.110 Results of benchmark 3-09 for pipe nr. 3, Deflection of the pipeline . . . . . . 3.111 Results of benchmark 3-09 for pipe nr. 3, Implosion . . . . . . . . . . . . . . 3.112 Results of benchmark 3-09 for pipe nr. 4, Strength calculation for Combination 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.113 Results of benchmark 3-09 for pipe nr. 4, Strength calculation for Combination 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.114 Results of benchmark 3-09 for pipe nr. 4, Strength calculation for Combination 2 3.115 Results of benchmark 3-09 for pipe nr. 4, Strength calculation for Combination 3 3.116 Results of benchmark 3-09 for pipe nr. 4, Strength calculation for Combination 4 3.117 Results of benchmark 3-09 for pipe nr. 4, Maximum allowable stresses . . . . 3.118 Results of benchmark 3-09 for pipe nr. 4, Deflection of the pipeline . . . . . . 3.119 Results of benchmark 3-09 for pipe nr. 4, Implosion . . . . . . . . . . . . . . 3.120 Results of benchmark 3-09 for pipe nr. 5, Strength calculation for Combination 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.121 Results of benchmark 3-09 for pipe nr. 5, Strength calculation for Combination 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.122 Results of benchmark 3-09 for pipe nr. 5, Strength calculation for Combination 2 3.123 Results of benchmark 3-09 for pipe nr. 5, Strength calculation for Combination 3 3.124 Results of benchmark 3-09 for pipe nr. 5, Strength calculation for Combination 4 3.125 Results of benchmark 3-09 for pipe nr. 5, Maximum allowable stresses . . . . 3.126 Results of benchmark 3-09 for pipe nr. 5, Deflection of the pipeline . . . . . . Deltares 44 44 45 45 45 45 46 46 46 46 46 47 47 47 47 47 48 48 48 48 48 49 49 49 49 50 50 50 50 50 51 51 51 51 51 52 52 52 52 52 53 53 53 xi D-G EO P IPELINE, Verification Report 3.127 Results of benchmark 3-09 for pipe nr. 5, Implosion . . . . . . . . . . . . . . 3.128 Pipe material data (benchmark 3-10) . . . . . . . . . . . . . . . . . . . . . 3.129 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-10) for the equivalent pipe . . . . . . . . 3.130 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-10) for pipe nr. 1 . . . . . . . . . . . . . 3.131 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-10) for pipe nr. 2 . . . . . . . . . . . . . 3.132 Results of benchmark 3-10, Buoyancy control . . . . . . . . . . . . . . . . . 3.133 Results of benchmark 3-10, Pulling forces in the pipeline . . . . . . . . . . . 3.134 Pipe material data (benchmark 3-11) . . . . . . . . . . . . . . . . . . . . . 3.135 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-11) for the equivalent pipe . . . . . . . . 3.136 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-11) for pipe nr. 1 . . . . . . . . . . . . . 3.137 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-11) for pipe nr. 2 . . . . . . . . . . . . . 3.138 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-11) for pipe nr. 3 . . . . . . . . . . . . . 3.139 Results of benchmark 3-11, Buoyancy control . . . . . . . . . . . . . . . . . 3.140 Results of benchmark 3-11, Pulling forces in the pipeline . . . . . . . . . . . 3.141 Analytical results for the calculation of the face support pressures . . . . . . . 3.142 Analytical results for the calculation of the uplift safety factor . . . . . . . . . 3.143 Results of benchmark 3-12a, Vertical soil stresses . . . . . . . . . . . . . . 3.144 Results of benchmark 3-12a, Neutral horizontal soil stress and bearing capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.145 Results of benchmark 3-12a, Vertical and horizontal moduli of subgrade reaction 3.146 Results of benchmark 3-12a, Maximal axial friction and displacements . . . . 3.147 Results of benchmark 3-12a, Face support pressures . . . . . . . . . . . . 3.148 Results of benchmark 3-12a, Thrust forces . . . . . . . . . . . . . . . . . . 3.149 Results of benchmark 3-12b, Thrust forces . . . . . . . . . . . . . . . . . . 3.150 Results of benchmark 3-12a, Uplift safety factor . . . . . . . . . . . . . . . . 3.151 Results of benchmark 3-12a, Trough . . . . . . . . . . . . . . . . . . . . . 3.152 Results of benchmark 3-12a, Subsidence at different horizontal distances of Z axis (from 0 to 0.7W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.153 Results of benchmark 3-12a, Subsidence at different horizontal distances of Z axis (from 1W to 2.5W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.154 Results of benchmark 3-13, Vertical and horizontal moduli of subgrade reaction 3.155 Results of benchmark 3-14, Vertical soil stresses . . . . . . . . . . . . . . . 3.156 Results of benchmark 3-14, Neutral horizontal soil stress and bearing capacities 3.157 Results of benchmark 3-14, Vertical and horizontal moduli of subgrade reaction 3.158 Results of benchmark 3-14, Maximal axial friction and displacements . . . . . 3.159 Results of benchmark 3-14, Face support pressures . . . . . . . . . . . . . 3.160 Results of benchmark 3-14, Thrust forces . . . . . . . . . . . . . . . . . . . 3.161 Results of benchmark 3-14, Uplift safety factor . . . . . . . . . . . . . . . . 3.162 Results of benchmark 3-14, Trough . . . . . . . . . . . . . . . . . . . . . . 3.163 Results of benchmark 3-14, Subsidence at different horizontal distances of Z axe (from 0 to 0.7W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.164 Results of benchmark 3-14, Subsidence at different horizontal distances of Z axe (from 1W to 2.5W) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.165 Configuration of the 3 trench sections (benchmark 3-15a) . . . . . . . . . . . 3.166 Analytical results for the calculation of the uplift safety factor . . . . . . . . . 3.167 Analytical results for the hydraulic heave check . . . . . . . . . . . . . . . . 3.168 Results of benchmark 3-15a, Vertical and horizontal soil stresses . . . . . . . xii 53 54 55 55 55 56 56 56 57 57 58 58 58 59 60 60 60 61 61 61 62 62 62 63 63 63 64 64 65 65 66 66 66 67 67 67 68 68 69 70 70 70 Deltares List of Tables 3.169 Results of benchmark 3-15a, Initial vertical stress qk for sand poorly compacted 3.170 Results of benchmark 3-15b, Initial vertical stress qk for stiff clay poorly compacted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.171 Results of benchmark 3-15c, Initial vertical stress qk for soft soil poorly compacted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.172 Results of benchmark 3-15d, Initial vertical stress qk for sand well compacted . 3.173 Results of benchmark 3-15e, Initial vertical stress qk for stiff clay well compacted 3.174 Results of benchmark 3-15f, Initial vertical stress qk for soft soil well compacted 3.175 Results of benchmark 3-15a, Horizontal modulus of subgrade reaction and bearing capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.176 Results of benchmark 3-15a, Vertical moduli of subgrade reaction upward . . 3.177 Results of benchmark 3-15a, Vertical moduli of subgrade reaction downward . 3.178 Results of benchmark 3-15a, Maximal axial friction and displacements . . . . 3.179 Results of benchmark 3-15a, Uplift check . . . . . . . . . . . . . . . . . . . 3.180 Results of benchmark 3-15a, Hydraulic heave check . . . . . . . . . . . . . 3.181 Analytical results for the hydraulic heave check . . . . . . . . . . . . . . . . 3.182 Results of benchmark 3-16, Hydraulic heave check . . . . . . . . . . . . . . 3.183 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-17) for the equivalent pipe . . . . . . . . 3.184 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-17) for pipe nr. 1 . . . . . . . . . . . . . 3.185 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-17) for pipe nr. 2 . . . . . . . . . . . . . 3.186 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-17) for pipe nr. 3 . . . . . . . . . . . . . 3.187 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-17) for pipe nr. 4 . . . . . . . . . . . . . 3.188 Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-17) for pipe nr. 5 . . . . . . . . . . . . . 3.189 Results of benchmark 3-17, Buoyancy Control . . . . . . . . . . . . . . . . 3.190 Results of benchmark 3-17, Pulling forces in the pipeline . . . . . . . . . . . 3.191 Position of the 6 characteristic points (bm3-18a) for case a (positive angle between radii) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.192 Position of the 6 characteristic points (bm3-18b) for case b . . . . . . . . . . 3.193 Results of benchmark 3-18a, Pulling forces in the pipeline . . . . . . . . . . . 3.194 Results of benchmark 3-18b, Pulling forces in the pipeline . . . . . . . . . . . 3.195 Results of benchmark 3-19, Buoyancy Control . . . . . . . . . . . . . . . . 3.196 Results of benchmark 3-19, Pulling forces in the pipeline . . . . . . . . . . . 3.197 Results of benchmark 3-19 for vertical nr. 1, Strength calculation for Combination 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.198 Results of benchmark 3-19 for vertical nr. 1, Strength calculation for Combination 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.199 Results of benchmark 3-19 for vertical nr. 1, Strength calculation for Combination 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.200 Results of benchmark 3-19 for vertical nr. 1, Strength calculation for Combination 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.201 Results of benchmark 3-19 for vertical nr. 1, Strength calculation for Combination 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.202 Results of benchmark 3-19 for vertical nr. 1, Maximum allowable stresses . . . 3.203 Results of benchmark 3-19 for vertical nr. 1, Deflection of the pipeline . . . . . 3.204 Results of benchmark 3-19 for vertical nr. 1, Implosion . . . . . . . . . . . . 3.205 Results of benchmark 3-19 for vertical nr. 2, Strength calculation for Combination 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deltares 71 71 71 72 72 72 73 73 73 74 74 74 75 75 76 77 77 77 78 78 78 79 80 80 81 81 83 83 83 83 84 84 84 84 84 85 85 xiii D-G EO P IPELINE, Verification Report 3.206 Results of benchmark 3-19 for vertical nr. 2, Strength calculation for Combination 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.207 Results of benchmark 3-19 for vertical nr. 2, Strength calculation for Combination 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.208 Results of benchmark 3-19 for vertical nr. 2, Strength calculation for Combination 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.209 Results of benchmark 3-19 for vertical nr. 2, Strength calculation for Combination 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.210 Results of benchmark 3-19 for vertical nr. 2, Maximum allowable stresses . . 3.211 Results of benchmark 3-19 for vertical nr. 2, Deflection of the pipeline . . . . 3.212 Results of benchmark 3-19 for vertical nr. 2, Implosion . . . . . . . . . . . 3.213 Results of benchmark 3-19 for vertical nr. 3, Strength calculation for Combination 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.214 Results of benchmark 3-19 for vertical nr. 3, Strength calculation for Combination 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.215 Results of benchmark 3-19 for vertical nr. 3, Strength calculation for Combination 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.216 Results of benchmark 3-19 for vertical nr. 3, Strength calculation for Combination 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.217 Results of benchmark 3-19 for vertical nr. 3, Strength calculation for Combination 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.218 Results of benchmark 3-19 for vertical nr. 3, Maximum allowable stresses . . 3.219 Results of benchmark 3-19 for vertical nr. 3, Deflection of the pipeline . . . . 3.220 Results of benchmark 3-19 for vertical nr. 3, Implosion . . . . . . . . . . . 3.221 Results of benchmark 3-20, Buoyancy Control . . . . . . . . . . . . . . . 3.222 Results of benchmark 3-20, Pulling forces in the pipeline . . . . . . . . . . 3.223 Results of benchmark 3-20 for vertical nr. 1, Strength calculation for Combination 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.224 Results of benchmark 3-20 for vertical nr. 1, Strength calculation for Combination 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.225 Results of benchmark 3-20 for vertical nr. 1, Strength calculation for Combination 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.226 Results of benchmark 3-20 for vertical nr. 1, Strength calculation for Combination 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.227 Results of benchmark 3-20 for vertical nr. 1, Strength calculation for Combination 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.228 Results of benchmark 3-20 for vertical nr. 1, Maximum allowable stresses . . 3.229 Results of benchmark 3-20 for vertical nr. 1, Deflection of the pipeline . . . . 3.230 Results of benchmark 3-20 for vertical nr. 1, Implosion . . . . . . . . . . . 3.231 Results of benchmark 3-20 for vertical nr. 2, Strength calculation for Combination 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.232 Results of benchmark 3-20 for vertical nr. 2, Strength calculation for Combination 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.233 Results of benchmark 3-20 for vertical nr. 2, Strength calculation for Combination 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.234 Results of benchmark 3-20 for vertical nr. 2, Strength calculation for Combination 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.235 Results of benchmark 3-20 for vertical nr. 2, Strength calculation for Combination 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.236 Results of benchmark 3-20 for vertical nr. 2, Maximum allowable stresses . . 3.237 Results of benchmark 3-20 for vertical nr. 2, Deflection of the pipeline . . . . 3.238 Results of benchmark 3-20 for vertical nr. 2, Implosion . . . . . . . . . . . 3.239 Results of benchmark 3-20 for vertical nr. 3, Strength calculation for Combination 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv . 85 . 85 . 85 . . . . 86 86 86 86 . 86 . 87 . 87 . 87 . . . . . . 87 88 88 88 89 89 . 89 . 89 . 90 . 90 . . . . 90 90 90 91 . 91 . 91 . 91 . 91 . . . . 92 92 92 92 . 92 Deltares List of Tables 3.240 Results of benchmark 3-20 for vertical nr. 3, Strength calculation for Combination 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.241 Results of benchmark 3-20 for vertical nr. 3, Strength calculation for Combination 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.242 Results of benchmark 3-20 for vertical nr. 3, Strength calculation for Combination 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.243 Results of benchmark 3-20 for vertical nr. 3, Strength calculation for Combination 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.244 Results of benchmark 3-20 for vertical nr. 3, Maximum allowable stresses . . 3.245 Results of benchmark 3-20 for vertical nr. 3, Deflection of the pipeline . . . . 3.246 Results of benchmark 3-20 for vertical nr. 3, Implosion . . . . . . . . . . . 3.247 Properties of the different layers in benchmark 21a . . . . . . . . . . . . . 3.248 Values of constant C (according to table E.1 of NEN 3650-1 (NEN, 2012a)) . 3.249 Soil type as a function of the cohesion and the friction angle . . . . . . . . 3.250 Bending factor (acc. to table 6 of NEN 3650-3) . . . . . . . . . . . . . . . 3.251 Results of benchmark 3-21a, Allowable minimum radius for steel pipes . . . 3.252 Results of benchmark 3-21b, Allowable minimum radius for PE pipes . . . . 3.253 Analytical results for the calculation of the five components of the pulling force for the six characteristic points . . . . . . . . . . . . . . . . . . . . . . . 3.254 Results of benchmark 3-22, Pulling forces in the pipeline . . . . . . . . . . 3.255 Analytical results for the calculation of the five components of the pulling force for the six characteristic points . . . . . . . . . . . . . . . . . . . . . . . 3.256 Results of benchmark 3-23, Buoyancy Control . . . . . . . . . . . . . . . 3.257 Results of benchmark 3-23, Pulling forces in the pipeline . . . . . . . . . . 3.258 Results of benchmark 3-23, Implosion . . . . . . . . . . . . . . . . . . . 3.259 Analytical results for the calculation of the traffic load . . . . . . . . . . . . 3.261 Results of benchmark 3-24, Buoyancy control . . . . . . . . . . . . . . . . 3.262 Results of benchmark 3-24, Pulling forces in the pipeline . . . . . . . . . . 3.263 Results of benchmark 3-24, Strength calculation for Combination 1A . . . . 3.264 Results of benchmark 3-24, Strength calculation for Combination 1B . . . . 3.265 Results of benchmark 3-24, Strength calculation for Combination 2 . . . . . 3.266 Results of benchmark 3-24, Strength calculation for Combination 3 . . . . . 3.267 Results of benchmark 3-24, Strength calculation for Combination 4 . . . . . 3.268 Results of benchmark 3-24, Maximum allowable stresses . . . . . . . . . . 3.269 Results of benchmark 3-24, Deflection of the pipeline . . . . . . . . . . . . 3.270 Results of benchmark 3-24, Implosion . . . . . . . . . . . . . . . . . . . 3.272 Results of benchmark 3-25, Buoyancy Control . . . . . . . . . . . . . . . 3.273 Results of benchmark 3-25, Pulling forces in the pipeline . . . . . . . . . . 3.274 Results of benchmark 3-25, Strength calculation for Combination 1A . . . . 3.275 Results of benchmark 3-25, Strength calculation for Combination 1B . . . . 3.276 Results of benchmark 3-25, Strength calculation for Combination 2 . . . . . 3.277 Results of benchmark 3-25, Strength calculation for Combination 3 . . . . . 3.278 Results of benchmark 3-25, Strength calculation for Combination 4 . . . . . 3.279 Results of benchmark 3-25, Maximum allowable stresses . . . . . . . . . . 3.280 Results of benchmark 3-25, Deflection of the pipeline . . . . . . . . . . . . 3.281 Results of benchmark 3-25, Implosion . . . . . . . . . . . . . . . . . . . 3.283 Results of benchmark 3-26, Buoyancy control . . . . . . . . . . . . . . . . 3.284 Results of benchmark 3-26, Pulling forces in the pipeline . . . . . . . . . . 3.285 Results of benchmark 3-26, Strength calculation for Combination 1A . . . . 3.286 Results of benchmark 3-26, Strength calculation for Combination 1B . . . . 3.287 Results of benchmark 3-26, Strength calculation for Combination 2 . . . . . 3.288 Results of benchmark 3-26, Strength calculation for Combination 3 . . . . . 3.289 Results of benchmark 3-26, Strength calculation for Combination 4 . . . . . 3.290 Results of benchmark 3-26, Maximum allowable stresses . . . . . . . . . . Deltares . 93 . 93 . 93 . . . . . . . . . . 93 94 94 94 96 97 98 98 100 101 . 102 . 102 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 103 103 104 106 107 107 108 108 108 108 109 109 109 109 111 111 111 112 112 112 112 113 113 113 115 115 115 115 115 116 116 116 xv D-G EO P IPELINE, Verification Report 3.291 Results of benchmark 3-26, Deflection of the pipeline . . . . . . . . . . . . . 116 3.292 Results of benchmark 3-26, Implosion . . . . . . . . . . . . . . . . . . . . 116 4.1 Results of benchmark 4-01, Pulling forces in the pipeline . . . . . . . . . . . 117 5.1 5.2 5.3 5.4 Koppejan’s parameters (benchmark 5-1) . . . . . . . . . . . . . . . . . . Results of benchmark 5-01, Settlements according to Koppejan . . . . . . . Isotache’s parameters (bm5-02) . . . . . . . . . . . . . . . . . . . . . . . Results of benchmark 5-02a, Settlements according to Isotache with OCR consolidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results of benchmark 5-02b, Settlements according to Isotache with POP consolidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 xvi . 119 . 120 . 120 . 121 . 121 Deltares Introduction Deltares Systems commitment to quality control and quality assurance has leaded them to develop a formal and extensive procedure to verify the correct working of all of their geotechnical engineering tools. An extensive range of benchmark checks have been developed to check the correct functioning of each tool. During product development these checks are run on a regular basis to verify the improved product. These benchmark checks are provided in the following sections, to allow the user to overview the checking procedure and verify for themselves the correct functioning of D-G EO P IPELINE. The benchmarks are subdivided into five separate groups as described below. Group 1 [chapter 1] – Benchmarks from literature (exact solution) Simple benchmarks for which an exact analytical result is available from literature. Group 2 [chapter 2] – Benchmarks from literature (approximate solution) More complex benchmarks described in literature for which an approximate solution is known. Group 3 [chapter 3] – Benchmarks from spread sheets Benchmarks which test program features specific to MSheet. Group 4 [chapter 4] – Benchmarks generated by D-G EO P IPELINE Benchmarks for which the reference results are generated using D-G EO P IPELINE. Group 5 [chapter 5] – Benchmarks compared with other programs Benchmarks for which the results of D-G EO P IPELINE are compared with the results of other programs. The number of benchmarks in group 1 may grow in the future. The benchmarks in this chapter are well documented in literature. There are no exact solutions available for these problems, however in the literature estimated results are available. When verifying the program, the results should be close to the results found in the literature. The number of benchmarks in group 2 will grow as new versions of the program are released. These benchmarks are designed so that (new) features specific to the program can be verified. The benchmarks are kept as simple as possible so that only one specific feature is verified from one benchmark to the next. 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, proves 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 to produce wrong results. Hopefully by using the verification procedure the number of ways this can occur will be limited. The benchmarks are all described in sufficient detail for reproduction to be possible at any time. The results are presented in text format with each benchmark description. The results in graphic format are available in the appendix, together with a copy of a part of the output file. This information is enough to be able to make the calculation. For each benchmark at least one picture is presented which shows the relevant results. The different benchmarks from literature with an exact solution (group 1) are described in the following paragraphs. Deltares 1 of 126 D-G EO P IPELINE, Verification Report 2 of 126 Deltares 1 Group 1: Benchmarks from literature (exact solution) 1.1 1.1.1 Soil type and displacement at maximal friction (Micro-tunneling and Trenching) Description This benchmark checks the classification of the soil type and the displacement at maximal friction associated to each soil type. Many combinations of parameters c and ϕ are simulated as shown in Table 1.1. Table 1.1: Material properties of the different layers (benchmark 1-1) Vertical nr. