3D modelling of single piles and pile groups D-P...

Verification Report

D-Pile GrouP

3D modelling of single piles and pile groups

D-PILE GROUP

3D modelling of single piles and pile groups

Verification Report

Version: 15.1Revision: 00

13 April 2015

D-PILE GROUP, Verification Report

Published and printed by:DeltaresBoussinesqweg 12629 HV DelftP.O. 1772600 MH DelftThe Netherlands

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Copyright © 2015 DeltaresAll rights reserved. No part of this document may be reproduced in any form by print, photoprint, 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) 31.1 One pile with an user defined pile tip curve is loaded by a vertical displace-

ment, only end bearing is considered . . . . . . . . . . . . . . . . . . . . . 31.1.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Two piles in elastic soil loaded and then unloaded by a horizontal centric force 31.2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Single pile in elasto-plastic soil loaded and then unloaded by a horizontal force 41.3.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Single pile, with pile top 2 m above ground level, loaded by a force . . . . . . 51.4.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 One pile is loaded by a horizontal force, user defined lateral curve . . . . . . 51.5.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 61.5.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 6

1.6 Single pile loaded by soil displacements . . . . . . . . . . . . . . . . . . . 61.6.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.6.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 61.6.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 6

1.7 Pile group of 4 piles loaded by a horizontal load . . . . . . . . . . . . . . . . 71.7.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.7.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 71.7.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 7

1.8 Pile group of 100 piles loaded by several forces . . . . . . . . . . . . . . . . 71.8.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.8.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 71.8.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 8

1.9 Two floating piles loaded by a moment . . . . . . . . . . . . . . . . . . . . 81.9.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.9.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 81.9.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 8

1.10 Single pile loaded by two surface loads, symmetrically positioned around thepile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.10.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.10.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 91.10.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 9

1.11 Single pile loaded by two opposite surface loads (same position, different loadsign) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.11.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.11.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 91.11.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 10

1.12 Determination of EI and EA for different pile types . . . . . . . . . . . . . . 101.12.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

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1.12.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 101.12.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 11

1.13 One pile is loaded by a force, rotation around Z-axis zero - rotation aroundZ-axis free . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.13.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.13.2 Benchmark result . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.13.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Group 2: Benchmarks from literature (approximate solution) 132.1 Single laterally loaded pile; Lake Austin test . . . . . . . . . . . . . . . . . . 13

2.1.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Collision of a ship against a pile (Dynamic model) . . . . . . . . . . . . . . . 152.2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Group 3: Benchmarks from spreadsheets 173.1 Vertical and horizontal displacements due to a concentrated load on a semi-

infinite solid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.1.1 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 173.1.2 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Lateral P − Y curve for clay and static loading (API) . . . . . . . . . . . . . 203.2.1 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2.2 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3 Lateral P − Y curve for clay and cyclic loading (API cyclic) . . . . . . . . . . 233.3.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 Lateral P − Y curve for sand and static loading (API) . . . . . . . . . . . . 253.4.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 26

3.5 Lateral P − Y curve for sand and cyclic loading (API cyclic) . . . . . . . . . 273.5.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.5.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 273.5.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 27

3.6 Lateral P − Y curve for undrained sand (API undrained) . . . . . . . . . . . 283.6.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.6.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 283.6.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 30

3.7 Axial T − Z curve for clay (API) . . . . . . . . . . . . . . . . . . . . . . . 313.7.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.7.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 313.7.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 32

3.8 Axial T − Z curve for clay (Ratio) . . . . . . . . . . . . . . . . . . . . . . 343.8.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.8.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 343.8.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 35

3.9 Axial T − Z curve for sand (API) . . . . . . . . . . . . . . . . . . . . . . . 363.9.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.9.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 363.9.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 37

iv Deltares

Contents

3.10 Axial T − Z curve for sand (Cone) . . . . . . . . . . . . . . . . . . . . . . 373.10.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.10.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 383.10.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 38

4 Group 4: Benchmarks generated by D-PILE GROUP 414.1 One pile loaded by a force, two different directions are considered . . . . . . 41

4.1.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.1.2 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2 Two piles loaded by an eccentric force – two piles loaded by a centric forceand a moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.2.2 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 42

4.3 One pile with user defined lateral curve is loaded by a force . . . . . . . . . . 424.3.1 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 43

4.4 One pile with user defined axial curve is loaded by a force . . . . . . . . . . 434.4.1 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 43

4.5 One pile is loaded by a vertical force, only end bearing is considered . . . . . 434.5.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.5.2 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 44

4.6 Single pile, with pile top 2m above ground level, loaded by a moment, consid-ered around two different axis . . . . . . . . . . . . . . . . . . . . . . . . . 444.6.1 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 44

4.7 One pile is loaded by a force, the same pile is loaded by the displacement(result of the force) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.7.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.7.2 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 45

4.8 A pile group loaded by a horizontal force . . . . . . . . . . . . . . . . . . . 454.8.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.8.2 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 46

4.9 A pile group of 7 piles is loaded by a horizontal force, comparison of Poulosand Cap soil interaction models . . . . . . . . . . . . . . . . . . . . . . . . 474.9.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.9.2 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 48

4.10 Calculation of the plasticity factors for the Plasti-Poulos model . . . . . . . . . 484.10.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.10.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 484.10.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 52

5 Group 5: Benchmarks compared with other programs 555.1 Two inclined piles in layered soil, complex case . . . . . . . . . . . . . . . . 55

5.1.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.1.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 555.1.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 55

5.2 3-piles group under general loading (Poulos theory) . . . . . . . . . . . . . . 565.2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.2.2 Benchmark results . . . . . . . . . . . . . . . . . . . . . . . . . . 565.2.3 D-PILE GROUP results . . . . . . . . . . . . . . . . . . . . . . . . 56

References 59

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vi Deltares

List of Figures

List of Figures

2.1 Lake Austin test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Calculated and measured pile displacement (left) and bending moment (right)

along the pile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Benchmark 2-2 – Calculated and measured forces and displacements (at the

end of collision) for different velocities . . . . . . . . . . . . . . . . . . . . . 16

3.1 Pile displacements along the pile . . . . . . . . . . . . . . . . . . . . . . . 193.2 Soil and pile profiles for benchmark bm3-2 . . . . . . . . . . . . . . . . . . 213.3 Lateral P − Y curve for clay and static load at different depths (bm3-2) . . . . 223.4 Lateral P − Y curve for clay and cyclic load at different depths (bm3-3) . . . 243.5 Lateral P − Y curve for sand and static load at different depths (bm3-4) . . . 263.6 Lateral P − Y curve for sand and cyclic load at different depths (bm3-5) . . . 273.7 Lateral P − Y curve for undrained sand at different depths (bm3-6) . . . . . 303.8 Skin friction along the pile for T − Z curve for clay (API) . . . . . . . . . . . 333.9 Skin friction along the pile for T − Z curve for clay (API) . . . . . . . . . . . 35

4.1 Top view of the position of the 9 piles . . . . . . . . . . . . . . . . . . . . . 454.2 Curve Fx − Ux for a single pile for different models . . . . . . . . . . . . . . 504.3 Curve Fx − θz for a single pile for different models . . . . . . . . . . . . . . 514.4 Curve Fy − Uy for a single pile for different models . . . . . . . . . . . . . . 514.5 Curve Mz − Ux for a single pile for different models . . . . . . . . . . . . . 514.6 Curve Mz − θz for a single pile for different models . . . . . . . . . . . . . . 52

5.1 3-piles group under general loading . . . . . . . . . . . . . . . . . . . . . . 56

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viii Deltares

List of Tables

List of Tables

1.1 Results of benchmark 1-1 – Displacement and force at pile top . . . . . . . . 31.2 Results of benchmark 1-2 – Pile top displacement in X direction . . . . . . . 41.3 Results of benchmark 1-3 – Pile top displacement in X direction . . . . . . . 51.4 Results of benchmark 1-4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Results of benchmark 1-5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.6 Results of benchmark 1-6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.7 Results of benchmark 1-7 – Results for pile 1 . . . . . . . . . . . . . . . . . 71.8 Results of benchmark 1-8 . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.9 Results of benchmark 1-9 . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.10 Results of benchmark 1-10 . . . . . . . . . . . . . . . . . . . . . . . . . . 91.11 Results of benchmark 1-11 . . . . . . . . . . . . . . . . . . . . . . . . . . 101.12 Results of benchmark 1-11 . . . . . . . . . . . . . . . . . . . . . . . . . . 101.13 Results of benchmark 1-12 . . . . . . . . . . . . . . . . . . . . . . . . . . 111.14 Results of benchmark 1-13a at pile top . . . . . . . . . . . . . . . . . . . . 121.15 Results of benchmark 1-13b at pile top . . . . . . . . . . . . . . . . . . . . 12

2.1 Results of benchmark 2-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Results of benchmark 2-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1 Results of benchmark bm3-1a (vertical point load) . . . . . . . . . . . . . . 193.2 Results of benchmark bm3-1b (horizontal point load) . . . . . . . . . . . . . 203.3 Soil properties for benchmark bm3-2 . . . . . . . . . . . . . . . . . . . . . 213.4 Results of benchmark 3-2 – Lateral soil resistance at depth -0.6 m . . . . . . 233.5 Results of benchmark 3-2 – Lateral soil resistance at depth -6.3 m . . . . . . 233.6 Results of benchmark 3-3 – Lateral soil resistance at depth -0.6 m . . . . . . 243.7 Results of benchmark 3-3 – Lateral soil resistance at depth -6.3 m . . . . . . 253.8 Soil properties for benchmark bm3-4 . . . . . . . . . . . . . . . . . . . . . 253.9 Results of benchmark 3-4 – Lateral soil resistance at depth -0.6 m . . . . . . 263.10 Results of benchmark 3-4 – Lateral soil resistance at depth -6.3 m . . . . . . 263.11 Results of benchmark 3-5 – Lateral soil resistance at depth -0.6 m . . . . . . 273.12 Results of benchmark 3-5 – Lateral soil resistance at depth -6.3 m . . . . . . 283.13 Soil properties for benchmark bm3-6 . . . . . . . . . . . . . . . . . . . . . 283.14 Results of benchmark 3-6 – Lateral soil resistance at depth -0.6 m . . . . . . 303.15 Results of benchmark 3-6 – Lateral soil resistance at depth -2.1 m . . . . . . 303.16 Results of benchmark 3-6 – Lateral soil resistance at depth -9.8 m . . . . . . 313.17 Soil properties for benchmark bm1-30 . . . . . . . . . . . . . . . . . . . . . 313.18 Results of benchmark 3-7 – Friction along the pile at load-step 10 (compres-

sive load) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.19 Results of benchmark 3-7 – Friction along the pile at load-step 20 (tensile load) 333.20 Soil properties for benchmark bm3-8 . . . . . . . . . . . . . . . . . . . . . 343.21 Results of benchmark 3-8 – Friction along the pile at load-step 10 (compres-



sive load) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.28 Results of benchmark 3-10 – Friction along the pile at load-step 20 (tensile load) 39

4.1 Results of benchmark 4-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

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4.2 Results of benchmark 4-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.3 Results of benchmark 4-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.4 Results of benchmark 4-4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.5 Results of benchmark 4-5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.6 Results of benchmark 4-6 at pile top . . . . . . . . . . . . . . . . . . . . . 444.7 Results of benchmark 4-7 . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.8 Results of benchmark 4-8b (Poulos model) compare to results of benchmark

