Initial top plate bearing of a suction pile

Delft University of Technology

Master thesis

Optimization of a suction pile foundation

Initial top plate bearing of a suction pile

Author:

Simon Lembrechts

Student number: 1386549

Supervisors:

Prof. dr. ir. C. van Rhee

Prof. ir. A.F. van Tol

Ir. G.L.M. van der Schrieck

Ir. T. Visser

January 28, 2013

Master ThesisOptimization of a Suction Pile Foundation

Administrative data

Student

Simon LembrechtsVoorstraat 95-22611JM DelftThe [email protected](+)31 647229631

Committee

Prof. Dr. Ir. C. van Rhee - ChairmanDelft University of TechnologyFaculty Mechanical, Maritime and Materials Engineering, Room [email protected](+)31 152783973

Ir. A.F. van Tol - Mentor Geo-engineeringDelft University of TechnologyFaculty of Civil Engineering and Geosciences, Room KG [email protected](+)31 152782092

Ir. G.L.M. van der Schrieck - Daily mentor TUDelftFaculty of Civil Engineering and Geosciences, Room HG [email protected](+)31 152788592

Ir. T. Visser - Daily mentor SPT O�shoretvi@spto�shore.com(+)31 622565753

Addresses

Delft University of TechnologyFaculty of Civil Engineering and Geo-sciencesDepartment of Geo-TechnologyStevingweg 12628CN DelftThe Netherlandswww.tudelft.nl

SPT O�shoreKorenmolenlaan 23447GG WoerdenThe Netherlandswww.spto�shore.com

iii


Preface

This report is the �nal result of eight months of research as a conclusion of the Master programGeotechnical Engineering at Delft University of Technology. The subject investigated in this MasterThesis originates from a practical challenge encountered by SPT O�shore, an o�shore contractorwith Suction Pile Technology as its core business. I performed most of my research at their o�cesin Woerden, the Netherlands.

Throughout the entire research project I have received lots of advice, support and help from manypeople. Working on this Master Thesis was without any doubt the most satisfactory part of myEngineering studies. That is why I would like to seize the opportunity to express my sincere thanksto everyone who has contributed to the completion of this project.

I would like to express my gratitude to the members of my committee, who supported me through-out this entire research project. To my mentor at SPT O�shore, Thijs Visser, for his patience,his enthusiasm and guidance. Numerous discussions helped me to get a good understanding of allrelevant geotechnical phenomena. To Bart van der Schrieck, my mentor at the TU Delft, for hisinterest, constructive criticism and the e�ort he took to teach me the tricks of physical modeling.I have appreciated the feedback I got, as even in weekends and in the middle of the night my ques-tions were answered. To Professor Cees van Rhee and Professor Frits van Tol, for giving me theopportunity to do my own, independent research project and for answering my questions wheneverneeded.

Besides my committee, I would like to thank my colleagues at SPT O�shore, for their interest inmy research project and their varying contributions to the completion of my thesis. Furthermoremy thanks go to Han de Visser, for his practical and cheerful assistance during my model tests.Last but not least, I would like to thank my girlfriend, family and friends, who had to listen foreight months to my, undoubtedly very interesting, stories about suction pile foundations.

January 28, 2013

Simon Lembrechts

v


Contents

Administrative data iii

Preface v

Contents vii

List of Figures xi

List of Tables xiv

List of Symbols xv

1 Introduction 11.1 Background information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Problem de�nition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Readers manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 A suction pile 32.1 De�nition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 The installation principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Groundwater �ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.1 The pressure gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3.2 Pore pressure at pile tip, next to the skirt . . . . . . . . . . . . . . . . . . . 62.3.3 Average pore pressure at pile tip level . . . . . . . . . . . . . . . . . . . . . 6

2.4 Prediction of the installation resistance . . . . . . . . . . . . . . . . . . . . . . . . . 82.4.1 Self-weight penetration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4.2 Suction-assisted penetration: Empirical reduction . . . . . . . . . . . . . . . 142.4.3 Suction-assisted penetration: Pressure-related reduction . . . . . . . . . . . 15

3 Gap between top plate and soil after installation 173.1 Plug heave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.1 Plug heave due to the soil which is pushed in by the skirt's penetration volume 173.1.2 Elastic plug heave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.1.3 Plug loosening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2 Erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4 Sollutions to the gap problem 254.1 Variants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1.1 Onshore measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.1.2 O�shore measures, prior to installation . . . . . . . . . . . . . . . . . . . . 274.1.3 O�shore measures, after installation . . . . . . . . . . . . . . . . . . . . . . 27

4.2 First evaluation of the di�erent variants . . . . . . . . . . . . . . . . . . . . . . . . 27

5 Calculation model 315.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.2 Soil structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Contents vii


5.3 Installation resistance and bearing capacity model . . . . . . . . . . . . . . . . . . 335.4 Groundwater �ow model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.4.1 Groundwater �ow equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.4.2 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.4.3 Numerical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.4.4 Programming considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 405.4.5 Veri�cation of the numerical model . . . . . . . . . . . . . . . . . . . . . . . 43

5.5 Erosion-rate model and plug loosening . . . . . . . . . . . . . . . . . . . . . . . . . 44

6 Results 476.1 Installation resistance and bearing capacity model . . . . . . . . . . . . . . . . . . 476.2 Erosion-rate model and plug loosening . . . . . . . . . . . . . . . . . . . . . . . . . 48

7 Bearing capacity of a second top plate 537.1 General design criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537.2 Bearing capacity in each construction phase . . . . . . . . . . . . . . . . . . . . . . 53

7.2.1 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537.2.2 Load phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

7.3 Second top plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557.3.1 Di�erent designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557.3.2 Numerical investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

8 Veri�cation 598.1 Physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

8.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598.1.2 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598.1.3 Scaling laws at earth's normal gravitational acceleration (1g) [22] . . . . . . 608.1.4 Scaling e�ects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658.1.5 The suction pile model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678.1.6 The tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698.1.7 The sand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698.1.8 Test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

8.2 Analysis of existing projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 768.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 768.2.2 Installation resistance and bearing capacity model . . . . . . . . . . . . . . 768.2.3 Erosion-rate model and plug loosening . . . . . . . . . . . . . . . . . . . . . 778.2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

8.3 Design considerations and procedure for the new calculation model . . . . . . . . . 81

9 Conclusion and recommendations 859.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 859.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Appendices 87

A Calculation models 89A.1 Calculation model based on homogeneous soil and cone resistance . . . . . . . . . . 89A.2 Calculation model based on non-homogeneous soil and cone resistance . . . . . . . 98

A.2.1 Parameters Project 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98A.2.2 Parameters Project 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

A.3 Calculation model based on Brinch-Hansen . . . . . . . . . . . . . . . . . . . . . . 100A.4 Strength parameters of the soil during the model tests . . . . . . . . . . . . . . . . 107

B Technical drawings of the model 109B.1 The tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109B.2 The procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110B.3 Views of the di�erent test set-ups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Contents viii


C Soil characterization model test 115C.1 Permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Contents ix


List of Figures

1.1 F3FA-platform for Centrica. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 A suction pile on a transport barge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2.1 Initial phase: own weight penetration, no suction is applied. . . . . . . . . . . . . . . . 3

2.2 Second phase: suction assisted penetration, there is a pressure di�erence along the top

plate. Plug heave occurs inside the pile. . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3 Result after installation in sand. Notice the gap between top plate and soil. . . . . . . . 4

2.4 For installations in sand, initial contact between top plate and soil is impossible due to

erosion and plug settlement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.5 Flowlines due to the applied pressure di�erence. . . . . . . . . . . . . . . . . . . . . . . 5

2.6 The pore pressure factor (a) at the pile tip according to Junaideen [2004], veri�ed by the

author in Plaxis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.7 At shallow depths, the pore pressure factor in the center is much higher (0.83) compared

to the factor at the skirt tip (0.40). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.8 At higher depths, the absolute di�erence between the pore pressure factor in the center

(0.31) and the factor at the skirt tip (0.16) is much smaller. . . . . . . . . . . . . . . . 7

2.9 The pore pressure factor (a) at the pile tip compared with the average pore pressure at the

base of the suction pile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.10 The 2-dimensional failure mechanism according to Brinch-Hansen. . . . . . . . . . . . . 9

2.11 Equilibrium of a slice of soil inside the suction pile, in�uenced by the skirt friction. [13] . 10

2.12 The inner and outer area of in�uence. . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.13 The inner area of in�uence is signi�cantly smaller than the outer area. . . . . . . . . . . 11

2.14 Houlsby's method [13] makes the assumption that the load distribution on the right may

be simpli�ed to the one on the left. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.15 E�ective stress over depth, in case of self-weight penetration (no reduction due to suction

is applied). (D=8m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.16 Critical suction versus L/D-ratio, according to di�erent approaches. . . . . . . . . . . . 16

3.1 Displacement of the particles due to the skirt's penetration volume (s/γ′D = 0.75). [20] . 18

3.2 Plug heave below and above the critical gradient, tested in a permeability apparatus. 1.

Original compacted sand at rest. 2. Upward �ow: i < icrit. 3. Upward �ow: i > icrit. 4.

Settled again i = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3 Displacement of the particles. (L/D = 0.2, s/γ′D = 4.1) [20] . . . . . . . . . . . . . . . 20

3.4 Displacement of the particles. (L/D = 0.3, s/γ′D = 5.1) [20] . . . . . . . . . . . . . . . 20

3.5 Erosion of the bed due to horizontal �ow on the bed. . . . . . . . . . . . . . . . . . . . 20

3.6 Example of �ow velocity and discharge for di�erent r/R-ratio's. (D = 8m, L = 8m, distance

between top plate and soil = 0.1m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.1 Top plate design 1: a plate which is slightly smaller than the top plate of the suction pile. 26

4.2 Top plate design 2: a perforated plate of the same size as the top plate of the suction pile. 26

4.3 Legend of �gures 4.4 to 4.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.4 Installation pressure below critical pressure. No plug heave occurs. . . . . . . . . . . . . 29

4.5 Once the top plate touches the soil, the gradient increases and locally liquefaction occurs. 29

4.6 Installation pressure above critical pressure. Plug heave occurs and the entire plug has lost

its e�ective stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

List of Figures xi


4.7 The second top plate sinks into the lique�ed soil. The �ow lines change direction and in

the middle e�ective stress can build up. . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.8 Installation pressure above critical pressure. A perforated top plate with geotextile is used. 29

4.9 The water �ows through the perforated top plate, while the soil stays in the plug. E�ective

stress can build up. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.1 For a homogeneous soil, the e�ective stress increases linearly with depth. (Di�erent relative

densities) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.2 Relation between the cone resistance and the e�ective stress of a soil pro�le, for di�erent

relative densities. [15] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.3 The cone resistance over depth, for di�erent relative densities. . . . . . . . . . . . . . . 33

5.4 Required installation pressure to overcome the total soil resistance, calculated for di�erent

relative densities. The dotted lines show the critical pressure, also for di�erent relative

densities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.5 Required suction pressure to overcome the soil resistance according to Brinch Hansen

(equation 2.18). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.6 In- and outgoing �ux for an elementary volume.[5] . . . . . . . . . . . . . . . . . . . . 36

5.7 Schematic representation of the domain and its boundaries, the axes are the same as in

�gure 2.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.8 De�nition of the central di�erence method. . . . . . . . . . . . . . . . . . . . . . . . . 38

5.9 Dirichlet boundaries (constant pressure), far from the suction pile . . . . . . . . . . . . 41

5.10 Neumann boundaries (no �ow), far from the suction pile . . . . . . . . . . . . . . . . . 41

5.11 Dirichlet boundaries (constant pressure), close to the suction pile . . . . . . . . . . . . . 41

5.12 Neumann boundaries (no �ow), close to the suction pile . . . . . . . . . . . . . . . . . 41

5.13 Example of a course mesh (5x6), with a suction pile with radius 2 and depth 2 (red line).

The skirt has to have a width of at least two nodes to be able to model it. . . . . . . . . 42

5.14 First part of the band matrix [A] (size: 30x30), belonging to the example of �gure 5.13.

The column on the right is the vector with the potentials of the �xed nodes [B]. ([A][V]=[B]) 42

5.15 The pore pressure factor at the pile tip, as a percentage of the actual pressure di�erence

between in- and outside the suction pile. . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.16 The discharge at a speci�c location (r/R) on the bed. . . . . . . . . . . . . . . . . . . . 45

5.17 The shape of the gap inside a conventional suction pile (D50 = 0.0002) . . . . . . . . . . 46

6.1 Calculated pressures for two existing projects. Feld's method is compared with the DNV

method, the relevant parameters are added in appendix A.2. . . . . . . . . . . . . . . . 47

6.2 The horizontal �ow speed and the discharge on the bed for a conventional suction pile and

one with a second top plate as in �gure 4.1. . . . . . . . . . . . . . . . . . . . . . . . . 48

6.3 The erosion- and installation velocity for a conventional suction pile. If the erosion velocity

is higher than the installation velocity, a gap will remain. . . . . . . . . . . . . . . . . . 50

6.4 The erosion- and installation velocity for a suction pile with a second top plate. The erosion

velocity is signi�cantly reduced. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.1 Bearing capacity in equilibrium with submerged weigh of the caisson: penetration due to

self-weight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

7.2 Bearing capacity in equilibrium with submerged weight and suction force: suction assisted

penetration. Note that the inner resistance is reduced compared to the outer resistance. . 54

7.3 Contact between top plate and soil. Pile behaves unplugged. . . . . . . . . . . . . . . . 55

7.4 Contact between top plate and soil. Pile behaves plugged. . . . . . . . . . . . . . . . . 55

7.5 Soil resistance in case of a compressible plug (unplugged behaviour). Settlement of the

anchor is required before the pile will behave plugged. . . . . . . . . . . . . . . . . . . 57

7.6 Soil resistance in case of a non-compressible plug. The pile, with second top plate, behaves

fully plugged (which is the situation with maximum bearing capacity for a suction pile). . 57

7.7 The design of the second top plate is variable. It is important to make a con�guration

which mobilizes the entire plug with as little settlement as possible. . . . . . . . . . . . 58

8.1 Gravity controlled test set-up. The out�ow nozzle can be tweaked. . . . . . . . . . . . . 62

8.2 Test set-up with a centrifugal pump. The out�ow nozzle can be tweaked. . . . . . . . . . 62

List of Figures xii


8.3 Pressure characteristics of a gravitation driven pump system. . . . . . . . . . . . . . . . 62

8.4 Pressure distribution for di�erent Rsp/Rt ratio's. The picture in the middle represents the

situation of the model test (Rsp/Rt = 0.33). The top �gure has an Rsp/Rt-ratio of 0.2

while the bottom one has a ratio of 0.8. . . . . . . . . . . . . . . . . . . . . . . . . . . 67