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Deltares Material description c ϕ Dense sand 1 Dense sand 2 Stiff clay 1 Medium dense sand 1 Medium dense sand 2 Stiff clay 2 Loose sand 1 Loose sand 2 Stiff sandy clay 1 Stiff sandy clay 2 Stiff clay 3 Clayey sand 1 Clayey sand 2 Stiff sandy clay 3 Medium stiff clay 1 Medium stiff clay 2 Stiff clay 4 Soft clay 1 Soft clay 2 Medium stiff clay 3 Stiff clay 5 Organic clay Peat [kPa] 0.2 0.5 3 0.3 0.5 1 0.1 1 5 10 35 4 5 12 6 10 15 4.9 5 5.3 10 15 30 [◦ ] 32.6 40 35 30.1 32 32.5 25.1 26 27 29 30 22.6 23 25 20.1 21 22.5 17.1 18 19 20 17 14 Friction displac. [mm] 2 2 3 4 4 3 7 7 5 3 3 7 7 3 5 5 4 8 8 5 5 10 13 Global soil type Sand Sand Clay Sand Sand Clay Sand Sand Clay Clay Clay Sand Sand Clay Clay Clay Clay Clay Clay Clay Clay Peat Peat 3 of 126 D-G EO P IPELINE, Verification Report Figure 1.1: Geometry of benchmark 1-1a (Construction in Trench) 1.1.2 Benchmark results The displacement necessary to develop the maximal axial friction along the pipeline and the classification of global soil types are determined using Table 1.2. Table 1.2: Displacement at maximal friction and classification of the soil type Soil type Global soil type ϕ ◦ [ ] Dense sand Medium dense sand Medium dense sand Loose sand Stiff sandy clay Stiff sandy clay Clayey sand Stiff clay Medium stiff clay Stiff clay Medium stiff clay Soft clay Peat / organic clay Sand Sand Sand Sand Clay Clay Sand Clay Clay Clay Clay Clay Peat ϕ > 32.5 30 < ϕ ≤ 32.5 ϕ > 30 25 < ϕ ≤30 25 < ϕ ≤ 30 22.5 < ϕ 25 22.5 < ϕ ≤ 25 20 < ϕ ≤ 22.5 20 < ϕ ≤ 22.5 17 < ϕ ≤ 20 17 < ϕ ≤ 20 17 < ϕ ≤ 20 ϕ ≤ 17 c [kN/m2 ] c ≤ 0.5 c ≤ 0.5 c > 0.5 c≤1 c>1 c>5 c≤5 c > 10 c ≤ 10 c > 10 5 < c ≤ 10 c≤5 Displacement [mm] 1-3 3-5 3-5 5-8 4-6 2-4 5-8 2-4 4-6 2-4 4-6 6-10 10-15 The Construction in trench model (bm1-1a) and the Micro-tunneling model (bm1-1b) are checked. Benchmark results are presented in both tables below. 4 of 126 Deltares Group 1: Benchmarks from literature (exact solution) 1.1.3 D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report. Table 1.3: Results of benchmark 1-1a, Global soil type for Construction in Trench Vertical nr. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Deltares Benchmark Sand Sand Clay Sand Sand Clay Sand Sand Clay Clay Clay Sand Sand Clay Clay Clay Clay Clay Clay Clay Clay Peat Peat D-G EO P IPELINE Sand Sand Clay Sand Sand Clay Sand Sand Clay Clay Clay Sand Sand Clay Clay Clay Clay Clay Clay Clay Clay Peat Peat Result OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK 5 of 126 D-G EO P IPELINE, Verification Report Table 1.4: Results of benchmark 1-1a, Maximal displacement for Construction in Trench Vertical nr. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 6 of 126 Benchmark [mm] 2 2 3 4 4 3 7 7 5 3 3 7 7 3 5 5 4 8 8 5 5 10 13 D-G EO P IPELINE [mm] 2 2 3 4 4 3 7 7 5 3 3 7 7 3 5 5 4 8 8 5 5 10 13 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Deltares Group 1: Benchmarks from literature (exact solution) Table 1.5: Results of benchmark 1-1b, Global soil type for Micro Tunneling Vertical nr. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Deltares Benchmark Sand Sand Clay Sand Sand Clay Sand Sand Clay Clay Clay Sand Sand Clay Clay Clay Clay Clay Clay Clay Clay Peat Peat D-G EO P IPELINE Sand Sand Clay Sand Sand Clay Sand Sand Clay Clay Clay Sand Sand Clay Clay Clay Clay Clay Clay Clay Clay Peat Peat Error OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK OK 7 of 126 D-G EO P IPELINE, Verification Report Table 1.6: Results of benchmark 1-1b, Maximal displacement for Micro Tunneling Vertical nr. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Benchmark [mm] 2 2 3 4 4 3 7 7 5 3 3 7 7 3 5 5 4 8 8 5 5 10 13 D-G EO P IPELINE [mm] 2 2 3 4 4 3 7 7 5 3 3 7 7 3 5 5 4 8 8 5 5 10 13 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input files bm1-1a.dri and bm1-1b.dri to run this benchmark. 8 of 126 Deltares 2 Group 2: Benchmarks from literature (approximate solution) The different benchmarks from literature for which an approximate solution is known are described in this chapter. Currently, no benchmarks are available. Deltares 9 of 126 D-G EO P IPELINE, Verification Report 10 of 126 Deltares 3 Group 3: Benchmarks from spreadsheets The benchmarks in this chapter (group 3) check if the output of D-G EO P IPELINE is according to the formula’s given in the User Manual of D-G EO P IPELINE [Deltares] using spreadsheets. Those formula’s are based on the Dutch standards NEN 3650-1, NEN 3650-2, NEN 3650-3 and NEN 3651 (NEN, 2012a,b,c,d). 3.1 3.1.1 HDD with 2D geometry – Steel pipe in two compressible undrained layers Description The pipe is constructed in two compressible undrained layers (clay and sand) with the characteristics given in Table 3.1. The boundaries between compressible/incompressible layers and drained/undrained layers are situated at the bottom of the sand layer. The ground level is at depth Z = 0 m and the phreatic line is at depth Z = -3 m. The steel pipe properties are given in Table 3.2. Calculations are performed for 8 verticals with L coordinates of 20, 50, 100, 200, 350, 500, 650 and 680 m. The configuration of the pipeline is given by: Xleft 10 m X-coordinate of the left entry point Xright 690 m X-coordinate of the right exit point ϕleft 13 deg Left angle of the pipe ϕright 15 deg Right angle of the pipe Zlowest -50 m Lowest level of the pipe Rleft 600 m Bending radius of the pipe at the left side Rright 800 m Bending radius of the pipe at the right side Rrol 1000 m Bending radius in pipe string (on rollers) Table 3.1: Soil material properties (bm3-1) Bottom depth of the layer Unit weight above phreatic level Unit weight below phreatic level Cohesion Friction angle Undrained cohesion at the top Undrained cohesion at the bottom Young modulus at the top Young modulus at the top Poisson ratio Deltares Zlowest γunsat γsat c ϕ cu;top cu;bot Etop Ebot ν [m] [kN/m3 ] [kN/m3 ] [kN/m2 ] [deg] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [-] Sand -60 18 20 0.2 30 0.2 0.5 20000 25000 0.45 Clay -15 14 16 5 22.5 25 30 1500 2000 0.4 11 of 126 D-G EO P IPELINE, Verification Report Table 3.2: Pipe material data (bm3-1) Material Negative wall thickness tolerance Yield strength Partial material factor Partial material factor for test pressure Young’s modulus Outer diameter Nominal wall thickness Unit weight Design pressure Test pressure Temperature variation δt Reb γm γm;test Eb D0 dn γb pd pt ∆t [%] [N/mm2 ] [-] [-] [N/mm2 ] [m] [mm] [kN/m3 ] [kN/m2 ] [kN/m2 ] [◦ ] Steel 15 235 1.1 1 205800 0.8 19 78.5 600 834 10 Figure 3.1: 2D Geometry of benchmark 3-1 (steel pipeline in two compressible undrained layers) 3.1.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Soil mechanical data The soil mechanical data’s are determined using the formulas given in chapter Calculation of soil mechanical data in the Background section of the User Manual of D-G EO P IPELINE. The maximal axial friction between the pipe and the drilling fluid is constant along the pipeline and equal to f2 = 50 N/m2 . The displacement necessary to develop the maximal axial friction along the pipeline is estimated between 6 and 9 mm (= 7.5 mm). 12 of 126 Deltares Group 3: Benchmarks from spreadsheets Minimum drilling fluid pressures For the minimum drilling fluid pressures, calculations are performed during the three stages of the drilling process using the formulas given in paragraph “Minimum required drilling fluid pressure” in the Background section of the User Manual of D-G EO P IPELINE [Deltares]. The minimum required pressure dp/dz is the optimal value for which the calculated flow rate Q is equal to the requested flow rate Qreq (necessary to initiate flow of drilling fluid). Calculations are performed in an Excel spreadsheet using the solver option and lead to the values of dp/dz given in Table 3.3. Table 3.3: Analytical results for the calculation of dp/dz for the three stages Pipe diameter Hole radius Circulation loss factor floss Annular back flow rate Qann Request back flow rate Qreq Minimum required pressure dp/dz [m] [m] [-] [m3 /s] [m3 /s] [kN/m3 ] Pilot 0.114 0.1 0.3 0.0025 0.00175 0.63631 Pre-ream 0.5 0.3 0.2 0.0067 0.00536 0.56048 Pull back 0.8 0.45 0.2 0.0033 0.00264 0.56018 Maximum drilling fluid pressures For the maximum drilling fluid pressures in undrained conditions, calculations are performed using the formulas given in paragraph Maximum required drilling fluid pressure in the Background section of the User Manual of D-G EO P IPELINE. Analytical results are given in the table below. Table 3.4: Analytical results for the calculation of the maximum drilling fluid pressures Vert. u 0.9 plimit plastic zone related to : [-] [kN/m2 ] [kN/m2 ] 1 0 88.6 2 62.35 122.71 3 177.78 107.92 4 394.42 222.39 5 470 264.87 6 404.81 228.21 7 77.18 129.29 8 0 91.95 ppilot ppreream pback deformation bore hole [kN/m2 ] [kN/m2 ] [kN/m2 ] 95.29 80.21 69.47 136.09 134.22 131.85 119.49 117.92 117.01 246.97 246.52 246.25 294.21 293.81 293.56 253.45 253 252.74 143.47 142.02 140.14 99.75 87.08 77.24 ppilot [kN/m2 ] 95.29 136.09 119.49 246.97 294.21 253.45 143.47 99.75 ppreream soil cover [kN/m2 ] 80.21 134.22 117.92 246.52 293.81 253 142.02 87.08 pback [kN/m2 ] 69.47 131.85 117.01 246.25 293.56 252.74 140.14 77.24 Strength calculation For the buoyancy control, the pulling forces in the pipeline and the strength calculation, calculations are performed using the formulas given in chapter “Strength pipeline calculation” in the Background section of the User Manual of D-G EO P IPELINE. The length of the pipe in the borehole at the characteristic points (Figure 3-2) is: LA = 0 m LB = LA + |Zlowest + Rleft × (1 − cos ϕleft )| / sin ϕleft = 153.909 m LC = LB + ϕleft × Rleft = 290.045 m Ld = LC + Xright − |Zlowest + Rright (1 − cos ϕright )| / tan ϕright − Rright × sin ϕright − Xleft − |Zlowest + Rleft × (1 − cos ϕleft )| / tan ϕleft − Rleft × sin ϕleft = 393.185 m LE = Ld + ϕright × Rright = 602.625 m Deltares 13 of 126 D-G EO P IPELINE, Verification Report LF = LE + |Zlowest + Rright × (1 − cos ϕright )| / sin ϕright = 690.488 m entry point exit point ground level T6 T1 T5 T2 T3 T4 Figure 3.2: Locations of the characteristic points T1 to T6 Hereafter are some intermediate results used for the pulling force and the strength calculations: Factor of friction pipe-roller Friction pipe-mud Factor of friction pipe-soil Load factor - Design pressure Load factor - Design pressure (combination) Load factor - Test pressure Load factor - Installation Load factor - Soil load Qn Load factor - Temperature Contingency factor - E-modulus Contingency factor - Pulling force Contingency factor - Modulus of subgrade reaction Contingency factor - Soil load Qn Contingency factor - Bending moment Contingency factor - Bending radius Contingency factor - Pressure borehole Effective weight of pipe Weight of pipeline (incl. filling) Uplift force Moment coefficient indirect bottom Moment coefficient indirect top Moment coefficient direct bottom Moment coefficient direct top Direct deflection factor Indirect deflection factor Part of pipe filled with water during pull back Cross sections of the pipe 14 of 126 f1 f2 f3 fpd fpd;comb fpt finstall fQn1 ftemp fE fpull fkv fQn2 fM fR fpress;bore geff gfill gupw kb ’ kt ’ kb kt ky ky ’ Pwater A Atrek 0.1 0.00005 0.2 1.25 1.15 1.1 1.1 1.5 1.1 1.25 1.4 1.6 1.1 1.27 1.1 1.1 1.414 0.456 5.529 0.083 0.061 0.138 0.131 0.089 0.048 10 39769.979 46618.093 [-] [N/mm2 ] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [N/mm] [N/mm] [N/mm] [-] [-] [-] [-] [-] [-] [%] [mm2 ] [mm2 ] Deltares Group 3: Benchmarks from spreadsheets Minimal wall thickness Outer radius of the pipeline Inner radius of the pipeline Average radius of the pipeline Moment of inertia of the pipe Moment of inertia of the wall Pipe resisting moment Wall resisting moment Unit weight of drilling fluid Maximum modulus of subgrade reaction Maximum neutral vertical soil load Maximum corrected reduced soil load Maximum neutral horizontal soil load Soil reaction - Left curve Soil reaction - Right curve Soil reaction - Left curve (long term) Soil reaction - Right curve (long term) Characteristic stiffness pipeline-soil Characteristic stiffness pipeline-soil (long term) Ainw dn;min re ri rg Ib Iw Wb Ww γdrill fluid kv;max qv;n;r;max qn qh;n;r qr;left qr;right qr;left qr;right λ λlong 456036.731 16.15 400 381 390.5 3556505999 571.583 8891265 60.167 11 30945.502 184.15 303.847 136.488 49.727 37.295 n.a. n.a. 0.0003032 n.a. [mm2 ] [mm] [mm] [mm] [mm] [mm4 ] [mm3 ] [mm4 m] [mm3 m] [kN/m3 ] [kN/m3 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [mm-1 ] [mm-1 ] The total pulling force is the contribution of five components. Results are given in Table 3-5. Table 3.6: Results of benchmark 3-01, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 284 154 284 290 468 393 468 603 622 690 622 5187 D-G EO P IPELINE Length Force [m] [kN] 0 284 154 284 290 468 393 468 603 622 690 622 5187 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 The maximum combined stress at the top or the bottom, and inside or outside the pipe is calculated in the tables below and used for checking the calculated stresses. Table 3.7: Set for calculation of the maximum stresses for load combination 1A σx [N/mm2 ] σy [N/mm2 ] σV [N/mm2 ] Deltares Top outside 115.5 0 115.5 Top inside 115.5 0 115.5 Bottom inside 137.51 0 137.51 Bottom outside 137.51 0 137.51 15 of 126 D-G EO P IPELINE, Verification Report Table 3.8: Set for calculation of the maximum stresses for load combination 1B 2 σx [N/mm ] σy [N/mm2 ] σV [N/mm2 ] Top outside 186.75 -15.81 195.14 Top inside 186.75 15.81 179.37 Bottom inside 234.92 21.51 224.94 Bottom outside 234.92 -21.51 246.38 Table 3.9: Set for calculation of the maximum stresses for load combination 3 σx;2 [N/mm2 ] σy;2 [N/mm2 ] σV;2 [N/mm2 ] σx;3 [N/mm2 ] σy;3 [N/mm2 ] σV;3 [N/mm2 ] σx;4 [N/mm2 ] σy;4 [N/mm2 ] σV;4 [N/mm2 ] Top outside 0 -207.43 207.43 -210.84 0 210.84 -210.84 -223.23 217.3 Top inside 0 207.43 207.43 -210.84 0 210.84 -210.84 223.23 375.97 Bottom inside 0 218.51 218.51 210.84 0 210.84 210.84 240.02 226.84 Bottom outside 0 -218.51 218.51 210.84 0 210.84 210.84 -240.02 390.72 Table 3.10: Set for calculation of the maximum stresses for load combination 4 σx;1 [N/mm2 ] σy;1 [N/mm2 ] σV;1 [N/mm2 ] σx;2 [N/mm2 ] σy;2 [N/mm2 ] σV;2 [N/mm2 ] σx;3 [N/mm2 ] σy;3 [N/mm2 ] σV;3 [N/mm2 ] σx;4 [N/mm2 ] σy;4 [N/mm2 ] σV;4 [N/mm2 ] 16 of 126 Top outside 8.37 16.74 14.5 8.37 -179.93 184.26 -202.46 16.74 211.33 -202.46 -195.29 198.97 Top inside 8.37 16.74 14.5 8.37 213.42 209.36 -202.46 16.74 211.33 -202.46 228.78 373.7 Bottom inside 8.37 16.74 14.5 8.37 223.93 219.86 219.21 16.74 211.33 219.21 244.82 233.07 Bottom outside 8.37 16.74 14.5 8.37 -190.44 194.76 219.21 16.74 211.33 219.21 -211.33 372.88 Deltares Group 3: Benchmarks from spreadsheets 3.1.3 D-G EO P IPELINE results D-G EO P IPELINE results presented in the tables below can be found in the Report. Table 3.11: Results of benchmark 3-01, Maximum allowable drilling fluid pressure (plastic zone related to deformation bore hole) Vert. [-] 1 2 3 4 5 6 7 8 Benchmark Pilot PrePull ream back [kN/m2 ] [kN/m2 ] [kN/m2 ] 89 80 69 185 185 185 286 286 286 617 617 617 735 735 735 633 633 633 206 206 206 92 87 77 D-G EO P IPELINE Pilot PrePull ream back [kN/m2 ] [kN/m2 ] [kN/m2 ] 89 80 69 185 185 185 286 286 286 617 617 617 735 735 735 634 634 634 206 206 206 92 87 77 Pilot [%] 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.00 Relative error PrePull ream back [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.16 0.16 0.00 0.00 0.00 0.00 Table 3.12: Results of benchmark 3-01, Maximum allowable drilling fluid pressure (plastic zone related to soil cover) Vert. [-] 1 2 3 4 5 6 7 8 Benchmark PrePull ream back [kN/m2 ] [kN/m2 ] [kN/m2 ] 89 80 69 185 185 185 286 286 286 617 617 617 735 735 735 633 633 633 206 206 206 92 87 77 Pilot D-G EO P IPELINE PrePull ream back [kN/m2 ] [kN/m2 ] [kN/m2 ] 89 80 69 185 185 185 286 286 286 617 617 617 735 735 735 634 634 634 206 206 206 92 87 77 Pilot Pilot [%] 0.00 0.00 0.00 0.00 0.00 0.16 0.00 0.00 Relative error PrePull ream back [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.16 0.16 0.00 0.00 0.00 0.00 Table 3.13: Results of benchmark 3-01, Minimum required drilling fluid pressure (from left to right) Vert. [-] 1 2 3 4 5 6 7 8 Deltares Benchmark PrePull ream back 2 2 [kN/m ] [kN/m ] [kN/m2 ] 32 31 31 128 125 125 287 280 280 591 576 576 770 743 743 794 602 588 531 144 141 462 36 35 Pilot D-G EO P IPELINE PrePull ream back 2 2 [kN/m ] [kN/m ] [kN/m2 ] 32 31 31 129 125 125 290 281 281 597 578 577 780 747 745 808 608 590 551 145 142 483 36 35 Pilot Pilot [%] 0.00 0.78 1.03 1.01 1.28 1.73 3.63 4.35 Relative error PrePull ream back [%] [%] 0.00 0.00 0.00 0.00 0.36 0.36 0.35 0.17 0.54 0.27 0.99 0.34 0.69 0.7 0.00 0.00 17 of 126 D-G EO P IPELINE, Verification Report Table 3.14: Results of benchmark 3-01, Minimum required drilling fluid pressure (from right to left) Vert. [-] 1 2 3 4 5 6 7 8 Benchmark PrePull ream back [kN/m2 ] [kN/m2 ] [kN/m2 ] 458 32 31 515 128 125 609 287 280 782 591 576 770 744 743 602 588 588 144 141 141 36 35 35 Pilot D-G EO P IPELINE PrePull ream back [kN/m2 ] [kN/m2 ] [kN/m2 ] 479 32 31 534 129 125 627 290 281 797 597 578 780 747 745 608 590 589 145 142 141 36 35 35 Pilot Pilot [%] 4.38 3.56 2.87 1.88 1.28 0.99 0.69 0.00 Relative error PrePull ream back [%] [%] 0.00 0.00 0.78 0.00 1.03 0.36 1.01 0.35 0.4 0.27 0.34 0.17 0.7 0.00 0.00 0.00 Table 3.15: Results of benchmark 3-01, Equilibrium between drilling fluid pressure and pore pressure Vert. [-] 1 2 3 4 5 6 7 8 Benchmark Drilling Water Safety fluid [kN/m2 ] [kN/m2 ] [-] 25.4 0 101.58 62.35 1.63 228.56 177.78 1.29 466.86 394.42 1.18 550 470 1.17 478.29 404.81 1.18 117.9 77.18 1.53 29.47 0 - D-G EO P IPELINE Drilling Water Safety fluid [kN/m2 ] [kN/m2 ] [-] 25.4 0 101.58 62.35 1.63 228.56 177.78 1.29 466.86 394.42 1.18 550 470 1.17 478.29 404.81 1.18 117.9 77.18 1.53 29.47 0 Relative error Drilling Water Safety fluid [%] [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.16: Results of benchmark 3-01, Vertical soil stresses Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error qv;p qv;n qv;r;n qv;p qv;n qv;r;n qv;p qv;n qv;r;n [kN/m2 ] 47 234 916 1656 1887 1688 253 60 [kN/m2 ] 28 77 169 385 461 396 86 33 [kN/m2 ] 28 62 114 178 184 179 68 33 [kN/m2 ] 47 234 916 1656 1887 1688 253 60 [kN/m2 ] 28 77 169 385 461 396 86 33 [kN/m2 ] 28 62 114 178 184 179 68 33 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 18 of 126 Deltares Group 3: Benchmarks from spreadsheets Table 3.17: Results of benchmark 3-01, Neutral horizontal soil stress and bearing capacities Benchmark Vert. [-] 1 2 3 4 5 6 7 8 ph;n Pv;e 2 D-G EO P IPELINE Ph;e 2 ph;n 2 Pv;e 2 Relative error Ph;e 2 ph;n 2 [kN/m ] [kN/m ] [kN/m ] [kN/m ] [kN/m ] [kN/m ] [%] 21 508 105 21 508 105 0.00 46 1090 234 46 1090 234 0.00 84 4612 916 84 4612 916 0.00 132 10388 1656 132 10388 1656 0.00 136 12404 1887 136 12404 1887 0.00 133 10665 1688 133 10665 1688 0.00 50 1199 253 50 1199 253 0.00 24 568 121 24 568 122 0.00 Pv;e Ph;e [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.82 Table 3.18: Results of benchmark 3-01, Vertical and horizontal moduli of subgrade reaction Benchmark Vert. [-] 1 2 3 4 5 6 7 8 kv;top kv;bot D-G EO P IPELINE kv;bot kh [kN/m ] [kN/m ] [kN/m ] [kN/m ] [kN/m ] [kN/m ] [%] 797 865 606 797 865 606 0.00 904 992 695 904 992 695 0.00 12768 13121 9185 12768 13121 9185 0.00 14365 14720 10304 14365 14720 10304 0.00 14924 15280 10696 14924 15280 10696 0.00 14441 14797 10358 14441 14797 10358 0.00 931 1317 922 931 1317 922 0.00 800 872 611 800 872 611 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3 kv;top 3 kv;bot Relative error kv;top 3 kh 3 kh 3 3 Table 3.19: Results of benchmark 3-01, Maximal axial friction and displacements Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error tmax dv dmax tmax dv dmax tmax dv dmax [kN/m2 ] 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 [mm] 5 10 20 40 80 60 50 35 [mm] 8 8 8 8 8 8 8 8 [kN/m2 ] 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 [mm] 5 10 20 40 80 60 50 35 [mm] 8 8 8 8 8 8 8 8 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.20: Results of benchmark 3-01, Buoyancy control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe Deltares Unit [kg/m] [kg/m] [kg/m] Benchmark 553 412 141 D-G EO P IPELINE 553 412 141 Error [%] 0.00 0.00 0.00 19 of 126 D-G EO P IPELINE, Verification Report Table 3.21: Results of benchmark 3-01, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 284 154 284 290 468 393 468 603 622 690 622 5187 D-G EO P IPELINE Length Force [m] [kN] 0 284 154 284 290 468 393 468 603 622 690 622 5187 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.22: Results of benchmark 3-01, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 127 11 138 138 D-G EO P IPELINE 127 11 138 138 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.23: Results of benchmark 3-01, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 211 24 235 0.000303 0.04973 22 22 246 D-G EO P IPELINE 211 24 235 0.000303 0.04973 22 22 246 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.24: Results of benchmark 3-01, Strength calculation for Combination 2 Result σpy σpx σptest σpm Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 18 9 22 16 D-G EO P IPELINE 18 9 22 16 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.25: Results of benchmark 3-01, Strength calculation for Combination 3 Result σb σa;max σqr σqr σt;max σV;max 20 of 126 Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 211 211 22 219 240 391 D-G EO P IPELINE 211 211 22 219 240 391 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.26: Results of benchmark 3-01, Strength calculation for Combination 4 Result σb σpy σpx σptest σptemp σa;max σqr σqr σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 211 17 8 22 26 219 22 219 374 D-G EO P IPELINE 211 17 8 22 26 219 22 219 374 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.27: Results of benchmark 3-01, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Benchmark 235 213.64 235 363.18 n.a. n.a. Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] D-G EO P IPELINE 235 213.64 235 363.18 n.a. n.a. Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.28: Results of benchmark 3-01, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 6.7 136 64 D-G EO P IPELINE 6.7 136 64 Rel. error [%] 0.00 0.00 0.00 Table 3.29: Results of benchmark 3-01, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark n.a. n.a. n.a. n.a. D-G EO P IPELINE n.a. n.a. n.a. n.a. Error Use D-G EO P IPELINE input file bm3-1.dri to run this benchmark. 3.2 HDD with 2D geometry – Vertical bearing capacity in homogeneous compressible undrained layer with ϕ = 0 Deltares 21 of 126 D-G EO P IPELINE, Verification Report 3.2.1 Description The same configuration as benchmark 3-1 (section 3.1) is used, except that both layers have the same properties: Unit weight above phreatic level Unit weight below phreatic level Cohesion Friction angle 3.2.2 [kN/m3 ] [kN/m3 ] [kN/m2 ] [◦ ] γunsat γsat c ϕ 14 16 5 0 Analytical results Analytical results for the ultimate vertical bearing capacity Pv;e with ϕ = 0 are worked out in an Excel spreadsheet using the formula given in paragraph ”Ultimate vertical bearing capacity” in the Background section of the User Manual of D-G EO P IPELINE. Intermediate results are given in the tables below. Table 3.30: Analytical results for the calculation of the vertical bearing capacity Vert. [-] 1 2 3 4 5 6 7 8 3.2.3 L Z σV ’ hh dC sC Pv;e [m] 20 50 100 200 350 500 650 680 [m] -2.309 -9.235 -20.778 -42.442 -50 -43.481 -10.718 -2.679 [kN/m2 ] 32.322 79.408 148.669 278.651 324 284.883 88.308 37.513 [m] 2.309 9.235 20.778 42.442 50 43.481 10.718 2.679 [-] 0.513 0.595 0.613 0.621 0.622 0.621 0.6 0.527 [-] 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 [kN/m2 ] 68.156 114.885 181.123 304.792 347.901 310.717 123.447 73.41 D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report. Table 3.31: Results of benchmark 3-02, Ultimate vertical bearing capacity Vert. nr. [-] 1 2 3 4 5 6 7 8 Benchmark [kN/m2 ] 68.16 114.88 181.12 304.79 347.9 310.72 123.45 73.41 D-G EO P IPELINE [kN/m2 ] 68.16 114.88 181.12 304.79 347.9 310.72 123.45 73.41 Relative error [kN/m2 ] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-2.dri to run this benchmark. 