4-8a (Cap model) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.9 Results of benchmark 4-8c (Cap soil interaction model) compare to results of

benchmark 4-8a (Cap model) . . . . . . . . . . . . . . . . . . . . . . . . . 464.10 Results of benchmark 4-8d (Cap layered soil interaction model) compare to

results of benchmark 4-8a (Cap model) . . . . . . . . . . . . . . . . . . . . 474.11 Results of benchmark 4-9 for pile 1 . . . . . . . . . . . . . . . . . . . . . . 484.12 Plasticity factors calculated with both methods – Curve Fx − Ux . . . . . . . 494.13 Plasticity factors calculated with both methods – Curve Fx − θz . . . . . . . 494.14 Plasticity factors calculated with both methods – Curve Fy − Uy (compression) 494.15 Plasticity factors calculated with both methods – Curve Fy − Uy (tension) . . 504.16 Plasticity factors calculated with both methods – Curve Mz − Uz . . . . . . . 504.17 Plasticity factors calculated with both methods – Curve Mz − θz . . . . . . . 504.18 Results of benchmark 4-10 – Plasticity factors for curve Fx − Ux . . . . . . . 524.19 Results of benchmark 4-10 – Plasticity factors for curve Fx − θz . . . . . . . 534.20 Results of benchmark 4-10 – Plasticity factors for curve Fy − Uy (compression) 534.21 Results of benchmark 4-10 – Plasticity factors for curve Fy − Uy (tension) . . 534.22 Results of benchmark 4-10 – Plasticity factors for curve Mz − Uz . . . . . . 534.23 Results of benchmark 4-10 – Plasticity factors for curve Mz − θz . . . . . . . 54

5.1 Results of benchmark 5-1 for pile 1 . . . . . . . . . . . . . . . . . . . . . . 555.2 Results of benchmark 5-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

x Deltares

Introduction

Deltares Systems commitment to quality control and quality assurance has leaded them todevelop a formal and extensive procedure to verify the correct working of all of their geotech-nical engineering tools. An extensive range of benchmark checks have been developed tocheck the correct functioning of each tool. During product development these checks are runon a regular basis to verify the improved product. These benchmark checks are provided inthe following sections, to allow the users to overview the checking procedure and verify forthemselves the correct functioning of D-PILE GROUP.

The benchmarks for D-PILE GROUP are subdivided into five separate groups:

1 Group 1 (chapter 1) – Benchmarks from literature (exact solution)Simple benchmarks for which an exact analytical result is available from literature.

2 Group 2 (chapter 2) – Benchmarks from literature (approximate solution)More complex benchmarks described in literature, for which an approximate solution isknown.

3 Group 3 (chapter 3) – Benchmarks from spreads sheetsBenchmarks which test program features specific to D-PILE GROUP.

4 Group 4 (chapter 4) – Benchmarks generated by D-PILE GROUP

Benchmarks for which the reference results are generated using D-PILE GROUP.5 Group 5 (chapter 5) – Benchmarks compared with other programs

Benchmarks for which the results of D-PILE GROUP are compared with the results of otherprograms.

The number of benchmarks in group 1 will probably remain the same in the future. The reasonfor this is that they are very simple, using only the most basic features of the program.

The number of benchmarks in group 2 may grow in the future. The benchmarks in this chapterare well documented in literature. There are no exact solutions for these problems available;however in the literature estimated results are available. When verifying the program, theresults should be close to the results found in the literature.

Groups 3 and 4 of benchmarks will grow as new versions of the program are released. Thesebenchmarks are designed in such a way that (new) features specific to the program can beverified. The benchmarks are kept as simple as possible so that, per benchmark, only onespecific feature is verified.

As much as software developers would wish they could, it is impossible to prove the correct-ness of any non-trivial program. Re-calculating all the benchmarks in this report, and makingsure the results are as they should be, will prove to some degree that the program works as itshould.

Nevertheless there will always be combinations of input values that will cause the program tocrash or produce wrong results. Hopefully by using the verification procedure the number oftimes this occurs will be limited.

The benchmarks will all be described to such detail that reproduction is possible at any time.The results are presented in text format with each benchmark description. The results ingraphic 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 leastone picture is presented which shows the relevant results.

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1 Group 1: Benchmarks from literature (exact solution)

The number of benchmarks in group 1 will probably remain the same in the future. The reasonfor this is that they are very simple, using only the most basic features of the program.

1.1 One pile with an user defined pile tip curve is loaded by a vertical displacement, onlyend bearing is considered

1.1.1 Description

This benchmark checks the functioning of a user-defined pile tip curve.

� In the first case (bm1-1a), a pile with a user defined axial T − Z curve of T = 0.01 kN/m,an user defined pile tip curve (Rp = 100 %; zp = 0.04 m) and an end bearing capacity of100 kN is loaded by a vertical displacement of -0.04 m.

� In the second case (bm1-1b), the same pile is loaded by a vertical displacement of -0.05 m.

The Cap model is used for both cases.

1.1.2 Benchmark results

For the first case (bm1-1a), the elastic part of the pile tip curve is considered. After a verticaldisplacement (zp) of -0.04 m, when elastic deformation of the pile is included, the measuredvalue should be 98.5 kN.

For the second case (bm1-1b) also the plastic part of the pile tip curve is considered. After avertical displacement (zp) of -0.05 m the axial force should be 100 kN.

1.1.3 D-PILE GROUP results

D-PILE GROUP results can be found in Charts window from the Results menu using the ViewData option.

Table 1.1: Results of benchmark 1-1 – Displacement and force at pile top

Benchmark D-PILE GROUP Relative error [%]bm1-1a Displacement – Y ”

[m]-0.040 -0.040 0.00

Axial force – Y ” [kN] -98.50 -98.46 0.04bm1-1b Displacement – Y ”

[m]-0.050 -0.050 0.00

Axial force – Y ” [kN] -100.00 -100.00 0.00

Use D-PILE GROUP input files bm1-1a.pii and bm1-1b.pii to run this benchmark.

1.2 Two piles in elastic soil loaded and then unloaded by a horizontal centric force

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1.2.1 Description

Two piles with the following positions are loaded by a centric horizontal force of 100 kN (steps0-10):

� Pile 1: (-1, 0, 0)� Pile 2: (1, 0, 0)

The lateral curve is user defined (P = 10000 kN/m; Y = 0.1 m). After loading, the force willbe taken away (steps 10-20). The Cap model is used for D-PILE GROUP calculations.


Only the elastic part of the lateral curve P − Y is considered. When the force is taken away,the pile should go back to its former position.



Table 1.2: Results of benchmark 1-2 – Pile top displacement in X direction

Benchmark[m]

D-PILE GROUP

[m]Relative error[%]

Start 0.0 0.0000000 0.00Load step 10 - 0.0006435 -Load step 20 0.0 0.0000004a 0.00a is 0 within calculation accuracy

Use D-PILE GROUP input file bm1-2.pii to run this benchmark.

1.3 Single pile in elasto-plastic soil loaded and then unloaded by a horizontal force

1.3.1 Description

One pile with a length of metricconverter10 m is loaded by a horizontal force of 200 kN (steps0-10). The lateral curve is user defined (P = 25 kN/m; Y = 0.1 m). After loading, the force willbe taken away (steps 10-20). Rotation around Z-axis is 0 degrees. The Cap model is usedfor D-PILE GROUP calculations.


The soil will partially deform plastically, so the pile won’t go back to its original position.

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Group 1: Benchmarks from literature (exact solution)



Table 1.3: Results of benchmark 1-3 – Pile top displacement in X direction

Benchmark[m]

D-PILE GROUP


Start 0.000 0.0000 0.00Load step 10 Not 0 0.6715 -Load step 20 Not 0 0.4742 -


1.4 Single pile, with pile top 2 m above ground level, loaded by a force

1.4.1 Description

A pile, which pile top reaches two meters above ground level, is loaded by a force in X-direction of 100 kN. The Cap model is used for the D-PILE GROUP calculation.


For the upper two meters above ground level the shear force should be constant (100 kN).The moment at the pile top should be 0 and linearly increasing to 200 kNm at ground level.



Table 1.4: Results of benchmark 1-4

Benchmark D-PILE GROUP Relative error [%]Shear force – X” [kN] - Pile top 100.00 100.00 0.00Moment – Z” [kNm] - Pile top 0.00 0.00 0.00Moment – Z” [kNm] – GL (-2 m) 200.00 200.00 0.00


1.5 One pile is loaded by a horizontal force, user defined lateral curve

1.5.1 Description

A pile is loaded by a horizontal force of 100 kN. The user defined lateral curve is fully elastic(P = 90000 kN/m; Y = 10 m). The number of pile-nodes is only four. The Cap model is usedfor the D-PILE GROUP calculations.

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A very small displacement in X-direction is expected. The shear force in X-direction at pile-top level should be 100 kN. The moment around the Z-axis should be negative, but zero atpile top level.


D-PILE GROUP results can be found in Charts window from the Results menu using the ViewData option. D-PILE GROUP results are the same as the expected benchmark results.


Benchmark D-PILE GROUP Relative error [%]Displacement – X” [m] Pile top Very small 0.004194 -Moment - Z” [kNm] Pile top 0.000 0.000 0.00Maximum moment - Z” [kNm] Negative -28.150 -Shear force - X” [kN] Pile top 100.00 100.00 0.00


1.6 Single pile loaded by soil displacements

1.6.1 Description

A vertical pile with position (0, 0, 0) and a length of 10 m is loaded by horizontal soil displace-ments of 0.150 m in X-direction. Over the complete length of the pile the soil displacementsare the same:

� Level –0 m, UX = 0.150 m� Level –5 m, UX = 0.150 m� Level –10 m, UX = 0.150 m

The Cap model is used for D-PILE GROUP calculations.


The displacement of the pile should be over the complete length of the pile the same. Nomoments should be present.


D-PILE GROUP results can be found in Charts window from the Results menu using the ViewData option. D-PILE GROUP results are according to the expected benchmark results.


Benchmark D-PILE GROUP Relative error [%]Displacement - X” [m] Pile top 0.150 0.150 0.00Displacement - X” [m] Pile tip 0.150 0.150 0.00Moment – Z” [kNm] Pile top 0.000 0.000 0.00Moment - Z” [kNm] Pile tip 0.000 0.000 0.00

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1.7 Pile group of 4 piles loaded by a horizontal load

1.7.1 Description

A pile group of four piles is loaded by a horizontal force of 100 kN. The piles positions are:

� Pile 1 (2, 0, -2)� Pile 2 (2, 0, 2)� Pile 3 (-2, 0, -2)� Pile 4 (-2, 0, 2)

The Poulos model is used for D-PILE GROUP calculations.


The horizontal force should result in a positive shear force in X-direction of 25 kN at eachpile-top. It should also result in a positive displacement in X-direction.


D-PILE GROUP results can be found in the Report, in the Top View or in the Charts window fromthe Results menu. D-PILE GROUP results are according to the expected benchmark results.

Table 1.7: Results of benchmark 1-7 – Results for pile 1

Benchmark D-PILE GROUP Relative error [%]Displacement - X” [m] Pile top Positive 0.012653 -Moment - Z” [kNm] Pile top - 44.29 -Shear force - X” [kN] Pile top 25.000 25.000 0.00


1.8 Pile group of 100 piles loaded by several forces

1.8.1 Description

A pile group of 100 piles is loaded by a horizontal force in X-direction of 100 kN, a horizontalforce in Z-direction of 100 kN and a vertical force of 50 kN. The Poulos model is used forD-PILE GROUP calculations.