8.5 Required distance of the boundary to minimize its in�uence on the model test. . . . . . . 68

8.6 A sketch of the tank which is used for the model. A technical drawing is included in

appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

8.7 Sieve curves of the soil inside the model test tank. . . . . . . . . . . . . . . . . . . . . 70

8.8 The suction pressures for two model tests in a sand bed prepared with two di�erent vibra-

tion periods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

8.9 Permeability k as a function of porosity n for several Dutch sand types [22]. . . . . . . . 71

8.10 The reduction in relative density (and so in bearing capacity) of the soil plug, due to plug

loosening. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

8.11 Gap remaining after installation of a conventional suction pile in the lab. . . . . . . . . . 74

8.12 Mark of the second top plate. Contact between the second top plate and the soil seems

possible. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

8.13 Initial penetration of the suction pile, the top has to be installed. . . . . . . . . . . . . . 74

8.14 The top plate "sinks" in the soil in case of critical suction. . . . . . . . . . . . . . . . . 74

8.15 Measured suction pressures compared to the predicted suction pressure for tests in loosely

packed sand. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

8.16 Measured suction pressures compared to the predicted suction pressure for tests in densely

packed sand. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

8.17 Project 1, actual installation data compared to the predicted installation pressures. . . . 78

8.18 Project 2, actual installation data compared to the predicted installation pressures. . . . 78

8.19 Depth measurements of a suction pile, schematized. . . . . . . . . . . . . . . . . . . . . 79

8.20 Penetration depth: echo sounder compared with depth sensor, plug heave starts with 2.5m

to go. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

8.21 Penetration depth: echo sounder compared with depth sensor, plug heave starts with 2m

to go. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

8.22 Pressure distribution inside the model before contact between second top plate and soil. . 83

8.23 Pressure distribution once the top plate touches the soil. The top plate is modelled as a

no-�ow boundary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

B.1 Technical drawing of the tank [6] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

B.2 Installation of the pile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

B.3 Test 1, without second top plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

B.4 Test 2, with second top plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

B.5 Side view of test 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

B.6 Top view of test 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

B.7 Side view of test 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

B.8 Top view of test 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

List of Figures xiii


List of Tables

4.1 Analysis of the e�ectiveness of the proposed solutions. . . . . . . . . . . . . . . . . 27

5.1 Relationship between relative density and angle of internal friction of cohesion lesssoils. [9] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

8.1 Summary of the scaling factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658.2 Permeability of the soil inside the tank (D50 is 0.25mm, D10 is 0.18mm). . . . . . . 72

C.1 Falling head test for vibrated sand, in a loose state . . . . . . . . . . . . . . . . . . 115C.2 Falling head test for vibrated sand, in a dense state . . . . . . . . . . . . . . . . . . 115

List of Tables xiv


List of Symbols

Variable Description Unit

a Pore pressure factor at pile tip [−]A Area of the cross section of the pile [m2]Aannulus,o Area of the outer annulus [m2]Aannulus,i Area of the inner annulus [m2]Ar/R Vertical cross section of the �ow on the bed at distance r [m2]c0 0.45 [−]c1 0.36 [−]c2 0.48 [−]cb Near bed concentration [−]D Diameter of the suction pile [m]D∗ Dimensionless particle diameter [−]Di Inner diameter of the suction pile [m]Do Outer diameter of the suction pile [m]Dpart Particle diameter [m]Dr Relative density [−]D10 10% of the grains has a smaller diameter this value [m]D50 50% of the grains has a smaller diameter this value [m]E Youngs' modulus [kN/m2]f0 coe�cient of friction of sediment bed [−]F1 Unplugged soil resistance [kN ]F2 Plugged soil resistance [kN ]F3 Di�erence between plugged and unplugged behaviour [kN ]fi Parameter to calculate the inner area of in�uence [−]Fi Inner friction force [kN ]Finst Installation force [kN ]fo Parameter to calculate the outer area of in�uence [−]Fo Outer friction force [kN ]Fres Resistance force [kN ]Fw Submerged weight [kN ]g Gravitational constant (= 9.81) [m/s2]i Pressure gradient [−]icrit Critical gradient [−]I Mass/Volume �owing in []k Permeability [m/s]kf Dimensionless coe�cient CPT-method [−]K Relates vertical to horizontal stress (= 0.8) [−]K0 Lateral earth pressure at rest [−]L Embedded length of the suction pile [m]n0 Bed porosity prior to erosion [−]Nq Dimensionless factor [26] [−]Nγ Dimensionless factor [26] [−]O Mass/Volume �owing out []pcrit Critical pressure [kPa]ptip Pressure at the pile tip [kPa]ps Applied suction pressure [kPa]Ptogo Penetration to go [m]q Flow [m/s]qc Cone resistance [MPa]r Distance to the center of the suction pile [m]R Radius of the suction pile [m]Rsp Radius of the suction pile [m]

List of Tables xv


Variable Description Unit

Rt Radius of the tank [m]Rp Reynolds particles number [−]Q Total discharge [m3/s]Qpenetration Discharge due to penetration in the soil [m3/s]Qr/R Discharge on the bed at distance r from the center [m3/s]Qsoil Discharge through the soil [m3/s]Qtip Tip bearing [kN ]s Seepage length [m]t Depends on context: Wall thickness of the suction pile [m]t Depends on context: Time [s]u Depth-averaged �ow velocity [m/s]V Potential [kPa]ve Erosion velocity [m/s]vinst Installation velocity [m/s]vr/R Flow velocity on the bed at distance r from the center [m/s]ws Settling velocity [m/s]xgap Distance between top plate and soil [m]z Depth [m]Zecho Penetration to go inside the suction pile [m]Zout Depth of the top plate compared to water level [m]Zref Depth of the bed [m]α Reduction factor for the soil resistance [−]αi Reduction factor for the inner friction [−]αo Reduction factor for the outer friction [−]αt Reduction factor for the pile tip resistance [−]γ Unit weight of the soil [kN/m3]γ′ E�ective unit weight of the soil [kN/m3]γw Unit weight of water [kN/m3]δ Angle of friction between soil and skirt [rad]∆ Relative sediment density [−]ε Strain [−]θ Shields parameter [−]θcrit Critical Shields parameter [−]θ1crit Modi�ed critical Shields parameter [−]ν Kinematic viscosity [m2/s]ρ Relative density [kg/m3]ρs Relative density of the soil [kg/m3]ρw Relative density of water [kg/m3]σ Stress [kN/m2]σ′end E�ective stress at pile tip level [kN/m2]σ′h Horizontal e�ective stress [kN/m2]σ′m Mean e�ective stress [kN/m2]σ′v Vertical e�ective stress [kN/m2]σ′vi Vertical e�ective stress, inside of the skirt [kN/m2]σ′vo Vertical e�ective stress, outside of the skirt [kN/m2]τskirt Shear stress [kN/m2]φ Angle of internal friction [rad]φp Dimensionless pick-up �ux [−]

List of Tables xvi


1 | Introduction

1.1. Background information

The core business of SPT O�shore is the design, fabrication and installation of foundations andanchors for o�shore constructions using suction pile technology. This technology is increasinglypopular in the o�shore industry (i.e. oil&gas and wind), but as it is a relatively young technology,there is still much room for development and improvement. Suction piles are also known under anumber of di�erent names [18], such as suction caissons, suction anchors, bucket foundations etc.In this thesis the term "suction pile" will be used.

A suction pile is a hollow cylindrical steel tube, closed on the topside and open at the bottom.The size typically varies between a diameter of 5 to 15 metres, and the height of the cylinder is forsandy soils typically about equal to the diameter (in clay typical L/D-ratios are around 2 till 6).The pile is installed with the closed part of the cylinder at the top and the open part at the bottom.The installation goes in two steps: First the pile penetrates the soil under its own weight, thenwater is pumped out of the pile, creating a pressure di�erence over the top plate. This pressuredi�erence across the top plate of the pile pushes the pile into the soil until the required penetrationdepth is reached.

A big advantage of the suction pile technology is the cost e�ectiveness of the installation method.The installation time, normally around 12-24 hours per foundation, is much shorter than the instal-lation time of a conventional platform foundation, which can last several days. Further, relativelysimple marine equipment can be used to install suction piles. Besides the easy installation, asuction pile can also be reused, just by reverse pumping. This makes this foundation method alsohighly e�cient in case of temporary foundations and mooring constructions. Last but not least,also for environmental reasons a suction pile is often the preferred solution, because comparedto driving piles, a suction pump is a very silent method which doesn't disturb the environment.Restrictions on this topic often result in the use of suction piles.

As an example of a structure founded on suction piles, the F3FA platform for Centrica is shownin �gure 1.1. This 9.000 ton platform is installed on the Dutch North Sea. Figure 1.2 shows anexample of a suction pile on a barge.

Figure 1.1: F3FA-platform for Centrica. Figure 1.2: A suction pile on a transport barge.

Chapter 1. Introduction 1


1.2. Problem de�nition

In installation practice of suction piles in sandy, permeable soils, it appears to be impossible to getinitial contact between the top plate of the suction pile and the soil. It even seems that in somecases after installation a gap of about 50 centimetres between top plate and soil remains. Thismeans that the bearing capacity of these suction piles is only delivered by the skirt friction andtip bearing. This is often not su�cient, because in the design protocols of the foundation, full topplate bearing is assumed. As a result of the gap, the construction will settle �rst before full contactbetween top plate and soil is obtained. Settlements are in general not desired, and certainly forasymmetrically loaded constructions on more than one suction pile, di�erential settlements canoccur. This could be problematic for the top structure, as cracks or other failures could arise.

Nowadays it is common practice to overcome this problem by injecting a grout mixture in the gapbetween top plate and soil. If the gap is entirely �lled with grout, top plate bearing is obtained andthe top structure can be installed without signi�cant settlements. However, this grouting procedureis an expensive o�shore operation. As it is an operation on the seabed and inside a suction pile,it is di�cult to visually control what happens and it is hard to predict how the grout will bedistributed in the gap. Because of this: a di�erent solution should be found, making groutingunnecessary. This brings us to the research question of this thesis: investigate the possibilitiesto overcome initial settlements due to the gap remaining after installation of a suction pile in apermeable soil. Focus hereby on the introduction of a second top plate inside the suction pile,attached to the sti�eners of the top plate. This second top plate should be designed in a way thatno gap remains after installation. This thesis can be read as a feasibility study of this possiblynew suction pile design, but also other possible solutions are discussed.

1.3. Readers manual

In chapter 4 di�erent ideas to initiate initial contact between top plate and soil are mooted.However before these ideas can be weighed, the reasons why this gap between top plate and soilarises should be well understood. This research is described in chapter 3. The output of thischapter is used to build a calculation model, which can be used to evaluate the feasibility of thedi�erent solutions and is explained in chapter 5. In chapter 8 the calculation model is veri�edusing existing model tests, measurements from the �eld, existing calculation methods and a self-developed physical model test. Readers interested in the conclusions and recommendations of thisthesis, are advised to read chapter 9.

Chapter 1. Introduction 2


2 | A suction pile

2.1. De�nition

A suction pile foundation is, next to the more famous drilled and driven pile foundations, a methodto connect o�shore structures with the seabed. Conveniently, this foundation type is used as ananchoring system for �oating platforms, which makes it a foundation suitable to be loaded intension. However, nowadays this system gains in applicability as it has also proven to be suitablefor foundations loaded to pressure.

A suction pile has a cylindrical shape with a closed top and an open bottom. The dimensionsdepend on the load and the soil type, with typically larger lengths in softer soils. In sandy soilsthe length/diameter (L/D)-ratio is typically somewhere between 0.5 and 1, as sand normally has ahigh bearing capacity (which makes it harder to penetrate). The diameter can vary between 5 and15 meters for foundations loaded to pressure, while smaller diameters occur in case of anchoringapplications.

2.2. The installation principle

The installation method (as illustrated in �gures 2.1 and 2.2) is divided in two main phases: �rstthere is a penetration into the bed due to the self-weight of the steel suction pile. This penetrationcontinues until an equilibrium between the weight and the soil resistance is reached. Dependingon the soil type, this initial phase varies between a couple of decimetres in very dense sands to afew meters for very soft soils. Once this equilibrium is reached, suction is applied and a di�erentialpressure along the top plate forces the remaining part of the suction pile to penetrate the soil. Asexplained in the introduction of this thesis, it is unlikely to get initial contact between the topplate and the soil for installations in permeable sands (see �gures 2.3 and 2.4). The installation aswell as the calculation methods will be explained in this chapter.

Figure 2.1: Initial phase: own weightpenetration, no suction is applied.

Figure 2.2: Second phase: suction assistedpenetration, there is a pressure di�erence alongthe top plate. Plug heave occurs inside the pile.

Chapter 2. A suction pile 3


Figure 2.3: Result after installation in sand.Notice the gap between top plate and soil.

Figure 2.4: For installations in sand, initialcontact between top plate and soil is impossible

due to erosion and plug settlement.

During the self-weight penetration phase, the installation force equals the submerged weight of thesuction pile. Penetration will continue until the installation force is in equilibrium with the soilresistance (as in equation 2.1).

Finst = Fw = Fres (2.1)

Where

Finst = the installation force [kN]Fw = the submerged weight [kN]Fres = the resistance force [kN]

This self-weight installation is an essential part of the installation process, because in order toallow suction-assisted penetration, the presence of a closed seal at the bottom of the suction pileis required. Without a closed seal, it is not possible to generate a pressure di�erence along the topplate. If this �rst requirement is met and self-weight penetration is a fact, there is an equilibriumbetween the installation and the resistance force (see 2.1). The resistance force is de�ned by thefriction between skirt and soil (both the inner friction force and outer friction force) and by thetip bearing of the skirt (see �gure 2.3):

Fres = Fi + Fo +Qtip (2.2)

Where Fi is the inner friction force, Fo the outer friction force and Qtip the tip bearing, all in [kN].

Because the soil resistance increases with increasing depth, further installation requires suction inorder to meet equation 2.3.

The suction phase is the main characteristic of a suction pile foundation. Both for piles in sandand in clay, a reduction of the pressure inside the pile generates a di�erential pressure over the topplate. Regardless the soil type, this di�erential pressure is needed to push the pile into the soil.For impermeable soils like clay, the installation principle is pretty straightforward and is basicallynothing more than the weight of the pile plus the di�erential pressure being higher than the soilresistance [13],[8](see equation 2.3).



Finst = Fw + ps ·πD2

i

4Finst > Fres (2.3)

Where ps is the applied suction pressure in [kN/m2] and Di the inner diameter of the suction pilein [m].

If equation 2.3 is true, the pile goes down until a new equilibrium is reached. Once this is the case,the pressure inside the suction pile should be decreased further (and so the pressure di�erence willincrease) if a higher installation depth is required. Equation 2.3 can be considered as the basisprinciple for the installation of a suction pile. This basis principle will be elaborated and explainedfurther below, focussing on permeable soils.

2.3. Groundwater �ow

2.3.1. The pressure gradient

The pressure di�erence between the in- and the outside of the suction pile causes a groundwater�ow from high to low pressure [11]. This means that during suction, water from outside thesuction pile is attracted and �ows inside the pile (see �gure 2.5). In order to calculate this �ow,it is necessary to know the pressure gradient inside the soil. The pressure gradient i, according toDarcy, is de�ned as:

i =dh

dz=q

k(2.4)

Figure 2.5: Flowlines due to the applied pressure di�erence.



In which i is the pressure gradient [−], q the �ow in [m/s] and k the permeability, also in [m/s].

The applied pressure depends on the total soil resistance at a certain depth and determines thehydraulic gradient inside the soil. It is important to make an accurate prediction of the hydraulicgradient, because in a later stage this gradient will be used to predict the reduction of the skirtfriction and the amount of �ow through the soil inside the suction pile [13]. To know the in�uenceof the hydraulic gradient on the skirt friction, it is important to know the pressure gradient nextto the skirt, both at the in- and outside of the suction pile. To do so, the pressure at the piletip is determined for di�erent L/D-ratio's in section 2.3.2. It should be noted that the "pressure"mentioned in this thesis is usually an under pressure, as suction lowers the pore pressure in thesoil.