3.3 HDD with 2D geometry – Polyethylene (PE 80) pipe in two compressible undrained layers 22 of 126 Deltares Group 3: Benchmarks from spreadsheets 3.3.1 Description The same data used for benchmark 3-1 (section 3.1) is used except that polyethylene is used as pipe material instead of steel as shown in Table 3.32. Table 3.32: Pipe material data (benchmark 3-3) Material Young’s modulus (long term) Young’s modulus (short term) Allowable strength (long term) Allowable strength (short term) Tensile factor Outer diameter Nominal wall thickness Unit weight Design pressure Test pressure Temperature variation 3.3.2 Polyethylene Epipe;long Epipe;short Re;long Re;short α D0 dn γb pd pt ∆t PE 80 200 N/mm2 1000 N/mm2 6.3 N/mm2 8 N/mm2 0.65 0.8 m 47.4 mm 9.54 kN/m3 600 kN/m2 834 kN/m2 10◦ Analytical results Analytical results are worked out in an Excel spreadsheet. Strength calculation For the buoyancy control, the pulling forces in the pipeline and the strength calculation, calculations are performed using the formulas given in chapter “Strength pipeline calculation” in the Background section of the User Manual of D-G EO P IPELINE. Intermediate results are given below. Factor of friction pipe-roller Friction pipe-mud Factor of friction pipe-soil Load factor - Design pressure Load factor - Design pressure (combination) Load factor - Test pressure Load factor - Installation Load factor - Soil load Qn Load factor - Temperature Contingency factor - E-modulus Contingency factor - Pulling force Contingency factor - Modulus of subgrade reaction Contingency factor - Soil load Qn Contingency factor - Bending moment Contingency factor - Bending radius Contingency factor - Pressure borehole Effective weight of pipe Weight of pipeline (incl. filling) Uplift force Moment coefficient indirect bottom Moment coefficient indirect top Moment coefficient direct bottom Moment coefficient direct top Deltares f1 f2 f3 fpd fpd;comb fpt finstall fQn1 ftemp fE fpull fkv fQn2 fM fR fpress;bore geff gfill gupw kb ’ kt ’ kb kt 0.1 0.00005 0.2 n.a. n.a. n.a. n.a. n.a. n.a. 1.25 1.4 1.6 1.1 1.4 n.a. 1.1 4.069 0.391 5.529 0.083 0.061 0.138 0.131 [-] [N/mm2 ] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [N/mm] [N/mm] [N/mm] [-] [-] [-] [-] 23 of 126 D-G EO P IPELINE, Verification Report Direct deflection factor Indirect deflection factor Part of pipe filled with water during pull back Cross sections of the pipe Minimal wall thickness Outer radius of the pipeline Inner radius of the pipeline Average radius of the pipeline Moment of inertia of the pipe Moment of inertia of the wall Pipe resisting moment Wall resisting moment Unit weight of drilling fluid Maximum modulus of subgrade reaction Maximum neutral vertical soil load Maximum corrected reduced soil load Maximum neutral horizontal soil load Soil reaction - Left curve Soil reaction - Right curve Soil reaction - Left curve (long term) Soil reaction - Right curve (long term) Characteristic stiffness pipeline-soil Characteristic stiffness pipeline-soil (long term) ky ky ’ Pwater A Atrek Ainw dn;min re ri rg Ib Iw Wb Ww γdrill fluid kv;max qv;n;r;max qn qh;n;r qr;left qr;right qr;left qr;right λ λlong 0.089 0.048 10 112070.789 112070.789 390584.036 47.4 400 352.6 376.3 7966181061 8874.702 19915453 374.46 11 51037.814 184.15 202.565 136.488 6.057 4.543 2.709 2.031 0.0010639 0.001591 [-] [-] [%] [mm2 ] [mm2 ] [mm2 ] [mm] [mm] [mm] [mm] [mm4 ] [mm3 ] [mm4 m] [mm3 m] [kN/m3 ] [kN/m3 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [mm-1 ] [mm-1 ] The total pulling force is the contribution of five components. Results are given in the table below. Table 3.34: Analytical results for the calculation of the five components of the pulling force for the six characteristic points Charac. point 1 2 3 4 5 6 3.3.3 Length [m] 0 153.91 290.04 393.19 602.62 690.49 T1 T2 T3a T3b T3c [kN] 100.79 78.33 58.45 43.4 12.83 0 [kN] 0 144.61 0 45.17 0 82.55 [kN] 0 0 127.91 0 196.78 0 [kN] 0 0 5.72 0 4.29 0 [kN] 0 0 15.25 0 31.55 0 Total [kN] 100.79 222.93 351.94 433.79 635.84 705.56 D-G EO P IPELINE results D-G EO P IPELINE results presented in the tables below can be found in the Report. Table 3.35: Results of benchmark 3-03, Buoyancy control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe 24 of 126 Unit [kg/m] [kg/m] [kg/m] Benchmark 553 146 407 D-G EO P IPELINE 553 146 407 Error [%] 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.36: Results of benchmark 3-03, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 100.79 153.91 222.93 290.04 351.94 393.19 433.79 602.62 635.84 690.49 705.56 829 D-G EO P IPELINE Length Force [m] [kN] 0 100.79 153.91 222.93 290.05 351.94 393.19 433.79 602.63 635.84 690.49 705.56 829 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.37: Results of benchmark 3-03, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.56 1.26 1.62 n.a. D-G EO P IPELINE 0.56 1.26 1.62 n.a. Rel. error [%] 0.00 0.00 0.00 Table 3.38: Results of benchmark 3-03, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.93 8.81 9.42 0.001064 0.00606 0.4 0.4 n.a. D-G EO P IPELINE 0.93 8.81 9.42 0.001064 0.00606 0.4 0.4 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.39: Results of benchmark 3-03, Strength calculation for Combination 2 Result σpy σpx σptest σpm Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 4.78 2.39 6.65 4.14 D-G EO P IPELINE 4.78 2.39 6.65 4.14 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.40: Results of benchmark 3-03, Strength calculation for Combination 3 Result σb σa;max σqr σqr σt;max σV;max Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.19 0.12 0.18 22.47 14.72 n.a. D-G EO P IPELINE 0.19 0.12 0.18 22.47 14.72 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 25 of 126 D-G EO P IPELINE, Verification Report Table 3.41: Results of benchmark 3-03, Strength calculation for Combination 4 Result σb σpy σpx σptest σptemp σa;max σqr σqr σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.19 4.78 2.39 6.65 0.36 2.51 0.18 22.47 n.a. D-G EO P IPELINE 0.19 4.78 2.39 6.65 0.36 2.51 0.18 22.47 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.42: Results of benchmark 3-03, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Benchmark 8 6.3 n.a. n.a. 8 6.3 Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] D-G EO P IPELINE 8 6.3 n.a. n.a. 8 6.3 Rel. error [%] 0.00 0.00 8 6.3 Table 3.43: Results of benchmark 3-03, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 121.4 64 40 D-G EO P IPELINE 121.4 64 40 Rel. error [%] 0.00 0.00 0.00 Table 3.44: Results of benchmark 3-03, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark 396.55 39.66 0 0 D-G EO P IPELINE 396.55 39.66 0 0 Error 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-3.dri to run this benchmark. 3.4 3.4.1 HDD with 2D geometry – Steel pipe in two incompressible drained layers Description The same input values as benchmark 3-1 (section 3.1) are used, only the position of the boundaries between compressible/incompressible layers and drained/undrained layers is different: the boundary coincides with the surface level.Calculations of the pulling forces and the minimum drilling fluid pressure are independent of the soil material. Therefore, in this benchmark, only the calculation of the maximum drilling fluid pressure and the reduced vertical stress are checked. 26 of 126 Deltares Group 3: Benchmarks from spreadsheets 3.4.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Soil mechanical data The soil mechanical data’s are determined using the formulas given in chapter “Calculation of soil mechanical data” in the Background section of the User Manual of D-G EO P IPELINE. Intermediate results are given in the tables below. Table 3.45: Analytical results – General data’s Vert. [-] 1 2 3 4 5 6 7 8 L Z hp HL hh σV ’ σv;H ’ [m] 20 50 100 200 350 500 650 680 [m] -2.309 -9.235 -20.778 -42.442 -50 -43.481 -10.718 -2.679 [m] 1.859 8.785 20.328 41.992 49.55 43.031 10.268 2.229 [m] 1.898 8.824 20.368 42.037 49.6 43.077 10.304 2.265 [m] 2.309 9.235 20.778 42.442 50 43.481 10.718 2.679 [kN/m2 ] 32.322 79.408 171.781 388.418 464 398.806 88.308 37.513 [kN/m2 ] 26.574 76.945 167.676 384.367 460 394.773 85.823 31.715 Table 3.46: Analytical results for the calculation of the neutral reduced vertical stress Vert. [-] 1 2 3 4 5 6 7 8 B1 Fr Fr;max qnr1 qnr2 qv;n qv;r;n [m] 0.935 0.935 0.862 0.862 0.862 0.862 0.935 0.935 [kN/m] n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. [kN/m] n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. [kN/m2 ] n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. [kN/m2 ] n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. [kN/m2 ] 27.808 77.474 168.557 385.237 460.858 395.638 86.322 32.813 [kN/m2 ] 27.808 28.587 26.621 28.21 28.448 28.247 28.299 32.813 Maximum drilling fluid pressures For the maximum drilling fluid pressures in drained conditions, calculations are performed using the formulas given in paragraph “Maximum required drilling fluid pressure” in the Background section of the User Manual of D-G EO P IPELINE [Deltares]. Intermediate results are given in the table below. Deltares 27 of 126 D-G EO P IPELINE, Verification Report Table 3.47: Analytical results for the calculation of the maximum drilling fluid pressures Vert. u 0.9 plimit plastic zone related to : [-] [kN/m2 ] [kN/m2 ] 1 0 85.33 2 62.35 111.81 3 177.78 163.77 4 394.42 285.63 5 470 328.15 6 404.81 291.48 7 77.18 116.82 8 0 88.25 3.4.3 ppilot ppreream pback deformation bore hole [kN/m2 ] [kN/m2 ] [kN/m2 ] 93.1 83.32 75.01 124.13 123.26 122.1 181.95 181.77 181.53 317.36 317.32 317.26 364.6 364.57 364.53 323.86 323.82 323.76 129.72 129.07 128.19 96.77 88.89 81.63 ppilot [kN/m2 ] 93.1 124.13 181.95 317.36 364.6 323.86 129.72 96.77 ppreream soil cover [kN/m2 ] 83.32 123.26 181.77 317.32 364.57 323.82 129.07 88.89 pback [kN/m2 ] 75.01 122.1 181.53 317.26 364.53 323.76 128.19 81.63 D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report. Table 3.48: Results of benchmark 3-04, Vertical soil stresses Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error qv;p qv;n qv;r;n qv;p qv;n qv;r;n qv;p qv;n qv;r;n [kN/m2 ] 47 234 916 1656 1887 1688 253 60 [kN/m2 ] 28 77 169 385 461 396 86 33 [kN/m2 ] 28 29 27 28 28 28 28 33 [kN/m2 ] 47 234 916 1656 1887 1688 253 60 [kN/m2 ] 28 77 169 385 461 396 86 33 [kN/m2 ] 28 29 27 28 28 28 28 33 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.49: Results of benchmark 3-04, Maximum allowable drilling fluid pressure (plastic zone related to deformation bore hole) Vert. [-] 1 2 3 4 5 6 7 8 Benchmark PrePull ream back 2 2 [kN/m ] [kN/m ] [kN/m2 ] 48 48 48 152 152 152 503 503 503 992 992 992 1153 1153 1153 1014 1014 1014 175 175 175 53 53 53 Pilot 28 of 126 D-G EO P IPELINE PrePull ream back 2 2 [kN/m ] [kN/m ] [kN/m2 ] 48 48 48 152 152 152 503 503 503 992 992 992 1153 1153 1153 1015 1015 1015 175 175 175 53 53 53 Pilot Pilot [%] 0.00 0.00 0.00 0.00 0.00 0.1 0.00 0.00 Relative error PrePull ream back [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.1 0.1 0.00 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.50: Results of benchmark 3-04, Maximum allowable drilling fluid pressure (plastic zone related to soil cover) Benchmark PrePull ream back [kN/m2 ] [kN/m2 ] [kN/m2 ] 88 74 62 221 221 221 800 800 800 1545 1545 1545 1785 1785 1785 1579 1579 1579 249 249 249 96 86 74 Vert. Pilot [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE PrePull ream back [kN/m2 ] [kN/m2 ] [kN/m2 ] 88 74 62 221 221 221 800 800 800 1545 1545 1545 1785 1785 1785 1579 1579 1579 249 249 249 96 86 74 Pilot Pilot [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Relative error PrePull ream back [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-4.dri to run this benchmark. 3.5 3.5.1 HDD with 2D geometry – Steel pipe in a sequence of a compressible undrained layer and a compressible drained layer Description The same input data’s as benchmark 3-1 (section 3.1) are used, except that the position of the boundary between undrained/drained layers is different: the boundary coincides with the top of the sand layer. Changing the position of the boundary between undrained/drained layers will only effect the maximum drilling fluid pressures calculation. 3.5.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Maximum drilling fluid pressures For the maximum drilling fluid pressures in drained conditions, calculations are performed using the formulas given in paragraph “Maximum required drilling fluid pressure” in the Background section of the User Manual of D-G EO P IPELINE [Deltares]. Intermediate results are given in the table below. Table 3.51: Analytical results for the calculation of the maximum drilling fluid pressures Vert. u 0.9 plimit plastic zone related to : [-] [kN/m2 ] [kN/m2 ] 1 0 88.6 2 62.35 122.71 3 177.78 180.76 4 394.42 302.62 5 470 345.13 6 404.81 308.46 7 77.18 129.29 8 0 91.95 Deltares ppilot ppreream pback deformation bore hole [kN/m2 ] [kN/m2 ] [kN/m2 ] 95.29 80.21 69.47 136.09 134.22 131.85 200.46 197.59 194.1 336.23 336.09 335.9 383.47 383.39 383.27 342.72 342.59 342.41 143.47 142.02 140.14 99.75 87.08 77.24 ppilot [kN/m2 ] 95.29 136.09 200.46 336.23 383.47 342.72 143.47 99.75 ppreream soil cover [kN/m2 ] 80.21 134.22 197.59 336.09 383.39 342.59 142.02 87.08 pback [kN/m2 ] 69.47 131.85 194.1 335.9 383.27 342.41 140.14 77.24 29 of 126 D-G EO P IPELINE, Verification Report The intermediate analytical results for the calculation of the maximum drilling fluid pressures in drained conditions are the same as benchmark 3-4 (see section 3.4.2). 3.5.3 D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report. Table 3.52: Results of benchmark 3-05, Maximum allowable drilling fluid pressure (plastic zone related to deformation bore hole) Benchmark PrePull ream back [kN/m2 ] [kN/m2 ] [kN/m2 ] 89 80 69 185 185 185 503 503 503 992 992 992 1153 1153 1153 1014 1014 1014 206 206 206 92 87 77 Pilot 1 2 3 4 5 6 7 8 D-G EO P IPELINE PrePull ream back [kN/m2 ] [kN/m2 ] [kN/m2 ] 89 80 69 185 185 185 502 502 502 992 992 992 1153 1153 1153 1014 1014 1014 206 206 206 92 87 77 Pilot Pilot [%] 0.00 0.00 0.2 0.00 0.00 0.00 0.00 0.00 Relative error PrePull ream back [%] [%] 0.00 0.00 0.00 0.00 0.2 0.2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.53: Results of benchmark 3-05, Maximum allowable drilling fluid pressure (plastic zone related to soil cover) nr. [-] 1 2 3 4 5 6 7 8 Benchmark PrePull ream back 2 2 [kN/m ] [kN/m ] [kN/m2 ] 89 80 69 185 185 185 800 767 697 1545 1545 1545 1785 1785 1785 1579 1579 1579 206 206 206 92 87 77 Pilot D-G EO P IPELINE PrePull ream back 2 2 [kN/m ] [kN/m ] [kN/m2 ] 89 80 69 185 185 185 799 766 696 1545 1545 1545 1785 1785 1785 1578 1578 1578 206 206 206 92 87 77 Pilot Pilot [%] 0.00 0.00 0.13 0.00 0.00 0.06 0.00 0.00 Relative error PrePull ream back [%] [%] 0.00 0.00 0.00 0.00 0.13 0.14 0.00 0.00 0.00 0.00 0.06 0.06 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-5.dri to run this benchmark. 3.6 3.6.1 HDD with 2D geometry – Steel pipe in a sequence of an incompressible undrained layer and an incompressible drained layer Description The same input data’s as benchmark 3-1 (section 3.1) are used, except for the position of the boundary between undrained/drained layers which coincides with the top of the sand layer and for the boundary between compressible/incompressible layers which coincides with the top of the ground line. Changing the position of the boundary between undrained/drained layers will only affect the maximum drilling fluid pressures calculation and changing the position of the boundary between compressible/incompressible layers will only affect the neutral reduced 30 of 126 Deltares Group 3: Benchmarks from spreadsheets vertical stress. 3.6.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Soil mechanical data The soil mechanical data’s are determined using the formulas given in chapter “Calculation of soil mechanical data” in the Background section of the User Manual of D-G EO P IPELINE. Intermediate results are given in the tables below. Analytical results for the neutral reduced vertical stress are the same as benchmark 3-4 (section 3.4.2) because the position of the boundary between compressible/incompressible layers is the same. Maximum drilling fluid pressures For the maximum drilling fluid pressures in drained conditions, calculations are performed using the formulas given in paragraph “Maximum required drilling fluid pressure” in the Background section of the User Manual of D-G EO P IPELINE [Deltares]. Analytical results for the maximum drilling fluid pressures are the same as benchmark 3-5 (section 3.5.2) because the position of the boundary between undrained/drained layers is the same. 3.6.3 D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report. Table 3.54: Results of benchmark 3-06, Vertical soil stresses Benchmark nr. [-] 1 2 3 4 5 6 7 8 qv;p qv;n 2 D-G EO P IPELINE qv;r;n 2 qv;p 2 qv;n 2 Relative error qv;r;n 2 qv;p 2 [kN/m ] [kN/m ] [kN/m ] [kN/m ] [kN/m ] [kN/m ] [%] 47 28 28 47 28 28 0.00 234 77 29 234 77 29 0.00 916 169 27 916 169 27 0.00 1656 385 28 1656 385 28 0.00 1887 461 28 1887 461 28 0.00 1688 396 28 1688 396 28 0.00 253 86 28 253 86 28 0.00 60 33 33 60 33 33 0.00 qv;n qv;r;n [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-6.dri to run this benchmark. 3.7 3.7.1 HDD with 3D geometry – Steel pipe in 4 layers – Compressible border above drainage border Description The pipe is constructed in four compressible undrained layers with the characteristics given in Table 3.57. The boundaries between compressible/uncompressible layers and drained/undrained layers are respectively situated at the bottom of the second and third layers. The ground level is not plane as shown in Figure 3.3 and the phreatic line is at depth Zphreatic = -5 m. The hydraulic head at the surface level is 1 m and 10 m at the bottom (i.e. Z = -46 m). The steel pipe properties are given in Table 3.56. Calculations are performed for 8 verticals with Deltares 31 of 126 D-G EO P IPELINE, Verification Report L coordinates of 60, 100, 150, 170, 1000, 1650, 1775 and 1800 m. The configuration of the pipeline is given by: Xleft 50 m X-coordinate of the left entry point Yleft -5 m Y-coordinate of the left entry point Zleft -2 m Z-coordinate of the left entry point Xright 1800 m X-coordinate of the right exit point Yright 104.21 m Y-coordinate of the right exit point Zright 10 m Z-coordinate of the right exit point ϕleft 13◦ Left angle of the pipe ϕright 15◦ Right angle of the pipe Zbottom -45 m Lowest level of the pipe Rleft 1300 m Bending radius of the pipe at the left side Rright 1050 m Bending radius of the pipe at the right side Rrol 800 m Bending radius in pipe string (on rollers) with two horizontal bendings: X-coordinate of the first point X1 Z-coordinate of the first point Z1 X-coordinate of the second point X2 Z-coordinate of the second point Z2 Bending radius Direction [m] [m] [m] [m] [m] bending 1 450 10 687.664 61.157 700.004 Right bending 2 800 106.880 1313.615 171.288 1000.008 Left Table 3.55: Soil material properties (benchmark 3-07) Unit weight above phreatic level Unit weight below phreatic level Cohesion Angle of internal friction Undrained cohesion top Undrained cohesion bottom Young modulus top Young modulus bottom Poisson ratio γunsat γsat c ϕ Cu;top Cu;bottom Eu;top Eu;bottom ν [kN/m3 ] [kN/m3 ] [kN/m2 ] [◦ ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [-] Mat 1 18 20 0.2 35 1 2 20000 25000 0.5 Mat 2 17 19 1.5 30 3 5 30000 40000 0.45 Mat 3 14 16 5 0 30 25 1500 2000 0.25 Mat 4 11 13 20 15 50 40 1000 500 0.35 Table 3.56: Pipe material data (benchmark 3-07) Material Negative wall thickness tolerance Yield strength Partial material factor Partial material factor for test pressure Young’s modulus Outer diameter Nominal wall thickness Unit weight Design pressure Test pressure Temperature variation 32 of 126 δt Re γm γm;test Eb D0 dn γb pd pt ∆t [%] [N/mm2 ] [-] [-] [N/mm2 ] [m] [mm] [kN/m3 ] [kN/m2 ] [kN/m2 ] [◦ ] Steel 25 200 1.3 1.15 180500 1.5 35 65 500 900 10 Deltares Group 3: Benchmarks from spreadsheets Figure 3.3: 3D view of the pipeline configuration (benchmark 3-7) 3.7.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Soil mechanical data The soil mechanical data’s are determined using the formulas given in chapter “Calculation of soil mechanical data” in the Background section of the User Manual of D-G EO P IPELINE. The maximal axial friction between the pipe and the drilling fluid is constant along the pipeline and equal to f2 = 50 N/m2 . The displacement necessary to develop the maximal axial friction along the pipeline is estimated between 6 and 9 mm (= 7.5 mm). Strength calculation For the buoyancy control, the pulling forces in the pipeline and the strength calculation, calculations are performed using the formulas given in chapter “Strength pipeline calculation” in the Background section of the User Manual of D-G EO P IPELINE. The length of the pipe in the borehole at the 10 characteristic points (see Figure 3.3) is: Table 3.57: Position of the characteristic points (benchmark 3-07a) Point 1 2 3 4 5 6 7 8 9 10 Deltares L-coord. [m] 50 91.93 384.37 450.28 694.63 815.91 1339.51 1487 1758.76 1830.5 X-coord. [m] 50 91.9 384.13 450 687.66 800 1313.62 1459.72 1728.93 1800 Z-coord. [m] -2 -11.68 -45 -45 -45 -45 -45 -45 -9.22 10 Traject length [m] 0 43.036 337.997 403.908 648.255 769.539 1293.138 1440.628 1715.518 1789.786 33 of 126 D-G EO P IPELINE, Verification Report Hereafter are some intermediate results used for the pulling force and the strength calculations: f1 f2 f3 fpd fpd;comb fpt finstall fQn1 ftemp fE fpull fkv fQn2 fM fR fpress;bore geff gfill gupw kb ’ kt ’ kb kt ky ky ’ Pwater A Atrek Ainw Minimal wall thickness dn;min Outer radius of the pipeline re Inner radius of the pipeline ri Average radius of the pipeline rg Moment of inertia of the pipe Ib Moment of inertia of the wall Iw Pipe resisting moment Wb Wall resisting moment Ww Unit weight of drilling fluid γdrill fluid Maximum modulus of subgrade reaction kv;max Maximum neutral vertical soil load qv;n;r;max Maximum traffic load qT;max Max. red. neutral vertical soil load (incl. traffic load) qv;n;r;maxT Max. corrected red. soil load (without traffic load) qn Max. corrected red. soil load (incl. traffic load) qnT Maximum neutral horizontal soil load qh;n;r Soil reaction - Left curve qr;left Soil reaction - Right curve qr;right Soil reaction - Left curve (long term) qr;left Soil reaction - Right curve (long term) qr;right Characteristic stiffness pipeline-soil λ Factor of friction pipe-roller Friction pipe-mud Factor of friction pipe-soil Load factor - Design pressure Load factor - Design pressure (combination) Load factor - Test pressure Load factor - Installation Load factor - Soil load Qn Load factor - Temperature Contingency factor - E-modulus Contingency factor - Pulling force Contingency factor - Modulus of subgrade reaction Contingency factor - Soil load Qn Contingency factor - Bending moment Contingency factor - Bending radius Contingency factor - Pressure borehole Effective weight of pipe Weight of pipeline (incl. filling) Uplift force Moment coefficient indirect bottom Moment coefficient indirect top Moment coefficient direct bottom Moment coefficient direct top Direct deflection factor Indirect deflection factor Part of pipe filled with water during pull back Cross sections of the pipe 34 of 126 0.2 0.00035 0.3 1.1 1.3 0.9 1.2 1.3 1.2 1.4 1.1 1.1 1.2 1.15 1.3 1.15 10.093 2.409 22.973 0.073 0.056 0.139 0.139 0.091 0.043 15 121535.457 161085.163 1606060.704 26.25 750 715 732.5 43240291745 3572.917 57653722 204.167 13 20467.554 154.787 5 154.787 241.467 241.467 101.846 52.606 65.131 n.a. n.a. 0.0001771 [-] [N/mm2 ] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [N/mm] [N/mm] [N/mm] [-] [-] [-] [-] [-] [-] [%] [mm2 ] [mm2 ] [mm2 ] [mm] [mm] [mm] [mm] [mm4 ] [mm3 ] [mm4 m] [mm3 m] [kN/m3 ] [kN/m3 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [mm-1 ] Deltares Group 3: Benchmarks from spreadsheets Characteristic stiffness pipeline-soil (long term) λlong [mm-1 ] n.a. The total pulling force is the contribution of five components. Two cases are checked: Case A (bm3-7a): pulling direction from left to right (see results in Table 3.59); Case B (bm3-7b): pulling direction from right to left (see results in Table 3.60). Table 3.59: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points for case a Charac. point 1 2 3 4 5 6 7 8 9 10 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 4610.36 4499.5 3739.7 3569.92 2940.5 2628.08 1279.33 899.4 191.31 0 [kN] 0 201.29 0 308.29 0 567.29 0 689.86 0 347.38 [kN] 0 0 1379.62 0 2702.75 0 3540.94 0 1285.74 0 [kN] 0 0 839.93 0 889.15 0 1797.78 0 1039.92 0 [kN] 0 0 418.44 0 0 0 0 0 823.38 0 Total [kN] 4610.36 4700.79 6578.99 6717.5 9679.98 9934.85 13924.82 14234.75 16675.7 16831.77 Table 3.60: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points for case b Charac. point 10 9 8 7 6 5 4 3 2 1 Deltares Length [m] 0 74.27 349.16 496.65 1020.25 1141.53 1385.88 1451.79 1746.75 1789.79 T1 T2 T3a T3b T3c [kN] 4610.36 4419.05 3710.95 3331.03 1982.28 1669.86 1040.44 870.66 110.86 0 [kN] 0 347.38 0 689.86 0 567.29 0 308.29 0 201.29 [kN] 0 0 1285.74 0 3540.94 0 2702.75 0 1379.62 0 [kN] 0 0 1039.92 0 1372.13 0 1336.7 0 839.93 0 [kN] 0 0 499.97 0 0 0 0 0 724.1 0 Total [kN] 4610.36 4766.42 6883.96 7193.89 10758.22 11013.08 14423.12 14561.63 16745.49 16835.92 35 of 126 D-G EO P IPELINE, Verification Report 3.7.3 D-G EO P IPELINE results D-G EO P IPELINE results presented in the tables below can be found in the Report. Table 3.61: Results of benchmark 3-07a, Vertical soil stresses Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error qv;p qv;n qv;r;n qv;p qv;n qv;r;n qv;p qv;n qv;r;n [kN/m2 ] 24 74 582 913 2006 1610 284 203 [kN/m2 ] 19 24 114 156 442 346 155 83 [kN/m2 ] 19 24 52 60 52 107 155 83 [kN/m2 ] 24 74 582 913 2006 1610 284 204 [kN/m2 ] 19 24 114 156 442 346 155 83 [kN/m2 ] 19 24 53 59 52 107 155 83 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.49 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 1.89 1.69 0.00 0.00 0.00 0.00 Table 3.62: Results of benchmark 3-07a, Neutral horizontal soil stress and bearing capacities Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error qh;n Pv;e Ph;e qh;n Pv;e Ph;e qh;n Pv;e Ph;e [kN/m2 ] 12 16 34 39 34 71 102 55 [kN/m2 ] 442 196 3332 4449 21154 16672 1233 831 [kN/m2 ] 98 115 794 1020 2006 1610 284 211 [kN/m2 ] 12 16 35 39 34 71 102 55 [kN/m2 ] 442 196 3332 4449 21154 16672 1233 831 [kN/m2 ] 99 115 794 1020 2006 1610 284 211 [%] 0.00 0.00 2.86 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 1.