The positive loads should result in positive shear forces in all directions. Moreover, the shearforces in the X and Z directions should be the same.

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D-PILE GROUP results can be found in the Report, in the Top View or in the Charts windowfrom the Results menu.


Results for pile 1 Benchmark D-PILE GROUP Relative error [%]Shear force - X” [kN] Pile top Positive 3.379 -Axial force – Y ” [kN] Pile top Positive 5.850 -Shear force - Z” [kN] Pile top Positive 3.379 -


1.9 Two floating piles loaded by a moment

1.9.1 Description

Two piles with each a total length of 4 m above surface level. Their positions are:

� Pile 1 (0, 4, -2)� Pile 2 (0, 4, 2)

The cap is also situated 4 m above surface level with a position of (0, 4, 0). The cap isloaded by a negative moment around the Z-axis of 200 kNm. The Poulos model is used forD-PILE GROUP calculations.


The positive moment should be equally divided over the two piles. Pile 1 should get a negativemoment of 100 kNm. The upper four meters of the piles are above surface level. Here themoment around the Z-axis should be constant -100 kNm.




Moment - Z” Benchmark[kNm]

D-PILE GROUP

[kNm]Relative error[%]

Pile 1 Pile top -100.00 -100.00 0.00Ground level (-4 m) -100.00 -100.00 0.00

Pile 2 Pile top -100.00 -100.00 0.00Ground level (-4 m) -100.00 -100.00 0.00


1.10 Single pile loaded by two surface loads, symmetrically positioned around the pile

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1.10.1 Description

A pile is loaded by two vertical surface loads of magnitude -175 kN/m2, situated on each sideof the pile. The magnitude of both loads and the dimensions are the same, so that the effectof the loads will be neutralized. The Cap soil interaction model is used for D-PILE GROUP

calculations.


The pile should keep its basic position in the X and Z directions.




Benchmark D-PILE GROUP Relative error [%]Displacement - X” [m] Pile top 0.000 0.0000873 0.00Displacement - X” [m] Pile tip 0.000 0.0000118 0.00Displacement - Z” [m] Pile top 0.000 0.0000593 0.00Displacement - Z” [m] Pile tip 0.000 0.0000114 0.00


1.11 Single pile loaded by two opposite surface loads (same position, different load sign)

1.11.1 Description

A pile is loaded by two surface loads, both situated on one side of the pile. The positioningand magnitude of both loads are the same, the direction in which the loads point are oppositefrom each other, so that the effect of the loads will be neutralized:

� horizontal surface load in X-direction of -175 kN/m2 on the right side;� horizontal surface load in X-direction of +175 kN/m2 on the right side.

Both loads are situated at the same co-ordinates.

The Cap soil interaction model is used for D-PILE GROUP calculations.


The pile should keep its basic position in all directions.

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Benchmark D-PILE GROUP Relative error [%]Displacement - X” [m] Pile top 0.00 0.0000000 0.00Displacement - X” [m] Pile tip 0.00 0.0000000 0.00Displacement – Y ” [m] Pile top 0.00 0.0000000 0.00Displacement - Y” [m] Pile tip 0.00 0.0000000 0.00Displacement - Z” [m] Pile top 0.00 0.0000000 0.00Displacement - Z” [m] Pile tip 0.00 0.0000000 0.00


1.12 Determination of EI and EA for different pile types

1.12.1 Description

The automatic calculation ofEI andEA by D-PILE GROUP in the Pile Types window, [§ 12.3.1]in the User Manual, is checked in this benchmark. Four different pile types are used and theirproperties are given in Table 1.12 below.


Pile type Wood Steel Concreteround

Concretesquare

Width [m] b 0.3Diameter [m] D 0.5 0.4 0.6Wall thickness [m] w 0.006Young’s modulus [kN/m2] E 2 × 107 108 6 × 107 3 × 107


The inertia I and the section A of a pile depend on its geometry:

A =

{b2 for a square pileπ D2/4 for a round pileπ w (D − w) for a tubular pile

(1.1)

I =

b4/12 for a square pileπ R4/4 for a round pileπ[R4 − (R− w)4

]/4 for a tubular pile

(1.2)

This leads to:

For wood EA = 2× 107× π × 0.52 / 4 = 3926990.82 kN

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EI = 2× 107× π × (0.5/2)4 / 4 = 61359.23 kNm2

For steel EA = 108 × π × 0.06 × (0.4 – 0.06) = 742672.50 kNEI = 108× π × [(0.4/2)4 - (0.4/2 – 0.06)4] / 4 = 14414.53 kNm2

For concrete round EA = 6 × 107 × π × 0.62 / 4 = 16964600.33 kNEI = 6× 107× π × (0.6/2)4 / 4 = 381703.51 kNm2

For concrete square EA = 3 × 107 × 0.52 = 2700000 kNEI = 3× 107× 0.3 / 12 = 20250 kNm2


D-PILE GROUP results can be found in Calculation Messages window displayed at the end ofthe calculation. D-PILE GROUP results are according to the expected benchmark results.


Pile type Benchmark D-PILE GROUP Relative error [%]Wood EI [kN/m2] 6.1359 × 104 6.1359 × 104 0.00

EA [kN] 3.9270 × 106 3.9270 × 106 0.00Steel EI [kN/m2] 1.4415 × 104 1.4415 104 0.00

EA [kN] 7.4267 × 105 7.4267 × 105 0.00Concrete EI [kN/m2] 3.8170 × 105 3.8170 105 0.00round EA [kN] 1.6965 × 107 1.6965 × 107 0.00Concrete EI [kN/m2] 2.0250 104 2.0250 × 104 0.00square EA [kN] 2.7000 × 106 2.7000 × 106 0.00


1.13 One pile is loaded by a force, rotation around Z-axis zero - rotation around Z-axis free

1.13.1 Description

This benchmark checks the functioning of the rotation of the cap.

� In the first case (bm1-13a), a pile is loaded by a horizontal force of 100 kN. The rotationof the cap around the Z-axis is 0 degrees. The pile top is fixed.

� In the second case (bm1-13b), the same pile is loaded by a horizontal force of 100 kN,now the rotation of the cap around the Z-axis is free. The pile top is also fixed.


1.13.2 Benchmark result

The displacement of the pile top of bm1-13a should be less than the displacement of the piletop of bm1-13b. At the pile top of bm1-13a there should be a positive moment. At the pile topof bm1-13b there should be no moment.

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Table 1.14: Results of benchmark 1-13a at pile top

Benchmark D-PILE GROUP Relative error [%]Displacement – X” [m] < 0.04743 0.010805 -Moment – Z” [kNm] Positive 126.52 -

Table 1.15: Results of benchmark 1-13b at pile top

Benchmark D-PILE GROUP Relative error [%]Displacement – X” [m] - 0.04743 -Moment – Z” [kNm] 0.00 0.00 0.00


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2 Group 2: Benchmarks from literature (approximate solution)

2.1 Single laterally loaded pile; Lake Austin test

2.1.1 Description

This benchmark describes the Lake Austin test. This test is one of the tests that form thebasis of the API. Therefore calculation of this test should result in computed displacementsand bending moments that are (almost) equal to the ones that were measured. The pile andload data are given in Figure 2.1.

Figure 2.1: Lake Austin test

The soil has an undrained cohesion of 38.3 kN/m2 and a saturated weight of 20 kN/m3. Theend bearing capacity of the pile isQp= 500 kN, the empirical constant J is 0.25 and the strainwhich occurs at one-half the maximum stress is ε50 = 0.012.


The measured displacements and moments along the pile are given by Matlock in Matlock(1970) and written in an Excel spreadsheet for comparison with D-PILE GROUP results.


D-PILE GROUP results are found in the Charts window using the View data option. The resultsshow that the agreement between the measured and the calculated values is good. Thisshows that the basic modules of D-PILE GROUP (P − Y generation according to the API andthe beam on springs) are working properly. Calculation results and measured values are alsopresented in Figure 2.2.

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Figure 2.2: Calculated and measured pile displacement (left) and bending moment (right)along the pile


Benchmark D-PILE GROUP Relative error [%]Lateral displacement 0.03478 0.03466 0.35Moment – Z” [kNm] at depth:0 0.00 0.00 0.00-0.32 -23.81 -24.43 2.54-0.64 -43.17 -45.81 5.76-0.928 -60.95 -62.32 2.20-1.28 -75.56 -78.93 4.27-1.568 -87.62 -89.53 2.13-1.792 -97.14 -95.93 1.26-2.08 -100.32 -101.72 1.38-2.432 -103.17 -105.14 1.87-2.656 -106.35 -105.24 1.05-3.04 -102.22 -101.92 0.29-3.328 -97.14 -96.70 0.46-3.648 -88.89 -88.32 0.65-4 -76.19 -76.36 0.22-4.576 -58.41 -53.41 9.36-5.152 -32.70 -31.83 2.73-5.44 -21.90 -22.78 3.86-6.08 -6.98 -7.97 12.42-6.656 0.00 -0.40 -


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Group 2: Benchmarks from literature (approximate solution)

2.2 Collision of a ship against a pile (Dynamic model)

2.2.1 Description

This benchmark compares the experimental results of the collision of a ship against a pile withD-PILE GROUP predictions using the Dynamic model. The geometry is the same as for Tutorial7 “Collision of a ship against a pile” in [§ 13] in the User Manual, see Figure (13-1).

Three different velocities are used:

� V = 0.20 m/s (bm2-2a)� V = 0.35 m/s (bm2-2b)� V = 0.56 m/s (bm2-2c)


The measured displacements and forces (at the end of collision) for different velocities (from0.20 to 0.56 m/s) are given in Bijnagte (1990) and written in an Excel spreadsheet for com-parison with D-PILE GROUP results. They are shown in Table 2.2.


In order to take into account the contact effect, the calculated lateral displacement x must beadapted to get the pile displacement xpile:

xpile = x− F

E(2.1)

where F is the calculated collision force andE = 10000 kN/m is the contact stiffness betweenthe ship and the pile.

Results of D-PILE GROUP version 5.2 (i.e. Tilly 4) are slightly different from the results ofversion 5.1 (Tilly 3). However these differences occur only in a less relevant part of the results(when the ship is moving back) and are considered acceptable.


Velocity Collision Pile displacementforce D-PILE GROUP Adapted Measurement Error

[m/s] [N] [m] [m] [m] [%]bm2-2a 0.2 261.6903 0.09543 0.06926 0.07800 12.62bm2-2b 0.35 451.6839 0.16825 0.12308bm2-2c 0.56 711.129 0.27122 0.20011 0.18200 9.05

D-PILE GROUP results are found in the Ducbots window using the View data option. Calculatedand measured values are presented in Figure 2.3 and show that the agreement is good.

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Figure 2.3: Benchmark 2-2 – Calculated and measured forces and displacements (at theend of collision) for different velocities

Use D-PILE GROUP input files bm2-2a.pii, bm2-2b.pii and bm2-2c.pii to run this benchmark.

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3 Group 3: Benchmarks from spreadsheets

3.1 Vertical and horizontal displacements due to a concentrated load on a semi-infinitesolid

Description

The Cap soil interaction model is used as the results of a surface loading is checked. Aconcentrated load, described as a very small surface loading is placed on a semi-infinitesolid. The pile is loaded with:

� a vertical surface load of Qy = 10 000 kN/m2 in benchmark bm3-1a� a horizontal surface load of Qx = 10 000 kN/m2 in benchmark bm3-1b

with a load factor of f = 1000 on a surface of A = 0.01 m2.