As the pressure distribution inside the suction pile is not entirely uniform, the pressure at the piletip can't be used to estimate total in�ow of water. To do so, the average pressure over the wholehorizontal suction pile area at pile tip level (see �gure 2.7) should be used instead of the pressureat the skirt tip. The di�erence between both values is explained in section 2.3.3.

2.3.2. Pore pressure at pile tip, next to the skirt

In the previous section is explained how a pressure gradient causes a groundwater �ow in the soilplug. In order to calculate this pressure gradient, literature suggests to use the di�erence in porepressure between the pile tip and the soil surface inside the suction pile [13]. This means that thepore pressure at the tip of the pile should be determined for di�erent L/D-ratio's.

In case of the classic example of groundwater �ow underneath a sheet pile wall, a pore pressurefactor of 0.5 is found at the pile tip [26]. This means that at the tip of the sheet pile wall, the porepressure is half the applied pressure di�erence. For a suction pile this is slightly di�erent, becausethe inner area is a lot smaller than the outer area (the 3D-e�ect). This results in a smaller pressuregradient outside the suction pile, because the groundwater �ow streamlines can spread over a widercross area. This means that the pore pressure factor at the pile tip is expected to be smaller than0.5 and decreasing with increasing L/D-ratio (as is shown in �gure 2.6). The continuous curvein this �gure is the result of an extended �nite element analysis by Junaideen [13]. This curveis veri�ed by the author using Plaxis, and it can be concluded that Junaideen's equation gives agood approach for the pore pressure factor at the pile tip as a function of the L/D-ratio:

a = c0 − c1[1− exp

(− L

c2D

)](2.5)

Where a is the dimensionless pore pressure factor, c0 is 0.45, c1 = 0.36 and c2 is 0.48. L is theembedded length of the suction pile and D the diameter, both in [m].

2.3.3. Average pore pressure at pile tip level

Conventional methods used to predict the �ow inside a suction pile [13], make use of the curvefrom equation 2.5 to estimate the pore pressure at the pile tip. With this value a pressure gradientis calculated and then an estimation of the groundwater �ow can be made using Darcy's law:

Qsoil = ks(1− a)

L

A

γw(2.6)

Where Qsoil is the discharge through the soil in [m3/s], s is the applied pressure, a is the porepressure factor at the skirt tip, A is the area of the cross section of the pile in [m2] and γw is therelative density of water in [kN/m3].



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

L/D

Pore

pressure

factor(a)

Pore pressure factor

Theoretical pore pressure factor (equation 2.5)

Result from Plaxis (D=15m)



Figure 2.6: The pore pressure factor (a) at the pile tip according to Junaideen [2004], veri�ed by theauthor in Plaxis.

So the pressure gradient i equals s(1−a)L . It is important to notice that this is the gradient alongside

the skirt, which is not the same as the overall gradient in the entire plug. The groundwater �owcalculated with equation 2.6 overestimates the �ow, because the gradient next to the skirt is higherthan the gradient averaged over the entire surface (|AB| in �gure 2.5). Figures 2.7 and 2.8 showthat especially for shallow penetration depths large di�erences between the center and the skirt ofthe suction pile are found. If the pressure at the pile tip is assumed to be the same as the pressureat the center of the suction pile (which is often done in literature), the pressure gradient is largelyoverestimated, resulting in an overestimation of the in�ow.

20 40 60

20

40

60

0

0.2

0.4

0.6

0.8

Figure 2.7: At shallow depths, the pore pressurefactor in the center is much higher (0.83)

compared to the factor at the skirt tip (0.40).

20 40 60

20

40

60

0

0.2

0.4

0.6

0.8

Figure 2.8: At higher depths, the absolutedi�erence between the pore pressure factor in thecenter (0.31) and the factor at the skirt tip (0.16)

is much smaller.

The calculation model developed in the context of this thesis (chapter 5) makes a clear distinctionbetween the pore pressure at the tip and the average pore pressure at the tip level. With the nu-merical groundwater �ow calculations integrated in the calculation-model, a much higher accuracycan be achieved. Conventional methods only predict the in�ow relatively accurate at high L/D



ratio, while the presented calculation model in this thesis doesn't use the pore pressure at the tipto calculate the in�ow, but uses the average pore pressure over the entire width of the caisson base.

2.4. Prediction of the installation resistance

2.4.1. Self-weight penetration

There are di�erent methods available to calculate the installation resistance of a suction pilefoundation in sand. In this section two methods are distinguished, namely the 2D-Brinch-Hansenmethod and a 3D-CPT-based method. Brinch-Hansen relates the soil resistance to the expectede�ective stress at a certain depth (see equation 2.8), for a 2D strip foundation. This 2D theoreticalmodel is a fairly good simulation of the 2D situation at the tip of the skirt and is very useful tomake initial predictions and calculations for model tests.

However, in engineering practice, the prediction of the soil resistance of a suction pile is often doneusing a CPT-based approach. This method is based on the relation between the tip- and frictionalresistance and a measured cone resistance [16], which is practical because a CPT is a reliable insitu test that measures the actual failure of the soil. This way e�ects as e.g. compressibility ofthe grains are also taken into account, which is not the case for the Brinch Hansen method. Animportant disadvantage of the empirical character of the CPT-method is that it is impossible toscale it to a resistance prediction for a scaled model. Besides that, the CPT-measurement is notreliable at low soil stresses (so in the �rst meter of penetrated soil) [15]. However, for suction pileinstallations in practice, this approach has proven to give reliable predictions of the soil resistance.The method is described in detail in section 2.4.1.2.

2.4.1.1. Brinch-Hansen method

The Brinch-Hansen method is usually used to calculate the bearing capacity of strip foundations.However, with just little adaptions, this method can also be used to estimate the bearing capacity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

L/D

Pore

pressure

factor(a)

Junaideen [2004] (equation 2.5)

Result from Matlab (at skirt)

Result from Matlab (averaged over the entire base)

Figure 2.9: The pore pressure factor (a) at the pile tip compared with the average pore pressure at thebase of the suction pile.



Figure 2.10: The 2-dimensional failure mechanism according to Brinch-Hansen.

of a suction pile. Just as in conventional foundation design, the total bearing capacity is determinedby the skirt friction Fi and Fo and the tip bearing Qtip (see equationsoilresistance2. But �rst, someessential geotechnical relations are highlighted, which are used in equation 2.8 [26]:

σ′h = K · σ′vτskirt = σ′h · tan(δ)

γ = ρn · gγ′ = (ρs − ρw) · g (2.7)

Where σ′h and σ′v are respectively the e�ective horizontal and vertical e�ective stress (in [kN/m2]),

K is a dimensionless factor to relate horizontal to vertical soil stress (= 0.8), τskirt is the shearstress in [kN/m2], δ (typically around 2/3 · φ [26]) is the angle of friction between soil and skirt in[rad], γ and γ′ are respectively the unit weight and the e�ective unit weight of the soil in [kN/m3],ρs and ρw the relative densities of water and soil in [kg/m3] and g is the gravitational constant(=9.81) in [m/s2].

With these relations in mind, the bearing capacity of a conventional strip foundation can now becalculated as follows:

Fres = Fi + Fo +Qtip

Fres =γ′L2

2· (Ktan(δ))o · πDo

+γ′L2

2· (Ktan(δ))i · πDi

+(γ′L ·Nq + γ′t

2Nγ) · (πDt) (2.8)



In which Do and Di are the outer and inner diameter of the suction pile (in [m]), Nq and Nγ aredimensionless factors [26] and t is the wall thickness of the suction pile in [m].

Compared to a conventional strip foundation at a certain depth, the bearing capacity of a suctionpile is also in�uenced by the mobilized stress due to penetration of the skirt. The skirt frictionresults in an increase in vertical e�ective stress, which makes that the bearing capacity calcu-lated with equation 2.8 is an underestimation. Houlsby [13] has developed a method to take thisadditional vertical e�ective stress into account.

Suction piles with high L/D-ratio: Slim suction piles will mobilize the entire plug inside thepile. In order to be able to calculate the in�uence of this extra mobilized soil stress, Houlsby'smethod starts with the analysis of a slice of soil inside such a pile with an entirely mobilized soilplug. This slice of soil is schematically shown in �gure 2.11.

Figure 2.11: Equilibrium of a slice of soil inside the suction pile, in�uenced by the skirt friction. [13]

The increase in vertical stress over this slice of soil with thickness dz is the result of the weight ofthe slice and the additional stress caused by the friction of the skirt. Expressed in a formula, thisbecomes:

dσ′

v

dz= γ′ +

σ′

v(Ktanδ)i(πDi)

πD2i /4

= γ′ +4σ′

v(Ktanδ)iDi

(2.9)

In order to simplify this formula, Houlsby introduces a new parameter, Zi, which is:

Zi =Di

4(Ktanδ)i(2.10)



With the introduction of this new parameter, equation 2.9 is expressed as:

dσ′

v

dz− σ

′

v

Zi= γ′ (2.11)

This is a di�erential equation with an analytical solution. However, this is only valid for the innerfriction for suction piles with a high L/D-ratio.

Suction piles with a low L/D-ratio: The considered suction piles in this thesis typically havesmaller L/D-ratio's, as they are used as foundations loaded to pressure and not as tension piles. Forthis type of suction piles only part of the inner plug is mobilized, depending on the so called "areaof in�uence". This parameter (fo and fi, for respectively the inner and outer area of in�uence)varies, depending on the soil type. In this thesis (and often in geotechnical practice) the regionof spreading of the extra vertical forces caused by friction is assumed to be limited to the innerside of a 45 degrees plane downwards (see hatched area in �gure 2.10) [26]. This means that forL/D < 0.5, the above formula is not valid as not the entire plug is mobilized. For these casesHoulsby adapted equation 2.10 to:

Zo =Do

{[1 + (2foz/Do)]

2 − 1}

4(Ktanδ)o(2.12)

and

Zi =Di

{1− [1− (2fiz/Di)]

2}

4(Ktanδ)i(2.13)

Figure 2.12: The inner and outer area ofin�uence.

Figure 2.13: The inner area of in�uence issigni�cantly smaller than the outer area.

This is true because the mobilized area is not an entire circle anymore, but an annulus in- andoutside the suction pile, and:



Aannulus,o =(Do + 2 · fo · z)2 · π −D2

o · π4

=π

4·D2

o ·(

(1 + 2foz/Do)2 − 1

)(2.14)

Aannulus,i =D2i · π − (Di − 2 · fi · z)2 · π

4

=π

4·D2

i ·(

1− (1− 2fiz/Di)2)

(2.15)

The area of the mobilized soil increases with increasing depth and is shown in �gure 2.13. Fromthis �gure it is clear that it is more likely that at the inside of the caisson higher stresses aregenerated than at the outside, as the area inside the suction pile is smaller. Houlsby [13] proposesa simpli�cation by assuming that the increase in vertical stress does not vary with radial coordinate(see �gure 2.14) and that there is no shear stress on the vertical planes at the outside of the areaof in�uence.

Figure 2.14: Houlsby's method [13] makes the assumption that the load distribution on the right maybe simpli�ed to the one on the left.

The di�erential equations for the vertical e�ective stress in- and outside the suction pile become:

dσ′

v

dz− σ

′

v

Zi/o= γ′ (2.16)

With Zi and Zo as in equation 2.13. This di�erential equation has no analytical solution, so it issolved numerically to calculate the vertical e�ective stress at the in- and the outside of the suctionpile.

Next, the tip bearing is calculated using the e�ective stress at the outside of the skirt, as thisstress is smaller than inside (which means failure will occur in outward direction for the self-weightpenetration phase):

σ′

end = σ′

voNq + γ′tNγ (2.17)



0 20 40 60 80 100 120 140 160 180

0

2

4

6

8

Vertical e�ective stress [kPa]

Depth

[m]

E�ective stress inside pileE�ective stress outside pile

Figure 2.15: E�ective stress over depth, in case of self-weight penetration (no reduction due to suctionis applied). (D=8m)

To know the vertical stress at the in- and outside of the skirt, the graphs of �gure 2.15 need to beintegrated over depth. In this �gure the total vertical stress over depth is shown, which is increaseddue to the in�uence of the skirt friction. Together with the end bearing of the pile tip, the totalsoil resistance in the self-weight penetration phase becomes:

Fres =

h∫0

σ′vodz(Ktanδ)o(πDo)

+

h∫0

σ′vidz(Ktanδ)i(πDi)

+σ′end(πDt) (2.18)

The result of this calculation is shown in �gure 2.15. From this �gure can be concluded that theenhancement of vertical stress inside the caisson is indeed larger than outside. The pile calculatedin this example has a diameter of 8 m and a depth of 8 m. The details of the calculation are addedin appendix A.3.

2.4.1.2. CPT-based method

The CPT-approach is described by di�erent researchers. Senders [16] proposes to use the DNV[10] approach for equation 2.8, and this is also the method used in this graduation thesis:



Fres = Fi + Fo +Qtip

Fi = πDikf

L∫0

qc(z)dz

Fo = πDokf

L∫0

qc(z)dz

Qtip = Atipkpqc(L) (2.19)

The coe�cient kf varies between 0.001 (most probable case) and 0.003 (highest expected). For kpa factor 0.3 to 0.6 is suggested. These factors are used to relate the cone resistance to the bearingcapacity of the pile. In engineering practice the calculation is done for both the "most probable"as the "highest expected" case, resulting in a lower and an upper bound for the soil resistance overdepth. Equation 2.19 doesn't include the suction phase, so the equation in this form is only usedto predict the soil resistance for the self-weight penetration phase. The equation is not valid forthe suction phase, as the applied suction, required to install the foundation, has an extra e�ect onpiles installed in permeable soils.

2.4.2. Suction-assisted penetration: Empirical reduction

Besides the di�erential pressure along the top plate of the suction pile, the pressure gradient insidethe soil is one of the driving forces in the installation of a suction pile. Due to this pressure gradient,the e�ective stress of the soil inside the suction pile, reduces signi�cantly. As the inner friction aswell as the tip resistance depend on the e�ective stress, it should be clear that the upward gradientalso reduces the soil resistance during installation [19]. Literature is not consequent on how thisreduction should be taken into account and in engineering practice the only available guidance isusually based on project experience, using empirical factors to predict the friction resistance at thepile tip and the inner skirt. Expressed as a formula, this means that all elements of equation 2.19change due to the seepage �eld in the soil plug:

Fres = αiFi + αoFo + αtQtip (2.20)

For the outer friction a small increase in friction is expected, because at the outside of the suctionpile the �ow has a downward direction, which results in higher e�ective stresses. At the tip andthe inside of the skirt, an upward �ow reduces the e�ective stresses and a lower soil resistanceis expected. This means that αi and αt are expected to be lower than 1, while αi should beslightly higher than 1. SPT O�shore uses empirical values for these reduction factors. This meansthat their soil resistance calculations are based on equations 2.19 and 2.20, and once suction isapplied, a reduction factor 1 is used to calculate the outer friction, 0.5 for the prediction of the tipresistance and a factor 0 for the inner friction. These factors are not theoretically supported andmeasurements from engineering practice show that they are rather conservative.

Besides the empirical method used by SPT o�shore to calculate the reduction factors, literaturealso provides more theoretically supported methods to predict the reduction. These methods arebased on the relation between the skirt friction and the e�ective stress of the sand. This e�ectivestress reduces inside the suction pile due to the upward �ow, but increases at the outside becausethere a downward groundwater �ow is present. In chapter 2.4.3 the quanti�cation of this de- orincrease in e�ective stress is explained.