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.63: Results of benchmark 3-07a, Vertical and horizontal moduli of subgrade reaction Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error kv;top kv;bot kh kv;top kv;bot kh kv;top kv;bot kh [kN/m3 ] 253 188 3871 9140 8287 10516 184 233 [kN/m3 ] 190 2365 12208 13024 9074 7949 309 166 [kN/m3 ] 133 1655 8546 9117 6352 5564 216 116 [kN/m3 ] 253 188 3871 9140 8287 10516 184 233 [kN/m3 ] 190 2365 12208 13024 9074 7949 309 166 [kN/m3 ] 133 1655 8546 9117 6352 5564 216 116 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 36 of 126 Deltares Group 3: Benchmarks from spreadsheets Table 3.64: Results of benchmark 3-07a, Maximal axial friction and displacements Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error tmax dv dmax tmax dv dmax tmax dv dmax [kN/m2 ] 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 [mm] 5 10 20 40 80 60 50 35 [mm] 8 8 8 8 8 8 8 8 [kN/m2 ] 0 0 0 0 0 0 0 0 [mm] 5 10 20 40 80 60 50 35 [mm] 8 8 8 8 8 8 8 8 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.65: Results of benchmark 3-07a, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 4610 43 4701 338 6579 1441 14235 1716 16676 1790 16832 0 D-G EO P IPELINE Length Force [m] [kN] 0 4610 43 4701 338 6579 1441 14235 1716 16676 1790 16832 0 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.66: Results of benchmark 3-07b, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 4610 74 4766 349 6884 1452 14562 1747 16745 1790 16836 0 D-G EO P IPELINE Length Force [m] [kN] 0 4610 74 4766 349 6884 1452 14562 1747 16745 1790 16836 0 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input files bm3-7a.dri and bm3-7b.dri to run this benchmark. 3.8 3.8.1 Special strength analysis Description The same input values as for benchmark 3-7a (section 3.7) are used. Calculations are performed using the Special Stress Analysis calculation which means that the maximum modulus of subgrade reaction and the maximum reduced soil load are input values instead of calculated values: kV;max = 45000 kN/m3 , qn;max = 0.14 N/mm2 and R = 700 m. Deltares 37 of 126 D-G EO P IPELINE, Verification Report 3.8.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Strength calculation For the buoyancy control, the pulling forces in the pipeline and the strength calculation, calculations are performed using the formulas given in chapter “Strength pipeline calculation” in the Background section of the User Manual of D-G EO P IPELINE. The total pulling force is the contribution of five components. Results are given in Table 3.67. Table 3.67: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-08) Charac. point 2 3 4 5 6 7 8 9 10 3.8.3 Length [m] 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 0 T1 T2 T3a T3b T3c [kN] 4499.5 3739.7 3569.92 2940.5 2628.08 1279.33 899.4 191.31 0 0 [kN] 201.29 0 308.29 0 567.29 0 689.86 0 347.38 0 [kN] 0 1379.62 0 3042.32 0 3778.64 0 1285.74 0 0 [kN] 0 1022.78 0 944.88 0 1926.4 0 1266.3 0 0 [kN] 0 430.86 0 0 0 0 0 856.4 0 0 Total [kN] 4700.79 6774.25 6912.76 10270.54 10525.4 14881.69 15191.62 17891.97 18048.04 0 D-G EO P IPELINE results A Special Stress Analysis calculation must be performed by selecting Special Stress Analysis for the Start menu. D-G EO P IPELINE results presented in the tables below can be found in the Report. Table 3.68: Results of benchmark 3-08, Buoyancy Control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe Unit [kg/m] [kg/m] [kg/m] Benchmark 2297 1288 1009 D-G EO P IPELINE 2297 1288 1009 Error [%] 0.00 0.00 0.00 Table 3.69: Results of benchmark 3-08, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force 38 of 126 Benchmark Length Force [m] [kN] 0 4610 43 4701 338 6774 1441 15192 1716 17892 1790 18048 0 D-G EO P IPELINE Length Force [m] [kN] 0 4610 43 4701 338 6774 1441 15192 1716 17892 1790 18048 0 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.70: Results of benchmark 3-08, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 304 50 354 354 D-G EO P IPELINE 304 50 354 354 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.71: Results of benchmark 3-08, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 347 196 543 0.000216 0.1449 57 57 574 D-G EO P IPELINE 347 196 543 0.000216 0.1449 57 57 574 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.72: Results of benchmark 3-08, Strength calculation for Combination 2 Result σpy σpx σptest σpm Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 15 8 23 13 D-G EO P IPELINE 15 8 23 13 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.73: Results of benchmark 3-08, Strength calculation for Combination 3 Result σb σa;max σqr σqr σt;max σV;max Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 347 347 57 164 222 496 D-G EO P IPELINE 347 347 57 164 222 496 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 39 of 126 D-G EO P IPELINE, Verification Report Table 3.74: Results of benchmark 3-08, Strength calculation for Combination 4 Result σb σpy σpx σptest σptemp σa;max σqr σqr σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 347 18 9 23 15 356 57 164 484 D-G EO P IPELINE 347 18 9 23 15 356 57 164 484 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.75: Results of benchmark 3-08, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Benchmark 173.91 153.85 169.23 261.54 n.a. n.a. Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] D-G EO P IPELINE 173.91 153.85 169.23 261.54 n.a. n.a. Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.76: Results of benchmark 3-08, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 16.1 255 120 D-G EO P IPELINE 16.1 255 120 Rel. error [%] 0.00 0.00 0.00 Table 3.77: Results of benchmark 3-08, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark n.a. n.a. n.a. n.a. D-G EO P IPELINE n.a. n.a. n.a. n.a. Error Use D-G EO P IPELINE input file bm3-8.dri to run this benchmark. 3.9 HDD with 3D geometry – Bundled pipeline (3 steel pipes and 2 PE pipes) 40 of 126 Deltares Group 3: Benchmarks from spreadsheets 3.9.1 Description The same input as for benchmark 3-7a (section 3.7) is used except that five pipes are used instead of one. Their characteristics are given in Table 3.78. Table 3.78: Pipe material data (benchmark 3-09) PE80 Synthetic Material δt Eb Epipe;long Reb Reb;long γm γm;test α D0 dn γb pd pt ∆T 3.9.2 [%] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [-] [-] [-] [mm] [mm] [kN/m3 ] [Bar] [Bar] [◦ C] 1000 200 8 6.3 FE385 Steel 10 205800 385 PE100 Synthetic 1200 300 10 8 1.2 1.1 0.65 50 3.7 9.54 3 6 5 219.1 22.2 85 3 6 4 0.5 355 26.1 13 5 5.5 6 FE360 Steel 15 205800 Steel 1 Steel 25 180500 360 200 1.1 1.05 1.3 1.15 457 9.52 78.5 4 6.5 8 1000 35 65 5 9 10 Analytical results Analytical results are worked out in an Excel spreadsheet. Strength calculation for bundled pipelines For the buoyancy control, the pulling forces in the pipeline and the strength calculation, calculations are performed using the formulas given in chapter “Strength pipeline calculation” in the Background section of the User Manual of D-G EO P IPELINE. The pulling force is calculated for an equivalent pipeline with the parameters of the bundle: EIeq = n X EIi (3.1) i=1 Gtot = n X π i=1 Deq = f × 4 2 − D0;i n X π (D0;i − 2 × dn;i )2 × γi 4 D0;i (3.2) (3.3) i=1 Gtot π 2 = Deq − (Deq − 2 × dn;eq )2 γeq 4 Deltares (3.4) 41 of 126 D-G EO P IPELINE, Verification Report q Deq − dn;eq = 2 − Deq Pn i=1 2 − (D0;i − 2 × dn;i )2 D0;i (3.5) 2 The properties of the equivalent pipe are: Deq dn;eq γeq Ieq Eeq kV;max;eq [mm] [mm] [kN/m3 ] [m4 ] [N/mm2 ] [kN/m3 ] 1284.11 41.16 58.92 0.031073 74520.87 24550.63 The calculated pulling force is acting on all the pipelines in the bundle. The magnitude of the pulling force of a single pipeline can be determined as follows: Ai Ti = Pn i=1 Ai × Ttotal where Ai = π 2 π D0;i − (D0;i − 2 × dn;i )2 4 4 (3.6) The total pulling force is the contribution of five components. Results are given in the 6 tables below, for the equivalent pipeline and for each single pipeline. Table 3.79: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-09) Charac. point 1 2 3 4 5 6 7 8 9 10 42 of 126 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 3887.97 3794.48 3153.74 3010.56 2479.76 2216.29 1078.88 758.48 161.33 0 [kN] 0 103.16 0 157.99 0 290.72 0 353.53 0 178.02 [kN] 0 0 707.01 0 1216.92 0 1696.91 0 658.9 0 [kN] 0 0 339.9 0 549.03 0 989.82 0 420.82 0 [kN] 0 0 292.32 0 0 0 0 0 417.14 0 Total [kN] 3887.97 3897.64 4596.13 4610.93 5846.09 5873.34 7422.66 7455.79 8355.52 8372.2 Deltares Group 3: Benchmarks from spreadsheets Table 3.80: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-09) Charac. point 1 2 3 4 5 6 7 8 9 10 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 2.6 2.54 2.11 2.02 1.66 1.48 0.72 0.51 0.11 0 [kN] 0 2.6 0 3.98 0 7.33 0 8.92 0 4.49 [kN] 0 0 17.83 0 14.77 0 31.65 0 16.62 0 [kN] 0 0 0 0 3.66 0 10.66 0 0 0 [kN] 0 0 1.53 0 0 0 0 0 8.25 0 Total [kN] 2.6 5.14 24.08 27.97 46.05 53.21 94.76 103.46 127.93 132.31 Table 3.81: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-09) Charac. point 1 2 3 4 5 6 7 8 9 10 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 430.7 420.34 349.36 333.5 274.7 245.52 119.52 84.02 17.87 0 [kN] 0 19.57 0 29.98 0 55.16 0 67.08 0 33.78 [kN] 0 0 134.16 0 124.15 0 247.26 0 125.03 0 [kN] 0 0 7.01 0 62.31 0 120.77 0 8.67 0 [kN] 0 0 34.65 0 0 0 0 0 66.45 0 Total [kN] 430.7 439.92 544.75 558.87 686.52 712.5 954.53 986.12 1120.12 1136.03 Table 3.82: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-09) Charac. point 1 2 3 4 5 6 7 8 9 10 Deltares Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 164.16 160.21 133.16 127.11 104.7 93.58 45.55 32.03 6.81 0 [kN] 0 27.49 0 42.1 0 77.47 0 94.21 0 47.44 [kN] 0 0 188.42 0 156.95 0 335.07 0 175.59 0 [kN] 0 0 0.46 0 49.7 0 124.81 0 0.57 0 [kN] 0 0 23.74 0 0 0 0 0 88.3 0 Total [kN] 164.16 187.7 373.27 409.33 593.56 659.91 1071.77 1152.45 1391.71 1432.33 43 of 126 D-G EO P IPELINE, Verification Report Table 3.83: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-09) Charac. point 1 2 3 4 5 6 7 8 9 10 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 456.95 445.96 370.66 353.83 291.44 260.48 126.8 89.14 18.96 0 [kN] 0 32.68 0 50.04 0 92.09 0 111.98 0 56.39 [kN] 0 0 223.95 0 229.82 0 428.55 0 208.71 0 [kN] 0 0 23.85 0 86.94 0 187.44 0 29.53 0 [kN] 0 0 44.23 0 0 0 0 0 111.14 0 Total [kN] 456.95 478.64 695.36 728.57 982.95 1044.07 1526.37 1600.7 1879.89 1917.32 Table 3.84: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-09) Charac. point 1 2 3 4 5 6 7 8 9 10 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 2833.56 2765.42 2298.45 2194.1 1807.25 1615.24 786.29 552.78 117.58 0 [kN] 0 76.94 0 117.84 0 216.84 0 263.69 0 132.78 [kN] 0 0 527.34 0 1039.44 0 1357.92 0 491.46 0 [kN] 0 0 324.47 0 425.87 0 782.44 0 401.73 0 [kN] 0 0 219.2 0 0 0 0 0 323.45 0 Total [kN] 2833.56 2842.36 3446.4 3459.89 4538.35 4563.17 5874.58 5904.76 6686.2 6701.4 In this benchmark, the stiffness of the steel and PE materials is significantly different. Therefore, a different approach is applied. In addition to the previous equation, the total pulling force is divided over the stiff steel pipelines. Table 3.85 gives the maximal calculated pulling forces for each pipeline in both cases: single and bundled calculation. Table 3.85: Maximal pulling forces without partial factors (bm3-09) Ai Tmax;i (Single) [mm2 ] [kN] PE80 538.19 132.31 FE385 13732.47 1346.74 PE100 26968.34 1432.33 FE360 13383.21 892.91 Steel 1 106107.29 6369.34 Bundled (all) 160729.50 8024.37 Bundled (only steel) 133222.97 1) 827.11 = 8024.37 × 13732.47 / 133222.97 2) 806.11 = 8024.37 × 13383.21 / 133222.97 3) 6391.12 = 8024.37 × 106107.29 / 133222.97 44 of 126 Tmax;i (Bundled steel pipes) [kN] 132.56 827.111) 1432.33 806.112) 6391.123) Deltares Group 3: Benchmarks from spreadsheets 3.9.3 D-G EO P IPELINE results D-G EO P IPELINE results presented in the tables below can be found in the Report. Table 3.86: Results of benchmark 3-09, Buoyancy control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe Benchmark 1414 1086 328 Unit [kg/m] [kg/m] [kg/m] D-G EO P IPELINE 1415 1086 328 Error [%] 0.07 0.00 0.00 Table 3.87: Results of benchmark 3-09, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 3887.97 43.04 3897.64 338 4596.13 1440.63 7455.79 1715.52 8355.52 1789.79 8372.2 4 D-G EO P IPELINE Length Force [m] [kN] 0 3887.97 43.04 3897.64 338 4596.13 1440.63 7455.8 1715.52 8355.52 1789.79 8372.21 4 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.88: Results of benchmark 3-09 for pipe nr. 1, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.04 5.32 5.34 n.a. D-G EO P IPELINE 0.04 5.32 5.34 n.a. Rel. error [%] 0.00 0.00 0.00 Table 3.89: Results of benchmark 3-09 for pipe nr. 1, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.04 270.44 270.46 0.016823 0.00038 0.01 0.01 n.a. D-G EO P IPELINE 0.04 270.44 270.46 0.016823 0.00038 0.01 0.01 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 45 of 126 D-G EO P IPELINE, Verification Report Table 3.90: Results of benchmark 3-09 for pipe nr. 1, Strength calculation for Combination 2 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σpy σpx σptest σpm Benchmark 1.89 0.94 3.78 1.64 D-G EO P IPELINE 1.89 0.94 3.78 1.64 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.91: Results of benchmark 3-09 for pipe nr. 1, Strength calculation for Combination 3 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σb σa;max σqr σqn σt;max σV;max Benchmark 0.01 0.01 0.01 5.96 3.88 n.a. D-G EO P IPELINE 0.01 0.01 0.01 5.96 3.88 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 Table 3.92: Results of benchmark 3-09 for pipe nr. 1, Strength calculation for Combination 4 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Benchmark 0.01 1.89 0.94 3.78 0.18 0.95 0.01 5.96 n.a. D-G EO P IPELINE 0.01 1.89 0.94 3.78 0.18 0.95 0.01 5.96 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.93: Results of benchmark 3-09 for pipe nr. 1, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 6.4 5.04 n.a. n.a. 6.4 5.04 D-G EO P IPELINE 6.4 5.04 n.a. n.a. 6.4 5.04 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.94: Results of benchmark 3-09 for pipe nr. 1, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) 46 of 126 Unit [mm] [mm] [mm] Benchmark 2.4 4 2.8 D-G EO P IPELINE 2.4 4 2.8 Rel. error [%] 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.95: Results of benchmark 3-09 for pipe nr. 1, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark 607.55 60.76 0 0 D-G EO P IPELINE 607.55 60.76 0 0 Error 0.00 0.00 0.00 0.00 Table 3.96: Results of benchmark 3-09 for pipe nr. 2, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 55.83 42.33 98.16 98.16 D-G EO P IPELINE 55.83 42.33 98.16 98.16 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.97: Results of benchmark 3-09 for pipe nr. 2, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 63.81 91.14 154.95 0.000831 0.02618 0.51 0.51 155.21 D-G EO P IPELINE 63.81 91.14 154.95 0.000831 0.02618 0.51 0.51 155.2 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 Table 3.98: Results of benchmark 3-09 for pipe nr. 2, Strength calculation for Combination 2 Result σpy σpx σptest σpm Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 1.66 0.83 2.69 1.44 D-G EO P IPELINE 1.66 0.83 2.69 1.44 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.99: Results of benchmark 3-09 for pipe nr. 2, Strength calculation for Combination 3 Result σb σa;max σqr σqn σt;max σV;max Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 63.81 63.81 0.51 4.06 4.57 66.21 D-G EO P IPELINE 63.81 63.81 0.51 4.06 4.57 66.21 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 47 of 126 D-G EO P IPELINE, Verification Report Table 3.100: Results of benchmark 3-09 for pipe nr. 2, Strength calculation for Combination 4 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Benchmark 63.81 1.96 0.98 2.69 11.56 64.79 0.51 4.06 66.27 D-G EO P IPELINE 63.81 1.96 0.98 2.69 11.56 64.79 0.51 4.06 66.27 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.101: Results of benchmark 3-09 for pipe nr. 2, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 350 320.83 352.92 545.42 n.a. n.a. D-G EO P IPELINE 350 320.83 352.92 545.42 n.a. n.a. Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.102: Results of benchmark 3-09 for pipe nr. 2, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 0 37.2 17.5 D-G EO P IPELINE 0 37.2 17.5 Rel. error [%] 0.00 0.00 0.00 Table 3.103: Results of benchmark 3-09 for pipe nr. 2, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark n.a. n.a. n.a. n.a. D-G EO P IPELINE n.a. n.a. n.a. n.a. Error Table 3.104: Results of benchmark 3-09 for pipe nr. 3, Strength calculation for Combination 1A Result σb σt σa;max σV;max 48 of 126 Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.31 6.7 6.85 n.a. D-G EO P IPELINE 0.31 6.7 6.85 n.a. Rel. error [%] 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.105: Results of benchmark 3-09 for pipe nr. 3, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.35 58.42 58.6 0.002253 0.0029 0.11 0.11 n.a. D-G EO P IPELINE 0.35 58.42 58.6 0.002253 0.0029 0.11 0.11 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.106: Results of benchmark 3-09 for pipe nr. 3, Strength calculation for Combination 2 Result σpy σpx σptest σpm Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 3.17 1.59 3.49 2.75 D-G EO P IPELINE 3.17 1.59 3.49 2.75 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.107: Results of benchmark 3-09 for pipe nr. 3, Strength calculation for Combination 3 Result σb σa;max σqr σqn σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.09 0.04 0.05 6.05 3.05 n.a. D-G EO P IPELINE 0.09 0.04 0.05 6.05 3.05 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 Table 3.108: Results of benchmark 3-09 for pipe nr. 3, Strength calculation for Combination 4 Result σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.09 3.17 1.59 3.49 0.32 1.63 0.05 6.05 n.a. D-G EO P IPELINE 0.09 3.17 1.59 3.49 0.32 1.63 0.05 6.05 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 49 of 126 D-G EO P IPELINE, Verification Report Table 3.109: Results of benchmark 3-09 for pipe nr. 3, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 8 6.4 n.a. n.a. 8 6.4 D-G EO P IPELINE 8 6.4 n.a. n.a. 8 6.4 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.110: Results of benchmark 3-09 for pipe nr. 3, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 11.7 28.4 19.9 D-G EO P IPELINE 11.7 28.4 19.9 Rel. error [%] 0.00 0.00 0.00 Table 3.111: Results of benchmark 3-09 for pipe nr. 3, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark 713.89 89.24 0 0 D-G EO P IPELINE 713.89 89.24 0 0 Error 0.00 0.00 0.00 0.00 Table 3.112: Results of benchmark 3-09 for pipe nr. 4, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 116.46 45.18 161.63 161.63 D-G EO P IPELINE 116.46 45.18 161.63 161.63 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.113: Results of benchmark 3-09 for pipe nr. 4, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max 50 of 126 Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 133.09 97.28 230.38 0.000569 0.02927 14.51 14.51 237.96 D-G EO P IPELINE 133.09 97.28 230.38 0.000569 0.02927 14.51 14.51 238 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 Deltares Group 3: Benchmarks from spreadsheets Table 3.114: Results of benchmark 3-09 for pipe nr. 4, Strength calculation for Combination 2 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σpy σpx σptest σpm Benchmark 12.2 6.1 16.23 10.57 D-G EO P IPELINE 12.2 6.1 16.23 10.57 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.115: Results of benchmark 3-09 for pipe nr. 4, Strength calculation for Combination 3 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σb σa;max σqr σqn σt;max σV;max Benchmark 133.09 133.09 14.51 103.79 118.3 217.84 D-G EO P IPELINE 133.09 133.09 14.51 103.79 118.3 217.8 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.02 Table 3.116: Results of benchmark 3-09 for pipe nr. 4, Strength calculation for Combination 4 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Benchmark 133.09 14.42 7.21 16.23 23.12 140.31 14.51 103.79 216.05 D-G EO P IPELINE 133.09 14.42 7.21 16.23 23.12 140.31 14.51 103.79 216.1 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 Table 3.117: Results of benchmark 3-09 for pipe nr. 4, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 342.86 327.27 360 556.36 n.a. n.a. D-G EO P IPELINE 342.86 327.27 360 556.36 n.a. n.a. Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.118: Results of benchmark 3-09 for pipe nr. 4, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Deltares Unit [mm] [mm] [mm] Benchmark 2.4 77.7 36.6 D-G EO P IPELINE 2.4 77.7 36.6 Rel. error [%] 0.00 0.00 0.00 51 of 126 D-G EO P IPELINE, Verification Report Table 3.119: Results of benchmark 3-09 for pipe nr. 4, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark n.a. n.a. n.a. n.a. D-G EO P IPELINE n.a. n.a. n.a. n.a. Error Table 3.120: Results of benchmark 3-09 for pipe nr. 5, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 223.5 50.9 274.41 274.41 D-G EO P IPELINE 223.5 50.9 274.41 274.41 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.121: Results of benchmark 3-09 for pipe nr. 5, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 255.43 109.61 365.04 0.000239 0.07646 13.31 13.31 371.88 D-G EO P IPELINE 255.43 109.61 365.04 0.000239 0.07646 13.31 13.31 371.9 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 Table 3.122: Results of benchmark 3-09 for pipe nr. 5, Strength calculation for Combination 2 Result σpy σpx σptest σpm Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 10.2 5.1 15.02 8.83 D-G EO P IPELINE 10.2 5.1 15.02 8.83 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.123: Results of benchmark 3-09 for pipe nr. 5, Strength calculation for Combination 3 Result σb σa;max σqr σqn σt;max σV;max 52 of 126 Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 255.43 255.43 13.31 44.12 57.43 288.47 D-G EO P IPELINE 255.43 255.43 13.31 44.17 57.48 288.5 Rel. error [%] 0.00 0.00 0.00 0.11 0.09 0.01 Deltares Group 3: Benchmarks from spreadsheets Table 3.124: Results of benchmark 3-09 for pipe nr. 5, Strength calculation for Combination 4 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Benchmark 255.43 12.06 6.03 15.02 25.34 261.46 13.31 44.12 287.87 D-G EO P IPELINE 255.43 12.06 6.03 15.02 25.34 261.46 13.31 44.17 287.9 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.11 0.01 Table 3.125: Results of benchmark 3-09 for pipe nr. 5, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 173.91 153.85 169.23 261.54 n.a. n.a. D-G EO P IPELINE 173.91 153.85 169.23 261.54 n.a. n.a. Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.126: Results of benchmark 3-09 for pipe nr. 5, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 1.8 170 80 D-G EO P IPELINE 1.8 170 80 Rel. error [%] 0.00 0.00 0.00 Table 3.127: Results of benchmark 3-09 for pipe nr. 5, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark n.a. n.a. n.a. n.a. D-G EO P IPELINE n.a. n.a. n.a. n.a. Error Use D-G EO P IPELINE input file bm3-9.dri to run this benchmark. 3.10 HDD with 3D geometry – Bundled pipeline (2 PE pipes) Deltares 53 of 126 D-G EO P IPELINE, Verification Report 3.10.1 Description The same input as for benchmark 3-7a (section 3.7) is used except that five pipes are used instead of one. Their characteristics are given in the table below. Table 3.128: Pipe material data (benchmark 3-10) Material Eb Epipe;long Reb Reb;long α D0 dn γb pd pt ∆T 3.10.2 [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [-] [mm] [mm] [kN/m3 ] [Bar] [Bar] [◦ C] PE80 Synthetic 1000 200 8 6.3 0.65 50 3.7 9.54 3 6 5 PE100 Synthetic 1200 300 10 8 0.5 355 26.1 13 5 5.5 6 Analytical results Analytical results are worked out in an Excel spreadsheet. Strength calculation for bundled pipelines For the buoyancy control, the pulling forces in the pipeline and the strength calculation, calculations are performed using the formulas given in chapter “Strength pipeline calculation” in the Background section of the User Manual of D-G EO P IPELINE. The properties of the equivalent pipe are: Deq [mm] 328.96 dn;eq [mm] 29.21 γeq [kN/m3 ] 12.93 Ieq [m4 ] 0.00031187 Eeq [N/mm2 ] 1412.43 kV;max;eq [kN/m3 ] 133262.93 The total pulling force is the contribution of five components. Results are given in the tables below for the equivalent pipeline and for the 2 single pipelines. 54 of 126 Deltares Group 3: Benchmarks from spreadsheets Table 3.129: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-10) for the equivalent pipe Charac. point 1 2 3 4 5 6 7 8 9 10 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 166.76 162.75 135.27 129.13 106.36 95.06 46.28 32.53 6.92 0 [kN] 0 26.49 0 40.58 0 74.67 0 90.8 0 45.72 [kN] 0 0 181.59 0 151.28 0 322.94 0 169.23 0 [kN] 0 0 0.46 0 48.58 0 121.04 0 0.57 0 [kN] 0 0 23.35 0 0 0 0 0 85.16 0 Total [kN] 166.76 189.25 367.16 401.6 578.69 642.06 1037.25 1114.31 1343.66 1382.46 Table 3.130: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-10) for pipe nr. 1 Charac. point 1 2 3 4 5 6 7 8 9 10 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 2.6 2.54 2.11 2.02 1.66 1.48 0.72 0.51 0.11 0 [kN] 0 2.6 0 3.98 0 7.33 0 8.92 0 4.49 [kN] 0 0 17.83 0 14.77 0 31.65 0 16.62 0 [kN] 0 0 0 0 3.66 0 10.66 0 0 0 [kN] 0 0 1.53 0 0 0 0 0 8.25 0 Total [kN] 2.6 5.14 24.08 27.97 46.05 53.21 94.76 103.46 127.93 132.31 Table 3.131: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-10) for pipe nr. 2 Charac. point 1 2 3 4 5 6 7 8 9 10 Deltares Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 164.16 160.21 133.16 127.11 104.7 93.58 45.55 32.03 6.81 0 [kN] 0 27.49 0 42.1 0 77.47 0 94.21 0 47.44 [kN] 0 0 188.42 0 156.95 0 335.07 0 175.59 0 [kN] 0 0 0.46 0 49.7 0 124.81 0 0.57 0 [kN] 0 0 23.74 0 0 0 0 0 88.3 0 Total [kN] 164.16 187.7 373.27 409.33 593.56 659.91 1071.77 1152.45 1391.71 1432.33 55 of 126 D-G EO P IPELINE, Verification Report 3.10.3 D-G EO P IPELINE results D-G EO P IPELINE results presented in the tables below can be found in the Report. Table 3.132: Results of benchmark 3-10, Buoyancy control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe Unit [kg/m] [kg/m] [kg/m] Benchmark 131 47 85 D-G EO P IPELINE 131 47 85 Error [%] 0.00 0.00 0.00 Table 3.133: Results of benchmark 3-10, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 167 43 189 338 367 1441 1114 1716 1344 1790 1382 4 D-G EO P IPELINE Length Force [m] [kN] 0 167 43 189 338 367 1441 1114 1716 1344 1790 1382 4 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-10.dri to run this benchmark. 3.11 3.11.1 HDD with 3D geometry – Bundled pipeline (3 steel pipes) Description The same input as for benchmark 3-7a (section 3.7) is used except that five pipes are used instead of one. Their characteristics are given in the table below. Table 3.134: Pipe material data (benchmark 3-11) Material δt Eb Reb γm γm;test D0 dn γb pd pt ∆T 3.11.2 [%] [N/mm2 ] [N/mm2 ] [-] [-] [mm] [mm] [kN/m3 ] [Bar] [Bar] [◦ C] FE385 Steel 10 205800 385 1.2 1.1 219.1 22.2 85 3 6 4 FE360 Steel 15 205800 360 1.1 1.05 457 9.52 78.5 4 6.5 8 Steel 1 Steel 25 180500 200 1.3 1.15 1000 35 65 5 9 10 Analytical results Analytical results are worked out in an Excel spreadsheet. 56 of 126 Deltares Group 3: Benchmarks from spreadsheets Strength calculation for bundled pipelines For the buoyancy control, the pulling forces in the pipeline and the strength calculation, calculations are performed using the formulas given in chapter “Strength pipeline calculation” in the Background section of the User Manual of D-G EO P IPELINE [Deltares]. The properties of the equivalent pipe are: Deq [mm] 1205.49 dn;eq [mm] 36.27 γeq [kN/m3 ] 68.42 4 Ieq [m ] 0.0227877 Eeq [N/mm2 ] 101597.36 kV;max;eq [kN/m3 ] 25604.32 The total pulling force is the contribution of five components. Results are given in the tables below for the equivalent pipeline and for the 3 single steel pipelines. Table 3.135: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-11) for the equivalent pipe Charac. point 1 2 3 4 5 6 7 8 9 10 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 3721.21 3631.73 3018.47 2881.43 2373.4 2121.23 1032.6 725.95 154.41 0 [kN] 0 88.51 0 135.55 0 249.44 0 303.33 0 152.74 [kN] 0 0 606.62 0 1130.34 0 1516.31 0 565.34 0 [kN] 0 0 338.05 0 515.78 0 915.32 0 418.54 0 [kN] 0 0 275.2 0 0 0 0 0 369.21 0 Total [kN] 3721.21 3720.24 4326.85 4325.36 5463.45 5460.71 6803.71 6800.39 7581.95 7580.28 Table 3.136: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-11) for pipe nr. 1 Charac. point 1 2 3 4 5 6 7 8 9 10 Deltares Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 430.7 420.34 349.36 333.5 274.7 245.52 119.52 84.02 17.87 0 [kN] 0 19.57 0 29.98 0 55.16 0 67.08 0 33.78 [kN] 0 0 134.16 0 124.15 0 247.26 0 125.03 0 [kN] 0 0 7.01 0 62.31 0 120.77 0 8.67 0 [kN] 0 0 34.65 0 0 0 0 0 66.45 0 Total [kN] 430.7 439.92 544.75 558.87 686.52 712.5 954.53 986.12 1120.12 1136.03 57 of 126 D-G EO P IPELINE, Verification Report Table 3.137: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-11) for pipe nr. 2 Charac. point 1 2 3 4 5 6 7 8 9 10 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 456.95 445.96 370.66 353.83 291.44 260.48 126.8 89.14 18.96 0 [kN] 0 32.68 0 50.04 0 92.09 0 111.98 0 56.39 [kN] 0 0 223.95 0 229.82 0 428.55 0 208.71 0 [kN] 0 0 23.85 0 86.94 0 187.44 0 29.53 0 [kN] 0 0 44.23 0 0 0 0 0 111.14 0 Total [kN] 456.95 478.64 695.36 728.57 982.95 1044.07 1526.37 1600.7 1879.89 1917.32 Table 3.138: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-11) for pipe nr. 3 Charac. point 1 2 3 4 5 6 7 8 9 10 3.11.3 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 2833.56 2765.42 2298.45 2194.1 1807.25 1615.24 786.29 552.78 117.58 0 [kN] 0 76.94 0 117.84 0 216.84 0 263.69 0 132.78 [kN] 0 0 527.34 0 1039.44 0 1357.92 0 491.46 0 [kN] 0 0 324.47 0 425.87 0 782.44 0 401.73 0 [kN] 0 0 219.2 0 0 0 0 0 323.45 0 Total [kN] 2833.56 2842.36 3446.4 3459.89 4538.35 4563.17 5874.58 5904.76 6686.2 6701.4 D-G EO P IPELINE results D-G EO P IPELINE results presented in the tables below can be found in the Report. Table 3.139: Results of benchmark 3-11, Buoyancy control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe 58 of 126 Unit [kg/m] [kg/m] [kg/m] Benchmark 1283 1040 244 D-G EO P IPELINE 1283 1040 244 Error [%] 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.140: Results of benchmark 3-11, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 3721 43 3720 338 4327 1441 6800 1716 7582 1790 7580 6493 D-G EO P IPELINE Length Force [m] [kN] 0 3721 43 3720 338 4327 1441 6800 1716 7582 1790 7580 6493 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-11.dri to run this benchmark. 3.12 3.12.1 Micro tunneling with 3D geometry – Steel pipe Description The same input data’s as for benchmark 3-7 (section 3.7) are used except that the calculation is performed for micro tunneling instead of horizontal directional drilling. Few input values must be added compare to HDD calculation: Friction with injection of lubricant 7.5 [kPa] Friction without injection of lubricant 10 [kPa] Allowable thrust force 200 [kN] Volume loss for surface settlement 15 [%] Two cases are checked: Case A (bm3-12a): thrusting direction from left to right; Case B (bm3-12b): thrusting direction from right to left. 3.12.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Soil mechanical data The soil mechanical data’s are determined using the formulas given in chapter “Calculation of soil mechanical data” in the Background section of the User Manual of D-G EO P IPELINE. Deltares 59 of 126 D-G EO P IPELINE, Verification Report Operation Parameters The face support pressures, the thrust forces and the uplift safety factor are determined using the formulas given in chapter “Micro Tunneling” in the Background section of the User Manual of D-G EO P IPELINE. Intermediate results are given in the tables below. Table 3.141: Analytical results for the calculation of the face support pressures Vert. [-] 1 2 3 4 5 6 7 8 σv ’ u C/D β O/A α K KA3 Qs [kN/m2 ] 25.396 27.34 120.537 162.667 448.99 353.117 161.58 89.894 [kN/m2 ] 0 116.373 192.742 218.871 352.192 250.214 0 0 [-] n.a. n.a. 3.199 6.643 21.924 7.226 n.a. n.a. [-] n.a. n.a. 66.706 66.706 68.683 68.683 n.a. n.a. [-] n.a. n.a. 6.645 6.645 7.125 7.125 n.a. n.a. [-] n.a. n.a. 1.432 1.465 1.489 1.468 n.a. n.a. [-] n.a. n.a. 0.417 0.417 0.349 0.349 n.a. n.a. [-] n.a. n.a. 0.214 0.212 0.167 0.168 n.a. n.a. [kN/m2 ] n.a. n.a. 3.376 3.842 9.702 9.343 n.a. n.a. Table 3.142: Analytical results for the calculation of the uplift safety factor Vert. [-] 1 2 3 4 5 6 7 8 3.12.3 Part dry [%] 100 0 0 0 0 0 66.256 100 guplift gweight fuplift [kN/m2 ] 0 7.854 7.854 7.854 7.854 7.854 2.65 0 [kN/m2 ] 6.897 6.897 6.897 6.897 6.897 6.897 6.897 6.897 [-] 999 4.009 15.493 20.858 57.269 45.074 61.495 999 D-G EO P IPELINE results D-G EO P IPELINE results presented in the tables below can be found in the Report. Table 3.143: Results of benchmark 3-12a, Vertical soil stresses Benchmark Vert. [-] 1 2 3 4 5 6 7 8 qv;p qv;n 2 D-G EO P IPELINE qv;r;n 2 qv;p 2 qv;n 2 Relative error qv;r;n 2 qv;p 2 [kN/m ] [kN/m ] [kN/m ] [kN/m ] [kN/m ] [kN/m ] [%] 32 21 21 32 21 21 0.00 106 25 45 106 25 45 0.00 830 116 79 830 116 79 0.00 1048 158 90 1048 158 90 0.00 2010 444 109 2010 444 109 0.00 1615 348 113 1615 348 141 0.00 284 157 102 284 157 102 0.00 213 85 85 213 85 85 0.00 60 of 126 qv;n qv;r;n [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 19.86 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.144: Results of benchmark 3-12a, Neutral horizontal soil stress and bearing capacities Benchmark qh;n Vert. [-] 1 2 3 4 5 6 7 8 Pv;e 2 D-G EO P IPELINE Ph;e 2 [kN/m ] [kN/m ] 16 455 19 494 58 3315 79 4434 189 21114 149 16630 116 1240 63 838 qh;n 2 [kN/m ] 208 147 1715 2364 12962 8152 702 451 Pv;e 2 Relative error Ph;e 2 [kN/m ] [kN/m ] 16 455 19 494 58 3315 79 4435 189 21114 149 16630 116 1240 63 838 2 [kN/m ] 208 147 1715 2364 12962 8152 702 451 qh;n Pv;e Ph;e [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.145: Results of benchmark 3-12a, Vertical and horizontal moduli of subgrade reaction Benchmark kv;top Vert. [-] 1 2 3 4 5 6 7 8 kv;bot 3 [kN/m ] 371 253 9424 16574 12499 16911 254 327 D-G EO P IPELINE kh 3 [kN/m ] 303 544 17421 18611 13305 11410 367 260 kv;top 3 [kN/m ] 212 380 12195 13028 9313 7987 257 182 kv;bot Relative error kv;top kv;bot kh [kN/m ] [kN/m ] [kN/m ] [%] 371 303 212 0.00 253 544 380 0.00 9424 17421 12195 0.00 16574 18611 13028 0.00 12499 13305 9313 0.00 16911 11410 7987 0.00 254 367 257 0.00 327 260 182 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3 kh 3 3 Table 3.146: Results of benchmark 3-12a, Maximal axial friction and displacements Benchmark Vert. [-] 1 2 3 4 5 6 7 8 Deltares D-G EO P IPELINE Relative error tmax dv dmax tmax dv dmax tmax dv dmax [kN/m2 ] 17 19 25 27 35 33 32 27 [mm] 5 10 20 40 80 60 50 35 [mm] 12 12 5 5 2 2 12 12 [kN/m2 ] 17 19 25 27 35 36 32 27 [mm] 5 10 20 40 80 60 50 35 [mm] 12 12 5 5 2 2 12 12 [%] 0.00 0.00 0.00 0.00 0.00 8.33 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 61 of 126 D-G EO P IPELINE, Verification Report Table 3.147: Results of benchmark 3-12a, Face support pressures Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error Pmax Pmin Ptarget Pmax Pmin Ptarget Pmax Pmin Ptarget [kN/m2 ] 21 120 261 318 668 503 135 75 [kN/m2 ] 0 128 248 242 390 277 0 0 [kN/m2 ] 19 137 253 300 544 401 120 67 [kN/m2 ] 21 120 261 318 668 503 135 75 [kN/m2 ] 0 128 248 242 389 276 0 0 [kN/m2 ] 19 137 253 300 544 401 120 67 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.26 0.36 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.148: Results of benchmark 3-12a, Thrust forces Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error Flubricated Fnormal Flubricated Fnormal Flubricated Fnormal [kN] 337 1719 3414 4089 30386 50715 54517 55288 [kN] 498 2525 5021 6015 45366 75915 81728 82906 [kN] 337 1719 3414 4089 30386 50715 54517 55288 [kN] 498 2525 5021 6015 45366 75915 81728 82906 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.149: Results of benchmark 3-12b, Thrust forces Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error Flubricated Fnormal Flubricated Fnormal Flubricated Fnormal [kN] 55920 54723 53211 52611 26696 6142 1899 1044 [kN] 83873 82031 79718 78798 39830 9056 2802 1540 [kN] 55920 54723 53211 52611 26696 6142 1899 1044 [kN] 83873 82031 79718 78798 39830 9056 2802 1540 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 62 of 126 Deltares Group 3: Benchmarks from spreadsheets Table 3.150: Results of benchmark 3-12a, Uplift safety factor Benchmark Calculated Required [-] [-] n.a. 1.15 4.01 1.15 15.49 1.15 20.86 1.15 57.27 1.15 45.07 1.15 61.49 1.15 n.a. 1.15 Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Calculated Required [-] [-] 999 1.15 4 1.15 15.48 1.15 20.85 1.15 57.27 1.15 45.07 1.15 57.7 1.15 999 1.15 Relative error Calculated Required [%] [%] 0.00 0.25 0.00 0.06 0.00 0.05 0.00 0.00 0.00 0.00 0.00 6.57 0.00 0.00 Table 3.151: Results of benchmark 3-12a, Trough v1 v2 v3 v4 v5 v6 v7 v8 Benchmark ftrough Trough [-] [-] 0.02156 2.093 0.00746 6.052 0.00433 10.431 0.00376 12 0.00235 19.235 0.0026 17.349 0.00608 7.416 0.00978 4.614 Depth [m] 2.309 11.516 21.699 25.349 49.182 41.18 14.689 8.172 D-G EO P IPELINE ftrough Trough Depth [-] [-] [m] 0.02156 2.093 2.309 0.00746 6.052 11.516 0.00433 10.431 21.699 0.00376 12 25.349 0.00235 19.235 49.182 0.0026 17.349 41.18 0.00608 7.416 14.689 0.00978 4.614 8.172 Relative error ftrough Trough Depth [%] [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.152: Results of benchmark 3-12a, Subsidence at different horizontal distances of Z axis (from 0 to 0.7W) 0 Benchmark [mm] 0.1 0.2 0.4 0.7 0 D-G EO P IPELINE [mm] 0.1 0.2 0.4 0.7 ×W v1 v2 v3 v4 v5 v6 v7 v8 22 7 4 4 2 3 6 10 Deltares 21 7 4 4 2 3 6 10 21 7 4 3 2 2 6 9 0 Relative error [%] 0.1 0.2 0.4 0.7 ×W 20 6 3 3 1 2 4 8 16 3 1 1 0 1 2 5 22 7 4 4 2 3 6 10 21 7 4 4 2 3 6 10 21 7 4 3 2 2 6 9 ×W 20 6 3 3 1 2 4 8 16 3 1 1 0 1 2 5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 63 of 126 D-G EO P IPELINE, Verification Report Table 3.153: Results of benchmark 3-12a, Subsidence at different horizontal distances of Z axis (from 1W to 2.5W) 1 Benchmark [mm] 1.3 1.6 2 2.5 1 D-G EO P IPELINE [mm] 1.3 1.6 2 2.5 ×W v1 v2 v3 v4 v5 v6 v7 v8 12 1 0 0 0 0 1 2 8 0 0 0 0 0 0 1 5 0 0 0 0 0 0 0 Relative error [%] 1.3 1.6 2 2.5 1 ×W 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 1 0 0 0 0 1 2 8 0 0 0 0 0 0 1 ×W 5 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Use D-G EO P IPELINE input files bm3-12a.dri and bm3-12b.dri to run this benchmark. 3.13 3.13.1 Micro tunneling with 3D geometry – Synthetic pipe Description The same input data’s as for benchmark 3-12a (section 3.12) are used except that a synthetic pipe (with a Young’s modulus at short term of 30000 kPa) instead of a steel pipe is used. Results are expected to be the same as bm3-12a except for the moduli of subgrade reaction. 3.13.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Soil mechanical data The moduli of subgrade reaction are determined using the formulas given in chapter “Calculation of soil mechanical data” in the Background section of the User Manual of D-G EO P IPELINE. 3.13.3 D-G EO P IPELINE results D-G EO P IPELINE results presented in the table below can be found in the Report. Table 3.154: Results of benchmark 3-13, Vertical and horizontal moduli of subgrade reaction Benchmark Vert. [-] 1 2 3 4 5 6 7 8 kv;top kv;bot 3 [kN/m ] 405 277 10477 18504 13924 18883 278 358 64 of 126 D-G EO P IPELINE kh 3 [kN/m ] 331 594 19458 20827 14829 12703 402 285 kv;top 3 [kN/m ] 232 416 13620 14579 10380 8892 281 199 kv;bot Relative error kv;top kv;bot kh [kN/m ] [kN/m ] [kN/m ] [%] 405 331 232 0.00 277 594 416 0.00 10477 19458 13620 0.00 18504 20827 14579 0.00 13924 14829 10380 0.00 18883 12703 8892 0.00 278 402 281 0.00 358 285 199 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3 kh 3 3 Deltares Group 3: Benchmarks from spreadsheets Use D-G EO P IPELINE input file bm3-13.dri to run this benchmark. 3.14 3.14.1 Micro tunneling with 3D geometry – Concrete pipe Description The same input data’s as for benchmark 3-12a (section 3.12) are used except that a concrete pipe instead of a steel pipe is used, but the properties are the same. Therefore, results are expected to be the same as bm3-12a. 3.14.2 Analytical results The same Excel spreadsheet as for benchmark 3-12a (section 3.12) is used. 3.14.3 D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report and are identical to the results of benchmark 3-12a (section 3.12) . Table 3.155: Results of benchmark 3-14, Vertical soil stresses Benchmark Vert. [-] 1 2 3 4 5 6 7 8 qv;p qv;n 2 D-G EO P IPELINE qv;r;n 2 qv;p 2 qv;n 2 Relative error qv;r;n 2 qv;p 2 [kN/m ] [kN/m ] [kN/m ] [kN/m ] [kN/m ] [kN/m ] [%] 32 21 21 32 21 21 0.00 106 25 45 106 25 45 0.00 830 116 79 830 116 79 0.00 1048 158 90 1048 158 90 0.00 2010 444 109 2010 444 109 0.00 1615 348 113 1615 348 141 0.00 284 157 102 284 157 102 0.00 213 85 85 213 85 85 0.00 qv;n qv;r;n [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 19.86 0.00 0.00 Table 3.156: Results of benchmark 3-14, Neutral horizontal soil stress and bearing capacities Benchmark Vert. [-] 1 2 3 4 5 6 7 8 Deltares qh;n Pv;e 2 D-G EO P IPELINE Ph;e 2 [kN/m ] [kN/m ] 16 455 19 494 58 3315 79 4434 189 21114 149 16630 116 1240 63 838 qh;n 2 [kN/m ] 208 147 1715 2364 12962 8152 702 451 Pv;e 2 Relative error Ph;e 2 [kN/m ] [kN/m ] 16 455 19 494 58 3315 79 4435 189 21114 149 16630 116 1240 63 838 2 [kN/m ] 208 147 1715 2364 12962 8152 702 451 qh;n Pv;e Ph;e [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 65 of 126 D-G EO P IPELINE, Verification Report Table 3.157: Results of benchmark 3-14, Vertical and horizontal moduli of subgrade reaction Benchmark Vert. [-] 1 2 3 4 5 6 7 8 kv;top kv;bot 3 [kN/m ] 371 253 9424 16574 12499 16911 254 327 D-G EO P IPELINE kh 3 [kN/m ] 303 544 17421 18611 13305 11410 367 260 kv;top 3 [kN/m ] 212 380 12195 13028 9313 7987 257 182 kv;bot Relative error kv;top kv;bot kh [kN/m ] [kN/m ] [kN/m ] [%] 371 303 212 0.00 253 544 380 0.00 9424 17421 12195 0.00 16574 18611 13028 0.00 12499 13305 9313 0.00 16911 11410 7987 0.00 254 367 257 0.00 327 260 182 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3 kh 3 3 Table 3.158: Results of benchmark 3-14, Maximal axial friction and displacements Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error tmax dv dmax tmax dv dmax tmax dv dmax [kN/m2 ] 16.83 18.93 24.55 26.97 35.39 33.21 32.4 26.77 [mm] 5 10 20 40 80 60 50 35 [mm] 12 12 5 5 2 2 12 12 [kN/m2 ] 17 19 25 27 35 36 32 27 [mm] 5 10 20 40 80 60 50 35 [mm] 12 12 5 5 2 2 12 12 [%] 0.00 0.00 0.00 0.00 0.00 8.33 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.159: Results of benchmark 3-14, Face support pressures Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error Pmax Pmin Ptarget Pmax Pmin Ptarget Pmax Pmin Ptarget [kN/m2 ] 21 120 261 318 668 503 135 75 [kN/m2 ] 0 128 248 242 390 277 0 0 [kN/m2 ] 19 137 253 300 544 401 120 67 [kN/m2 ] 21 120 261 318 668 503 135 75 [kN/m2 ] 0 128 248 242 389 276 0 0 [kN/m2 ] 19 137 253 300 544 401 120 67 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.26 0.36 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 66 of 126 Deltares Group 3: Benchmarks from spreadsheets Table 3.160: Results of benchmark 3-14, Thrust forces Benchmark Vert. [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error Flubricated Fnormal Flubricated Fnormal Flubricated Fnormal [kN] 337 1719 3414 4089 30386 50715 54517 55288 [kN] 498 2525 5021 6015 45366 75915 81728 82906 [kN] 337 1719 3414 4089 30386 50715 54517 55288 [kN] 498 2525 5021 6015 45366 75915 81728 82906 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.161: Results of benchmark 3-14, Uplift safety factor Vert. [-] 1 2 3 4 5 6 7 8 Benchmark Calculated Required [-] [-] 999 1.15 4.01 1.15 15.49 1.15 20.86 1.15 57.27 1.15 45.07 1.15 61.49 1.15 999 1.15 D-G EO P IPELINE Calculated Required [-] [-] 999 1.15 4 1.15 15.48 1.15 20.85 1.15 57.27 1.15 45.07 1.15 57.7 1.15 999 1.15 Relative error Calculated Required [%] [%] 0.00 0.00 0.25 0.00 0.06 0.00 0.05 0.00 0.00 0.00 0.00 0.00 6.57 0.00 0.00 0.00 Table 3.162: Results of benchmark 3-14, Trough v1 v2 v3 v4 v5 v6 v7 v8 Benchmark ftrough Trough [-] [-] 0.02156 2.093 0.00746 6.052 0.00433 10.431 0.00376 12 0.00235 19.235 0.0026 17.349 0.00608 7.416 0.00978 4.614 Deltares Depth [m] 2.309 11.516 21.699 25.349 49.182 41.18 14.689 8.172 D-G EO P IPELINE ftrough Trough Depth [-] [-] [m] 0.02156 2.093 2.309 0.00746 6.052 11.516 0.00433 10.431 21.699 0.00376 12 25.349 0.00235 19.235 49.182 0.0026 17.349 41.18 0.00608 7.416 14.689 0.00978 4.614 8.172 Relative error ftrough Trough Depth [%] [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 67 of 126 D-G EO P IPELINE, Verification Report Table 3.163: Results of benchmark 3-14, Subsidence at different horizontal distances of Z axe (from 0 to 0.7W) 0 Benchmark [mm] 0.1 0.2 0.4 0.7 0 D-G EO P IPELINE [mm] 0.1 0.2 0.4 0.7 ×W v1 v2 v3 v4 v5 v6 v7 v8 22 7 4 4 2 3 6 10 21 7 4 4 2 3 6 10 21 7 4 3 2 2 6 9 0 Relative error [%] 0.1 0.2 0.4 0.7 ×W 20 6 3 3 1 2 4 8 16 3 1 1 0 1 2 5 22 7 4 4 2 3 6 10 21 7 4 4 2 3 6 10 21 7 4 3 2 2 6 9 ×W 20 6 3 3 1 2 4 8 16 3 1 1 0 1 2 5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Table 3.164: Results of benchmark 3-14, Subsidence at different horizontal distances of Z axe (from 1W to 2.5W) 1 Benchmark [mm] 1.3 1.6 2 2.5 1 D-G EO P IPELINE [mm] 1.3 1.6 2 2.5 ×W v1 v2 v3 v4 v5 v6 v7 v8 12 1 0 0 0 0 1 2 8 0 0 0 0 0 0 1 5 0 0 0 0 0 0 0 1 Relative error [%] 1.3 1.6 2 2.5 ×W 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 1 0 0 0 0 1 2 8 0 0 0 0 0 0 1 5 0 0 0 0 0 0 0 ×W 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Use D-G EO P IPELINE input file bm3-14.dri to run this benchmark. 