The simulated concentrated load is:

� F= Qy × f × A = 10 000× 1 000× 0.01 = 100 000 kN for bm3-1a� Q = Qx × f × A = 10 000× 1 000× 0.01 = 100 000 kN for bm3-1b.

The load is placed on (X, Y, Z) = (-10, 0, -5).


The theoretical solution can be found in Mindlin theory (Mindlin, 1953).

Case A: Vertical surface load

The displacements in the X , Y and Z directions resulting from a vertical point load P (bm3-1a) are given by the following Mindlin’s equations:

ux =P x

16πG (1− ν)× (3.1)[

(y − c)R3

1

+(3− 4ν) (y − c)

R32

− 4 (1− ν) (1− 2ν)

R2 (R2 + y + c)+

6cy (y + c)

R52

]uy =

P

16πG (1− ν)3− 4ν

R1

+8 (1− ν)2 − (3− 4ν)

R2

+(y − c)2

R31

(3.2)

+(3− 4ν) (y + c)2 − 2cy

R32

+6cy (y + c)2

R52

uz =P z

16πG (1− ν)× (3.3)[

(y − c)R3

1

+(3− 4ν) (y − c)

R32

− 4 (1− ν) (1− 2ν)

R2 (R2 + y + c)+

6cy (y + c)

R52

]where:

R1 =√x2 + (y − c)2 + z2

R2 =√x2 + (y + c)2 + z2

x, y, z are the co-ordinates of the calculated point, in m;

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ux, uy, uz are the displacements at the calculated point, in m;P is the vertical point load, in kN;E is the Young’s modulus of the soil, in kN/m2;ν is the Poisson ratio of the soil;G is the shear modulus of the soil, in kN/m2;c > 0 is the depth beneath the surface where the load is acting, in m.

As the vertical load acts at the surface level (i.e. c = 0), this problem is equivalent to Boussi-nesq’s theory and the Mindlin’s equations become:

ux =P x (1 + ν)

2π E R

[y

R2− (1− 2ν)

R + y

](3.4)

uy =P (1 + ν)

2π E R

[2 (1− 2ν) +

y2

R2

](3.5)

uz =P z (1 + ν)

2π E R

[y

R2− (1− 2ν)

R + y

](3.6)

with R =√x2 + y2 + z2.

Case B: Horizontal surface load

The displacements in the X , Y and Z directions resulting from a horizontal point load Q(bm3-1b) are given by the following Mindlin’s equations:

ux =Q

16πG (1− ν)×

(3− 4ν)

R1

+1

R2

+x2

R31

+(3− 4ν)x2

R32

+2cy

R32

(1− 3x2

R22

)+

4 (1− ν) (1− 2ν)

(R2 + y + c)×(

1− x2

R2 (R2 + y + c)

)

(3.7)

uy =Q x

16πG (1− ν)×

y − cR3

1

+(3− 4ν) (y − c)

R32

−6cy (y + c)

R52

+4 (1− ν) (1− 2ν)

R2 (R2 + y + c)

(3.8)

uz =Q x z

16πG (1− ν)×[1

R31

+(3− 4ν)

R32

− 6cy

R52

− 4 (1− ν) (1− 2ν)

R2 (R2 + y + c)2

](3.9)

As the horizontal load acts at the surface level (i.e. c = 0), this problem is equivalent to Cerruti’stheory and the Mindlin’s equations become:

ux =P (1 + ν)

2π E R

[1 +

x2

R2+

(1− 2ν

R + t

) (r − x2

R + y

)](3.10)

uy =P x (1 + ν)

2π E R

[1− 2ν

R + y+

y

R2

](3.11)

uz =P x z (1 + ν)

2π E R

[1

R2− 1− 2ν

(R + y)2

](3.12)

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Group 3: Benchmarks from spreadsheets

Calculations using those formulas are performed in an Excel spreadsheet for different depthsbelow the pile head.



Calculation results according to Boussinesq’s theory and D-PILE GROUP are also compared inFigure 3.1.

Figure 3.1: Pile displacements along the pile

Table 3.1: Results of benchmark bm3-1a (vertical point load)

Benchmark[m]

D-PILE GROUP


Displacement - X” [m]at depth m0 m (pile top) -0.6621 -0.6621 0.00at depth 12 m 0.3851 0.3851 0.00at depth 16 m 0.3258 0.3258 0.00at depth 20 m (pile tip) 0.2598 0.2598 0.00Displacement - Y” [m]at depth 0 m (pile top) -2.5908 -2.5908 0.00at depth 5 m -2.6371 -2.6371 0.00at depth 10 m -2.6166 -2.6166 0.00at depth ?15 m -2.4414 -2.4414 0.00at depth 16 m -2.1962 -2.1962 0.00at depth 20 m (pile tip) -1.9522 -1.9522 0.00Displacement - Z” [m]at depth 0 m (pile top) -0.3310 -0.3310 0.00at depth 5 m 0.0276 0.0276 0.00at depth 10 m 0.1801 0.1801 0.00at depth ?15 m 0.1925 0.1925 0.00at depth 16 m 0.1629 0.1629 0.00at depth 20 m (pile tip) 0.1299 0.1299 0.00

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Table 3.2: Results of benchmark bm3-1b (horizontal point load)

Benchmark[m]

D-PILE GROUP


Displacement - X” [m]at depth 0 m (pile top) 3.479 3.479 0.00at depth 12 m 1.959 1.959 0.00at depth 16 m 1.538 1.538 0.00at depth 20 m (pile tip) 1.248 1.248 0.00Displacement - Y” [m]at depth 0 m (pile top) -0.6621 -0.6621 0.00at depth 5 m -0.9334 -0.9334 0.00at depth 10 m -0.9138 -0.9138 0.00at depth 15 m -0.7404 -0.7404 0.00at depth 16 m -0.5645 -0.5645 0.00at depth 20 m (pile tip) -0.4282 -0.4282 0.00Displacement - Z” [m]at depth 0 m (pile top) 0.4441 0.4441 0.00at depth 5 m 0.4796 0.4796 0.00at depth 10 m 0.3345 0.3345 0.00at depth 15 m 0.2032 0.2032 0.00at depth 16 m 0.1223 0.1223 0.00at depth 20 m (pile tip) 0.0762 0.0762 0.00


3.2 Lateral P − Y curve for clay and static loading (API)

Description

The lateral PY curve for clay and static loading according to the API (1984) is determined inthis benchmark. A pile composed of two sections in a soil composed of two clay layers withthe properties given in the table below is laterally loaded (Figure 3.2).

20 of 62 Deltares


Figure 3.2: Soil and pile profiles for benchmark bm3-2

Table 3.3: Soil properties for benchmark bm3-2

Top layer Bottom layerSoil type Soft clay Soft clayWet weight Top [kN/m3] 16 14

Bottom 18 16Dry weight Top [kN/m3] 11 11

Bottom 13 13su Top [kN/m2] 30 6

Bottom 22 15J [-] 0.25 0.3ε50 [-] 0.02 0.01

Calculations are performed at two different depths:

� Depth 0.6 m below surface level in dry Top layer with top pile section� Depth 6.3 m below surface level in wet Bottom layer with bottom pile section


According to the API (1984), the relation between the lateral force and the horizontal displace-ment for clay and static loading is given by the following equation:

p =

{0.5 pu (y/y50)

1/3 for y < 8 y50pu for y ≥ 8 y50

(3.13)

where:

p is the actual lateral soil resistance at depth H in kN/m2;

Deltares 21 of 62


pu is the ultimate lateral soil resistance at depth H [kN/m2]:p = min (pus; pud);

y is the actual lateral deflection, in m;y50 y50 = 2.5× ε50× D;ε50 is the strain which occurs at one-half the maximum stress on laboratory undrained

compression tests of undisturbed soil samples;D is the pile diameter, in m;pus is the ultimate lateral soil resistance at shallow depth, in kN/m2:

pus = 3 su + γ′ H + J suHD

;pud is the ultimate lateral soil resistance at deep depth, in kN/m2:

pud = 9 su;su is the undrained shear strength, in kN/m2;γ’ is the effective unit weight of the soil, in kN/m3;H is the depth below soil surface, in m;j is the dimensionless empirical constant. A value ranging from 0.25 to 0.5 is rec-

ommended.

The soil weight of each layer is the average between the top and the bottom whereas thecohesion is a linear interpolation. Results of the analytical calculations can be found in anExcel spreadsheet.


In the Calculation window the checkbox Create P − Y Curve dumpfile must be marked.Results can be found in the P −Y Plots window from the Results menu selecting the desireddepth and using the View Data option. D-PILE GROUP results are according to the expectedbenchmark results.

Figure 3.3: Lateral P − Y curve for clay and static load at different depths (bm3-2)

22 of 62 Deltares


Table 3.4: Results of benchmark 3-2 – Lateral soil resistance at depth -0.6 m

Horizontal displacement[mm]

Benchmark[kN/m]

D-PILE GROUP

[kN/m]Relative error[%]

0 0.00 0.00 0.000.006 26.95 26.97 0.070.018 38.87 38.90 0.080.06 58.07 58.11 0.070.18 83.75 83.81 0.070.48 116.14 116.22 0.070.5 116.14 116.22 0.07


Horizontal displacement[mm]

Benchmark[kN/m]

D-PILE GROUP


0 0.00 0.00 0.000.0025 18.71 18.70 0.050.0075 26.98 26.97 0.040.025 40.31 40.29 0.050.075 58.13 58.11 0.030.2 80.61 80.58 0.040.5 80.61 80.58 0.04


3.3 Lateral P − Y curve for clay and cyclic loading (API cyclic)

3.3.1 Description

The lateral PY curve for clay and cyclic loading according to the API is determined in thisbenchmark. The same geometry (??) and soil properties as for benchmark 3-2 (section 3.2)are used.


According to the API (1984), the relation between the lateral force and the horizontal displace-ment for clay and cyclic loading is given by the following equation:

p

pu=

{0.5 (y/y50)

13 for y < 3 y500.72 for y ≥ 3 y50

for H > HR (3.14)

p

pu=

0.5 (y/y50)

13 for y < 3 y50(0.06 y

y50+ 0.54

) (HHR− 1)

for 15 y50 ≥ y ≥ 3 y500.72 (H/HR) for y > 15 y50

for H ≤ HR

(3.15)

where:

Deltares 23 of 62


HR is the depth below soil surface to bottom of reduced resistance zone, in m:

HR =6D

γ′ D/c+ J

The soil weight of each layer is the average between the top and the bottom whereas thecohesion is a linear interpolation.

Results of the analytical calculations can be found in an Excel spreadsheet.



0

10

20

30

40

50

60

70

80

90

0 0.05 0.1 0.15 0.2

Lateral deflection Y [m]

Latera

l soil r

esista

nce P

[kN/m

]

Analytical P-Y curve at depth -0.6 m

D-Pile Group at depth -0.6 m

Analytical P-Y curve at depth -6.3 m

D-Pile Group at depth -6.3 m

Figure 3.4: Lateral P − Y curve for clay and cyclic load at different depths (bm3-3)


Horizontal displace-ment[mm]

Benchmark[kN/m]

D-PILE GROUP

[kN/m]Relative error [%]

0 0.00 0.00 0.000.006 26.95 26.97 0.070.018 38.87 38.90 0.080.06 58.07 58.11 0.070.18 83.62 83.81 0.230.5 83.62 83.81 0.23

24 of 62 Deltares




Benchmark[kN/m]

D-PILE GROUP


0 0.00 0.00 0.000.0025 18.71 18.70 0.050.0075 26.98 26.97 0.040.025 40.31 40.29 0.050.075 58.04 58.11 0.120.5 58.04 58.11 0.12


3.4 Lateral P − Y curve for sand and static loading (API)

3.4.1 Description

The lateral P −Y curve for sand and static loading according to the API is determined in thisbenchmark. The same geometry as for benchmark 3-2 (section 3.2) is used (see ??). Thesoil properties of the two sand layers are given in ??.