2.4.3. Suction-assisted penetration: Pressure-related reduction

2.4.3.1. Critical suction

As the suction pressure increases, also the gradient inside the soil plug increases. At a certainmoment, the gradient will be so high that the e�ective stress becomes zero and the soil inside theplug will liquefy. This gradient is called the critical gradient and the applied pressure which isneeded to achieve this critical gradient, is called the critical pressure. The critical gradient dependson the ratio of the e�ective weights of soil and up �owing water:

icrit =γ′

γw(2.21)

The critical gradient is a well-known concept in geotechnical engineering, but the critical pressureinside a suction pile is harder to de�ne. Di�erent researches proposed di�erent empirical methodsto predict the critical suction pressure for varying L/D-ratios [7], [16], [13], [12] but in general onecan say that the critical suction pressure is calculated using the critical gradient times the seepagelength s:

pcrit = sγwicrit (2.22)

The di�culty in this de�nition lies in the interpretation of the seepage length by the di�erentresearchers. For the 2-dimensional case of a sheet pile wall, the minimum seepage length is typicallytwice the penetration dept. However, in case of an axial symmetric suction pile, most of the pressuredissipation happens inside the pile (3D-e�ect), with the highest gradient close to the pile tip. Asliquefaction is �rst to be expected at the location with the highest upward gradient, this wouldbe close to the pile tip (see �gure 2.8). However, liquefaction (in terms of a free moving lique�edsand-water mixture), requires an increase in volume to overcome the dilatancy necessary to shear.This is not possible at pile tip level because at this depth the soil is con�ned by non-lique�ed soil.This would mean that not the gradient at pile tip level is the limiting factor, but the exit-gradientat bed level is.

According to Feld [12], the loss of e�ective stress is a progressive phenomenon starting at the soil bedinside the suction pile. Once the critical gradient close to the bed is exceeded, the critical pressureis reached and the soil plug will liquefy. In this case the friction reduction is at its maximum. In�gure 2.16, a comparison is made between the critical suction according to Feld [12], Bruggeman[7] and �nite element calculations performed by the author, using the numerical model describedin chapter 5. From this �gure can be concluded that an approach with a gradient calculated overthe entire plug ((p − ptip)/L) results in an underestimation of the critical pressure. Besides thatit can be concluded that the exit gradient calculated by the numerical model developed for thisthesis approaches the proposed formula by Feld (equation 2.23) very well.

pcrit = 1.32 · γ′ ·D(L

D

)0.75

(2.23)

The reduction factors in equation 2.20 vary between no reduction (factor 1) and total loss of friction(or a reduction factor equal to 0). It is assumed that in case of an entirely lique�ed soil plug nomore inner friction occurs, while the friction is at its maximum in case there is no upward gradientinside the plug.

Following this reasoning, and assuming that the inner friction reduces linearly between minimumand maximum reduction [16], it is concluded that the reduction factor for the inner friction couldbe predicted as follows:



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.2

0.4

0.6

0.8

1

1.2

1.4

L/D

Pcrit/γeffD

FEM gradient over entire lengthFEM exit gradient

Bruggeman [7]

Feld (Equation 2.23)

Figure 2.16: Critical suction versus L/D-ratio, according to di�erent approaches.

α = 1− p

pcrit(2.24)

Once the suction pressure is equal to the critical suction pressure, reduction is at its maximumas α becomes 0. If no suction pressure is applied, α is 1, resulting in no reduction. This is validfor the inner friction and the reduction at the pile tip. According to Senders [16], the in�uenceof the suction pressure on the outside friction can be neglected and remains the external frictionuna�ected by the applied suction. This means that the reduction factor at the outside is assumedto be 1 and that equation 2.20 can be written as:

Fres + 0.25 · πD2p = Fo +

(1− p

pcrit

)(Fi +Qtip) (2.25)

Once pcrit > p, the reduction factor is 0, as the plug is lique�ed in this case and maximal reductionis reached. The way this problem is included in the calculation model is described in chapter 5.



3 | Gap between top plate and soilafter installation

As explained in chapter 2, the main di�erence between an installation in sand and one in clay,is the presence of a groundwater �ow. Besides that, clay is a cohesive material, while sand hasan angle of internal friction and can be more easily eroded. These two di�erences are the mainreasons why an installation in sand will result in a gap between top plate and soil, whereas this isnot the case for an installation in clay. (Remark: in clay other problems can arise, but this is notin the scope of this thesis.)

It is assumed that there are two main reasons why the gap arises. The �rst is as a result of thepressure gradient in the soil, which results in an upward groundwater �ow. Due to this gradientbetween the low pressure inside the suction pile and the high pressure at the outside, the plugin the pile could become less densely packed. This results in an increase of volume of the soilinside the pile and as a consequence, an increase in permeability. Once the suction is stopped,the gradient disappears and the packing will possibly decrease again. However, for an initiallydensely packed sand, a permanent expansion will remain. According to Tran [20], who did severalcentrifuge experiments to investigate the e�ect of the installation on the permeability of the soilplug inside a suction pile, a plug heave of about 6% of the embedded wall length is expected,caused both by the volumetric expansion of the loosened sand and the sand in�ow.

The second reason why the gap arises is due to the horizontal �ow on the bed. The horizontal �owis a result of water �owing to the out�ow opening in the center of the suction pile. This �ow, incombination with the vertical �ow through the bed, results in erosion of the bed. If the erosionvelocity is higher than the installation velocity of the suction pile, it becomes impossible to obtaincontact between the top plate and the soil.

Both the e�ect of plug loosening and the e�ect of erosion are investigated and described in thischapter.

3.1. Plug heave

The total plug heave is caused by three independent processes, which could (in some combinations)occur at the same time:

1. Plug heave due to the soil which is pushed in by the skirt's penetration volume

2. Elastic plug heave

3. Plug loosening (increase of the porosity of the plug)

It is important to distinguish these three processes, because they all have a di�erent e�ect on thegap between the top plate and the soil.

3.1.1. Plug heave due to the soil which is pushed in by the skirt'spenetration volume

Plug heave due to the skirt's penetration volume will occur for any (suction) pile installation. Theinward gradient makes it more likely that the failure plane beneath the pile tip is at the inside of

Chapter 3. Gap between top plate and soil after installation 17


the suction rather than outside, so that the entire skirt volume will contribute to the plug heaveinside the pile.

Tran [20] measured the soil deformation using PIV, a photo analysis method which shows thedisplacement of soil particles for a scaled model. For this method, the suction pile is cut in halfand is installed against the wall of a Perspex box, allowing to follow each particle during installation.The result of this investigation is shown in �gure 3.1. It is clear that most displacements occur ina triangular-shaped zone close to the suction pile. It is also clear, from this �gure, that the in�owof sand particles is limited, as the little arrows outside the pile show limited or no displacement.

Figure 3.1: Displacement of the particles due to the skirt's penetration volume (s/γ′D = 0.75). [20]

In the middle of the suction pile, no displacement of the bed is measured. The actual displacements,close to the skirt are permanent and do not much in�uence the relative density of the soil. It is notdue to this type of displacement that Tran measured a plug heave of 6% of the embedded length,because this large displacement can only occur as a result of a decrease in relative density of thewhole volume of the plug.

3.1.2. Elastic plug heave

As long as the critical pressure is not exceeded during installation, only some elastic heave willoccur due to the reduction of the load on top of the soil. However, the elastic heave as a result ofthis phenomenon, will be limited to a few centimetres (using Hooke's law):

∆σ = E ·∆ε (3.1)

Assume, as an example, an average decrease in vertical e�ective stress of 2bar (200kPa), a meansti�ness of a densely packed sand (mean because the sti�ness depends on the e�ective stress) of50MPa [3] and a penetration depth of 8m, following heave is found:

0.2MPa = 50MPa · ∆L

8m⇒ ∆L = 0.032[m] (3.2)

Which means that the elastic heave in case of an installation pressure below the critical pressureis in the order of magnitude of 0.5 procent. It is important to notice that this type of plug heaveis no plug loosening, as it is assumed to be elastic.

3.1.3. Plug loosening

A third process causing plug heave is the so-called plug loosening. Plug loosening is primarilycaused by a volume increase of the soil plug. It should be noticed that plug loosening occurs atsuction pressures above the critical suction pressure. This is an important remark, because if the



pressure gradient inside the soil stays below the critical gradient, a positive stress between thegrains will remain and the relative density won't change dramatically. This can easily be provedin a permeability apparatus, where an upward �ow can be set up using a hydraulic head. This testshows that an upward �ow doesn't in�uence the packing of the soil, as long as the critical gradientisn't exceeded. Once the critical gradient is reached, the entire plug is lifted up and lique�es.

Figure 3.2: Plug heave below and above the critical gradient, tested in a permeability apparatus. 1.Original compacted sand at rest. 2. Upward �ow: i < icrit. 3. Upward �ow: i > icrit. 4. Settled again

i = 0.

On �gure 3.2 this test is shown schematically. The soil has an initial density and a hydraulicgradient is applied (2). This hydraulic gradient is gradually increased until the critical gradientis reached (3). The soil increases in volume and the relative density decreases dramatically. Nextthe gradient is removed and the soil particles settles (4). However, without vibration the initialrelative density isn't obtained and a permanent volume increase remains. The most importantconclusions from this relatively simple test set-up are:

• There is no permanent plug heave in a permeability apparatus in case of a gradient belowthe critical gradient.

• Once the critical gradient is exceeded, the soil plug lique�es and increases in volume.

• Once the hydraulic head is removed, the lique�ed plug will settle again into a loose sand.

• A permanent increase in volume remains, as the initial relative density can't be reachedwithout vibration.

Given the critical gradient is exceeded, Tran could quantify the plug loosening as follows. Hedid the experiment on a dense sand (initial relative density of about 91% and a particle sizeD50 of 0.18mm) and calculated the plug loosening by measuring the �ow through the soil duringinstallation. By keeping the applied pressure constant, Darcy's law can be used to calculate thedischarge through the soil for a certain permeability. Because all discharges were higher thanexpected for the initial permeability, he could conclude that the plug inside the pile was loosenedduring installation. This phenomenon is also con�rmed comparing CPT logs inside a jacked pileand a pile installed using suction[20]. From his investigation can be concluded that plug looseningstarts at a penetration depth of about L/D=0.2 and that the permeability after installation is onaverage a factor 1.5 higher than the initial permeability. In terms of relative density this meansthat a sand sample with a relative density of 90% reaches after installation on average a relativedensity of about 60%. This reduction could a�ect the inner friction resistance of the skirt.



On �gures 3.3 and 3.4 the displacement of particles of an installation above the critical gradientis shown. It is clear that in this case the soil of the entire plug moves upward, which was not thecase in section 3.1.1. The highest concentration of activity is still close to the skirt, because herethe gradient is the highest and the skirt's volume is pushed in. An important di�erence with �gure3.1 is that the plug loosening measured in this case could be partly reversible, as the soil can goback to a denser packing once the hydraulic head is removed.

Figure 3.3: Displacement of the particles.(L/D = 0.2, s/γ′D = 4.1) [20]

Figure 3.4: Displacement of the particles.(L/D = 0.3, s/γ′D = 5.1) [20]

3.2. Erosion

In chapter 2, the concept "critical suction" is explained. For installation pressures below the criticalsuction pressure, the soil plug won't liquefy and the relative density of the plug won't change. Inthis case only limited plug heave will occur, because only the displaced sand due to the penetrationof the skirt will result in plug heave. For this type of installations, the bed will remain stable andno loosening will occur due to the vertical gradient. However, it could still be impossible to getinitial contact between top plate and soil because of erosion of the top of the plug.

Figure 3.5: Erosion of the bed due to horizontal �ow on the bed.

As shown in �gure 3.5, a horizontal �ow is present on the bed. This �ow arises because water ispumped out of the suction pile in order to get it installed. All the water has to �ow to the middleof the pile, where it is extracted by the pump. Because of the cylindrical shape of a suction pile,the �ow velocity will increase towards the middle, as the water �ows in the direction of decreasing



radius. As the top plate approaches the soil and the gap becomes smaller, the �ow velocity willincrease, with a theoretical limit to an in�nitely high �ow velocity once the top plate is in�nitelyclose to the soil. In �gure 3.6 an example of the �ow velocity pro�le above the bed is given. Atr/R = 0, or in other words, in the center of the suction pile, the �ow velocity is at its maximum.

0 0.2 0.4 0.6 0.8 10

2 · 10−2

4 · 10−2

r/R [-]

Flowspeed[m/s]

Conventional suction pile

0 0.2 0.4 0.6 0.8 10

5 · 10−3

1 · 10−2

1.5 · 10−2

r/R [-]

Q[m3/s]

Figure 3.6: Example of �ow velocity and discharge for di�erent r/R-ratio's. (D = 8m, L = 8m, distancebetween top plate and soil = 0.1m)

Due to the horizontal �ow above the soil, erosion could occur and the bed could become unstable.Depending on the soil structure, the size of the grains and the �ow velocity, the erosion velocitycan be determined. The erosion velocity is perpendicular to the soil bed, and becomes problematicfor the installation of the suction pile once it is higher than the installation velocity. As the sizeof the gap decreases during installation, the �ow will theoretically always increase to an in�nitelyhigh value. The erosion velocity of the bed is indicated on �gure 3.5 by the downward arrows.

Besides the horizontal �ow on the bed, an upward gradient in the soil plug is present. This gradientfacilitates the pick-up rate of the grains, so that the erosion velocity is higher than what's to beexpected in case of erosion solely due to a horizontal �ow. In order to include these two "erosion-inducing-processes" in one single calculation model, it is proposed to use equations derived andveri�ed by van Rhee [23].

In general one can say that the �ow inside the pile acts as a shear force on the bed, which isrepresented by the (dimensionless) Shields' parameter (θ) and depends (i.a.) on the height ofthe �ow velocity. Erosion occurs once this shear exceeds a critical shear value, called the criticalShields' parameter (θcrit). This is the boundary which has to be exceeded to get erosion. As longas the shear is below this critical value, the bed remains stable and no pick-up occurs [24].

The dimensionless Shield's parameter is de�ned as:

θ =fo8· u2

∆gDpart(3.3)

with fo is the coe�cient of friction of the sediment bed, u is the mean �ow velocity, ∆ the relativesediment density and Dpart the particle diameter. As soon as this value exceeds the critical shieldsparameter, which is a function of Reynolds particle number, grains will be picked up by the �ow.

θcr = 0.22R−0.6p + 0.06exp

(−17.77R−0.6

p

)(3.4)

The upward gradient in the soil plug lowers this critical value and erosion will start at lower �owvelocity. Van Rhee and van Bezuijen [24] derived an equation to take into account this in�uence



of a hydraulic gradient on the erosion. They used following expression to derive a new value forthe critical Shields parameter:

θ1cr =

(1 +A

i

∆

)θcr (3.5)

with A = 1/(1 − n0) and ∆ is the speci�c weight of a particle (∆ = (ρs − ρw)/ρw). In terms ofthis thesis, where a continuum and not a single particle is considered, this is the same as:

∆

A= icrit (3.6)

As soon as the present gradient exceeds icrit, the bed will be unstable, even without horizontal�ow. The entire plug will be in suspension, so small horizontal �ows are enough to transport theparticles (as they are already in suspension due to the upward gradient).