3.15 3.15.1 Trenching (3 sections) – 3D geometry in four layers – Compressible border above drainage border Description The same input data’s as for benchmark 1-7 (section 3.7) are used except that a construction in trench is modeled. The trenching configuration (3 trench sections) is given in Table 3-114. Calculations are performed for 8 verticals with L coordinates of 70, 150, 400, 600, 900, 1200, 1500 and 1800 m. Six cases are considered depending on the type of filling of the trench: Case A (bm3-15a): sand poorly compacted; Case B (bm3-15b): stiff clay poorly compacted; Case C (bm3-15c): soft soil poorly compacted; Case D (bm3-15d): sand well compacted; Case E (bm3-15e): stiff clay well compacted; Case F (bm3-15f): soft soil well compacted. The type of filling will influence only the actual soil stress. 68 of 126 Deltares Group 3: Benchmarks from spreadsheets Table 3.165: Configuration of the 3 trench sections (benchmark 3-15a) Xbegin Ybegin Zbegin Xend Yend Zend Eb D0 dn γb Width Slope of the wall [1:x] Offset [m] [m] [m] [m] [m] [m] [N/mm2 ] [mm] [mm] [kN/m3 ] [mm] [-] [m] Trench 1 50 0 -1 400 10 -4 1500 500 35 78.5 550 2 0.1 Trench 2 400 10 -4 1300 -6 -2 2000 300 20 90 400 3 0.2 Trench 3 1300 -6 -2 1900 5 0.5 3500 600 50 56 700 4 0.3 Figure 3.4: Lateral view of the 3 trench sections (benchmark 3-15) 3.15.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Soil mechanical data The soil mechanical data’s are determined using the formulas given in chapter “Calculation of soil mechanical data” in the Background section of the User Manual of D-G EO P IPELINE. Deltares 69 of 126 D-G EO P IPELINE, Verification Report Operation Parameters The safety factors for uplift and hydraulic heave are determined using the formulas given in chapter “Trench” in the Background section of the User Manual of D-G EO P IPELINE. Intermediate results are given in the tables below. Table 3.166: Analytical results for the calculation of the uplift safety factor Vert. [-] 1 2 3 4 5 6 7 8 Part dry [%] 0 0 0 0 0 0 0 100 σv;top ’ qpipe quplift f [kN/m2 ] 0.367 4.458 30.326 27.931 23.082 19.085 12.564 6.774 [kN/m2 ] 4.014 4.014 4.014 1.583 1.583 1.583 4.838 4.838 [kN/m2 ] 1.963 1.963 1.963 0.707 0.707 0.707 2.827 0 [-] 2.138 3.179 9.767 14.094 12.036 10.34 4.377 999 Table 3.167: Analytical results for the hydraulic heave check v1 v2 v3 v4 v5 v6 v7 v8 3.15.3 a b d2;d fBous [m] 2.6 4 8.7 12.1 10.8 9.4 10.2 6.1 [m] 0.28 0.28 0.28 0.2 0.2 0.2 0.35 0.35 [m] 2.08 1.39 -0.84 -0.47 0.09 0.65 1.34 2.48 [-] 0.34 0.15 -0.04 -0.01 0 0.03 0.05 0.2 σv 54.7 54.7 55.1 55.4 55.8 56.2 56.7 57.1 σbot Wbot 16.6 28.2 71.9 64.7 54.1 44 33.1 16.7 [kN/m2 ] 38.1 16.6 26.5 28.2 -16.8 71.9 -9.4 64.7 1.7 54.1 12.3 44 23.6 33.1 40.4 16.7 Wtop Ww 10.2 17.1 38.5 34.1 27.4 20.7 12.7 0.2 uopw ϕ f 28.5 28.5 27.7 27.1 26.1 25.1 24.1 23.1 [m] -0.8 -0.8 -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 [-] 1.9 1.7 100 100 1.1 1.4 1.6 1.9 D-G EO P IPELINE results D-G EO P IPELINE results presented in the tables below can be found in the Report. Table 3.168: Results of benchmark 3-15a, Vertical and horizontal soil stresses Benchmark qv;p qv;n 2 v1 v2 v3 v4 v5 v6 v7 v8 D-G EO P IPELINE qh;n 2 qv;p 2 qv;n 2 Relative error qh;n 2 qv;p 2 [kN/m ] [kN/m ] [kN/m ] [kN/m ] [kN/m ] [kN/m ] [%] 1 1 0 1 1 0 0.00 9 5 4 9 5 4 0.00 99 31 13 99 31 13 0.00 127 28 12 127 28 12 0.00 95 23 12 95 23 12 0.00 70 19 18 70 19 18 0.00 23 13 13 23 13 13 0.00 10 7 6 10 8 6 0.00 70 of 126 qv;n qh;n [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 12.5 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.169: Results of benchmark 3-15a, Initial vertical stress qk for sand poorly compacted Vertical nr. [-] 1 2 3 4 5 6 7 8 Benchmark [kN/m2 ] 1 6 99 127 95 70 16 8 D-G EO P IPELINE [kN/m2 ] 1 6 99 127 95 70 16 8 Relative error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.170: Results of benchmark 3-15b, Initial vertical stress qk for stiff clay poorly compacted Vertical nr. [-] 1 2 3 4 5 6 7 8 Benchmark [kN/m2 ] 1 8 99 127 95 70 19 9 D-G EO P IPELINE [kN/m2 ] 1 8 99 127 95 70 19 9 Relative error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.171: Results of benchmark 3-15c, Initial vertical stress qk for soft soil poorly compacted Vertical nr. [-] 1 2 3 4 5 6 7 8 Deltares Benchmark [kN/m2 ] 1 9 99 127 95 70 21 9 D-G EO P IPELINE [kN/m2 ] 1 9 99 127 95 70 21 9 Relative error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 71 of 126 D-G EO P IPELINE, Verification Report Table 3.172: Results of benchmark 3-15d, Initial vertical stress qk for sand well compacted Vertical nr. [-] 1 2 3 4 5 6 7 8 Benchmark [kN/m2 ] 1 5 99 127 95 36 14 8 D-G EO P IPELINE [kN/m2 ] 1 5 99 127 95 36 14 8 Relative error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.173: Results of benchmark 3-15e, Initial vertical stress qk for stiff clay well compacted Vertical nr. [-] 1 2 3 4 5 6 7 8 Benchmark [kN/m2 ] 1 6 99 127 95 70 16 8 D-G EO P IPELINE [kN/m2 ] 1 6 99 127 95 70 16 8 Relative error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.174: Results of benchmark 3-15f, Initial vertical stress qk for soft soil well compacted Vertical nr. [-] 1 2 3 4 5 6 7 8 72 of 126 Benchmark [kN/m2 ] 1 7 99 127 95 70 17 8 D-G EO P IPELINE [kN/m2 ] 1 7 99 127 95 70 17 8 Relative error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.175: Results of benchmark 3-15a, Horizontal modulus of subgrade reaction and bearing capacities Benchmark kh Pv;e 3 [kN/m ] 2970 3699 15130 16398 10278 767 1212 4105 v1 v2 v3 v4 v5 v6 v7 v8 D-G EO P IPELINE Ph;e 2 [kN/m ] 64 261 1622 1433 733 615 52 363 kh 2 [kN/m ] 36 59 448 416 234 15 23 53 Pv;e 3 [kN/m ] 2970 3699 15130 16407 10301 774 1217 4095 Relative error Ph;e 2 [kN/m ] 64 261 1622 1433 733 615 52 363 2 [kN/m ] 36 59 448 416 234 16 23 53 kh Pv;e Ph;e [%] 0.00 0.00 0.00 0.05 0.22 0.9 0.41 0.24 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 6.25 0.00 0.00 Table 3.176: Results of benchmark 3-15a, Vertical moduli of subgrade reaction upward Benchmark v1 v2 v3 v4 v5 v6 v7 v8 D-G EO P IPELINE Relative error kv;top1 kv;top2 kv;top1 kv;top2 kv;top1 kv;top2 [kN/m3 ] 1 37 158782 734587 129440 3080 76 12 [kN/m3 ] 6 85 231275 945256 172065 4265 170 57 [kN/m3 ] 1 37 158781 735567 129743 3084 76 12 [kN/m3 ] 6 85 231274 946483 172460 4270 170 57 [%] 0.00 0.00 0.00 0.13 0.23 0.13 0.00 0.00 [%] 0.00 0.00 0.00 0.13 0.23 0.12 0.00 0.00 Table 3.177: Results of benchmark 3-15a, Vertical moduli of subgrade reaction downward Benchmark v1 v2 v3 v4 v5 v6 v7 v8 D-G EO P IPELINE Relative error kv;bot1 kv;bot2 kv;bot1 kv;bot2 kv;bot1 kv;bot2 [kN/m3 ] 1621 7876 39240 55098 31184 29860 812 3695 [kN/m3 ] 324 1575 7848 11020 6237 5972 162 591 [kN/m3 ] 1621 7876 39240 55116 31186 29863 813 3692 [kN/m3 ] 324 1575 7848 11023 6237 5973 163 591 [%] 0.00 0.00 0.00 0.03 0.01 0.01 0.12 0.08 [%] 0.00 0.00 0.00 0.03 0.00 0.02 0.61 0.00 Deltares 73 of 126 D-G EO P IPELINE, Verification Report Table 3.178: Results of benchmark 3-15a, Maximal axial friction and displacements Benchmark v1 v2 v3 v4 v5 v6 v7 v8 D-G EO P IPELINE Relative error tmax dv dmax tmax dv dmax tmax dv dmax [kN/m2 ] 19.76 7.09 12.59 11.03 9.6 11.11 14.05 25.53 [mm] 5 10 20 40 80 60 50 35 [mm] 12 15 2 2 5 15 15 12 [kN/m2 ] 24 7 13 11 10 11 14 26 [mm] 5 10 20 40 80 60 50 35 [mm] 12 15 2 2 5 15 15 12 [%] 16.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.179: Results of benchmark 3-15a, Uplift check Benchmark Vertical [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error fcalc freq fcalc freq fcalc freq [-] 2.14 3.18 9.77 14.09 12.04 10.34 4.38 999 [-] 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.15 [-] 2.14 3.18 9.77 14.1 12.04 10.34 4.38 999 [-] 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1.15 [%] 0.00 0.00 0.00 0.07 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.180: Results of benchmark 3-15a, Hydraulic heave check Benchmark Vertical [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error fcalc freq fcalc freq fcalc freq [-] 1.89 1.68 100 100 1.11 1.36 1.58 1.89 [-] 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 [-] 1.89 1.68 100 100 1.11 1.36 1.58 1.89 [-] 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input files bm3-15a.dri until bm3-15f to run this benchmark. 3.16 3.16.1 Trenching (3 sections) – 3D geometry in four layers – Drainage border above compressible border Description The same input values as benchmark 3-15 (section 3.15) are used, only the positions of the boundaries between compressible/incompressible layers and drained/undrained layers have 74 of 126 Deltares Group 3: Benchmarks from spreadsheets been turned around. This modification will only have an influence on the hydraulic heave check. 3.16.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Operation Parameters The safety factors for hydraulic heave are determined using the formulas given in chapter “Trench” in the Background section of the User Manual of D-G EO P IPELINE. Intermediate results are given in the table below. Table 3.181: Analytical results for the hydraulic heave check v1 v2 v3 v4 v5 v6 v7 v8 3.16.3 a b d2;d fBous [m] 2.6 4 8.7 12.1 10.8 9.4 10.2 6.1 [m] 0.28 0.28 0.28 0.2 0.2 0.2 0.35 0.35 [m] 0.48 -0.21 -2.27 -1.77 -1.01 -0.25 0.64 1.98 [-] 0.04 0 -0.13 -0.08 -0.04 0 0.02 0.15 σv 24.3 24.3 27.8 30.7 34.9 39.1 43.4 47.6 σbot Wbot 16.6 28.2 71.9 64.7 54.1 44 33.1 16.7 [kN/m2 ] 7.7 16.6 -3.9 28.2 -44 71.9 -34.1 64.7 -19.2 54.1 -4.8 44 10.3 33.1 30.9 16.7 Wtop Ww 10.2 17.1 38.5 34.1 27.4 20.7 12.7 0.2 uopw ϕ f 16.5 16.5 16.8 17.1 17.6 18 18.6 19.1 [m] -0.4 -0.4 -0.4 -0.4 -0.5 -0.5 -0.6 -0.6 [-] 1.1 100 100 100 100 100 1.3 1.8 D-G EO P IPELINE results D-G EO P IPELINE results presented in the tables below can be found in the Report. Table 3.182: Results of benchmark 3-16, Hydraulic heave check Benchmark Vertical [-] 1 2 3 4 5 6 7 8 D-G EO P IPELINE Relative error fcalc freq fcalc freq fcalc freq [-] 1.13 100 100 100 100 100 1.27 1.76 [-] 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 [-] 1.13 100 100 100 100 100 1.26 1.75 [-] 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.79 0.57 [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-16.dri to run this benchmark. 3.17 Bundled pipeline with Special Stress Analysis Deltares 75 of 126 D-G EO P IPELINE, Verification Report 3.17.1 Description The same input data’s as for benchmark 3-9 (section 3.9) are used except that calculations are performed using the Special Stress Analysis calculation which means that the maximum modulus of subgrade reaction and the maximum reduced soil load are input values instead of calculated values: kV;max = 45000 kN/m3 , qn;max = 0.14 N/mm2 and R = 700 m. 3.17.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Strength calculation for bundled pipelines For the buoyancy control, the pulling forces in the pipeline and the strength calculation, calculations are performed using the formulas given in chapter “Strength pipeline calculation” in the Background section of the User Manual of D-G EO P IPELINE. The properties of the equivalent pipe are: D0;eq [mm] 1284.11 dn;eq [mm] 41.16 γeq [kN/m3 ] 58.92 Ieq [m4 ] 0.031073 Eeq [N/mm2 ] 74520.87 kV;max;eq [kN/m3 ] 45000 The total pulling force is the contribution of five components. Results are given in the tables below for the equivalent pipeline and for each single pipelines. Table 3.183: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-17) for the equivalent pipe Charac. point 1 2 3 4 5 6 7 8 9 10 76 of 126 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 3887.97 3794.48 3153.74 3010.56 2479.76 2216.29 1078.88 758.48 161.33 0 [kN] 0 103.16 0 157.99 0 290.72 0 353.53 0 178.02 [kN] 0 0 707.01 0 1320.17 0 1769.18 0 658.9 0 [kN] 0 0 395.49 0 565.97 0 1028.93 0 489.65 0 [kN] 0 0 296.1 0 0 0 0 0 427.18 0 Total [kN] 3887.97 3897.64 4655.49 4670.3 6025.65 6052.89 7713.58 7746.72 8725.31 8742 Deltares Group 3: Benchmarks from spreadsheets Table 3.184: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-17) for pipe nr. 1 Charac. point 1 2 3 4 5 6 7 8 9 10 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 2.6 2.54 2.11 2.02 1.66 1.48 0.72 0.51 0.11 0 [kN] 0 2.6 0 3.98 0 7.33 0 8.92 0 4.49 [kN] 0 0 17.83 0 14.77 0 31.65 0 16.62 0 [kN] 0 0 0 0 3.66 0 10.66 0 0 0 [kN] 0 0 1.53 0 0 0 0 0 8.25 0 Total [kN] 2.6 5.14 24.08 27.97 46.05 53.2 94.76 103.46 127.93 132.31 Table 3.185: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-17) for pipe nr. 2 Charac. point 1 2 3 4 5 6 7 8 9 10 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 430.7 420.34 349.36 333.5 274.7 245.52 119.52 84.02 17.87 0 [kN] 0 19.57 0 29.98 0 55.16 0 67.08 0 33.78 [kN] 0 0 134.16 0 121.3 0 245.27 0 125.03 0 [kN] 0 0 5.47 0 61.84 0 119.69 0 6.78 0 [kN] 0 0 34.54 0 0 0 0 0 66.17 0 Total [kN] 430.7 439.92 543.11 557.23 681.57 707.55 946.51 978.1 1109.92 1125.83 Table 3.186: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-17) for pipe nr. 3 Charac. point 1 2 3 4 5 6 7 8 9 10 Deltares Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 164.16 160.21 133.16 127.11 104.7 93.58 45.55 32.03 6.81 0 [kN] 0 27.49 0 42.1 0 77.47 0 94.21 0 47.44 [kN] 0 0 188.42 0 156.75 0 334.93 0 175.59 0 [kN] 0 0 0.36 0 49.67 0 124.74 0 0.44 0 [kN] 0 0 23.73 0 0 0 0 0 88.28 0 Total [kN] 164.16 187.7 373.16 409.21 593.22 659.57 1071.21 1151.9 1391 1431.63 77 of 126 D-G EO P IPELINE, Verification Report Table 3.187: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-17) for pipe nr. 4 Charac. point 1 2 3 4 5 6 7 8 9 10 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 456.95 445.96 370.66 353.83 291.44 260.48 126.8 89.14 18.96 0 [kN] 0 32.68 0 50.04 0 92.09 0 111.98 0 56.39 [kN] 0 0 223.95 0 226.19 0 426.01 0 208.71 0 [kN] 0 0 21.9 0 86.34 0 186.06 0 27.12 0 [kN] 0 0 44.09 0 0 0 0 0 110.78 0 Total [kN] 456.95 478.64 693.27 726.49 976.64 1037.76 1516.16 1590.48 1866.91 1904.33 Table 3.188: Analytical results for the calculation of the five components of the pulling force for the 10 characteristic points (bm3-17) for pipe nr. 5 Charac. point 1 2 3 4 5 6 7 8 9 10 3.17.3 Length [m] 0 43.04 338 403.91 648.25 769.54 1293.14 1440.63 1715.52 1789.79 T1 T2 T3a T3b T3c [kN] 2833.56 2765.42 2298.45 2194.1 1807.25 1615.24 786.29 552.78 117.58 0 [kN] 0 76.94 0 117.84 0 216.84 0 263.69 0 132.78 [kN] 0 0 527.34 0 1108.12 0 1405.99 0 491.46 0 [kN] 0 0 361.45 0 437.14 0 808.45 0 447.51 0 [kN] 0 0 221.71 0 0 0 0 0 330.13 0 Total [kN] 2833.56 2842.36 3485.89 3499.38 4657.8 4682.62 6068.11 6098.3 6932.19 6947.39 D-G EO P IPELINE results A Special Stress Analysis calculation must be performed by selecting Special Stress Analysis for the Start menu. D-G EO P IPELINE results can be found in the Report. Table 3.189: Results of benchmark 3-17, Buoyancy Control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe 78 of 126 Unit [kg/m] [kg/m] [kg/m] Benchmark 1414 1086 328 D-G EO P IPELINE 1415 1086 328 Error [%] 0.07 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.190: Results of benchmark 3-17, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 3887.97 43.04 3897.64 338 4655.49 1440.63 7746.72 1715.52 8725.31 1789.79 8742 4 D-G EO P IPELINE Length Force [m] [kN] 0 3887.97 43.04 3897.64 338 4655.49 1440.63 7746.72 1715.52 8725.31 1789.79 8742 4 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-17.dri to run this benchmark. 3.18 3.18.1 HDD with 3D geometry – Pipeline configuration not ending at surface and with an angle between radii Description The same input values as benchmark 3-1 (section 3.1) are used, only the pipeline configuration is slightly different: the configuration is not ending at surface but 5 meters below the surface and an angle between the radii is present. Two cases are checked: Case A (bm3-18a): the angle between the radii is positive; Case B (bm3-18b): the angle between the radii is negative. The configuration of the pipeline is given by: Xleft 10 m X-coordinate of the left entry point Yleft 10 m Y-coordinate of the left entry point Zleft 0m Z-coordinate of the left entry point Xright 690 m X-coordinate of the right exit point Yright -30 m Y-coordinate of the right exit point Zright -5 m Z-coordinate of the right exit point ◦ ϕleft 13 Left angle of the pipe ϕright 15◦ Right angle of the pipe Zbottom -50 m Lowest level of the pipe α ±2◦ Angle of pipe between radii Rleft 600 m Bending radius of the pipe at the left side Rright 800 m Bending radius of the pipe at the right side Rrol 1000 m Bending radius in pipe string (on rollers) 3.18.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Strength calculation For the buoyancy control, the pulling forces in the pipeline and the strength calculation, calculations are performed using the formulas given in chapter “Strength pipeline calculation” in the Background section of the User Manual of D-G EO P IPELINE. The position of the six characteristic points of the pipeline configuration is represented in Figure 3.5 and Figure 3.6. Their coordinates are given in the tables below. Deltares 79 of 126 D-G EO P IPELINE, Verification Report Table 3.191: Position of the 6 characteristic points (bm3-18a) for case a (positive angle between radii) Point 1 2 3 4 5 6 L-coord. [m] 10 161.55 317.46 350.59 441.52 620.66 X-coord. [m] 10 161.29 316.93 350 440.78 619.6 Z-coord. [m] 0 -34.99 -50 -48.84 -45.67 -18.9 Traject length [m] 0 155.534 312.614 345.764 436.752 618.266 Table 3.192: Position of the 6 characteristic points (bm3-18b) for case b Point 1 2 3 4 5 6 L-coord. [m] 10 144.81 258.84 350.59 369.51 604.49 X-coord. [m] 10 144.57 258.41 350 368.89 603.46 Z-coord. [m] 0 -31.12 -46.14 -49.34 -50 -23.23 Traject length [m] 0 138.353 253.545 345.35 364.287 601.652 Figure 3.5: Locations of the characteristic points T1 to T6 for case A (positive angle between radii) 80 of 126 Deltares Group 3: Benchmarks from spreadsheets Figure 3.6: Locations of the characteristic points T1 to T6 for case B (negative angle between radii) 3.18.3 D-G EO P IPELINE results D-G EO P IPELINE results presented in the tables below can be found in the Dumpfile. Table 3.193: Results of benchmark 3-18a, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 284.5 155.53 284.01 312.61 471.53 436.75 471.14 618.27 620.94 691.27 620.71 5188 D-G EO P IPELINE Length Force [m] [kN] 0 284.5 155.53 284.01 312.61 471.53 436.75 471.14 618.27 620.94 691.27 620.71 5188 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.194: Results of benchmark 3-18b, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Deltares Benchmark Length Force [m] [kN] 0 284.55 138.35 284.11 253.54 465.66 364.29 465.31 601.65 622.87 691.4 622.58 5187 D-G EO P IPELINE Length Force [m] [kN] 0 284.55 138.35 284.11 253.55 465.66 364.29 465.31 601.65 622.87 691.4 622.59 5187 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 81 of 126 D-G EO P IPELINE, Verification Report Use D-G EO P IPELINE input files bm3-18a.dri and bm3-18b.dri to run this benchmark. 3.19 3.19.1 HDD with 2D geometry – Stress Analysis per Vertical – Steel pipe Description The same sub-soil as benchmark 3-7 (section 3.7) is used, with a simple pipeline configuration as shown in Figure 3-7. A stress analysis per vertical is performed using 3 verticals at L = 70 m, L = 200 m and L = 1600 m. Figure 3.7: Locations of the characteristic points (T1 to T6) and the 3 verticals 3.19.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Soil mechanical data The soil mechanical data’s are determined using the formulas given in chapter “Calculation of soil mechanical data” in the Background section of the User Manual of D-G EO P IPELINE. Strength calculation For the buoyancy control, the pulling forces in the pipeline and the strength calculation, calculations are performed using the formulas given in chapter “Strength pipeline calculation” in the Background section of the User Manual of D-G EO P IPELINE. For the radius, the following values are used for each vertical: Vertical 1, situated in the first (left) descending straight part: R = 100 000 000 m; Vertical 2, situated in the left curved part: R = 1300 m; Vertical 3, situated in the right curved part: R = 1050 m. 82 of 126 Deltares Group 3: Benchmarks from spreadsheets 3.19.3 D-G EO P IPELINE results D-G EO P IPELINE results presented in the tables below can be found in the Report. Table 3.195: Results of benchmark 3-19, Buoyancy Control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe Unit [kg/m] [kg/m] [kg/m] Benchmark 2297 1288 1009 D-G EO P IPELINE 2297 1288 1009 Error [%] 0.00 0.00 0.00 Table 3.196: Results of benchmark 3-19, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 4532 43 4622 338 6477 1410 8730 1685 11136 1759 11292 36460 D-G EO P IPELINE Length Force [m] [kN] 0 4532 43 4622 338 6477 1410 8730 1685 11136 1759 11292 36460 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.197: Results of benchmark 3-19 for vertical nr. 1, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 304 49 353 353 D-G EO P IPELINE 304 49 353 353 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.198: Results of benchmark 3-19 for vertical nr. 1, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0 123 123 0.000065 0 0 0 123 D-G EO P IPELINE 0 123 123 0.000065 0 0 0 123 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 83 of 126 D-G EO P IPELINE, Verification Report Table 3.199: Results of benchmark 3-19 for vertical nr. 1, Strength calculation for Combination 2 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σpy σpx σptest σpm Benchmark 15 8 23 13 D-G EO P IPELINE 15 8 23 13 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.200: Results of benchmark 3-19 for vertical nr. 1, Strength calculation for Combination 3 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σb σa;max σqr σqn σt;max σV;max Benchmark 0 0 0 0 0 0 D-G EO P IPELINE 0 0 0 0 0 0 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.201: Results of benchmark 3-19 for vertical nr. 1, Strength calculation for Combination 4 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Benchmark 0 18 9 23 25 9 0 0 16 D-G EO P IPELINE 0 18 9 23 25 9 0 0 16 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.202: Results of benchmark 3-19 for vertical nr. 1, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 173.91 153.85 169.23 261.54 n.a. n.a. D-G EO P IPELINE 173.91 153.85 169.23 261.54 n.a. n.a. Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.203: Results of benchmark 3-19 for vertical nr. 1, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) 84 of 126 Unit [mm] [mm] [mm] Benchmark 0 255 120 D-G EO P IPELINE 0 255 120 Rel. error [%] 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.204: Results of benchmark 3-19 for vertical nr. 1, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark n.a. n.a. n.a. n.a. D-G EO P IPELINE n.a. n.a. n.a. n.a. Error Table 3.205: Results of benchmark 3-19 for vertical nr. 2, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 304 49 353 353 D-G EO P IPELINE 304 49 353 353 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.206: Results of benchmark 3-19 for vertical nr. 2, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 187 123 309 0.000174 0.05052 20 20 320 D-G EO P IPELINE 187 123 309 0.000174 0.05052 20 20 320 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.207: Results of benchmark 3-19 for vertical nr. 2, Strength calculation for Combination 2 Result σpy σpx σptest σpm Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 15 8 23 13 D-G EO P IPELINE 15 8 23 13 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.208: Results of benchmark 3-19 for vertical nr. 2, Strength calculation for Combination 3 Result σb σa;max σqr σqn σt;max σV;max Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 187 187 20 65 85 241 D-G EO P IPELINE 187 187 20 65 85 241 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 85 of 126 D-G EO P IPELINE, Verification Report Table 3.209: Results of benchmark 3-19 for vertical nr. 2, Strength calculation for Combination 4 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Benchmark 187 18 9 23 25 196 20 65 239 D-G EO P IPELINE 187 18 9 23 25 196 20 65 239 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.210: Results of benchmark 3-19 for vertical nr. 2, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 173.91 153.85 169.23 261.54 n.a. n.a. D-G EO P IPELINE 173.91 153.85 169.23 261.54 n.a. n.a. Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.211: Results of benchmark 3-19 for vertical nr. 2, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 6.1 255 120 D-G EO P IPELINE 6.1 255 120 Rel. error [%] 0.00 0.00 0.00 Table 3.212: Results of benchmark 3-19 for vertical nr. 2, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark n.a. n.a. n.a. n.a. D-G EO P IPELINE n.a. n.a. n.a. n.a. Error Table 3.213: Results of benchmark 3-19 for vertical nr. 3, Strength calculation for Combination 1A Result σb σt σa;max σV;max 86 of 126 Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 304 49 353 353 D-G EO P IPELINE 304 49 353 353 Rel. error [%] 0.00 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.214: Results of benchmark 3-19 for vertical nr. 3, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 231 123 354 0.000167 0.0578 23 23 366 D-G EO P IPELINE 231 123 354 0.000167 0.0578 23 23 366 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.215: Results of benchmark 3-19 for vertical nr. 3, Strength calculation for Combination 2 Result σpy σpx σptest σpm Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 15 8 23 13 D-G EO P IPELINE 15 8 23 13 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.216: Results of benchmark 3-19 for vertical nr. 3, Strength calculation for Combination 3 Result σb σa;max σqr σqn σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 231 231 23 95 117 307 D-G EO P IPELINE 231 231 23 95 117 307 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.217: Results of benchmark 3-19 for vertical nr. 3, Strength calculation for Combination 4 Result σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 231 18 9 23 25 240 23 95 304 D-G EO P IPELINE 231 18 9 23 25 240 23 95 304 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 87 of 126 D-G EO P IPELINE, Verification Report Table 3.218: Results of benchmark 3-19 for vertical nr. 3, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 173.91 153.85 169.23 261.54 n.a. n.a. D-G EO P IPELINE 173.91 153.85 169.23 261.54 n.a. n.a. Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.219: Results of benchmark 3-19 for vertical nr. 3, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 8.2 255 120 D-G EO P IPELINE 8.2 255 120 Rel. error [%] 0.00 0.00 0.00 Table 3.220: Results of benchmark 3-19 for vertical nr. 3, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark n.a. n.a. n.a. n.a. D-G EO P IPELINE n.a. n.a. n.a. n.a. Error Use D-G EO P IPELINE input file bm3-19.dri to run this benchmark. 3.20 3.20.1 HDD with 3D geometry – Stress Analysis per Vertical – PE pipe Description The same input as for benchmark 3-10 (section 3.10) is used except that a stress analysis per vertical instead of a standard analysis is performed using 3 verticals at L = 60 m, L = 170 m and L = 1000 m and only one synthetic pipe (PE 80) is used. 3.20.2 Analytical results Analytical results are worked out in an Excel spreadsheet. Strength calculation for bundled pipelines For the buoyancy control, the pulling forces in the pipeline and the strength calculation, calculations are performed using the formulas given in chapter “Strength pipeline calculation” in the Background section of the User Manual of D-G EO P IPELINE. For the radius, the following values are used for each vertical: Vertical 1, situated in the first (left) descending straight part: R = 100 000 000 m; Vertical 2, situated in the left curved part: R = 1300 m; Vertical 3, situated in the second bending: R = 1000.008 m. 88 of 126 Deltares Group 3: Benchmarks from spreadsheets 3.20.3 D-G EO P IPELINE results D-G EO P IPELINE results presented in the tables below can be found in the Report. Table 3.221: Results of benchmark 3-20, Buoyancy Control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe Unit [kg/m] [kg/m] [kg/m] Benchmark 653 166 488 D-G EO P IPELINE 654 166 488 Error [%] 0.15 0.00 0.00 Table 3.222: Results of benchmark 3-20, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 582 43 669 338 1353 1410 3510 1685 4387 1759 4537 897 D-G EO P IPELINE Length Force [m] [kN] 0 582 43 669 338 1353 1410 3510 1685 4387 1759 4537 897 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.223: Results of benchmark 3-20 for vertical nr. 1, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 1 6 6 n.a. D-G EO P IPELINE 1 6 6 n.a. Rel. error [%] 0.00 0.00 0.00 Table 3.224: Results of benchmark 3-20 for vertical nr. 1, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0 45 45 0.000398 0 0 0 n.a. D-G EO P IPELINE 0 45 45 0.000398 0 0 0 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 89 of 126 D-G EO P IPELINE, Verification Report Table 3.225: Results of benchmark 3-20 for vertical nr. 1, Strength calculation for Combination 2 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σpy σpx σptest σpm Benchmark 5 2 7 4 D-G EO P IPELINE 5 2 7 4 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.226: Results of benchmark 3-20 for vertical nr. 1, Strength calculation for Combination 3 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σb σa;max σqr σqn σt;max σV;max Benchmark 0 0 0 0 0 n.a. D-G EO P IPELINE 0 0 0 0 0 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 Table 3.227: Results of benchmark 3-20 for vertical nr. 1, Strength calculation for Combination 4 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Benchmark 0 5 2 7 0 2 0 0 n.a. D-G EO P IPELINE 0 5 2 7 0 2 0 0 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.228: Results of benchmark 3-20 for vertical nr. 1, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 6.4 5.04 n.a. n.a. 6.4 5.04 D-G EO P IPELINE 6.4 5.04 n.a. n.a. 6.4 5.04 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.229: Results of benchmark 3-20 for vertical nr. 1, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) 90 of 126 Unit [mm] [mm] [mm] Benchmark 0 64 44.8 D-G EO P IPELINE 0 64 44.8 Rel. error [%] 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.230: Results of benchmark 3-20 for vertical nr. 1, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark 297 30 0 0 D-G EO P IPELINE 297 30 0 0 Error 0.00 0.00 0.00 0.00 Table 3.231: Results of benchmark 3-20 for vertical nr. 2, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 1 6 6 n.a. D-G EO P IPELINE 1 6 6 n.a. Rel. error [%] 0.00 0.00 0.00 Table 3.232: Results of benchmark 3-20 for vertical nr. 2, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0 45 45 0.001125 0.00313 0 0 n.a. D-G EO P IPELINE 0 45 45 0.001125 0.00313 0 0 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.233: Results of benchmark 3-20 for vertical nr. 2, Strength calculation for Combination 2 Result σpy σpx σptest σpm Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 5 2 7 4 D-G EO P IPELINE 5 2 7 4 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.234: Results of benchmark 3-20 for vertical nr. 2, Strength calculation for Combination 3 Result σb σa;max σqr σqn σt;max σV;max Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0 0 0 4 3 n.a. D-G EO P IPELINE 0 0 0 4 3 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 91 of 126 D-G EO P IPELINE, Verification Report Table 3.235: Results of benchmark 3-20 for vertical nr. 2, Strength calculation for Combination 4 Result Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Benchmark 0 5 2 7 0 2 0 4 n.a. D-G EO P IPELINE 0 5 2 7 0 2 0 4 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.236: Results of benchmark 3-20 for vertical nr. 2, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 6.4 5.04 n.a. n.a. 6.4 5.04 D-G EO P IPELINE 6.4 5.04 n.a. n.a. 6.4 5.04 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.237: Results of benchmark 3-20 for vertical nr. 2, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 32.6 64 44.8 D-G EO P IPELINE 33 64 44.8 Rel. error [%] 1.22699386503067 0.00 0.00 Table 3.238: Results of benchmark 3-20 for vertical nr. 2, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark 297 30 0 0 D-G EO P IPELINE 297 30 0 0 Error 0.00 0.00 0.00 0.00 Table 3.239: Results of benchmark 3-20 for vertical nr. 3, Strength calculation for Combination 1A Result σb σt σa;max σV;max 92 of 126 Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 1 6 6 n.a. D-G EO P IPELINE 1 6 6 n.a. Rel. error [%] 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.240: Results of benchmark 3-20 for vertical nr. 3, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 1 45 45 0.000994 0.00302 0 0 n.a. D-G EO P IPELINE 1 45 45 0.000994 0.00302 0 0 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.241: Results of benchmark 3-20 for vertical nr. 3, Strength calculation for Combination 2 Result σpy σpx σptest σpm Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 5 2 7 4 D-G EO P IPELINE 5 2 7 4 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.242: Results of benchmark 3-20 for vertical nr. 3, Strength calculation for Combination 3 Result σb σa;max σqr σqn σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0 0 0 4 3 n.a. D-G EO P IPELINE 0 0 0 4 3 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 Table 3.243: Results of benchmark 3-20 for vertical nr. 3, Strength calculation for Combination 4 Result σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0 5 2 7 0 2 0 4 n.a. D-G EO P IPELINE 0 5 2 7 0 2 0 4 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 93 of 126 D-G EO P IPELINE, Verification Report Table 3.244: Results of benchmark 3-20 for vertical nr. 3, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 6.4 5.04 n.a. n.a. 6.4 5.04 D-G EO P IPELINE 6.4 5.04 n.a. n.a. 6.4 5.04 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.245: Results of benchmark 3-20 for vertical nr. 3, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 36.6 64 44.8 D-G EO P IPELINE 37 64 44.8 Rel. error [%] 1.09289617486339 0.00 0.00 Table 3.246: Results of benchmark 3-20 for vertical nr. 3, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark 297 30 0 0 D-G EO P IPELINE 297 30 0 0 Error 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-20.dri to run this benchmark. 3.21 3.21.1 HDD – Determination of the minimum allowable radius Description This benchmark checks the determination of the minimum allowable radius in two cases: Case A (bm3-21a): 4 different steel pipes with a diameter of 399, 400, 401 and 2000 mm are tested; Case B (bm3-21b): 20 different PE pipes with a diameter of 63, 100, 160, 180, 200, 225, 250, 290, 315, 335, 355, 380, 400, 500, 630, 680, 710, 760, 800 and 1000 mm are tested. 94 of 126 Deltares Group 3: Benchmarks from spreadsheets Case A In case A, two bending radius are present: a radius of 1750 m at the left and 500 m at the right as shown in Figure 3.8. Figure 3.8: Geometry of benchmark 3-21a The soil properties of the different are given in Table 3.247. Deltares 95 of 126 D-G EO P IPELINE, Verification Report Table 3.247: Properties of the different layers in benchmark 21a Name Dense sand Phi 35 Stiff clay Phi 22.5 Dense sand Phi 32.6 Stiff clay Phi 21 Med dense sand Phi 35 Stiff clay Phi 20 Med dense sand Phi 32.5 Stiff clay Phi 17.1 Med dense sand Phi 30.1 Med stiff clay Phi 22.5 Loose sand Phi 30 Med stiff clay Phi 21 Loose sand Phi 25.1 Med stiff clay Phi 20 Stiff sandy clay Phi 30 Med stiff clay Phi 17.1 Stiff sandy clay Phi 25 Soft clay Phi 20 Stiff sandy clay Phi 22.6 Soft clay Phi 17.1 Clayey sand Phi 25 Organic clay Phi 17 Clayey sand Phi 22.6 Organic clay Phi 16 Soil type Dense sand Stiff clay Dense sand Stiff clay Med dense sand Stiff clay Med dense sand Stiff clay Med dense sand Med stiff clay Loose sand Med stiff clay Loose sand Med stiff clay Stiff sandy clay Med stiff clay Stiff sandy clay Soft clay Stiff sandy clay Soft clay Clayey sand Organic clay Clayey sand Organic clay c [kN/m2 ] 1 15 0.5 10.1 0.6 15 2 10.1 0.6 10 1 7 0.1 10 1.1 5.1 5.1 5 12 3 5 15 4 30 ϕ ◦ [ ] 35 22.5 32.6 21 35 20 32.5 17.1 30.1 22.5 30 21 25.1 20 30 17.1 25 20 22.6 17.1 25 17 22.6 16 Top level [m] 0 -1 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30 -32 -34 -36 -38 -40 -42 -44 Constant C [-] 9400 10500 9400 10500 9400 10500 9400 10500 9400 11500 10500 11500 10500 11500 10500 11500 10500 12500 10500 12500 10500 12500 10500 12500 Case B In case B, four bending radius are present as shown in Figure 3.9. 96 of 126 Deltares Group 3: Benchmarks from spreadsheets Figure 3.9: Geometry of benchmark 3-21b 3.21.2 Analytical results Case A: Allowable curve radius for steel pipes The minimum allowable radius for steel pipes is: R ≥ 1000 √ × D0 for small pipe diameter (D0 ≤ 0.4 m) R ≥ C × D0 × dn for large pipe diameter (D0 > 0.4 m) where C is a constant (without dimension) depending on the soil type as shown in Table 3.248. Table 3.248: Values of constant C (according to table E.1 of NEN 3650-1 (NEN, 2012a)) Soil type Dense packed sand Moderate packed sand Loose packed sand Stiff clay Medium stiff clay Soft clay and peat Constant C [-] 8500 9400 10200 10500 11500 12500 In D-G EO P IPELINE, the soil type is a function of the cohesion and the friction angle of the soil, as shown in Table 3.249. Deltares 97 of 126 D-G EO P IPELINE, Verification Report Table 3.249: Soil type as a function of the cohesion and the friction angle Soil type Dense sand Medium dense sand Medium dense sand Loose sand Stiff sandy clay Stiff sandy clay Clayey sand Stiff clay Medium stiff clay Stiff clay Medium stiff clay Soft clay Peat /organic clay ϕ [◦ ] ϕ > 32.5 ϕ > 32.5 30 < ϕ ≤ 32.5 25 < ϕ ≤ 30 25 < ϕ ≤ 30 22.5 < ϕ ≤ 25 22.5 < ϕ ≤ 25 20 < ϕ ≤ 22.5 20 < ϕ ≤ 22.5 17 < ϕ ≤ 20 17 < ϕ ≤ 20 17 < ϕ ≤ 20 ϕ ≤ 17 c [kN/m2 ] c ≤ 0.5 c > 0.5 c≤1 c>1 c>5 c≤5 c > 10 c ≤ 10 c > 10 5 < c ≤ 10 c≤5 Constant C [-] 8500 9400 9400 10200 10500 10200 10500 10500 11500 10500 11500 12500 12500 In the case of a layered sub-soil, the highest C-value of a layer with a significant thickness is normative. In the case of a sub-soil with an alternation of layers with relative small thicknesses, a weighted interpolation can be performed to determine the C-value: Cd = n X i=1 Ci × di dtotal where dtotal = n X di (3.7) i=1 in which: n Total number of layers in the curve [-] Ci C-value of layer i [-] di Thickness of layer i [m] dtotal Total thickness of all layers in the curve [m] Case B: Allowable curve radius for polyethylene pipes According to article 8.6.4 of NEN 3650-3 (NEN, 2012c), the minimal curve-radius for PE pipes is equal to the bending factor as given in Table 3.250 times the diameter. Table 3.250: Bending factor (acc. to table 6 of NEN 3650-3) Diameter in mm 63 → 160 200 → 250 315 → 355 400 → 630 710 → 800 98 of 126 Bending factor 50 75 100 100 125 Deltares Group 3: Benchmarks from spreadsheets 3.21.3 D-G EO P IPELINE results The check for the minimum curve radius is performed in D-G EO P IPELINE by means of warning messages appearing when starting a calculation, as shown in Figure 3.10 and Figure 3.11. Figure 3.10: Warning message displayed for benchmark 3-21a Deltares 99 of 126 D-G EO P IPELINE, Verification Report Figure 3.11: Warning message displayed for benchmark 3-21b Table 3.251: Results of benchmark 3-21a, Allowable minimum radius for steel pipes Pipe R [m] → 399 mm 400 mm 401 mm 2000 mm 100 of 126 Benchmark 1750 398 [m] [m] 399 399 1631 2195 1633 2197 3647 4907 D-G EO P IPELINE 1750 398 [m] [m] 399 1000 1002 2082 2237 Error [%] 1750 398 [%] [%] 0 119.5 119.26 75.17 119.36 Deltares Group 3: Benchmarks from spreadsheets Table 3.252: Results of benchmark 3-21b, Allowable minimum radius for PE pipes R [m] → 63 mm 100 mm 160 mm 180 mm 200 mm 225 mm 250 mm 290 mm 315 mm 335 mm 355 mm 380 mm 400 mm 500 mm 630 mm 680 mm 710 mm 760 mm 800 mm 1000 mm 3 [m] 3 5 8 14 15 17 19 29 32 34 36 38 40 50 63 85 89 95 100 125 Benchmark 15 20 70 [m] [m] [m] 15 17 19 29 32 34 36 38 40 50 63 85 89 95 100 125 29 32 34 36 38 40 50 63 85 89 95 100 125 85 89 95 100 125 D-G EO P IPELINE 3 15 20 70 [m] [m] [m] [m] 3 5 8 14 15 15 17 17 19 19 29 29 29 32 32 32 34 34 34 36 36 36 38 38 38 40 40 40 50 50 50 63 63 63 85 85 85 85 89 89 89 89 95 95 95 95 100 100 100 100 125 125 125 125 3 [%] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Error [%] 15 20 [%] [%] 70 [%] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Use D-G EO P IPELINE input files bm3-21a.dri and bm3-21b.dri to run this benchmark. 3.22 3.22.1 HDD – PE pipe not filled with water on rollers Description This benchmark checks the effect of not-filling the pipe on rollers with water. The same input data’s as for benchmark 3-3 (section 3.3) are used except that the option Pipe filled with water on rollers is unchecked. This should have an influence on the calculation of T1 , the pulling force due to friction of the pipeline on the roller-lane. 3.22.2 Analytical results The pulling force due to friction of the pipeline on the roller-lane is: T1 = f1 × Lrol × g (3.8) where g = gpipe = 1.069 N/mm is the weight of the pipe on roller, without water filling, whereas for benchmark 3-3 (pipe filled with water on rollers) this weight is equal to: g = gpipe + gfill =1.069 + 0.391= 1.460 N/mm. Analytical results are worked out in an Excel spreadsheet. Results are given in the table below. Deltares 101 of 126 D-G EO P IPELINE, Verification Report Table 3.253: Analytical results for the calculation of the five components of the pulling force for the six characteristic points Charac. point 1 2 3 4 5 6 3.22.3 Length [m] 0 153.91 290.04 393.19 602.62 690.49 T1 T2 T3a T3b T3c [kN] 73.82 57.37 42.81 31.79 9.39 0 [kN] 0 144.61 0 45.17 0 82.55 [kN] 0 0 127.91 0 196.78 0 [kN] 0 0 5.72 0 4.29 0 [kN] 0 0 14.54 0 31.33 0 Total [kN] 73.82 201.97 335.59 421.47 631.48 704.64 D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report. Table 3.254: Results of benchmark 3-22, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 73.82 153.91 201.97 290.04 335.59 393.19 421.47 602.62 631.48 690.49 704.64 829 D-G EO P IPELINE Length Force [m] [kN] 0 73.82 153.91 201.98 290.05 335.59 393.19 421.47 602.63 631.48 690.49 704.64 829 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-22.dri to run this benchmark. 3.23 3.23.1 HDD – PE pipe always filled (100%) – Implosion Description This benchmark checks the effect of completely filling the pipe with fluid during pull back. The same input data’s as for benchmark 3-3 (section 3.3) are used except that the part of the pipe filled with fluid during pull back is 100% instead of 10%. This should have an influence on the calculation of the effective weight of the pipe (and the the pulling forces) and on the internal pressure during implosion check. 102 of 126 Deltares Group 3: Benchmarks from spreadsheets 3.23.2 Analytical results The weight of the filling with fluid is equal to: gfill = 100% ×γw × Ainw = 3.906 N/mm whereas for benchmark 3-3 (pipe filled with 10% fluid) this weight is equal to: gfill = 0.3906 N/mm. This will therefore have an infuence on the pulling forces. Analytical results are worked out in an Excel spreadsheet. Results are given in Table 3.255. Table 3.255: Analytical results for the calculation of the five components of the pulling force for the six characteristic points Charac. point 1 2 3 4 5 6 Length [m] 0 153.91 290.04 393.19 602.62 690.49 T1 T2 T3a T3b T3c [kN] 343.52 266.95 199.22 147.91 43.71 0 [kN] 0 36.4 0 11.37 0 20.78 [kN] 0 0 32.2 0 49.53 0 [kN] 0 0 5.72 0 4.29 0 [kN] 0 0 12.39 0 10.89 0 Total [kN] 343.52 303.35 285.93 259.01 219.53 196.6 During implosion check, the internal pressure due to complete filling is not nil but equal to: Pfilling = γfluid × [min (Zleft ; Zright ) − Zbottom ] (3.9) This leads to: Pfilling = 12 × (0 + 50) = 600 kN/m2 . 3.23.3 D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report. Table 3.256: Results of benchmark 3-23, Buoyancy Control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe Unit [kg/m] [kg/m] [kg/m] Benchmark 553 497 55 D-G EO P IPELINE 553 498 55 Error [%] 0.00 0.20 0.00 Table 3.257: Results of benchmark 3-23, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Deltares Benchmark Length Force [m] [kN] 0 343.52 153.91 303.35 290.04 285.93 393.19 259.01 602.62 219.53 690.49 196.6 829 D-G EO P IPELINE Length Force [m] [kN] 0 343.52 153.91 303.35 290.05 285.93 393.19 259.01 602.63 219.53 690.49 196.6 829 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 103 of 126 D-G EO P IPELINE, Verification Report Table 3.258: Results of benchmark 3-23, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark 396.55 39.66 600 600 D-G EO P IPELINE 396.55 39.66 600 600 Error 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-23.dri to run this benchmark. 