Top layer Bottom layerSoil type Sand SandWet weight Top [kN/m3] 16 14


Bottom 13 13Phi Top [◦] 32 22

Bottom 39 18


The relation between the lateral force and the horizontal displacement for clay and cyclicloading is given by the following equation:

P = A pu tanh

(k H

A puY

)(3.16)

where:

P Actual lateral soil resistance at depth H [kN/m]A Factor to account for loading conditions.

For static loads: A = 3− 0.8HD≥ 0.9

Pu Ultimate lateral soil resistance at depth H [kN/m]:pu = min (pus; pud).

k Initial modulus of subgrade reaction [kN/m3] determined by figure 6.8.7-1 ofthe API (1984).

H Depth below soil surface [m]D Pile diameter [m]Y Actual lateral deflection [m]

Deltares 25 of 62


The soil weight of each layer is the average between the top and the bottom whereas theangle of internal friction is a linear interpolation.




-11

-9

-7

-5

-3

-1

-60 -40 -20 0 20 40 60

Skin friction [kN/m]

Depth

[m]

Analytical - Compression load

D-Pile Group load-step 20

Analytical - Tension load


Figure 3.5: Lateral P − Y curve for sand and static load at different depths (bm3-4)



Benchmark[kN/m]

D-PILE GROUP


0 0.00 0.00 0.000.001611 24.31 24.38 0.290.003223 45.57 46.00 0.930.006445 73.72 75.81 2.760.009668 86.30 90.10 4.220.016113 92.82 98.21 5.49



Benchmark[kN/m]

D-PILE GROUP


0 0.00 0.00 0.000.00421 70.53 70.45 0.110.00841 132.88 132.92 0.030.01682 218.75 219.06 0.140.02524 259.78 260.36 0.220.04206 282.90 283.79 0.31

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3.5 Lateral P − Y curve for sand and cyclic loading (API cyclic)

3.5.1 Description

The lateral P −Y curve for sand and cyclic loading according to the API is determined in thisbenchmark. The same geometry as for benchmark 3-2 is used (see ??). The soil propertiesof the two sand layers are given in Table 3.8.


For cyclic lateral loads, the same equation that for static lateral loads (section 3.4.2) applyexcept for factor A which is constant and equal to 0.9. Results of the analytical calculationscan be found in an Excel spreadsheet.



-11

-9

-7

-5

-3

-1

-80 -60 -40 -20 0 20 40 60 80

Skin friction [kN/m]

Depth

[m]

Analytical - Compression load


Analytical - Tension load


Figure 3.6: Lateral P − Y curve for sand and cyclic load at different depths (bm3-5)



Benchmark[kN/m]

D-PILE GROUP


0 0.00 0.00 0.000.000558 8.42 8.44 0.230.001116 15.78 15.92 0.900.002231 25.52 26.24 2.760.003347 29.87 31.19 4.230.005578 32.13 34.00 5.49

Deltares 27 of 62




Benchmark[kN/m]

D-PILE GROUP


0 0.00 0.00 0.000.00421 70.53 70.45 0.110.00841 132.88 132.92 0.030.01682 218.75 219.06 0.140.02524 259.78 260.36 0.220.04206 282.90 283.79 0.31


3.6 Lateral P − Y curve for undrained sand (API undrained)

3.6.1 Description

The lateral P − Y curve for undrained sand and static loading according to the API is deter-mined in this benchmark. The same geometry as for benchmark 3-2 is used (see ??). Thesoil properties of the two sand layers are given in Table 3.13 below.




Bottom 13 13Phi Top [◦] 32 22

Bottom 39 18qc Top [kN/m2] 5000 8000

Bottom 10000 12000Void ratio Minimum [-] 0.5 0.6

Initial 0.6 0.9Maximum 0.8 1


The P − Y curve for undrained sand is obtained by multiplying the P − Y curve for drainedsand and static loading with a factor α = α(y ):

Puu (y) = α (y) ·Pu (y) (3.17)

where:

Puu(y) Actual lateral soil resistance at depth H [kN/m], for undrained sand.α(y) Factor [-], see equation (3.18) below.Pu(y) Actual lateral soil resistance at depth H [kN/m], for drained sand. See equa-

tion (3.16).

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y Actual lateral deflection [m]

The factor α is equal to:

α (y) =

1− 0.185 ur3

p1if |ur3| < |ueven|

1− uevenp1

[1− 0.815

(uevenur3

)0.226]if |ur3| ≥ |ueven|

(3.18)

with:

ur3 Excess pore water pressure [kN/m2]:

ur3 =kunload c1

1+e0

[e0 − c4 − c5 ln

(σ′v

p0

)]6 yD

ueven Maximum excess pore water pressure [kN/m2], limited in one hand by thecavity stress and in the other hand by the effective stress, ucav < ueven <σ′v, with:

ueven = σ′v − p0 exp(e0−c4c5

)ucav Cavitation stress [kN/m2]:

ucav = −pa − γw (H −Hw) with H −Hw ≥ 0pa Atmospheric pressure (pa = 100 kN/m2)γw Unit weight of water (9.81 kN/m3)H Actual depth [m]Hw Depth of water level [m]kunload Stiffness for unloading [kN/m2]: kunload = 4 qcqc Cone resistance [kN/m2]σ′v Initial effective stress [kN/m2]p0 Reference pressure (p0 = 100 kN/m2)c1, c4, c5 Constant terms [-]:

c1 = 13.86c4 = 0.61 emax + 0.39 eminc5 = 0.13 (emin - emax)

e0, emin, emax Initial, minimum and maximum void ratios [-]y Actual lateral deflection [m]D Pile diameter [m]

The soil weight of each layer is the average between the top and the bottom whereas the angleof internal friction and the cone resistance are linear interpolation.Results of the analyticalcalculations can be found in an Excel spreadsheet.

Deltares 29 of 62



In the Calculation window the checkbox Create P −Y Curve dumpfile must be marked. Thisspecial API-rule may only be used when the Dynamic model has been selected.Results canbe found in the P − Y Plots window from the Results menu selecting the desired depth andusing the View Data option. D-PILE GROUP results are according to the expected benchmarkresults.

0

200

400

600

800

1000

1200

1400

0 0.01 0.02 0.03 0.04 0.05

Lateral deflection Y [m]

Latera

l soil r

esista

nce P

[kN/m

]

at depth -0.6 m

at depth -2.1 m

at depth -9.8 m

Analytical

D-Pile Group

Figure 3.7: Lateral P − Y curve for undrained sand at different depths (bm3-6)



Benchmark[kN/m]

D-PILE GROUP


0 0.00 0.00 0.000.001611 147.33 147.36 0.020.003223 337.09 337.04 0.010.006445 638.58 638.59 0.000.009668 809.98 809.97 0.000.0016113 946.05 946.05 0.00



Benchmark[kN/m]

D-PILE GROUP


0 0.00 0.00 0.000.001388 200.78 200.83 0.020.002777 442.59 442.66 0.020.005554 819.22 819.34 0.010.008331 1028.76 1028.88 0.010.013885 1189.61 1189.73 0.01

30 of 62 Deltares




Benchmark[kN/m]

D-PILE GROUP


0 0.00 0.00 0.000.00492 96.56 96.54 0.020.00984 174.26 174.23 0.020.01968 276.01 275.98 0.010.02952 321.19 321.15 0.010.04919 341.60 341.57 0.01


3.7 Axial T − Z curve for clay (API)

3.7.1 Description

The axial T−Z curve for clay according to the API is checked in this benchmark by calculatingthe mobilized skin friction along the pile. The same geometry as for benchmark 1-25 is used(see ??) except that the lateral load is replaced by a compressive vertical load of Fc = 300 kN(from steps 1 to 10) and a tensile vertical load of FT = 300 kN (from steps 11 to 20). The soilproperties of the two clay layers are given in Table 3.17 below.




Bottom 13 13Cu Top [kN/m2] 30 6

Bottom 22 15dz at 100 % [m] 0.002 0.004


According to API, the relation between the mobilized skin friction T and the vertical displace-ment Z for clay is:

T =

{Z f As/dz if Z < dzf As if Z ≥ dz [kN ] (3.19)

where:

f Maximum skin friction [kN/m2] given by equation (15) in [§ 15.2.1] of theUser Manual

Az Side surface area of pile [m2]dz Displacement corresponding with the ultimate resistance Tmax = f As

Deltares 31 of 62


As the pile stiffness is large (EI = 1012 kN/m2 and EA = 1012 kN), the pile is rigid so thevertical displacement Z is constant along the pile and equal to the pile tip displacement:

Z = Ztip =

{Zu Q/Qmax if Q < Qmax

Zu if Q ≥ Qmax(3.20)

where:

Q Mobilized axial force [kN]:Q = F − T Htip where F =

Qmax End bearing capacity (Qmax = 400 kN)Zu Pile tip displacement corresponding with the end bearing capacity

(Zu = 0.1 m)

� Z = 2.282 mm at the end of the compression (load-step 10)� Z = 2.438 mm at the end of the traction (load-step 20)

Therefore, at load-step 10, the mobilized skin friction is equal to the maximum skin frictiononly for the Top layer.

The soil weight of each layer is the average between the top and the bottom whereas theundrained cohesion is a linear interpolation.



Results can be found in the Charts window from the Results menu using the View Data option.D-PILE GROUP results are according to the expected benchmark results.

32 of 62 Deltares


Figure 3.8: Skin friction along the pile for T − Z curve for clay (API)

Table 3.18: Results of benchmark 3-7 – Friction along the pile at load-step 10 (compres-sive load)

Depth[m]

Benchmark[kN/m]

D-PILE GROUP


-0.75 m -40.27 -40.27 0.00-2.37 m -38.68 -39.28 1.53-3.13 m -40.70 -41.73 2.47-5.75 m -14.79 -14.79 0.00-9.25 m -22.85 -22.85 0.00-11 m -26.88 -10.89 146.83

Table 3.19: Results of benchmark 3-7 – Friction along the pile at load-step 20 (tensileload)

Depth[m]

Benchmark[kN/m]

D-PILE GROUP


-0.75 m 49.09 40.27 21.90-2.37 m 47.15 39.28 20.04-3.13 m 49.61 41.73 18.88-5.75 m 15.80 15.80 0.00-9.25 m 24.41 24.41 0.00-11 m 28.72 1.98 1350.51


Deltares 33 of 62


3.8 Axial T − Z curve for clay (Ratio)

3.8.1 Description

The axial T − Z curve for clay according to the API using a user-defined factor alpha ischecked in this benchmark by calculating the mobilized skin friction along the pile. The samegeometry as for benchmark 3-2 is used (see ??) except that the lateral load is replaced by acompressive vertical load of 300 kN (from steps 1 to 10) and a tensile vertical load of 300 kN(from steps 11 to 20). The soil properties of the two clay layers are given in Table 3.20 below.