Van Rhee [23] also includes a phenomenon called "hindered erosion". For high shear velocities (forexample in case of jetting in dredging practice), densely packed sands dilate, causing an inwardgradient. This inward gradient reduces the erosion velocity. In the context of this research, theshear velocities are limited, because once θcrit is exceeded, erosion will enlarge the �ow surfaceinside the suction pile. This way, the high �ow velocities which are expected once the top plate isreally close to the soil, can theoretically never be reached. For this reason, the e�ect of this inwardgradient due to a high �ow velocity is not relevant and not considered.

This means that van Rijn's [25] pick up function becomes:

φp = 0.00033D0.3∗

(θ − θ1

cr

θ1cr

)1.5

(3.7)

with

D∗ = Dpart3

√∆g

ν2(3.8)

and ν is the kinematic viscosity of the water, which is at 10 degrees equal to 1.307 · 10−6m2/s.The erosion velocity perpendicular to the bed becomes than:

ve =1

1− n0 − cb

[0.00033D0.3

∗

(θ − θ1

cr

θ1cr

)1.5√g∆Dpart − cbws

](3.9)

Herein is cb the near-bed concentration and ws the settling velocity of a particle including thein�uence of concentration. Now the erosion velocity of the bed can be calculated for di�erentsand gradations. In the context of this thesis the most important aspect to consider regardingerosion, is the ratio between the erosion velocity and the installation velocity, because as long asthe erosion velocity stays lower than the installation velocity, it should be possible to get initialcontact between top plate and soil.



3.3. Conclusion

The three di�erent processes resulting in plug heave have a di�erent impact on the gap betweentop plate and soil. As long as the critical pressure isn't exceeded, only elastic heave and heavedue to the skirt's volume occur. However, for these installations erosion can make initial contactimpossible.

In case the critical gradient is exceeded, all described processes occur. However, the main reasonof the gap between top plate and soil is now the reversibility of the "plug loosening", because oncethe hydraulic head is removed, the soil will decrease in volume again and a gap will remain.

The plug heave is clearly concentrated along the skirt and less heave occurs in the middle of thesuction pile. It is possible that initial contact between top plate and soil is obtained in an annulusnext to the skirt, with a gap remaining in the middle.





4 | Sollutions to the gap problem

4.1. Variants

There are di�erent solutions possible to get initial contact between top plate and soil. In thischapter several possibilities are discussed. In order to choose the most favourable solution, thee�ectiveness of the di�erent possibilities should be compared. The maximum bearing capacity ofa suction pile is reached once the top plate is �ush with a densely packed soil bed. The goal ofthis research is to �nd a solution that approaches this situation immediately after installation.

The solutions mentioned in this chapter are investigated further in this thesis, and in chapter 9 anadvice is formulated. The solutions are divided in three subgroups, based on the moment in theinstallation operation when the new measures have to be taken:

1. Onshore measures, to be implemented during the construction phase of the suction pile.

2. O�shore measures, to be implemented before installation.

3. O�shore measures, to be implemented after installation.

In general o�shore measures are more expensive than adjustments in the onshore constructionphase, as extra vessels or extra o�shore construction time makes the operation more complicated.

4.1.1. Onshore measures

4.1.1.1. Improvement of the extraction nozzle

If more extraction nozzles would be implemented, this would reduce the horizontal �ow speedon the bed (as not all the water has to �ow to the same place). This way erosion of the bedcould be reduced. Besides that, a �lter could be placed inside the extraction nozzle, in a way itbecomes impossible to extract sand from the inside of the suction pile. If there is e�ectively nosand transport outside the suction pile, it could be argued that initial contact between top plateand soil should be possible. An important disadvantage is that this �lter could clog, preventingalso the water to �ow out and making installation impossible. This could be an important risk,which needs to be investigated. In general one can say: the bigger the �lter, the less chance ofclogging.

4.1.1.2. Extra bearing elements

Erosion occurs because of a high �ow velocity on the bed. This velocity increases if the top platecomes closer to the soil, as explained in chapter 3. If extra bearing elements are implemented in thesuction pile, they have to be designed in a way that the �ow velocity below these extra elementsstays low enough to avoid erosion. Possible con�gurations are:

Second top plate: A smaller, second top plate could be attached to the top plate of the suctionpile. If this plate is smaller than the original top plate, the extracted water will have to �ow aroundthis second top plate, through the open space at the outside of the cylinder. In the original designof the suction pile, the water �ows to an opening in the center of the pile. This means that thesecond top plate (as in �gures 4.1 and 4.4 to 4.7) inverts the �ow, resulting in much lower �ow

Chapter 4. Sollutions to the gap problem 25


velocities and less erosion. Further investigation is needed to determine if it is possible to get initialcontact between soil and second top plate, but if that turns out to be possible, this second topplate can replace the function of the original top plate. The feasibility of this second top plate isinvestigated in chapter 5, while the required size in relation to the bearing capacity of this secondtop plate is investigated in chapter 7.

Figure 4.1: Top plate design 1: a plate which isslightly smaller than the top plate of the suction

pile.

Figure 4.2: Top plate design 2: a perforatedplate of the same size as the top plate of the

suction pile.

Perforated top plate: A perforated top plate (as in �gures 4.2, 4.8 and 4.9) is basically thesame idea as the second top plate explained above. Due to the perforations, the horizontal �owvelocity is minimal as the water can �ow directly vertical through the plate. The size of the holes aswell as the amount has to be determined: an optimum is needed between horizontal �ow reductionand total bearing capacity of this top plate design.

Parallel I-beams: Besides a plate-solution, a solution with parallel I-beams could work as well.The gaps between the di�erent I-beams should be big enough to decrease the horizontal �ow velocitysu�ciently, but small enough to make sure the di�erent strip foundations will work together andincrease each other's bearing capacity. It could be necessary to use geotextile between the di�erentI-beams to avoid that sand will be squeezed through the gaps and settlements will occur in the"as-built" situation. This is investigated in chapter 7.

4.1.1.3. Implementation of a geotextile �lter

A geotextile �lter instead of a second top plate could have the same e�ect as a perforated steel topplate. A design with a gravel layer sealed with a geotextile, is permeable over the entire surface.This reduces the horizontal �ow velocity on the bed and at the same time the gravel has enoughstrength and sti�ness to transfer the load on the top plate to the soil, once there is contact betweenthe geotextile and the seabed. An important advantage of a geotextile over the entire surface ofthe suction pile, is that the risk of cogging is signi�cantly reduced compared to a geotextile �lterin the nozzle (as discussed in paragraph 4.1.1.1).



4.1.2. O�shore measures, prior to installation

4.1.2.1. Deposition of a gravel layer on the project location

To prevent erosion of the bed, a layer of gravel could be deposited on the project location. Thegravel will be too heavy to be picked up by the horizontal �ow, so erosion won't occur. Thissolution is only applicable in case the suction pressure stays below critical suction. Otherwise thesoil plug will �uidize and the gravel will probably sink into the soil (ρfluidized = 2000, ρrock = 2650:it could help to place the rock on a geotextile).

4.1.3. O�shore measures, after installation

4.1.3.1. Sand or grout injection

The injection of sand or grout in the gap between top plate and soil is what's currently beingused in engineering practice. This is an expensive extra o�shore operation, because it requiresexpensive equipment to get the grout at the project location and inject it at high water depths.Besides that, it is a relatively insecure measure, as it is impossible to see how the grout or the sandis distributed inside the gap, which makes it di�cult to prove that the entire gap is �lled. Thegoal of this research is to improve the current methods, so this solution will not be investigatedfurther.

4.2. First evaluation of the di�erent variants

The most favourable solutions are the onshore measures, because this is generally a lot cheaper thano�shore proceedings. This makes the extra bearing elements the most interesting to investigatefurther. In order to get the best insight in the di�erent solutions and their feasibility, feedbackwith chapter 3 is required, because in this chapter the origin of the gap is described.

In table 4.1 the di�erent solutions are listed and evaluated on their e�ectiveness to solve each partof the problem. This evaluation gives a �rst indication of the feasibility of a proposed solution.The coloured area's in table 4.1 indicate combinations of the problem from which is believed that itwouldn't occur: in case of critical suction the plug is loosened entirely, causing a signi�cant volumeincrease. Elastic heave can be neglected in this case. For sub-critical suction plug loosening won'toccur, as it is believed that the critical gradient should be exceeded before this can happen.

Table 4.1: Analysis of the e�ectiveness of the proposed solutions.

Critical suction Sub-critical suction Score

Gap caused by Loosening Heave Erosion Loosening Heave Erosion

Solution

Filter in nozzle - - + + - - + -1

Second top plate + - + + 2

Perforated top plate + This + This + + + 5

I-beams +/- doesn't - doesn't - + + 0

Geotextile �lter + + occur + + occur - + + 5

Gravel layer - - - - +/- + + -2

Grout injection - - - - - - - - -8

In general all solutions using �lter material, should be e�ective as protection against erosion. Thisbecause a �lter prevents sand grains of leaving the suction pile, while the water can still �ow out.Mainly in case of a lique�ed soil plug, these solutions are expected to be the most e�ective. For thenon-lique�ed soil plug (sub-critical suction), all solutions with reduced horizontal �ow velocities



have good scores in the erosion-column, as it should be possible to get initial contact with the topplate, (which is for example shown in �gure 4.4 and 4.5).

The gap due to plug loosening is expected to be solved using a geotextile �lter or a perforated topplate. These solutions can squeeze the water out of a lique�ed soil plug in a way that stress is buildup again (see �gure 4.8 and 4.9). This way the plug should settle again during installation, insteadof after installation. Still a loosened plug will remain, but it should make grouting super�uous.Parallel I-beams or a second top plate (�gure 4.6 and 4.7) could probably do this in a more limitedway. This idea should be con�rmed by model tests.

Elastic heave is expected to be solved best by a (perforated) second top plate. These solutionscan push the soil plug back by keeping on the pressure after contact between top plate and soil.Because the second top plate has a smaller surface than the normal top plate, the resulting forcewill be downward and the soil could possibly be pre-stressed. This should also be con�rmed bythe model test.

Grout injection is considered to be not a solution to the problem, as it deals with the symptoms(the gap) and not with the cause of the problem. All other proposed solutions prevent one or moreof the occurring processes, while grout injection is implemented afterwards, once the gap is alreadypresent.

Concluding from table 4.1, the geotextile in combination with the perforated top plate is themost promising solution, followed by the second top plate as shown in �gure 4.1. The parallelI-beams could be useful in certain circumstances, but in case it is possible to limit erosion usinga (perforated) second top plate, this solution is preferable. The other proposed solutions are onlyuseful to overcome one of the occurring phenomena, so they are not investigated any further. The(perforated) second top plate and the I-beams seem to be good solutions of the problem, but thisshould be con�rmed by calculations. Because of that, a calculation model is developed whichdescribes all of the occurring processes in a suction pile installation. The calculation model allowsto implement the proposed solutions and check their e�ectiveness against the occurrence of thegap due to erosion or due to the compaction of the plug after loosening.

Figure 4.3: Legend of �gures 4.4 to 4.9



Figure 4.4: Installation pressure below criticalpressure. No plug heave occurs.

Figure 4.5: Once the top plate touches the soil,the gradient increases and locally liquefaction

occurs.

Figure 4.6: Installation pressure above criticalpressure. Plug heave occurs and the entire plug

has lost its e�ective stress.

Figure 4.7: The second top plate sinks into thelique�ed soil. The �ow lines change direction and

in the middle e�ective stress can build up.

Figure 4.8: Installation pressure above criticalpressure. A perforated top plate with geotextile is

used.

Figure 4.9: The water �ows through theperforated top plate, while the soil stays in the

plug. E�ective stress can build up.





5 | Calculation model

5.1. Introduction

The suction piles considered in this thesis are installed in a homogeneous sandy soil, subject togroundwater �ow, erosion and plug heave. These processes result in a gap between the top plateand the soil surface, which could be problematic in certain circumstances (see chapter 3). Themain goal of the calculation model is to convert the present physical processes in a mathematicalform, in a way it becomes possible to predict the size of the gap inside the suction pile. Secondly,the calculation model should answer the question if it could be possible to install a second topplate that rests directly on the soil. To do so, two similar models are developed: one theoreticalcase with a homogeneous soil consisting of only one grain size, and one which can be used in case insitu soil data like CPT's are available. The calculation model couples di�erent sub-models, whichresults in a complete image of the processes present during a suction pile installation. First the soilstructure is determined, than the installation of the pile is modelled in the so-called "installationand bearing capacity model", than the groundwater �ow is modelled and �nally the erosion isincluded.

The objective of the model is to predict the size of the gap between the top plate and the soil.To predict this, an erosion calculation has to be made. So it is desired to make the entire modeldepending on parameters related to the erosion formulas (like grain size, porosity, density of thematerial...).

5.2. Soil structure

The properties of a soil are characterized by many di�erent parameters, which are mutually linkedby empirical relationships. This enables the possibility to reduce the amount of parameters in themodel. A disadvantage is that every empirical relationship between two soil parameters induces itsown imperfections and inaccuracies. The model also uses certain assumptions, so it is importantto interpret the results of the model with the inaccuracies of certain assumptions in mind. Thischapter describes all assumptions and relations to model a homogeneous sand layer, including allpossible inaccuracies and uncertainties induced by these assumptions and relations.

The conventional calculation methods used to predict the soil resistance during the installationphase, make use of the cone resistance of a CPT to predict the required installation pressures (seechapter 2.4). However, a homogeneous soil with constant grain size is a theoretical soil pro�le,so in situ data like the cone resistance are not available. The classical bearing capacity approachassumes a linear increase of the cone resistance with e�ective stress level, which would result ina linear relation between cone resistance and depth (as e�ective stress is linearly related to depthin case of a homogeneous soil, see �gure 5.1). However, from experience can be concluded thatthe cone resistance increases less than linearly with increasing stress [14],[16]. Several researchershave tried to formulate a relationship between e�ective stress, relative density and cone resistance.In order to predict a good estimation for the cone resistance in this theoretical soil pro�le, theempirical relation found by Baldi et al. [4], [15] is used (see also �gure 5.2):

qc =(C0 ∗ (σ

′

v)C1 ∗ exp(C2 ∗Dr)

)(5.1)

With σ′

v is the vertical e�ective stress and C0, C1 and C2 are constants. For normally consolidatedsands these parameters equal 157, 0.55 and 2.41. In case of over consolidated behaviour, equation5.1 becomes:

Chapter 5. Calculation model 31


0 20 40 60 80 100 120 140

0

2

4

6

8

10

12

10

Vertical e�ective stress [kPa]

Depth

[m]

Relative density1.000.920.830.740.640.530.420.290.150.00

Figure 5.1: For a homogeneous soil, the e�ective stress increases linearly with depth. (Di�erent relativedensities)

0 5 10 15 20 25 30

0

20

40

60

80

100

120

140

10

Cone resistance qc [MPa]

Verticale�ective

stress

[kPa] Relative density

1.000.920.830.740.640.530.420.290.150.00

Figure 5.2: Relation between the cone resistance and the e�ective stress of a soil pro�le, for di�erentrelative densities. [15]

qc =(C0 ∗ (σ

′

m)C1 ∗ exp(C2 ∗Dr))

(5.2)

Witch C0, C1 and C2 are equal to 181, 0.55 and 2.61. σ′

m is the mean e�ective stress, which isde�ned as:

σ′

m =σ′

v(1 + 2K0)

3(5.3)

With K0 = 1− sin(ϕ). ϕ is the angle of internal friction of the considered soil and can be relatedto the relative density Dr (as shown in tabel 5.1). This empirical relation makes it possible to



estimate the cone resistance based on the relative density [9], which is useful in view of the comingerosion calculations (see �gure 5.3).