3.24 3.24.1 HDD with 2D geometry – Effect of traffic loads Description This benchmark checks the effect of two traffic loads on the stress analysis. The same input data’s as for benchmark 3-1 (section 3.1) are used except that the Z co-ordinates of the top of the layers and the pipe configuration are divided by 10 in order to optimize the effect of the traffic load. The new geometry is given in Figure 3.12. The traffic loads have the following properties: Traffic Load 1: X co-ordinate at start X co-ordinate at end Load type Traffic Load 2: X co-ordinate at start X co-ordinate at end Load type 0m 110 m Graph I 600 m 700 m Graph II Figure 3.12: Geometry of benchmark 3-12 with 2 traffic loads 3.24.2 Analytical results According to article C.5.1 from NEN 3650-1 (NEN, 2012a), the traffic load qv is given by Figure 3.13, for both types of load and for four diameters: 200, 600, 1000 and 1600 mm. 104 of 126 Deltares Group 3: Benchmarks from spreadsheets Intermediary diameters are lineary interpolated. D-G EO P IPELINE uses the following formulas to convert this figure into numbers: For Graph I, For Graph I, For Graph I, For Graph I, For Graph II, For Graph II, For Graph II, For Graph II, 200 mm: qv = 53.988 ×Z −1.058 600 mm: qv = 51.403 ×Z −1.016 1000 mm: qv = 46.522 ×Z −0.94 1600 mm: qv = 39.448 ×Z −0.804 200 mm: qv = 31.716 ×Z −1.457 600 mm: qv = 29.501 ×Z −1.4 1000 mm: qv = 26.776 ×Z −1.324 1600 mm: qv = 21.963 ×Z −1.172 Figure 3.13: Traffic load as a function of the depth, for different pipe diameters, according to NEN 3650-1 In this benchmark, the pipe diameter is 800 mm, a linear interpolation between curves 600 mm and 1000 mm is performed and leads to the results given in Table 3.259. Deltares 105 of 126 D-G EO P IPELINE, Verification Report Table 3.259: Analytical results for the calculation of the traffic load Traffic Load 1 Vert. [-] 1 2 3 4 5 6 7 8 Z qv ; [m] -1.986 -4.686 -4.686 -4.686 -4.686 -4.686 -4.686 -2.34 [kN/m2 ] 34.556 14.448 14.448 n.a. n.a. n.a. n.a. n.a. 600 qv; 1000 [kN/m2 ] 32.949 14.705 14.705 n.a. n.a. n.a. n.a. n.a. Traffic Load 2 qv; 800 [kN/m2 ] 33.752 14.576 14.576 n.a. n.a. n.a. n.a. n.a. qv; 600 [kN/m2 ] n.a. n.a. n.a. n.a. n.a. n.a. 4.582 12.113 qv ; 1000 [kN/m2 ] n.a. n.a. n.a. n.a. n.a. n.a. 4.677 11.728 qv; 800 [kN/m2 ] n.a. n.a. n.a. n.a. n.a. n.a. 4.63 11.92 Hereafter are some intermediate results used for the pulling force and the strength calculations: Factor of friction pipe-roller Friction pipe-mud Factor of friction pipe-soil Load factor - Design pressure Load factor - Design pressure (combination) Load factor - Test pressure Load factor - Installation Load factor - Soil load Qn Load factor - Temperature Contingency factor - E-modulus Contingency factor - Pulling force Contingency factor - Modulus of subgrade reaction Contingency factor - Soil load Qn Contingency factor - Bending moment Contingency factor - Bending radius Contingency factor - Pressure borehole Factor of importance Allowable deflection of pipe (Steel) Piggability (Steel) Allowable deflection of pipe (PE) Piggability (PE) Unit weight water Safety factor cover (Drained layer) Safety factor cover (Undrained layer) Traffic load factor Effective weight of pipe Weight of pipeline (incl. filling) Uplift force Moment coefficient indirect bottom Moment coefficient indirect top Moment coefficient direct bottom Moment coefficient direct top Direct deflection factor Indirect deflection factor Part of pipe filled with water during pull back Cross sections of the pipe 106 of 126 f1 f2 f3 fpd fpd;comb fpt finstall fQn1 ftemp fE fpull fkv fQn2 fM fR fpress;bore S γw fqv geff gfill gupw kb ’ kt ’ kb kt ky ky ’ Pwater A 0.1 0.00005 0.2 1.25 1.15 1.1 1.1 1.5 1.1 1.25 1.4 1.6 1.1 1.27 1.1 1.1 1 17 8 n.a. n.a. 10 0.67 0.5 1.35 1.414 0.456 5.529 0.083 0.061 0.138 0.131 0.089 0.048 10 39769.979 [-] [N/mm2 ] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [%] [%] [%] [%] [N/mm3 ] [-] [-] [-] [N/mm] [N/mm] [N/mm] [-] [-] [-] [-] [-] [-] [%] [mm2 ] Deltares Group 3: Benchmarks from spreadsheets Atrek Ainw Minimal wall thickness dn;min Outer radius of the pipeline re Inner radius of the pipeline ri Average radius of the pipeline rg Moment of inertia of the pipe Ib Moment of inertia of the wall Iw Pipe resisting moment Wb Wall resisting moment Ww Unit weight of drilling fluid γdrill fluid Maximum modulus of subgrade reaction kv;max Maximum neutral vertical soil load qv;n;r;max Maximum traffic load qT;max Max. red. neutral vertical soil load (incl. traffic load) qv;n;r;maxT Max. corrected red. soil load (without traffic load) qn Max. corrected red. soil load (incl. traffic load) qnT Maximum neutral horizontal soil load qh;n;r Soil reaction - Left curve qr;left Soil reaction - Right curve qr;right Soil reaction - Left curve (long term) qr;left Soil reaction - Right curve (long term) qr;right Characteristic stiffness pipeline-soil λ Characteristic stiffness pipeline-soil (long term) λlong 3.24.3 46618.093 456036.731 16.15 400 381 390.5 3556505999 571.583 8891265 60.167 11 31637.947 57.835 33.752 43.258 71.376 95.427 42.866 502.806 377.104 n.a. n.a. 0.0003049 n.a. [mm2 ] [mm2 ] [mm] [mm] [mm] [mm] [mm4 ] [mm3 ] [mm4 m] [mm3 m] [kN/m3 ] [kN/m3 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [mm-1 ] [mm-1 ] D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report. Table 3.261: Results of benchmark 3-24, Buoyancy control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe Unit [kg/m] [kg/m] [kg/m] Benchmark 553 412 141 D-G EO P IPELINE 553 412 141 Error [%] 0.00 0.00 0.00 Table 3.262: Results of benchmark 3-24, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Deltares Benchmark Length Force [m] [kN] 0 280 15 280 29 2026 651 2024 672 3437 681 3437 0 D-G EO P IPELINE Length Force [m] [kN] 0 280 15 280 29 2026 651 2024 672 3437 681 3437 0 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 107 of 126 D-G EO P IPELINE, Verification Report Table 3.263: Results of benchmark 3-24, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 1265 11 1276 1276 D-G EO P IPELINE 1265 11 1276 1276 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.264: Results of benchmark 3-24, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 2108 133 2241 0.000305 0.5028 217 217 2358 D-G EO P IPELINE 2108 133 2241 0.000305 0.5028 217 217 2358 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.265: Results of benchmark 3-24, Strength calculation for Combination 2 Result σpy σpx σptest σpm Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 18 9 22 16 D-G EO P IPELINE 18 9 22 16 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.266: Results of benchmark 3-24, Strength calculation for Combination 3 Result σb σa;max σqr σqn σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] 108 of 126 Benchmark 2108 2108 217 69 286 2265 D-G EO P IPELINE 2108 2108 217 69 286 2265 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.267: Results of benchmark 3-24, Strength calculation for Combination 4 Result σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 2108 17 8 22 26 2117 217 69 2258 D-G EO P IPELINE 2108 17 8 22 26 2117 217 69 2258 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.268: Results of benchmark 3-24, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 235 213.64 235 363.18 n.a. n.a. D-G EO P IPELINE 235 213.64 235 363.18 n.a. n.a. Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.269: Results of benchmark 3-24, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 12.1 136 64 D-G EO P IPELINE 12.1 136 64 Rel. error [%] 0.00 0.00 0.00 Table 3.270: Results of benchmark 3-24, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark n.a. n.a. n.a. n.a. D-G EO P IPELINE n.a. n.a. n.a. n.a. Error Use D-G EO P IPELINE input file bm3-24.dri to run this benchmark. 3.25 3.25.1 HDD with safety factors from the European Standard CEN – Steel pipe Description This benchmark checks the use of the safety factors from the European Standard CEN in combination with a steel pipe. The same input data’s as for benchmark 3-7a (section 3.7) are used except that the safety factors are different: when selecting the European Standard CEN, no factor is apllied on the loads. The choice of a different standard will have effects only on the strength calculation. Deltares 109 of 126 D-G EO P IPELINE, Verification Report 3.25.2 Analytical results Hereafter are some intermediate results used for the pulling force and the strength calculations: Factor of friction pipe-roller Friction pipe-mud Factor of friction pipe-soil Load factor - Design pressure Load factor - Design pressure (combination) Load factor - Test pressure Load factor - Installation Load factor - Soil load Qn Load factor - Temperature Contingency factor - E-modulus Contingency factor - Pulling force Contingency factor - Modulus of subgrade reaction Contingency factor - Soil load Qn Contingency factor - Bending moment Contingency factor - Bending radius Contingency factor - Pressure borehole Factor of importance Allowable deflection of pipe (Steel) Piggability (Steel) Allowable deflection of pipe (PE) Piggability (PE) Unit weight water Safety factor cover (Drained layer) Safety factor cover (Undrained layer) Traffic load factor Effective weight of pipe Weight of pipeline (incl. filling) Uplift force Moment coefficient indirect bottom Moment coefficient indirect top Moment coefficient direct bottom Moment coefficient direct top Direct deflection factor Indirect deflection factor Part of pipe filled with water during pull back Cross sections of the pipe Minimal wall thickness Outer radius of the pipeline Inner radius of the pipeline Average radius of the pipeline Moment of inertia of the pipe Moment of inertia of the wall Pipe resisting moment Wall resisting moment Unit weight of drilling fluid Maximum modulus of subgrade reaction Maximum neutral vertical soil load 110 of 126 f1 f2 f3 fpd fpd;comb fpt finstall fQn1 ftemp fE fpull fkv fQn2 fM fR fpress;bore S γw fqv geff gfill gupw kb ’ kt ’ kb kt ky ky ’ Pwater A Atrek Ainw dn;min re ri rg Ib Iw Wb Ww γdrill fluid kv;max qv;n;r;max 0.2 0.00035 0.3 n.a n.a n.a n.a n.a n.a 1.4 1.1 1.1 1.2 n.a 1.3 1.15 1 17 8 n.a. n.a. 10 0.67 0.5 1.35 10.093 2.409 22.973 0.073 0.056 0.139 0.139 0.091 0.043 15 121535.457 161085.163 1606060.704 26.25 750 715 732.5 43240291745 3572.917 57653722 204.167 13 20467.554 154.787 [-] [N/mm2 ] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [%] [%] [%] [%] [N/mm3 ] [-] [-] [-] [N/mm] [N/mm] [N/mm] [-] [-] [-] [-] [-] [-] [%] [mm2 ] [mm2 ] [mm2 ] [mm] [mm] [mm] [mm] [mm4 ] [mm3 ] [mm4 m] [mm3 m] [kN/m3 ] [kN/m3 ] [kN/m2 ] Deltares Group 3: Benchmarks from spreadsheets Maximum traffic load Max. red. neutral vertical soil load (incl. traffic load) Max. corrected red. soil load (without traffic load) Max. corrected red. soil load (incl. traffic load) Maximum neutral horizontal soil load Soil reaction - Left curve Soil reaction - Right curve Soil reaction - Left curve (long term) Soil reaction - Right curve (long term) Characteristic stiffness pipeline-soil Characteristic stiffness pipeline-soil (long term) 3.25.3 qT;max qv;n;r;maxT qn qnT qh;n;r qr;left qr;right qr;left qr;right λ λlong 0 154.787 185.744 185.744 101.846 52.606 65.131 n.a. n.a. 0.0001771 n.a. [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [mm-1 ] [mm-1 ] D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report. Table 3.272: Results of benchmark 3-25, Buoyancy Control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe Unit [kg/m] [kg/m] [kg/m] Benchmark 2297 1288 1009 D-G EO P IPELINE 2297 1288 1009 Error [%] 0.00 0.00 0.00 Table 3.273: Results of benchmark 3-25, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 4610 43 4701 338 6579 1441 14235 1716 16676 1790 16832 3332 D-G EO P IPELINE Length Force [m] [kN] 0 4610 43 4701 338 6579 1441 14235 1716 16676 1790 16832 3332 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.274: Results of benchmark 3-25, Strength calculation for Combination 1A Result σb σt σa;max σV;max Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 220 42 262 262 D-G EO P IPELINE 220 42 262 262 Rel. error [%] 0.00 0.00 0.00 0.00 111 of 126 D-G EO P IPELINE, Verification Report Table 3.275: Results of benchmark 3-25, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 251 152 404 0.000177 0.0977 39 39 424 D-G EO P IPELINE 251 152 404 0.000177 0.0977 39 39 424 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.276: Results of benchmark 3-25, Strength calculation for Combination 2 Result σpy σpx σptest σpm Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 14 7 25 12 D-G EO P IPELINE 14 7 25 12 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.277: Results of benchmark 3-25, Strength calculation for Combination 3 Result σb σa;max σqr σqn σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 251 251 39 140 178 374 D-G EO P IPELINE 251 251 39 140 178 374 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.278: Results of benchmark 3-25, Strength calculation for Combination 4 Result σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] 112 of 126 Benchmark 251 14 7 25 13 258 39 140 365 D-G EO P IPELINE 251 14 7 25 13 258 39 140 365 Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Deltares Group 3: Benchmarks from spreadsheets Table 3.279: Results of benchmark 3-25, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 173.91 153.85 169.23 278 n.a. n.a. D-G EO P IPELINE 173.91 153.85 169.23 278 n.a. n.a. Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.280: Results of benchmark 3-25, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 10.5 255 120 D-G EO P IPELINE 10.5 255 120 Rel. error [%] 0.00 0.00 0.00 Table 3.281: Results of benchmark 3-25, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark n.a. n.a. n.a. n.a. D-G EO P IPELINE n.a. n.a. n.a. n.a. Error Use D-G EO P IPELINE input file bm3-25.dri to run this benchmark. 3.26 3.26.1 HDD with safety factors from the European Standard CEN – PE pipe Description This benchmark checks the use of the safety factors from the European Standard CEN in combination with a PE pipe. The same input data’s as for benchmark 3-24 (section 3.24) are used except that a PE pipe is used instead of a steel pipe. 3.26.2 Analytical results Hereafter are some intermediate results used for the pulling force and the strength calculations: Factor of friction pipe-roller Friction pipe-mud Factor of friction pipe-soil Load factor - Design pressure Load factor - Design pressure (combination) Load factor - Test pressure Load factor - Installation Load factor - Soil load Qn Load factor - Temperature Contingency factor - E-modulus Contingency factor - Pulling force Deltares f1 f2 f3 fpd fpd;comb fpt finstall fQn1 ftemp fE fpull 0.2 0.00035 0.3 n.a n.a n.a n.a n.a n.a 1.4 1.1 [-] [N/mm2 ] [-] [-] [-] [-] [-] [-] [-] [-] [-] 113 of 126 D-G EO P IPELINE, Verification Report Contingency factor - Modulus of subgrade reaction Contingency factor - Soil load Qn Contingency factor - Bending moment Contingency factor - Bending radius Contingency factor - Pressure borehole Factor of importance Allowable deflection of pipe (Steel) Piggability (Steel) Allowable deflection of pipe (PE) Piggability (PE) Unit weight water Safety factor cover (Drained layer) Safety factor cover (Undrained layer) Traffic load factor Effective weight of pipe Weight of pipeline (incl. filling) Uplift force Moment coefficient indirect bottom Moment coefficient indirect top Moment coefficient direct bottom Moment coefficient direct top Direct deflection factor Indirect deflection factor Part of pipe filled with water during pull back Cross sections of the pipe fkv fQn2 fM fR fpress;bore S γw fqv geff gfill gupw kb ’ kt ’ kb kt ky ky ’ Pwater A Atrek Ainw Minimal wall thickness dn;min Outer radius of the pipeline re Inner radius of the pipeline ri Average radius of the pipeline rg Moment of inertia of the pipe Ib Moment of inertia of the wall Iw Pipe resisting moment Wb Wall resisting moment Ww Unit weight of drilling fluid γdrill fluid Maximum modulus of subgrade reaction kv;max Maximum neutral vertical soil load qv;n;r;max Maximum traffic load qT;max Max. red. neutral vertical soil load (incl. traffic load) qv;n;r;maxT Max. corrected red. soil load (without traffic load) qn Max. corrected red. soil load (incl. traffic load) qnT Maximum neutral horizontal soil load qh;n;r Soil reaction - Left curve qr;left Soil reaction - Right curve qr;right Soil reaction - Left curve (long term) qr;left Soil reaction - Right curve (long term) qr;right Characteristic stiffness pipeline-soil λ Characteristic stiffness pipeline-soil (long term) λlong 114 of 126 1.1 1.2 n.a n.a. 1.15 1 n.a. n.a. 8 5 10 0.67 0.5 1.35 4.874 0.585 6.535 0.073 0.056 0.139 0.139 0.091 0.043 15 112735.141 112735.141 389919.683 47.7 400 352.3 376.15 8007444342 9044.278 20018611 379.215 13 61938.505 76.383 0 76.383 91.659 91.659 50.258 3.087 3.823 1.381 1.71 0.0011153 0.0016677 [-] [-] [-] [-] [-] [-] [%] [%] [%] [%] [N/mm3 ] [-] [-] [-] [N/mm] [N/mm] [N/mm] [-] [-] [-] [-] [-] [-] [%] [mm2 ] [mm2 ] [mm2 ] [mm] [mm] [mm] [mm] [mm4 ] [mm3 ] [mm4 m] [mm3 m] [kN/m3 ] [kN/m3 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [kN/m2 ] [mm-1 ] [mm-1 ] Deltares Group 3: Benchmarks from spreadsheets 3.26.3 D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report. Table 3.283: Results of benchmark 3-26, Buoyancy control Result Uplift forces Weight of pipeline (incl. filling) Effective weight of pipe Benchmark 653 166 487 Unit [kg/m] [kg/m] [kg/m] D-G EO P IPELINE 654 166 488 Error [%] 0.15 0.00 0.21 Table 3.284: Results of benchmark 3-26, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force Benchmark Length Force [m] [kN] 0 594.34 43.04 680.84 338 1364.62 1440.63 4234.93 1715.52 5116.67 1789.79 5265.94 860 D-G EO P IPELINE Length Force [m] [kN] 0 594.34 43.04 680.84 338 1364.62 1440.63 4234.93 1715.52 5116.67 1789.79 5265.94 860 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.285: Results of benchmark 3-26, Strength calculation for Combination 1A Result σb σt σa;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.5 5.8 6.12 n.a. D-G EO P IPELINE 0.5 5.8 6.12 n.a. Rel. error [%] 0.00 0.00 0.00 Table 3.286: Results of benchmark 3-26, Strength calculation for Combination 1B Result σb σt σa;max λ qr σqr σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [mm-1 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.57 51.38 51.75 0.001115 0.00573 0.33 0.33 n.a. D-G EO P IPELINE 0.57 51.38 51.75 0.001115 0.00573 0.33 0.33 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 3.287: Results of benchmark 3-26, Strength calculation for Combination 2 Result σpy σpx σptest σpm Deltares Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 4.75 2.38 6.6 4.11 D-G EO P IPELINE 4.75 2.38 6.6 4.11 Rel. error [%] 0.00 0.00 0.00 0.00 115 of 126 D-G EO P IPELINE, Verification Report Table 3.288: Results of benchmark 3-26, Strength calculation for Combination 3 Result σb σa;max σqr σqn σt;max σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.11 0.07 0.15 10.11 6.67 n.a. D-G EO P IPELINE 0.11 0.07 0.15 10.26 6.76 n.a. Rel. error [%] 0.00 0.00 0.00 1.48 1.35 Table 3.289: Results of benchmark 3-26, Strength calculation for Combination 4 Result σb σpy σpx σptest σptemp σa;max σqr σqn σV;max Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 0.11 4.75 2.38 6.6 0.36 2.45 0.15 10.11 n.a. D-G EO P IPELINE 0.11 4.75 2.38 6.6 0.36 2.45 0.15 10.26 n.a. Rel. error [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.48 Table 3.290: Results of benchmark 3-26, Maximum allowable stresses Result σptest σpy σpm σV;max σa/t (short) σa/t (long) Unit [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] [N/mm2 ] Benchmark 6.4 5.04 n.a. n.a. 6.4 5.04 D-G EO P IPELINE 6.4 5.04 n.a. n.a. 6.4 5.04 Rel. error [%] 0.00 0.00 0.00 0.00 Table 3.291: Results of benchmark 3-26, Deflection of the pipeline Result Calculated Max. allowable Max. allow. (piggability) Unit [mm] [mm] [mm] Benchmark 85.4 64 44.8 D-G EO P IPELINE 86.6 64 44.8 Rel. error [%] 1.41 0.00 0.00 Table 3.292: Results of benchmark 3-26, Implosion Result Max. allow. external pressure (short) Max. allow. external pressure (long) Int. pressure due to 100% filling (short) Int. pressure due to 100% filling (long) Unit [kPa] [kPa] [kPa] [kPa] Benchmark 303.46 30.35 0 0 D-G EO P IPELINE 303.46 30.35 0 0 Error 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm3-26.dri to run this benchmark. 116 of 126 Deltares 4 Group 4: Benchmarks generated by D-G EO P IPELINE This chapter contains benchmarks for which the reference results are generated using D-G EO P IPELINE. 4.1 4.1.1 HDD with 3D geometry – Check of the pulling direction Description This benchmark checks the pulling direction. The same input data’s as for benchmark 3-7b (section 3.7) are used except that the geometry is inversed (mirror symmetry) and the pulling direction is from left to right instead of right to left. Results for the pulling forces are therefore expected to be the same. 4.1.2 D-G EO P IPELINE results Both files give identical results. Table 4.1: Results of benchmark 4-01, Pulling forces in the pipeline Charac. points T1 T2 T3 T4 T5 T6 Max. rep. pulling force D-G EO P IPELINE (bm3-7b) Length Force [m] [kN] 0 4610 74 4766 349 6884 1452 14562 1747 16745 1790 16836 20468 D-G EO P IPELINE (bm4-1) Length Force [m] [kN] 0 4610 74 4766 349 6884 1452 14562 1747 16745 1790 16836 20467 Relative error Length Force [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm4-1.dri to run this benchmark. Deltares 117 of 126 D-G EO P IPELINE, Verification Report 118 of 126 Deltares 5 Group 5: Benchmarks compared with other programs These benchmarks are intended to verify specific features of D-G EO P IPELINE comparing D-G EO P IPELINE results with those from an other program. 5.1 5.1.1 Settlements according to Koppejan model Description The same input data’s as benchmark 1-1 (section 3.1) are used, except that a trapezoidal load (γunsat = 17 kN/m3 and γsat = 20 kN/m3 ) is added at the top of the Clay layer as shown in Figure 5.1. A settlement calculation is performed using the Koppejan model with the parameters given in Table 5.1. Table 5.1: Koppejan’s parameters (benchmark 5-1) Parameter OCR Cp Cp ’ Cs Cs ’ Unit [-] [-] [-] [-] [-] Sand 1.3 200 100 500 150 Clay 1.1 1.1 10 200 80 Figure 5.1: Geometry of benchmark 5-1 5.1.2 D-S ETTLEMENT results Benchmark results for the settlements calculation are calculated using the D-S ETTLEMENT program (formally known as MSettle). Calculations are performed for 8 verticals and the results for each vertical are worked out in an Excel spreadsheet. A linear interpolation is used to get the settlement at the desired depth. Results are given in Table 5.2. Deltares 119 of 126 D-G EO P IPELINE, Verification Report 5.1.3 D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report. Table 5.2: Results of benchmark 5-01, Settlements according to Koppejan Vert. nr. [-] 1 2 3 4 5 6 7 8 Settl. [mm] 1 2 21 35 18 32 2 1 Benchmark Add. dv [mm] [mm] 5 6 10 12 20 41 50 85 50 68 20 52 10 12 5 6 D-G EO P IPELINE Settl. Add. dv [mm] [mm] [mm] 1 5 6 2 10 12 21 20 41 35 50 85 18 50 68 32 20 52 2 10 12 1 5 6 Settl. [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Relative error Add. dv [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input file bm5-1.dri to run this benchmark. 5.2 5.2.1 Settlements according to Isotache model Description The same input data’s as benchmark 1-1 (section 3.1) are used, except that a trapezoidal load (γunsat = 17 kN/m3 and γsat = 20 kN/m3 ) is added at the top of the Clay layer (see section 5.1). A settlement calculation is performed using the Isotache model with the parameters given in Table 5.3. Benchmark 5-2a uses an OCR parameter whereas benchmark 5-2b uses a P OP parameter for the modelisation of the preconsolidation process. Table 5.3: Isotache’s parameters (bm5-02) Parameter OCR (bm5-2a) P OP (bm5-2b) a b c 5.2.2 Unit [-] [kN/m2 ] [-] [-] [-] Sand 1.3 15 0.005 0.05 0.005 Clay 1.1 20 0.001 0.01 0.001 D-S ETTLEMENT results Benchmark results for the settlements calculation are calculated using the D-S ETTLEMENT program (formally known as MSettle). Calculations are performed for 8 verticals and the results for each vertical are worked out in an Excel spreadsheet. A linear interpolation is used to get the settlement at the desired Z depth. Results are given in Table 5.4 and Table 5.5. 120 of 126 Deltares Group 5: Benchmarks compared with other programs 5.2.3 D-G EO P IPELINE results D-G EO P IPELINE results can be found in the Report. Table 5.4: Results of benchmark 5-02a, Settlements according to Isotache with OCR consolidation Vert. nr. [-] 1 2 3 4 5 6 7 8 Settl. [mm] 1524 1483 1339 702 397 659 1473 1522 Benchmark Add. dv [mm] [mm] 5 1529 10 1493 20 1359 50 752 50 447 20 679 10 1483 5 1527 D-G EO P IPELINE Settl. Add. dv [mm] [mm] [mm] 1524 5 1529 1483 10 1493 1339 20 1359 702 50 752 397 50 447 659 20 679 1473 10 1483 1522 5 1527 Relative error Settl. Add. dv [%] [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Table 5.5: Results of benchmark 5-02b, Settlements according to Isotache with POP consolidation Vert. nr. [-] 1 2 3 4 5 6 7 8 Settl. [mm] 1891 1867 1695 872 495 820 1859 1890 Benchmark Add. dv [mm] [mm] 5 1896 10 1877 20 1715 50 922 50 545 20 840 10 1869 5 1895 D-G EO P IPELINE Settl. Add. dv [mm] [mm] [mm] 1891 5 1896 1867 10 1877 1695 20 1715 872 50 922 495 50 545 820 20 840 1859 10 1869 1890 5 1895 Relative error Settl. Add. dv [%] [%] [%] 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Use D-G EO P IPELINE input files bm5-2a.dri and bm5-2b.dri to run this benchmark. Deltares 121 of 126 D-G EO P IPELINE, Verification Report 122 of 126 Deltares Bibliography Deltares. D-Geo Pipeline User Manual. Deltares. NEN, 2012a. NEN 3650-1:2012. Eisen voor buisleidingsystemen - Deel 1: Algemene eisen (Requirements for pipeline systems - Part 1: General requirements), in Dutch. NEN, 2012b. NEN 3650-2:2012. Eisen voor buisleidingsystemen - Deel 2: Aanvullende eisen voor leidingen van staal (Requirements for pipeline systems - Part 2: Additional specifications for steel pipelines), in Dutch. NEN, 2012c. NEN 3650-3:2012. Eisen voor buisleidingsystemen - Deel 3: Aanvullende eisen voor leidingen van kunststof (Requirements for pipeline systems - Part 3: Additional specifications for plastic pipelines), in Dutch. NEN, 2012d. NEN 3651:2012. Aanvullende eisen voor buisleidingen in of nabij belangrijke waterstaatswerken (Additional requirements for pipelines in or nearby important public works), in Dutch. Deltares 123 of 126 D-G EO P IPELINE, Verification Report 124 of 126 Deltares 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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