Bottom 13 13Cu Top [kN/m2] 30 6

Bottom 22 15Factor alpha [-] 0.5 0.7dz at 100 % [m] 0.002 0.004


The relation between the axial force T and the vertical displacement Z for clay is the same asfor benchmark 3-7.

As the pile stiffness is large (EI = 1012 kN/m2 and EA = 1012 kN), the pile is rigid so thevertical displacement Z is constant along the pile and equal to:





34 of 62 Deltares




0

5

10

15

20

25

30

0 0.01 0.02 0.03 0.04 0.05 0.06

Cap lateral deflection Ux [m ]

Cap

late

ral

forc

e F

x [

kN

]

Plasti-Poulos model (bm4-10a)

Cap model (bm4-10b)

Poulos model with E = 1366.21 kPa (bm4-10f)

Cap model - Elastic part (bm4-10b)

Figure 3.9: Skin friction along the pile for T − Z curve for clay (API)


Depth[m]

Benchmark[kN/m]

D-PILE GROUP


-0.75 m -53.72 -53.72 0.00-2.37 m -39.68 -39.68 0.00-3.13 m -37.29 -37.29 0.00-5.75 m -12.33 -12.33 0.00-9.25 m -19.05 -19.05 0.00-11 m -22.41 -15.06 48.80

Deltares 35 of 62



Depth[m]

Benchmark[kN/m]

D-PILE GROUP


-0.75 m 81.95 53.72 52.55-2.37 m 60.53 39.68 52.55-3.13 m 56.88 37.29 52.53-5.75 m 13.84 13.84 0.00-9.25 m 21.39 21.39 0.00-11 m 25.16 1.75 1337.71


3.9 Axial T − Z curve for sand (API)

3.9.1 Description

The axial T − Z curve for sand according to the API is checked in this benchmark by calcu-lating the mobilized skin friction along the pile. The same geometry as for benchmark 3-25is used (see ??) except that the lateral load is replaced by a compressive vertical load of300 kN (from steps 1 to 10) and a tensile vertical load of 300 kN (from steps 11 to 20). Thesoil properties of the two sand layers are given in Table 3.23 below.




Bottom 13 13Delta angle Top [◦] 20 15

Bottom 25 25Ko [-] 0.4 0.6dz at 100 % [m] 0.002 0.004


The relation between the axial force T and the vertical displacement Z for clay is the same asfor benchmark 3-7.





36 of 62 Deltares






Depth[m]

Benchmark[kN/m]

D-PILE GROUP


-0.75 m -5.19 -5.29 1.89-2.37 m -12.14 -12.14 0.00-3.13 m -15.76 -15.76 0.00-5.75 m -14.42 -14.42 0.00-9.25 m -26.83 -26.83 0.00-11 m -34.65 -113.51 69.47


Depth[m]

Benchmark[kN/m]

D-PILE GROUP


-0.75 m 10.18 5.29 92.44-2.37 m 23.80 12.14 96.05-3.13 m 30.88 15.76 95.94-5.75 m 25.40 25.40 0.00-9.25 m 47.26 47.26 0.00-11 m 61.02 4.10 1388.29


3.10 Axial T − Z curve for sand (Cone)

3.10.1 Description

The axial T −Z curve for sand according to the NEN using the cone resistance is checked inthis benchmark by calculating the mobilized skin friction along the pile. The same geometry asfor benchmark 3-2 is used (see ??) except that the lateral load is replaced by a compressivevertical load of 300 kN (from steps 1 to 10) and a tensile vertical load of 300 kN (from steps11 to 20). The soil properties of the two sand layers are given in Table 3.26 below.

Deltares 37 of 62





Bottom 13 13Cone resistance Top [kN/m2] 2000 1000

Bottom 3000 1500Factor alpha [-] 0.005 0.008dz at 100 % [m] 0.002 0.004


The relation between the axial force T and the vertical displacement Z for sand is the sameas for benchmark bm3-9.









Depth[m]

Benchmark[kN/m]

D-PILE GROUP


-0.75 m -41.30 -41.30 0.00-2.37 m -40.72 -40.72 0.00-3.13 m -43.71 -43.71 0.00-5.75 m -16.56 -16.56 0.00-9.25 m -20.24 -20.24 0.00-11 m -22.08 -5.35 312.71

38 of 62 Deltares



Depth[m]

Benchmark[kN/m]

D-PILE GROUP


-0.75 m 49.81 41.30 20.61-2.37 m 49.11 40.72 20.60-3.13 m 52.71 43.71 20.59-5.75 m 17.05 17.05 0.00-9.25 m 20.84 20.84 0.00-11 m 22.73 1.59 1329.56


Deltares 39 of 62


40 of 62 Deltares

4 Group 4: Benchmarks generated by D-PILE GROUP

4.1 One pile loaded by a force, two different directions are considered

4.1.1 Description

The two cases presented below are equivalent.

� In the first case (bm4-1a), a pile with position (0, 0, 0) is loaded by a horizontal force of100 kN on the top.

� In the second case (bm4-1b), the same pile has an angle of 45 degrees in the X − Zplane. The pile is also loaded by a force in X-direction of 70.7 kN and a force in Z-direction of -70.7 kN on the top. The angle of the force is also 45 degrees in the X − Zplane.



D-PILE GROUP results can be found in Charts window from the Results menu using the ViewData option. For both cases, D-PILE GROUP gives the same results.


D-PILE GROUP bm4-1a D-PILE GROUP bm4-1b Relative error [%]Maximum dis-placement – X”[m]

0.04808 0.04806 0.04

Maximum mo-ment – Z” [kNm]

-156.98 -156.95 0.02

Maximum shearforce – X” [kN]

100.00 99.98 0.02


4.2 Two piles loaded by an eccentric force – two piles loaded by a centric force and amoment

4.2.1 Description


� In the first case (bm4-2a), two piles are loaded by an eccentric horizontal force of magni-tude 100 kN and eccentricity 2 m. The pile positions are:

� position pile 1: (−1, − 2, 0)� position pile 2: (1, − 2, 0)

� In the second case (bm4-2b), these two piles are loaded by a centric force of 100 kN andalso a moment around Y -axis of 200 kNm. The pile positions are:

� position pile 1: (−1, 0, 0)� position pile 2: (1, 0, 0)

Deltares 41 of 62


For both cases the Cap model is used with a cap located at (0, 0, 0) and the rotation aroundZ-axis is set equal to 0 degrees.


D-PILE GROUP results can be found in Charts window from the Results menu using the ViewData option. For both piles D-PILE GROUP gives the same results.


D-PILE GROUP bm4-2a D-PILE GROUP bm4-2b Relative error [%]Max. displace-ment – X” [m]

0.004423 0.004423 0.00

Max. displace-ment – Z” [m]

0.010805 0.010805 0.00

Max. moment –Z” [kNm]

57.33 57.33 0.00

Max. moment –X” [kNm]

-126.52 -126.52 0.00

Max. shearforce – X” [m]

50.00 50.00 0.00

Max. shearforce – Z” [m]

100.00 100.00 0.00


4.3 One pile with user defined lateral curve is loaded by a force

Description

This benchmark checks the functioning of a user-defined lateral curve. In the first case (bm4-3a), the soil is just strong enough to handle the applied force whereas in the second case(bm4-3b) the pile and soil should collapse as the applied horizontal force is 1 kN more thanthe allowed horizontal force. The following inputs are used for each case:

� In the first case (bm4-3a), a pile at position (0, 0, 0) with a length of metricconverter10 mand a user defined lateral P − Y curve of P = 20 kN/m is loaded by a horizontal force of200 kN. The rotation around Z-axis is 0 degrees.

� In the second case (bm4-3b), the same pile is loaded by a horizontal force of 201 kN.


42 of 62 Deltares

Group 4: Benchmarks generated by D-PILE GROUP


D-PILE GROUP results can be found in Charts window from the Results menu using the ViewData option. As expected, the soil and the pile collapse for bm4-3b but not for bm4-3a.


D-PILE GROUP bm4-3a D-PILE GROUP bm4-3bDisplacement – X” [m] Pile top 1.2748 -4.8E+12 (Collapsed)


4.4 One pile with user defined axial curve is loaded by a force

Description

This benchmark checks the functioning of a user-defined axial curve. In the first case (bm4-4a), the soil is just strong enough to handle the applied vertical force whereas in the secondcase (bm4-4b) the pile and soil should collapse as the applied vertical force is 1 kN more thanthe allowed vertical force. The following inputs are used for each case:

� In the first case (bm4-4a), a pile with an end bearing capacity of 0 kN and a user definedaxial T − Z curve of T = 10 kN/m is loaded by a vertical force of 100 kN.

� In the second case (bm4-4b), the same pile is loaded by a vertical force of 101 kN.



D-PILE GROUP results for bm4-4a can be found in Charts window from the Results menu usingthe View Data option. For bm4-4a, a vertical load of 100 kN leading to instability, an updatedvalue of 99.949 kN is used.As expected, the soil and the pile collapse for bm4-4b but not forbm4-4a.


D-PILE GROUP bm4-4a D-PILE GROUP bm4-4bDisplacement – Y ” [m] -0.10012 Error (Collapsed)


4.5 One pile is loaded by a vertical force, only end bearing is considered

4.5.1 Description

This benchmark checks the functioning of end bearing. In the first case (bm4-5a), the soil isjust strong enough to handle the applied vertical force whereas in the second case (bm4-5b)the pile and soil should collapse as the applied vertical force is 1 kN more than the allowedvertical force. The following inputs are used for each case:

� In the first case (bm4-5a), a pile with an end bearing capacity of 100 kN and a user definedaxial T − Z curve of T = 0.01 kN/m is loaded by a vertical force of 100 kN.

� In the second case (bm4-5b), the same pile is loaded by a vertical force of 101 kN.

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D-PILE GROUP results for bm4-5a can be found in Charts window from the Results menu usingthe View Data option. For bm4-5a, a vertical load of 100 kN leading to instability, an updatedvalue of 99.949 kN is used.As expected, the soil and the pile collapse for bm4-5b but not forbm4-5a.


D-PILE GROUP bm4-5a D-PILE GROUP bm4-5bDisplacement – Y ” [m] Pile top -0.04090 Error (Collapsed)


4.6 Single pile, with pile top 2m above ground level, loaded by a moment, consideredaround two different axis

Description


� In the first case (bm4-6a), a pile, which pile top reaches two meters above ground level, isloaded by a moment around the X-axis of 100 kNm.

� In the second case (bm4-6b), the same pile is loaded by a moment around the Z-axis of100 kNm.

For both cases, the Cap model is used.

For bm4-6a and bm4-6b, D-PILE GROUP should give the same displacement. For the uppertwo meters above ground level the moment should be constant (100 kNm) and the shear forceshould be 0 kN.


Results can be found using the View data option in the Charts window selecting for bm1-9aand bm1-9b respectively directions Z and X .

Table 4.6: Results of benchmark 4-6 at pile top

D-PILE GROUP bm4-6a(direction Z)

D-PILE GROUP bm4-6b(direction X)

Relative error [%]

Displacement [m] 0.04114 -0.04114 0.00Moment [kNm] 100.00 100.00 0.00Shear force [kN] 0.000 0.000 0.00


4.7 One pile is loaded by a force, the same pile is loaded by the displacement (result ofthe force)

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4.7.1 Description

This benchmark checks the functioning of the soil displacement load by comparing the twofollowing cases which are equivalent and should therefore give the same results.