Table 5.1: Relationship between relative density and angle of internal friction of cohesion less soils. [9]

State of packing Relative density (%) Angle of internal friction ϕ

Very loose <20 <30Loose 20-40 30-35

Compact 40-60 35-40Dense 60-80 40-45

Very dence >80 >45

0 5 10 15 20 25 30

0

2

4

6

8

10

12

10

Cone resistance qc [MPa]

Depth

[m]


Figure 5.3: The cone resistance over depth, for di�erent relative densities.

5.3. Installation resistance and bearing capacity model

As explained in chapter 2, the installation pressures and the bearing capacity can be estimatedwith di�erent methods. In engineering practice the CPT-method is used, but it is also possibleto use Houlsby's method [13] which is based on Brinch Hansen. Initially the model is developedfor a homogeneous soil with uniform grains. Empirical relationships allowed to relate the relativedensities to a cone resistance, which made it possible to predict the installation pressures for allpossible homogeneous, permeable soils. As an example, a calculation is executed for a suction pilewith following dimensions: L = 8m, D = 8m and t = 0.04m. The chosen soil has uniform grainsof 0.2mm and the calculation is done for di�erent relative densities (see �gure 5.4).

Besides the required suction pressure, the critical suction pressure is also calculated for all possibleinput parameters. These pressures are plotted with the dotted lines in �gure 5.4. In case the suctionpressure exceeds the critical suction line, plug loosening and liquefaction is expected. Notice thatfor the considered soil conditions and this suction pile geometry, it is not expected to get criticalsuction.

The model allows to model all possible geometries and all possible uniform sandy soils. In a laterstage, an adaption is made to the model, which allows to make the calculation for layered soils,based on their CPT-pro�le. An example is given in chapter 8.



0 20 40 60 80 100 120 140

0

2

4

6

8

Required suction pressure [kPa]

Depth

[m]


Figure 5.4: Required installation pressure to overcome the total soil resistance, calculated for di�erentrelative densities. The dotted lines show the critical pressure, also for di�erent relative densities.

The challenge in the calculation of the required suction pressures is the iterative character of thecalculation. Because the reduction factor for the soil resistance depends on the applied suctionpressure, the right equilibrium needs to be found with an iterative procedure: as the resistanceincreases with depth, the required suction pressure increases as well. However, a higher suctionpressure results in a higher reduction in resistance, and so a decrease in required suction pressure.The way this is programmed is shown in appendix A.1, from line 246 till 266.

The same calculation is done with Houlsby's method, based on Brinch Hansen. The main inputparameters of this method are the internal friction and the e�ective weight of the soil. The methodis described in chapter 2 and the way it is programmed is shown in appendix A.3. In this appendixthe exact input parameters of the calculation in �gure 5.5 are included as well.

0 20 40 60 80 100

0

2

4

6


Depth

[m]

Required suction pressureCritical pressure

Figure 5.5: Required suction pressure to overcome the soil resistance according to Brinch Hansen(equation 2.18).



5.4. Groundwater �ow model

5.4.1. Groundwater �ow equation

[5] The considered soil is homogeneous and permeable, which means that the pressure distributioninside the suction pile is the same for di�erent permeability's. The �ow (q) increases linearly withincreasing permeability, so this means that for a certain penetration depth, the pressure gradientis a constant and can be calculated, no matter the exact soil conditions (given that you havepermeable and homogeneous soil).

In order to model the pressure distribution in a mathematical way (in Matlab), it is useful tostart with the di�erential equation for groundwater �ow. This equation is based on the physicalprinciple of mass conservation, meaning that for a given small volume, the mass �owing in, themass �owing out and the sources inside the volume equal the amount of mass stored in the system:

I(t)−O(t) = dM/dt (5.4)

If a steady state �ow is assumed, the in- and outgoing �uxes are constant in time and the changein storage inside the control volume is zero.

I −O = 0 (5.5)

Because mass can be expressed as density times volume and because water can be consideredincompressible, the mass �uxes across the boundary can be expressed as volume �uxes. This givesfor the ingoing �ux:

I = ρqx∆y∆z + ρqy∆x∆z + ρqz∆x∆y (5.6)

And for the outgoing �ux the equation becomes:

O =

(ρqx +

δ(ρqx)

δx∆x

)∆y∆z +

(ρqy +

δ(ρqy)

δy∆y

)∆x∆z +

(ρqz +

δ(ρqz)

δz∆x

)∆x∆y (5.7)

Because steady state �ow is assumed (equation 2.4), the di�erence between in and outgoing �uxbecomes (see also �gure 5.6):

I −O =

(δ (ρqx)

δx+δ (ρqy)

δy+δ (ρqz)

δz

)∆x∆y∆z = 0 (5.8)

Water is assumed to be incompressible, so the density doesn't change. Now equation (5.8) becomes:

I −O =δ (qx)

δx+δ (qy)

δy+δ (qz)

δz= 0 (5.9)

Darcy's law relates �ux to hydraulic heads (dh/dz = q/k), so equation (5.9) becomes:

I −O =δ

δx

(kδh

δx

)+

δ

δy

(kδh

δy

)+

δ

δz

(kδh

δz

)= 0 (5.10)



Figure 5.6: In- and outgoing �ux for an elementary volume.[5]

The soil is assumed to be homogeneous, which means that also the permeability is constant. Usingthis �nal assumption, the equation becomes the well-known Laplace equation:

δ2h

δx2+δ2h

δy2+δ2h

δz2= 0 (5.11)

This equation is valid for a rectangular domain in Cartesian coordinates. In case of a suction pileproblem, the domain is radial symmetric and will be modelled in cylindrical coordinates. TheLaplace equation in cylindrical coordinates can be derived in a similar way (starting with a massbalance, assumptions of homogeneous soil and incompressible �uid and using Darcy's equation torelate �ux to hydraulic head) and becomes (see also �gure 2.5):

δ2h

δr2+

1

r

δh

δr+δ2h

δz2+

1

r2

δ2h

δϑ2= 0 (5.12)

This means that the Laplace equation in cylindrical coordinates depends on the radius r and theangle ϑ. Because of radial symmetry of the problem, the ϑ term becomes zero and the Laplaceequation for cylindrical coordinates becomes:

δ2h

δr2+

1

r

δh

δr+δ2h

δz2= 0 (5.13)

Solving the Laplace equation with the right boundary conditions will give the pressure distributioninside the suction pile. A simple di�erential equation as the Laplace equation can be solvedanalytically in case the boundary conditions are straight forward (for example a rectangular domainwith two closed bounds and two Dirichlet bounds ( = a bound with a given head), but in the caseof a suction pile, the domain and boundaries are more complicated and require a numerical solutionto the boundary value problem (�gure 5.7).



(5)

(3) (6)

(1) (2)

(4)

z

r

Figure 5.7: Schematic representation of the domain and its boundaries, the axes are the same as in�gure 2.5.

5.4.2. Boundary conditions

In �gure 5.7 a sketch of the domain of the considered boundary value problem is given. Thedi�erent boundaries are numbered and refer to the numbers in the text. The di�erent boundarieshave di�erent properties, so they are all modelled in a speci�c way. The domain is radial symmetric,with boundary (3) is the mirror line and boundary (4) is the skirt of the suction pile.

Boundaries (1) and (2) are so called Dirichlet boundaries. A Dirichlet boundary is a boundarywhere every coordinate has an assigned value. Along boundary (1) an under pressure is applied, soalong this boundary all elements of the domain have a �xed potential equal to this under pressure.Boundary (2) equals the hydrostatic pressure of the sea bed, which is in case of suction a higherpotential than at boundary (1).

Because of the homogeneity of the soil, it doesn't matter which pressure is applied. In percent-age terms, the pressure distribution inside the suction pile will be equal for all chosen pressuredi�erences. It is only relevant to know the percentage of the applied pressure at a certain depth,so it is chosen to assign a potential of 1 to boundary (1) and a potential of 0 to boundary (2).These �xed potentials are then used to model the pressure distribution for all possible pressuredi�erences between in- and outside the suction pile.

Boundary (3) is the center line of the suction pile. For this boundary the so called Neumannboundary is applied. For this type of boundary, the values of the normal derivative are prescribedon the boundary. Boundary (3) is the mirror line of the model, which means that there is no �owacross this boundary, so the pressure gradient perpendicular to this boundary equals 0. The skirtof the suction pile, boundary (4), can be modelled in a similar way as boundary (3). The �owacross this boundary is also zero, which means that a gradient of zero can also be assigned to thisbound.

Boundaries (5) and (6) are more complicated to model in a correct way, because in practicethese boundaries are open. In the model they should allow the �uid to �ow through, in a radialsymmetric way. If the bounds are modelled as Dirichlet boundaries, a �xed potential is applied.This potential is mostly equal to the potential applied to the seabed boundary (2). This way anopen boundary is created, which allows in�owing water. For boundary (6) this could be comparedto a vertical side of an island in water. However, a constant potential alongside boundary (5) and(6) is not exactly what's to be expected in reality.

The other option, the Neumann boundary, assigns a �xed gradient to the cells on the boundary.A gradient of 0 is used to model a closed bound, which is also not an exact solution (as the boundis not closed in reality). For both the Dirichlet as the Neumann solution holds: the further awayfrom boundary (3) and (4) these bounds are placed, the better it is. It can be concluded that it isimportant to choose from both options the solution with the least impact on the problem, in order



to minimize the required size of the domain. The in�uence of this boundary will be investigatedin chapter 5.4.3.

5.4.3. Numerical model

Because of the complexity of the domain and its boundaries, it is not possible to �nd an analyticalsolution for the groundwater �ow equation. That's why the Laplace equation has to be discretized,in order to �nd a numerical solution. For this thesis, the discretization of the Laplace equation isdone by using the central di�erence method. The Laplace equation with cylindrical coordinatesis really similar to the one in Cartesian coordinates, so �rst the discretization of the CartesianLaplace equation is shown. Afterwards, the radial e�ect will be added. So, the Cartesian Laplaceequation in 2D is:

δ2h

δx2+δ2h

δy2= 0 (5.14)

The de�nition of the central di�erence method is (with h is the step size and not the hydraulichead as in equation 5.14), see also �gure 5.8:

Figure 5.8: De�nition of the central di�erence method.

δf(x) =f(x+ 1

2h)− f

(x− 1

2h)

h=f (x+ h)− f (x− h)

2h(5.15)

However, the Laplace equation requires a second order centered di�erence scheme, so equation(5.15) has to be discretized again:

δ [δf(x)] =f(x+ 1

2h−12h)− f

(x+ 1

2h+ 12h)− f

(x− 1

2h−12h)

+ f(x− 1

2h+ 12h)

h2

=f (x)− f (x+ h)− f (x− h) + f (x)

h2

=2f (x)− f (x+ h)− f (x− h)

h2(5.16)



Equation (5.16) is the discretization of the �rst term of the Laplace equation (the term dependenton x). The same holds for the term depending on y, so the �nal discretization of the groundwater�ow equation becomes:

0 = 2f(x, y)− f(x+ h, y)− f(x− h, y) + 2f(x, y)− f(x, y + h)− f(x, y − h)

⇒ f(x, y) =1

4[f(x+ h, y) + f(x− h, y) + f(x, y + h) + f(x, y − h)] (5.17)

In words we can say that the Cartesian Laplace equation is discretized by cons idering one gridpoint and equalize this grid point to the average of the four surrounding gridpoints. The cylindricalLaplace equation is discretized exactly in the same way (the �rst and the last term of equation(5.18) are equal to the Cartesian case), only the second term di�ers and is discretized as follows:

δ2h

δr2+

1

r

δh

δr+δ2h

δz2= 0 (5.18)

1

rδf(r) =

f(r − 1

2h)− f

(r + 1

2h)

rh(5.19)

So the total discretization of the cylindrical Laplace equation becomes:

4

h2f(r, z) =

f(r + h, z) + f(r − h, z) + f(r, z + h) + f(r, z − h)

h2

+f(r − 1

2h, z)− f

(r + 1

2h, z)

rh⇒ 4f(r, z) = f(r + h, z) + f(r − h, z) + f(r, z + h) + f(r, z − h)

+

[f(r − 1

2h, z)− f

(r + 1

2h, z)]h

r(5.20)

In terms of potential (V) in a considered grid point (ρ0, z0), equation (5.20) becomes:

4V (ρ0, z0) = V (ρ0, z0 + h) + V (ρ0, z0 − h) + V (ρ0 + h, z0) + V (ρ0 − h, z0)

+

[V(ρ0 + 1

2h, z0

)− V

(ρ0 − 1

2h, z0

)]h

ρ0(5.21)

Based on the de�nition of the central di�erence (equation (5.15)), equation (5.22) is true:

1

2

h

ρ0[V (ρ0 + h, z0) + V (ρ0 − h, z0)] =

h

ρ0

[V

(ρ0 +

1

2h, z0

)+ V

(ρ0 −

1

2h, z0

)](5.22)

So equation (5.21) can be rewritten as:



4V (ρ0, z0) = V (ρ0, z0 + h) + V (ρ0, z0 − h)

+

(1 +

1

2

h

ρ0

)V (ρ0 + h, z0) +

(1− 1

2

h

ρ0

)V (ρ0 − h, z0) (5.23)

In words this means that the considered grid point (ρ0, z0) equals the average of the surroundingcells, with an extra weighting factor added to the left and the right adjacent grid points. Physicallythis can be explained because in case of horizontal �ow over the boundaries of each cell, the out�owsurface increases the further you get away from the center line. To compensate for this inequalityin in- and out�ow area between the left and the right side of the considered cell, the compensation

factors(

1 + 12hρ0

)and

(1− 1

2hρ0

)appear in the discretization of the cylindrical Laplace equation.

5.4.4. Programming considerations

5.4.4.1. Boundary conditions

In section 5.4.4.1 is already indicated that two di�erent methods can be used to model the boundaryconditions, namely Dirichlet and Neumann boundaries. An investigation is done by changingthe bottom and the right side boundary. In �gure 5.9 these bounds are modelled as Dirichletboundaries, while in �gure 5.10 the bounds are modelled as Neumann boundaries. The investigationis done twice, once with the boundaries far away from the suction pile, and once with the boundariesclose-by.

From this investigation, two things can be concluded:

1. With the boundary far away from the suction pile, its in�uence becomes negligible. For bothNeumann and Dirichlet a similar result of the pressure distribution inside the suction pile isfound.

2. With the bottom boundary close to the suction pile, a clear di�erence is found for the pressuredistribution inside the pile. The �xed potential of the Dirichlet boundary turns out to bethe most similar solution, which makes in this case this type of boundary preferable abovethe Neumann boundary.

So the outer boundaries of the domain, except the left one, are modelled as Dirichlet boundaries,which means that the coordinates on these bounds get a �xed potential. This is really straightforward in programming (just assigning a value to the speci�c grid point of the mesh). All outerboundaries get a potential equal to 0 and inside the suction pile the boundary equals 1. Section5.4.4.1 explains why this is allowed and why it is not necessary to model the pressure distributionwith the actual applied suction pressure.