� In the first case (bm4-7a), a pile is loaded by a horizontal force of 150 kN. This results ina displacement of 0.291 m.

� In the second case (bm4-7b), the same pile is loaded by a displacement in X-direction of0.291 m.



D-PILE GROUP results can be found in Charts window from the Results menu using the ViewData option. Both cases give the same results.


D-PILE GROUP bm4-7a D-PILE GROUP bm4-7b Relative error [%]Max. displace-ment – X” [m]

0.2913 0.2910 0.10

Max. moment –Z” [kNm]

-286.92 -286.68 0.08

Max. shearforce – X” [kN]

-163.63 -163.44 0.12


4.8 A pile group loaded by a horizontal force

4.8.1 Description

A pile group of 9 piles is loaded by a horizontal force of 450 kN and the rotation around theZ-axis is free.

0

5

10

15

20

25

30

-0.02 -0.018 -0.016 -0.014 -0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0

Rotation around Z-axis θθθθz [rad]

Cap

late

ral

forc

e Fx

[k

N]


Cap model (bm4-10b)



Figure 4.1: Top view of the position of the 9 piles

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The D-PILE GROUP results for the four following models are compared:

� Cap model (bm4-8a)� Poulos model (bm4-8b)� Cap soil interaction model (bm4-8c)� Cap layered soil interaction model (bm4-8d)

The results of the four different models should be almost the same, with the exception of theCap model (bm4-8a) where all piles are loaded equally (no pile-soil-pile interaction).


Results can be found using the Top View window form the Results menu. The differencesbetween the results are acceptable.

Table 4.8: Results of benchmark 4-8b (Poulos model) compare to results of benchmark4-8a (Cap model)

Horizontal loadsat pile top

D-PILE GROUP bm4-8a[kN]

D-PILE GROUP bm4-8b[kN]

Relative error [%]

Corner pile (piles1, 3, 7 and 9)

50.0 52.6 4.94

“Side” row pile(piles 4 and 6)

50.0 48.7 2.67

“Front or back”row pile (piles 2and 8)

50.0 49.0 2.04

Centre pile (pile5)

50.0 44.4 12.61

Table 4.9: Results of benchmark 4-8c (Cap soil interaction model) compare to results ofbenchmark 4-8a (Cap model)



D-PILE GROUP bm4-8c[kN]

Relative error [%]

Corner pile (piles1, 3, 7 and 9)

50.0 52.4 4.58

“Side” row pile(piles 4 and 6)

50.0 48.6 2.88

“Front or back”row pile (piles 2and 8)

50.0 49.1 1.83

Centre pile (pile5)

50.0 44.8 11.61

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Table 4.10: Results of benchmark 4-8d (Cap layered soil interaction model) compare toresults of benchmark 4-8a (Cap model)



D-PILE GROUP bm4-8d[kN]

Relative error [%]

Corner pile (pile1)

50.0 52.1 4.03

Corner pile (pile3)

50.0 52.0 3.85

Corner pile (pile7)

50.0 52.2 4.21

Corner pile (pile9)

50.0 52.0 3.85

“Side” row pile(pile 4)

50.0 48.2 3.73

“Side” row pile(pile 6)

50.0 48.1 3.95

“Front or back”row pile (pile 2)

50.0 49.9 0.20

“Front or back”row pile (pile 8)

50.0 49.9 0.20

Centre pile (pile5)

50.0 45.6 9.65

Use D-PILE GROUP input files bm4-8a.pii to bm4-8d.pii to run this benchmark.

4.9 A pile group of 7 piles is loaded by a horizontal force, comparison of Poulos and Capsoil interaction models

4.9.1 Description

A pile group of 7 piles is loaded by a horizontal force in X-direction of 140 kN. The springstiffness is set high, so that the interaction between the piles and the soil is very stiff. ThePoisson ratio is 0.3 and the Young’s modulus is 1000 kN/m2. The results of two models arecompared:

� Poulos model (bm4-9a),� Cap soil interaction model (bm4-9b).

For bm4-9b, the lateral and axial curves are user defined:

� User defined lateral curve: P = 99 999 kN/m ; Y = 0.100 m� User defined axial curve: T = 99 999 kN/m ; Z = 0.100 m

It is expected that bm4-9a and bm4-9b should almost give the same results.

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D-PILE GROUP results can be found in Charts window from the Results menu using the ViewData option. Differences between both models are within acceptable limits.

Table 4.11: Results of benchmark 4-9 for pile 1

D-PILE GROUP bm4-9a D-PILE GROUP bm4-9b Relative error [%]Displacement –X” [m] Pile top

0.014342 0.013480 6.39

Moment – Z”[kNm] Pile top

17.813 22.479 20.76

Shear force – X”[kN] Pile top

13.185 14.096 6.46


4.10 Calculation of the plasticity factors for the Plasti-Poulos model

4.10.1 Description

The determination of the plasticity factors used for the Plasti-Poulos calculation is checked inthis benchmark. The same input data as Tutorial-8b are used (see Tutorial 8: "3-piles groupanalysis using four different models" in Chapter 14 and Figure 14-1 of the User Manual. Onlythe loading is different as a moment Mz = -40 kNm is added to the lateral load Fx = 80 kNand the vertical load Fy = -320 kN.

Plasticity factors are determined in the Plasticity Factors window from the Pile menu, usingthe following ranges:

� Force X : from 0 till 30 kN in 100 steps;� Force Y : from -210 till 130 kN in 100 steps;� Moment Z : from 0 till 70 kNm in 100 steps.


Two methods are used to check the calculation of the plasticity factors.

� Method 1: In D-PILE GROUP, the plasticity factors as given in the Plasticity Factors windowof the program are determined using the Cap model :fplastic = XCap/XCap,elasticwhereXCap can be whatever Fx, Fy, Ux, Uy, Mz, θz for a single pile and X − Cap, elasticis the elastic first part of the Cap curve.

� Method 2: D-PILE GROUP also automatically calculate an equivalent Young’s modulus insuch a way that the elastic stiffness of a single pile in the Poulos model is almost thesame as for the Cap model calculation. Therefore, the plasticity factor can also be writtenas:fplastic = XCap/XPoulos

In order to get the XCap values, four calculations with D-PILE GROUP are performed using theCap model for a single pile loaded by:

� (bm4-10b) a lateral load of Fx = 30 kN during the 100 last steps;� (bm4-10c) a compressive vertical load Fy = -210 kN during the 62 first steps;� (bm4-10d) a tensile vertical load Fy = 130 kN during 38 steps;� (bm4-10e) a moment Mz = 40 kN during 100 steps.

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The XCap,elastic values are deduced from the XCap values using the 10 first points (assumedto be in the elastic part) pf the Cap curve.

In order to get the XPoulos values, four calculations with D-PILE GROUP are performed usingthe Poulos model for a single pile with a Young’s modulus of E = 1366.21 kN/m2 as automat-ically calculated in the Calculation Messages window of bm4-10a. The single pile is loadedby:

� (bm4-10f) a lateral load of Fx = 30 kN;� (bm4-10g) a compressive vertical load Fy = -210 kN;� (bm4-10h) a tensile vertical load Fy = 130 kN;� (bm4-10i) a moment Mz = 40 kN.

Results of all those D-PILE GROUP input files can be found in an Excel spreadsheet and arepresented in the following tables and figures for both methods.

Table 4.12: Plasticity factors calculated with both methods – Curve Fx − Ux

Fx Ux;Cap Ux;CapEL Ux;Poulos Plasticity factor(bm4-10b) (bm4-10f) Cap/Cap EL Cap/Poulos

[kN] [m] [m] [m] [-] [-]0 0.00000 0.00000 0.00000 1.0000 1.00006 0.00326 0.00269 0.00274 1.2119 1.189812 0.01055 0.00538 0.00547 1.9610 1.928718 0.02174 0.00807 0.00821 2.6939 2.648024 0.03686 0.01076 0.01094 3.4257 3.369330 0.05543 0.01345 0.01368 4.1212 4.0519

Table 4.13: Plasticity factors calculated with both methods – Curve Fx − θz

Fx θz;Cap θz;Cap EL θz;Poulos Plasticity factor(bm4-10b) (bm4-10f) Cap/Cap EL Cap/Poulos

[kN] [rad] [rad] [rad] [-] [-]0 0.000000 0.000000 0.000000 1.0000 1.00006 -0.001535 -0.001304 -0.001277 1.1771 1.202012 -0.004373 -0.002608 -0.002553 1.6768 1.712918 -0.008147 -0.003911 -0.003830 2.0831 2.127224 -0.012803 -0.005215 -0.005107 2.4550 2.507030 -0.018062 -0.006519 -0.006383 2.7707 2.8297

Table 4.14: Plasticity factors calculated with both methods – Curve Fy−Uy (compression)

Fy Uy;Cap Uy;Cap EL Uyx;Poulos Plasticity factor(bm4-10c) (bm4-10g) Cap/Cap EL Cap/Poulos

[kN] [m] [m] [m] [-] [-]-210 -0.006212 -0.004697 -0.004540 1.3225 1.3683-182.903 -0.004330 -0.004091 -0.003954 1.0584 1.0951-132.097 -0.002956 -0.002955 -0.002856 1.0003 1.0350-105 -0.002349 -0.002349 -0.002270 1.0000 1.0348-77.903 -0.001743 -0.001743 -0.001684 1.0000 1.0350-27.097 -0.000606 -0.000606 -0.000586 1.0000 1.03410 0.000000 0.000000 0.000000 1.0000 1.0000

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Table 4.15: Plasticity factors calculated with both methods – Curve Fy − Uy (tension)

Fy Uy;Cap Uy;Cap EL Uy;Poulos Plasticity factor(bm4-10d) (bm4-10h) Cap/Cap EL Cap/Poulos

[kN] [m] [m] [m] [-] [-]0 0.000000 0.000000 0.000000 1.0000 1.000034.211 0.000886 0.000887 0.000739 0.9989 1.198965 0.001684 0.001685 0.001405 0.9994 1.198699.211 0.002571 0.002571 0.002144 1.0000 1.1992130 0.003396 0.003369 0.002810 1.0080 1.2085

Table 4.16: Plasticity factors calculated with both methods – Curve Mz − Uz

Mz Uz;Cap Uz;Cap EL Uz;Poulos Plasticity factor(bm4-10e) (bm4-10i) Cap/Cap EL Cap/Poulos

[kNm] [m] [m] [m] [-] [-]0 0.000000 0.000000 0.000000 1.0000 1.000014 -0.003470 -0.003044 -0.001258 1.1399 2.758328 -0.008920 -0.006087 -0.002517 1.4654 3.543942 -0.015920 -0.009131 -0.003775 1.7435 4.217256 -0.023780 -0.012175 -0.005034 1.9532 4.723970 -0.032950 -0.015218 -0.006292 2.1652 5.2368

Table 4.17: Plasticity factors calculated with both methods – Curve Mz − θz

Mz θz;Cap θz;Cap EL θz;Poulos Plasticity factor(bm4-10e) (bm4-10i) Cap/Cap EL Cap/Poulos

[kNm] [rad] [rad] [rad] [-] [-]0 0.000000 0.000000 0.000000 1.0000 1.000014 0.002981 0.002792 0.001627 1.0677 1.832228 0.006708 0.005584 0.003255 1.2013 2.060842 0.010900 0.008375 0.004882 1.3015 2.232756 0.015351 0.011167 0.006509 1.3747 2.358470 0.020144 0.013959 0.008137 1.4431 2.4756