The mirror line as well as the skirt of the suction pile, are Neumann boundaries. This means thatthese coordinates get a �xed gradient, which can be derived directly from the discretization of theLaplace equation. In case of the mirror line of the suction pile for example, the head in cell (i,-1) isequal to the head in cell (i,+1). Because cell (i,-1) is not part of the domain, a solution has to befound to model this. The head in the two cells is equal, which corresponds to a zero in- or decreaseof the change in head. In other words: there is no �ow through this boundary, which means:

δh

δr= 0 (5.24)

If this is �lled in the cylindrical Laplace equation (5.18), this becomes:



10 20 30 40 50 60 70 80 90

10

20

30

40

50

60

70

80

90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 5.9: Dirichlet boundaries (constantpressure), far from the suction pile

10 20 30 40 50 60 70 80 90

10

20

30

40

50

60

70

80

90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 5.10: Neumann boundaries (no �ow), farfrom the suction pile

10 20 30 40 50 60 70 80 90

10

20

30

40

50

60

70

80

90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 5.11: Dirichlet boundaries (constantpressure), close to the suction pile

10 20 30 40 50 60 70 80 90

10

20

30

40

50

60

70

80

90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 5.12: Neumann boundaries (no �ow),close to the suction pile

δ2h

δr2+δ2h

δz2= 0 (5.25)

Which is equal to the Cartesian Laplace equation and which is modelled as shown in equation(5.17). In this case, the left boundary, f(x − h, y) doesn't exist. However, this bound is a mirrorline, so it can be modelled using f(x+ h, y) twice:

0 = 2f(x, y)− 2f(x+ h, y) + 2f(x, y)− f(x, y + h)− f(x, y − h)

⇒ 4f(x, y) = 2f(x+ h, y) + f(x, y + h) + f(x, y − h) (5.26)

The same is valid for the skirt. This is also a no-�ow boundary with a gradient equal to zero, sothis can be modelled in the same way as the mirror line.

5.4.4.2. Iteration method versus band matrix method

The Laplace equation for groundwater �ow is a typical example of a partial di�erential equationwith a speci�c domain and boundary conditions. This type of problem is solved with a �nite



di�erence approach, the simple numerical technique explained in chapter 5.4.3. Equation 5.17clearly shows that the potential in a considered point is the average of the potentials at thesurrounding points. Two methods are commonly used to model the problem given in equation5.17: the Iteration Method and the Band Matrix Method.

Iteration Method - The iteration method starts with a grid with initial values assigned to everynode. The potentials at the �xed nodes (the boundaries) are left unchanged and on the other nodesequation (5.23) is applied. This operation is repeated with the new values, until a prescribedaccuracy is reached. The iteration method makes intensive use of the available computationalmemory of the computer, which makes it only useful for small grids with few calculation points.The method is not suitable for the scoop of this research, because a rather high accuracy of thepressure distribution is desired.

Band Matrix Method - The band matrix method uses the computational memory more ef-�cient to solve the �nite di�erence problem. The method uses a matrix equation which includesthe potential equation of every single grid point. This matrix equation is solved at once and hasfollowing form:

[A] [V ] = [B] (5.27)

1 2 3 4 5 6

7 8...

...

...

...30

Figure 5.13: Example of a course mesh (5x6), with a suction pile with radius 2 and depth 2 (red line).The skirt has to have a width of at least two nodes to be able to model it.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... [V] [B]

1 -1 0 0 V1 -12 0 -1 0 0 V2 -13 0 -1 0 0 V3 -14 0 -1 0 0 V4 05 0 -1 0 0 V5 06 0 -1 0 0 V6 07 1 0 -4 2 1 V7 08 1 1 -4 1 1 V8 09 1 2 -4 0 ... V9 010 1 0 -4 2 V10 011 1 1 -4 1 V11 012 0 0 -4 0 V12 013 1 0 -4 2 V13 014 1 1 -4 ... V14 0... ... ... ... ... ...

Figure 5.14: First part of the band matrix [A] (size: 30x30), belonging to the example of �gure 5.13.The column on the right is the vector with the potentials of the �xed nodes [B]. ([A][V]=[B])

[B], the right side of the matrix equation, is the matrix prescribing the potentials at the �xednodes, while [V ] is the column matrix consisting of the unknown potentials at the free nodes and



[A] is the band matrix. As an example we consider a 6x5 mesh, with a suction pile with a radiusand depth of 3 grid points. The nodes are numbered as shown in �gure 5.13. For every node ofthe grid, a unique equation can be drawn. For example, the potential in node 8 equals the averageof the potentials in node 2, node 7, node 9 and node 14. Or expressed as a formula:

−4V8 + V2 + V7 + V9 + V14 = 0 (5.28)

Node 8 is an example of a normal grid point, without in�uence of any boundary. All other pointswithout in�uence of a boundary are modelled in the same way and are displayed in black in �gure5.14.

The boundaries with �xed potential (Dirichlet boundaries; so the top, right and bottom boundary),are modelled as the green nodes in �gure 5.14. Most of the boundaries have a �xed potential equalto 0, only the nodes on the top boundary inside the suction pile, have a �xed potential of -1.Equation (5.29) and equation (5.30) show the equations for respectively node 2 (top bound) andnode 12 (right bound):

−1V2 = −1 (5.29)

−4V12 = 0 (5.30)

The left boundary and the skirt of the suction pile are modelled as Neumann boundaries (see chap-ter 5.4.4.1), so these nodes require a �xed gradient. Equation (5.26) describes the mathematicalinterpretation of this boundary. For the example given, nodes 7 and 13 are nodes on the left bound(the mirror line of the model), while node 9 and 10 de�ne the suction pile skirt. Equation (5.31)describes what equation (5.26) becomes in the band matrix for node nine. In �gure 5.14 the nodesbelonging to the skirt of the suction pile are marked in blue and the nodes on the mirror line aremarked in red.

−4V9 + 2V8 + 0V10 + V3 + V15 = 0 (5.31)

This way the entire band matrix is build up and by inverting matrix [A] in Matlab, the unknownpotentials for the free nodes can be calculated (=[V]). The results can be plotted for di�erent L/Dratio's and will be used to determine the amount of groundwater �owing in the suction pile.

[V ] = [A]−1

[B] (5.32)

5.4.5. Veri�cation of the numerical model

To evaluate the correctness of the pressure gradient calculated by the numerical model describedin chapter 5.4.3, a comparison is done between the results generated by this numerical model andsome Plaxis calculations for groundwater �ow. Previous investigations in Plaxis [1] resulted in abest-�t equation describing the pore pressure factor as a function of the L/D-ratio (see chapter2.3). This equation is plotted in �gure 5.15 and �ts the results of the Matlab model reasonablywell.



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1

0.2

0.3

0.4

0.5

L/D

Pore

pressure

factor(a)

Junaideen [2004] (equation 2.5)

Result from Plaxis (at skirt)

Result from Matlab (at skirt)

Figure 5.15: The pore pressure factor at the pile tip, as a percentage of the actual pressure di�erencebetween in- and outside the suction pile.

5.5. Erosion-rate model and plug loosening

The total discharge depends on both the discharge through the soil as on the installation velocity(see equation 5.33). These two processes are mutually coupled through the pump characteristics:the (centrifugal) pump delivers a certain head, high enough to install the suction pile, and depend-ing on the pump characteristics a certain discharge will be present. Part of this extracted volumecomes from groundwater �owing in due to the pressure head, and if the total discharged volumeis higher than the volume of extracted groundwater at a certain pressure head (= again pumpcharacteristic), than the pump will extract this extra volume from the area between top plate andsoil bed. This extraction of volume determines the installation velocity :

Q = Qsoil +Qpenetration

⇒ Q = k · i ·A+ vinst ·A (5.33)

This means that, if the soil is too permeable, installation won't occur because all discharge willcome from groundwater �owing in. On the other hand, equationtotaldischargenotscaled showsthat, if the soil is not permeable (like clay), all discharge comes from the penetration term. Thisresults in a maximal installation velocity.

Also the type of pump in�uences the installation velocity of a suction pile. Some centrifugal pumpscan install the suction pile at a constant installation velocity, while other pumps have a decreasinginstallation velocity throughout the installation. As the soil resistance increases with increasingdepth, the pumps of the �rst type can be adjusted in a way that a higher pressure can be reached.This is done by increasing the rounds per minute (rpm) of the centrifugal pump. Some pumps onlypump at a constant rpm, and for these pumps it is not possible to maintain a constant installationspeed. For these pumps the installation speed decreases during installation, because the possibledischarge decreases for increasing pressures.

Depending on the type of pump used, a pump characteristic has to be implemented in the cal-culation model. In installation practice it is always tried to keep a constant installation speedby increasing the rounds per minute of the used centrifugal pump. In case of a pump with aconstant power, the out�ow is tweaked to increase the pressure during installation. This way afairly constant installation velocity is maintained. Because of that, the calculation model uses alsoa constant installation speed. However, it is still possible to include pump characteristics and runthe model with a varying installation speed.



Through the pump characteristics the total discharge of the pump is now determined. This dis-charge is the driving force for the erosion on the bed, as all the discharged water �ows on the bedto the extraction nozzle (in case of a conventional suction pile). The erosion resulting from thishorizontal �ow is modelled below and the results are discussed in chapter 6. Starting from thetotal discharge, which originates from the pump characteristics, the horizontal �ow on the bed canbe calculated. As it is a radial problem, the �ow velocity will be higher in the center of the pile(see �gure 5.16). The formula used to calculate the �ow velocity is:

Qr/R =

(1− r2

R2

)·Q (5.34)

Figure 5.16: The discharge at a speci�c location (r/R) on the bed.

The discharge on the bed divided by the area at a speci�c location on the bed, results in the �owvelocity on the bed at this speci�c location:

Ar/R = 2π · r · xgap

vr/R =Qr/R

Ar/R(5.35)

The �ow velocity on the bed is the driving force of the erosion on the bed. Besides the horizontal�ow, the upward gradient is also included in the model as a driving force for the erosion. Asexplained in chapter 3.2, the upward gradient in�uences the critical velocity at which erosionstarts. The higher the upward gradient, the easier particles will be picked up by the �ow. Assoon as the critical gradient is exceeded, the calculation model will show an unstable bed andparticles will be picked up by the �ow, no matter the height of the horizontal �ow velocity. Theused formulas to calculate the vertical erosion velocity [23] are summarized below and are alreadyexplained in chapter 3:

θ =fo8· u2

∆gDpart(5.36)

θcr = 0.22R−0.6p + 0.06exp

(−17.77R−0.6

p

)(5.37)

θ1cr =

(1 +A

i

∆

)θcr (5.38)



∆

A= icrit (5.39)

φp = 0.00033D0.3∗

(θ − θ1

cr

θ1cr

)1.5

(5.40)

D∗ = Dpart3

√∆g

ν2(5.41)

ve =1

1− n0 − cb

[0.00033D0.3

∗

(θ − θ1

cr

θ1cr

)1.5√g∆Dpart − cbws

](5.42)

The results of the erosion-rate model are shown in chapter 6. As said before, the erosion ratedepends on the �ow velocity on the bed and the upward critical gradient in the plug. Once acertain threshold value is exceeded, erosion will occur and a gap will be formed. The gap causesan enlargement of the cross section of the �ow, which reduces the �ow velocity again. Using thecritical velocity, the shape of the gap can be predicted. In �gure 5.17 the result of such a calculationis shown. Due to the cylindrical shape of the suction pile, the �ow velocities in the center of thesuction pile behave asymptotic, which is in reality not true. The �ow velocity will be loweredbecause in the center of the pile the �ow changes from horizontal to vertical. This will result inturbulent �ow where particles will on one hand �ow out and on the other hand will settle on thebed. Therefore, the prediction of the gap in the center of the suction pile (as in �gure 5.17) is nota realistic representation of reality. However, out of the center, �gure 5.17 can be used to predictthe shape of the gap. The used parameters to get this particular shape, are shown in appendixA.1.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.1

0.2

0.3

0.4

0.5

r/R [-]

Gap[m]

Figure 5.17: The shape of the gap inside a conventional suction pile (D50 = 0.0002)

suc



6 | Results

6.1. Installation resistance and bearing capacity model

To present the results of the installation resistance and bearing capacity model, the calculation isdone for two projects in the Dutch North Sea. Existing projects are used, because this way theresults can be veri�ed using the actual installation data from the �eld. To be able to handle a realproject in the calculation model, the sheet is adapted to be able to analyse a soil with multiplelayers instead of a uniform, homogeneous sand. The installation analysis is done using the CPT-method, as the CPT data are available and reliable in-situ measures for both projects. The partof the code which is changed is added in chapter A.2.

The prediction of the installation pressures is done using Feld's [12] method and the DNV method[10] (chapter 2). The main di�erence between both methods is there approach of the reduction ofthe soil resistance due to the presence of the gradient. The DNV method uses empirical parametersto calculate the reduction, while Feld's method uses a pressure related reduction. The continuouslines in �gure 6.1 show the most probable and the highest expected installation pressures of thetwo projects. The thicker lines are the prediction using the DNV method, while the thinner linesare the pressure predictions according to Feld. The kink in the lines is caused by a change in thesoil properties due to the di�erent layers.

0 100 200 300 400

0

2

4

6


Depth

[m]

Project 1

0 100 200 300 400 500

0

2

4

6

8

10

12


Depth

[m]

Project 2

Feld - Lower boundFeld - Upper boundDNV - Most probable

DNV - Highest expectedCritical suction

Figure 6.1: Calculated pressures for two existing projects. Feld's method is compared with the DNVmethod, the relevant parameters are added in appendix A.2.

It is clear that the upper and lower limit of the suction pressure according to Feld forms a muchsmaller band than the upper and lower bound according to the empirical DNV-method. For the�rst project an initial penetration of about 1 meter is expected, and for the second project an initialpenetration of about 2 meter. For both projects the critical suction is exceeded, which means thatplug loosening is predicted for these two installations.

In engineering practice, the critical suction is not used in the design calculations of a suction pile.However, by introducing the critical suction in the design phase, important information about

Chapter 6. Results 47


the installation and bearing capacity of the pile becomes better predictable and some (simple)adjustments can be made to the suction pile to improve the design. As an example, project 2 isconsidered, and it is assumed that Feld's method gives an accurate prediction of the installationpressures (this is con�rmed in chapter 8). At -10m the prediction-band of Feld's method crossesthe critical suction line for this project, so almost the entire suction installation is possible withoutexceeding the critical suction line. If the critical suction pressure would be used in engineeringpractice, following considerations could be made already during the design phase:

• Lowering the L/D ratio by increasing the diameter or reducing the length. A slight increasein diameter lowers the required suction pressure signi�cantly.

• Adding some ballast weight. If the suction pile is heavier, less suction pressure is expected.

• A combination of both measures.

If it is possible to prevent critical suction, this will highly contribute to the �nal bearing capacity ofthe suction pile. If the plug doesn't loosen during installation, the inner friction is fully mobilizedand less settlements will occur in the load phase. Besides that, the sub-critical situation is alsodesired during installation of the second top plate, as it is expected to get initial bearing capacityof the top plate in this case.

6.2. Erosion-rate model and plug loosening

The erosion-rate model of chapter 5 is used both for a conventional suction pile and a suctionpile with a second top plate. As an example, a calculation is done for both cases, with randomlychosen soil parameters (see appendix A.1) and a randomly chosen L/D-ratio (in this particularcase L/D=1). These parameters are identical for both cases, so that a comparison of the horizontal�ow- and erosion velocity can be made. For both the conventional suction pile and the one withthe second top plate, a depth of L− 0.1m is considered. For this penetration depth, the e�ect ofthe second top on the horizontal �ow velocity on the bed is investigated in �gure 6.2.