-210

-160

-110

-60

-10

40

90

-0.008 -0.006 -0.004 -0.002 0 0.002 0.004

Cap vertical displacem ent Uy [m ]

Cap a

xial fo

rce Fy

[kN]


Cap model (bm4-10c and bm4-10d)

Poulos model with E = 1366.21 kPa (bm4-10g and bm4-10h)

Cap model - Elastic part (bm4-10c and bm4-10d)

Figure 4.2: Curve Fx − Ux for a single pile for different models

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0

10

20

30

40

50

60

70

-0.035 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0

Cap lateral deflection Ux [m ]

Bend

ing m

omen

t Mz [

kNm]


Cap model (bm4-10e)

Poulos model with E = 1366.21 kPa (bm4-10i)

Cap model - Elastic part (bm4-10e)

Figure 4.3: Curve Fx − θz for a single pile for different models

0

10

20

30

40

50

60

70

0 0.005 0.01 0.015 0.02 0.025


Bend

ing m

omen

t Mz [

kNm]


Cap model (bm4-10e)

Poulos model with E = 1366.21 kPa (bm4-10i)

Cap model - Elastic part (bm4-10e)

Figure 4.4: Curve Fy − Uy for a single pile for different models

0

5

10

15

20

25

30

-0.02 -0.018 -0.016 -0.014 -0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0


Cap l

ateral

force

Fx [k

N]


Cap model (bm4-10b)



Figure 4.5: Curve Mz − Ux for a single pile for different models

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0

5

10

15

20

25

30

-0.02 -0.018 -0.016 -0.014 -0.012 -0.01 -0.008 -0.006 -0.004 -0.002 0


Cap l

ateral

force

Fx [k

N]


Cap model (bm4-10b)



Figure 4.6: Curve Mz − θz for a single pile for different models

For all curves, the Cap model fits perfectly with the Plasti-Poulos plastic curves. This wasexpected as they are defined this way.

For curves Fx−Ux, Fx− θz and Fy −Uy (in compression), it can be seen that the Poulosmodel with the automatic calculated Young’s modulus (E = 1366.21 kN/m2) corresponds withthe elastic part of the Plasti-Poulos plastic curves. This is not right for the other curves. Thisis due to the way the Young’s modulus is estimated: the fit is made for the lateral and axialforces, but not for the moment.


General plasticity factors determined by D-PILE GROUP for the Plasti-Poulos model (bm4-10a)can be found in the Plasticity Factors window from the Pile menu.

Table 4.18: Results of benchmark 4-10 – Plasticity factors for curve Fx − Ux

Fx Benchmark D-PILE GROUP Relative errorCap/Cap EL Cap/Poulos (bm4-10a) Cap/Cap EL Cap/Poulos

[kN] [-] [-] [-] [%] [%]0 1.0000 1.0000 1.0000 0.00 0.006 1.2119 1.1898 1.2010 0.91 0.9312 1.9610 1.9287 1.9435 0.90 0.7618 2.6939 2.6480 2.6668 1.02 0.7024 3.4257 3.3693 3.3959 0.88 0.7830 4.1212 4.0519 4.0662 1.35 0.35

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Table 4.19: Results of benchmark 4-10 – Plasticity factors for curve Fx − θz

Fx Benchmark D-PILE GROUP Relative errorCap/Cap EL Cap/Poulos (bm4-10a) Cap/Cap EL Cap/Poulos

[kN] [-] [-] [-] [%] [%]0 1.0000 1.0000 1.0000 0.00 0.006 1.1771 1.2020 1.1686 0.73 2.8612 1.6768 1.7129 1.6567 1.21 3.3918 2.0831 2.1272 2.0542 1.41 3.5524 2.4550 2.5070 2.4182 1.52 3.6730 2.7707 2.8297 2.7238 1.72 3.89

Table 4.20: Results of benchmark 4-10 – Plasticity factors for curve Fy − Uy (compres-sion)

Fy Benchmark D-PILE GROUP Relative errorCap/Cap EL Cap/Poulos (bm4-10a) Cap/Cap EL Cap/Poulos

[kN] [-] [-] [-] [%] [%]-210 1.3225 1.3683 1.3223 0.02 3.48-182.903 1.0584 1.0951 1.0579 0.05 3.52-132.097 1.0003 1.0350 1.0000 0.03 3.50-105 1.0000 1.0348 1.0000 0.00 3.48-77.903 1.0000 1.0350 1.0000 0.00 3.50-27.097 1.0000 1.0341 1.0000 0.00 3.410 1.0000 1.0000 1.0000 0.00 0.00

Table 4.21: Results of benchmark 4-10 – Plasticity factors for curve Fy − Uy (tension)

Fy Benchmark D-PILE GROUP Relative errorCap/Cap EL Cap/Poulos (bm4-10a) Cap/Cap EL Cap/Poulos

[kN] [-] [-] [-] [%] [%]0 1.0000 1.0000 1.0000 0.00 0.0034.211 0.9989 1.1989 1.0178 1.86 17.7965 0.9994 1.1986 1.0187 1.89 17.6699.211 1.0000 1.1992 1.0191 1.87 17.67130 1.0080 1.2085 1.0273 1.88 17.64

Table 4.22: Results of benchmark 4-10 – Plasticity factors for curve Mz − Uz

Mz Benchmark D-PILE GROUP Relative errorCap/Cap EL Cap/Poulos (bm4-10a) Cap/Cap EL Cap/Poulos

[kNm] [-] [-] [-] [%] [%]0 1.0000 1.0000 1.0000 0.00 0.0014 1.1399 2.7583 1.1330 0.61 143.4528 1.4654 3.5439 1.4450 1.41 145.2542 1.7435 4.2172 1.7107 1.92 146.5256 1.9532 4.7239 1.9323 1.08 144.4770 2.1652 5.2368 2.1329 1.51 145.52

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Table 4.23: Results of benchmark 4-10 – Plasticity factors for curve Mz − θz

Mz Benchmark D-PILE GROUP Relative errorCap/Cap EL Cap/Poulos (bm4-10a) Cap/Cap EL Cap/Poulos

[kNm] [-] [-] [-] [%] [%]0 1.0000 1.0000 1.0000 0.00 0.0014 1.0677 1.8322 1.0646 0.29 72.1028 1.2013 2.0608 1.1948 0.54 72.4842 1.3015 2.2327 1.2928 0.67 72.7056 1.3747 2.3584 1.3695 0.38 72.2170 1.4431 2.4756 1.4367 0.45 72.31

Use D-PILE GROUP input files bm4-10a.pii and bm4-10i.pii to run this benchmark.

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5 Group 5: Benchmarks compared with other programs

5.1 Two inclined piles in layered soil, complex case

5.1.1 Description

A complex case with two inclined piles with different length in a layered soil is considered.

Pile 1 Pile 2Pile positions (−1.5, 0, 0) (1.5, 0, 0)Pile skewness 1:3 1:3Pile angle 0 degrees 180 degreesPile length 10 m 20 m

The cap is first loaded by a vertical force of 100 kN between steps 0 to 50. After that ahorizontal force of 250 kN is applied between steps 50 to 100.

The Cap model is used for D-PILE GROUP calculations.


No accurate predictions can be done. Testing this complex case no strange results may occur.A comparison is possible with the DOS-version of D-PILE GROUP.



No abnormal curves were found. One difference is found between the Dos and Windowsversion. The Y-reaction of the bottom pile-node differs. The results obtained from the Dos-version are not correct. The Windows-version takes end bearing for the bottom pile-node inaccount.

Note: The results shown in the menus Charts and Top View of the Windows version aredifferent, because in the Charts window the values are in the local system of the pile and inthe Top View the values are in the global system. The DOS values are in the local system, sofor comparison the local system values will be used.

Table 5.1: Results of benchmark 5-1 for pile 1

MPile(Dos 2.2.2)

D-PILE GROUP (Win-dows)

Relative error [%]

Displacement - X”[m] Pile top

-0.012 -0.012 0.00

Moment - Z”[kNm] Pile top

-42.2 -44.4 4.95

Shear force - X”[kN] Pile top

-75.4 -75.9 0.66

Displacement –Y ” [m] Pile top

0.024 0.024 0.00

Reaction - Y” [kN]Pile tip

30.9 (incorrect) 4.8 -

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5.2 3-piles group under general loading (Poulos theory)

5.2.1 Description

A group of 3 piles is subjected to a combination of axial load, lateral load and moment. Thepile and soil properties are given in Table 5.2. The Poulos model is used for D-PILE GROUP

calculations. Resulting loads, bending moments and displacements are compared with thoseobtain by three different programs.

Figure 5.1: 3-piles group under general loading


In Poulos (1980), Poulos compares the results given by three different programs (DEFPIG,Piglet Randolph (1996) and GEPAN Xu (2000)) for the described above project. Those pro-grams consider the presence of the soil, including the interaction effects between the pilesthrough the soil. Results are reported in the table below.


D-PILE GROUP results are found in the Report window. The results show a good agreementbetween D-PILE GROUP and the different programs, especially with Piglet.

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Group 5: Benchmarks compared with other programs


Benchmark D-PILE GROUP Relative error [%]Da Pa Ga Da Pa Ga

Axial force, Pile top 1 [kN] 55.8 55.7 54.0 55.9 0.18 0.36 3.40Axial force, Pile top 2 [kN] 155.1 155.0 156.0 155.8 0.45 0.51 0.13Axial force, Pile top 3 [kN] 389.1 389.3 390.0 388.3 0.21 0.26 0.44Lateral force, Pile top 1 [kN] 72.0 80.4 73.7 80.4 10.45 0.00 8.33Lateral force, Pile top 2 [kN] 56.0 39.3 50.9 39.2 42.86 0.26 29.85Lateral force, Pile top 3 [kN] 72.0 80.4 75.4 80.4 10.45 0.00 6.22Moment, Pile top 1 [kNm] 35.8 42.0 38.5 41.5 13.73 1.20 7.23Moment, Pile top 2 [kNm] 28.5 16.3 26.1 15.8 80.38 3.16 65.19Moment, Pile top 3 [kNm] 35.8 42.0 38.6 41.5 13.73 1.20 6.99Vert. displ., Pile top 3 [mm] 13.4 9.9 10.8 13.2 1.52 25.00 18.18Horiz. cap displac. [mm] 11.6 11.4 10.5 11.4 1.75 0.00 7.89Rotation of the cap [10-3 rad] 2.42 2.42 2.41 2.45 1.22 1.22 1.63a D = DEFPIG, P = Piglet, G = GEPAN


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References

API, 1984. “Recommended practice for planning, designing, and constructing fixed offshoreplatforms.” Washington D.C.

Bijnagte, J. L., 1990. Ducbots dynamisch modelleren van ducdalven. Tech. Rep. CO-294782/27, GeoDelft.

Matlock, H., 1970. “2nd Offsh. Techn. Conf., Texas.” In Correlations for design of laterallyloaded piles in soft clay, OTC 1204.

Mindlin, R. D., 1953. “1st Mid-west. Conf. Solid Mech., University of Illinois, Illinois.” In Forceat a point in the interior of a semi-infinite solid, pages 56-59.

Poulos, E. H., H. G. Davis, 1980. Pile foundation analysis and design. Wiley, New York.

Randolph, M. F., 1996. PIGLET, Analysis and Design of pile groups. University of WesternAustralia.

Xu, H. G., K. J. Poulos, 2000. “General elastic analysis of pile groups.” Int. J. Numer. Anal.Meth. Geomechs. 24: 1109-1138.

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