0 0.2 0.4 0.6 0.8 10

2 · 10−2

4 · 10−2

r/R [-]

Flowspeed[m/s]

Conventional suction pile

0 0.2 0.4 0.6 0.8 10

5 · 10−3

1 · 10−2

1.5 · 10−2

r/R [-]

Q[m3/s]

0.2 0.4 0.6 0.8 10

2 · 10−2

4 · 10−2

r/R [-]

Suction pile with second top plate

0 0.2 0.4 0.6 0.8 10

5 · 10−3

1 · 10−2

1.5 · 10−2

r/R [-]

Figure 6.2: The horizontal �ow speed and the discharge on the bed for a conventional suction pile andone with a second top plate as in �gure 4.1.

Due to the cylindrical shape of the suction pile, the discharge on the soil bed is not equal at everyspot inside the pile. For a conventional suction pile, the maximum discharge is in the centre, atr/R = 0. Most of the water comes from the outer region of the suction pile, as this is the biggerpart. From �gure 6.2 it is clear that the total discharge of a suction pile with second top plate



is equal to the total discharge of a conventional suction pile. However, because the vertical areabetween top plate and soil increases with increasing radius, the e�ect on the �ow velocity is clearlyvisual: the horizontal �ow speed in the conventional suction pile is signi�cantly higher (it goeseven in an in�nitely high asymptotic speed) than in case of a suction pile with a second top plate.

The horizontal �ow velocity is directly linked to the erosion velocity of the bed. The closer thetop plate approaches the soil, the higher the �ow velocity becomes. The erosion velocity is alsoanalysed for a suction pile with and a suction pile without second top (see �gures 6.3 and 6.4), andthe distance between top plate and soil at the considered moments is 50,10 and 5cm. The ratiobetween the erosion- and the installation velocity is calculated, and it is assumed that as soonas the erosion velocity exceeds the installation velocity, that it is impossible to get initial contactbetween top plate and soil at this location. On �gures 6.3 and 6.4, the erosion- and installationvelocities are plotted against the radius of a suction pile with L/D = 8/8 = 1. The analysis isdone for a densely packed homogeneous soil with a grain diameter of 0.0002m.

For the conventional suction pile it is expected that in the centre of the pile the erosion velocitieswill be high. In case the vertical �ow velocity is high enough to transport the particles upwardout of the suction pile, a gap will grow from the middle of the pile. Breaching will horizontallyincrease the size of the gap, in a way that the entire bed erodes. This process is also shown on�gures 6.3 and �gure 6.4.



0 1 2 3 40

2 · 10−4

4 · 10−4

Radius [m]

Velocity

[m/s]

Erosion velocityInstallation velocity

0 1 2 3 40

2 · 10−4

4 · 10−4

Radius [m]

Velocity

[m/s]


0 1 2 3 40

2 · 10−4

4 · 10−4

Radius [m]

Velocity

[m/s]


Figure 6.3: The erosion- and installation velocity for a conventional suction pile. If the erosion velocityis higher than the installation velocity, a gap will remain.



0 1 2 3 40

2 · 10−4

4 · 10−4

Radius [m]

Velocity

[m/s]


0 1 2 3 40

2 · 10−4

4 · 10−4

Radius [m]

Velocity

[m/s]


0 1 2 3 40

2 · 10−4

4 · 10−4

Radius [m]

Velocity

[m/s]


Figure 6.4: The erosion- and installation velocity for a suction pile with a second top plate. The erosionvelocity is signi�cantly reduced.





7 | Bearing capacity of a second topplate

7.1. General design criteria

The design of the second top plate should become a balance between following requirements:

1. The horizontal �ow in the gap has to be small enough, so that no signi�cant erosion occurs.A small horizontal �ow is achieved by large open spaces in or next to the second top platecompared to the conventional top plate.

2. The design has to be such that no or very little local failure occurs. The second top plateshould approach the bearing capacity of the original top plate as close as possible.

It should be noticed that it is not possible to maximize both requirements at once, because if thebearing capacity is at its maximum, the plate will have a very large surface, which will decreasethe vertical out�ow area and result in higher horizontal �ow velocities. The right balance needs tobe found between a construction with low horizontal �ow velocities and a high bearing capacity.

7.2. Bearing capacity in each construction phase

7.2.1. Installation

In the �rst stage of the installation (see �gure 7.1), the suction pile will penetrate the soil under itsown weight. At a certain depth, equilibrium between the submerged weight and the skin friction+ tip bearing will be reached. During this phase, no suction is applied and water is removed fromthe gap volume inside the suction pile through an opened valve. Because no suction is applied,there is no reduction in friction.

The second phase of the installation is the suction phase. As explained in chapter 2, the suctionreduces the wall friction and the tip bearing (depending on the used calculation method the amountof reduction varies, but the most favourable (Feld) has a reduction depending on the ratio betweenapplied suction pressure and the critical suction pressure). During this phase the applied suctionpressure has to be high enough to overcome the remaining bearing capacity arising from the reducedwall friction and tip resistance(see �gure 7.2). With increasing penetration depth and a constantsuction �ow also the suction pressure increases, until the maximum penetration depth is reached.Generally one can say that three factors determine the maximum penetration depth of a suctioninstallation:

1. The maximum pump capacity is reached. In this case maximum pressure di�erence over thetop plate is reached and further installation becomes physically impossible. Only a pumpwith higher capacity can increase penetration depth in this case.

2. The maximum allowable pressure is reached to prevent the construction from buckling. Thisrestriction prevents failure of the bucket. If this limit is reached during installation, immedi-ately pumping is stopped and maximum possible sucked installation is achieved.

3. The pump starts sucking mud and sediments.

Chapter 7. Bearing capacity of a second top plate 53


For all three cases maximum sucked installation depth is reached and for all three cases a gapbetween top plate and soil level remains present. In terms of bearing capacity this means that thesuction pile foundation draws its strength from the skirt friction and the skirt tip bearing (�gure7.2). Once suction is stopped, there is no more reduction in friction due to the upward �ow, whichmeans that only small additional settlement is required to mobilize the non-reduced skirt frictionand skirt tip bearing. The platform or other permanent load can now be installed.

Figure 7.1: Bearing capacity in equilibrium withsubmerged weigh of the caisson: penetration due

to self-weight.

Figure 7.2: Bearing capacity in equilibrium withsubmerged weight and suction force: suctionassisted penetration. Note that the inner

resistance is reduced compared to the outerresistance.

7.2.2. Load phase

7.2.2.1. Plugged versus unplugged behaviour

Because only sandy soils are considered, one can assume that settlements due to consolidation willbe negligible. Most of the settlements will occur immediately after loading (big waves can causeadditional settlements in a later stage) and will continue until enough soil resistance is mobilized,bringing the load/resistance ratio in equilibrium. Once this equilibrium is reached, it is assumedthat no more settlements occur, unless the load is increased for some reason. O� course this processis limited by the maximum bearing capacity at which failure of the soil will occur.

The behaviour of the suction pile foundation during the load phase is highly depending on theheight of the applied load. As long as the load is smaller than the applied pressure during thesuction phase, the situation of �gure 7.2 remains. Because there is no reduction in friction duringthe loading phase, the skirt friction is higher than during installation phase. This means that theskirt and the tip of the suction pile can carry an even higher load than the maximum appliedsuction pressure.

However, if skirt friction and pile tip bearing aren't su�cient to carry a heavy structure, the suctionpile will settle more, until the situation shown in �gure 7.3 is reached. In this phase the skirt andtip friction are fully mobilized and the top plate touches the soil. On this particular momentthe maximum "unplugged" bearing capacity of the pile is reached. If the load keeps increasing,settlements will gradually continue, while more and more soil resistance will be mobilized (the plugwill compact) and a transition between "unplugged" and "plugged" behaviour takes place. Thiscontinues until the pile behaves fully "plugged" and maximum bearing capacity is reached (see�gure 7.4).



As mentioned above, it is important to consider the amount of settlement needed to get "fullyplugged behaviour". It is of great importance to include a consideration on this topic in everydesign calculation, because if a structure requires the bearing capacity of a fully plugged suctionpile, it is possible that this stage can only be reached after unreasonably high settlements. Alsothe e�ect of "plug loosening" adds its unfavourable contribution to the sti�ness and total bearingcapacity of the soil (see chapter 3.1).

Figure 7.3: Contact between top plate and soil.Pile behaves unplugged.

Figure 7.4: Contact between top plate and soil.Pile behaves plugged.

7.2.2.2. E�ect of plug loosening on the bearing capacity

The plug loosening resulting from the upward seepage �ow during the installation of the suctionpile has following e�ects on the total bearing capacity of the suction pile in the loading phase:

1. In the unplugged loading phase, the density of the plug is less than it initially was. Thismeans that, compared to the outer friction, the inner friction will require a reduction factor(a lower density results in a lower cone resistance (see �gure 5.2), which will results in a lowerskirt friction [10].

2. In the transitional phase, between unplugged and plugged behaviour, the lower density resultsin a lower initial top plate bearing [10]. This means that in order to get fully pluggedbehaviour (or maximum bearing capacity), more settlement will be required compared witha calculation based on the original CPT values.

These e�ects of plug loosening should be taken into account in the calculations of the bearingcapacity of a suction pile and will a�ect the design of the second top plate.

7.3. Second top plate

7.3.1. Di�erent designs

As mentioned in Chapter 7.1, the second top plate has to be designed in a way that a balance isachieved between erosion rate and bearing capacity. This means that every possible design needsto be analysed �rst with the Erosion-rate model described above. The con�guration of the secondtop plate should be chosen such that the horizontal �ow velocity on the sea bed is low enough,



and erosion velocities are below the critical limit. Note that this is theoretically not possible, asthere will always be an erosion situation just before the top plate touches the soil. For the secondtop plate as designed above, the remaining gap is not bigger than 1 cm, so this is assumed to benegligible, compared to the relief of the seabed. Once this �rst requirement is met, the bearingcapacity can be analysed.

First of all one needs to determine the amount of force carried by the second top plate. Thesoil resistance mobilized by skirt friction and the resistance mobilized by top plate bearing aren'tmobilized the same way. Skirt friction only needs little settlements to get mobilized, while full topplate bearing requires more settlement. Because of this, and because the total bearing capacity ofa suction pile is a combination of skirt friction and top plate bearing, some assumptions are madeto be able to model the second top plate:

1. Under pure axial loading, whether compressive or tensile, the caisson may either behave asa plugged or a coring foundation. For compressive loading, the axial resistance is the lowervalue of �gure 7.3 and �gure 7.4 [27]. In general, suction piles with high L/D ratios behaveplugged way before the top plate touches the soil. For these cases, the design of the top platedoesn't really matter, because it has no e�ect on the total bearing capacity of the pile. Pileswith low L/D ratio however, will need a signi�cant contribution of the top plate before fullyplugged behaviour will occur. In this chapter is assumed that the considered pile has a lowL/D ratio, in a way that plugged behaviour can only occur once the (second) top plate hasmobilized su�cient soil inside the pile. This is an essential assumption, because if pluggedbehaviour occurs before contact between soil and top plate, the presence of the gap doesn'tin�uence the bearing capacity. If this assumption is met, and L/D is low enough such thatthe pile still behaves unplugged at initial contact between top plate and soil, than the designof the (second) top plate starts to matter.

2. All skirt friction is mobilized before top plate bearing comes in. This is a simpli�cation,because the settlement required to mobilize top plate bearing will activate an extra piece ofskirt. However, this assumption is a good approximation, as this extra piece of skirt frictionis signi�cantly small compared to the entire skirt (see �gure 7.5: once the top plate touchesthe soil, all skirt friction is mobilized and extra bearing capacity comes from the top plate).

3. The plug loosening inside the suction model is assumed to be uniform over the entire depth.This means that the permeability and relative density inside the suction pile are modelledas constant values.

4. The second top plate is designed in a way that it touches the soil the moment installationstops. This can be achieved using the Erosion-Rate model. For this item the same remarkas above is valid: theoretically contact is not possible, as horizontal �ows will be too highin an in�nitely small gap, but the size of this gap is negligible compared to the relief on theseabed.

Assuming that these assumptions are good approximations of reality, following reasoning is valid.

At the end of the suction installation, the second top plate touches the soil. Suction is stoppedand the load due to the top structure starts working on the foundation. If the weight of the topstructure is less than the applied suction pressure, the skirt friction will be su�cient to carry theload, without any extra settlements. Once the load exceeds the suction pressure, small settlementswill occur until the skirt friction is fully activated (see �gure 7.5). The load needed to bring thepile in this "unplugged" state, is called F1 and equals:

F1 = Fi + Fo +Qtip (7.1)

where Fi is the inner friction, Fo the outer friction and Qtip the tip end bearing. Any additionalload will result in more settlements and will activate the second top plate, until fully plugged



behaviour is reached and the bearing capacity is at its maximum. The load required to achievefully plugged behaviour is called F2 and equals:

F2 = Fo + Fplate (7.2)

where Fplate is the bearing capacity of a plate at pile tip level. Both F1 and F2 can be predictedusing conventional methods for pile design [10]. Now the di�erence between plugged (F1) and un-plugged (F2) behaviour is the force which needs to be mobilized by the second top plate (called F3).Depending on the design of this second top plate, a certain amount of settlement will occur beforethe required soil resistance is activated. The designing challenge is now to �nd a con�guration ofthis additional top plate, which encounters the least settlements once loaded with F3.

Figure 7.5: Soil resistance in case of acompressible plug (unplugged behaviour).

Settlement of the anchor is required before thepile will behave plugged.

Figure 7.6: Soil resistance in case of anon-compressible plug. The pile, with second top

plate, behaves fully plugged (which is thesituation with maximum bearing capacity for a

suction pile).

7.3.2. Numerical investigation

Any �nite element program can be used to calculate the load/settlement curves of di�erent topplate designs (ex. Plaxis). The calculation should be done "displacement-controlled", which meansthat for di�erent foundation designs a gradual increase in displacement is de�ned, resulting in aresistance force which increases with increasing depth. This way, di�erent possible top plate designscan be compared on their bearing capacity (see �gure 7.7 for an example).

It is advised to use a numerical investigation to do this calculation, as the complexity of thefoundation layout doesn't allow to solve this problem analytically. The radial e�ect and thein�uence of a skirt can easily be modelled in a �nite element model as Plaxis. Besides that,the calculation is meant as a comparison between di�erent possibilities. A �nite element programallows to keep all boundary conditions as a constant (same soil type, same size of suction pile,same loading rate...) and change only the layout of the foundation. This way the single relevantparameter, the geometry of the foundation, can be isolated and compared.



Figure 7.7: The design of the second top plate is variable. It is important to make a con�gurationwhich mobilizes the entire plug with as little settlement as possible.



8 | Veri�cation

8.1. Physical model

8.1.1. Introduction

The physical model described in this chapter will be used as a proof of concept of the theoriesexplained in this thesis. It is too expensive to test the second top plate in an unscaled experiment,so a small scale physical model test is developed. The physical model is a simpli�cation of realityand will not be used to measure all details used in the calculation model, but it will only be usedto get more insight and understanding in the following statements:

1. Initial top plate bearing is not likely to occur in case of a conventional suction pile design(see chapter 3).

2. Plug loosening only occurs in case of suction pressures above the so-called critical suctionpressure (theory formulated in chapter 3).

3. For installation below the critical suction pressure, initial bearing capacity of a second topplate is feasible (see chapter 6).

4. For installation above the critical suction pressure, the entire plug lique�es and subsidenceof the plug results in a gap (see chapter 6).

If a relatively easy test set-up shows that it is possible to get initial contact between second topplate and soil, with a substantial contribution to the bearing capacity of the suction pile, this canbe used to convince possible clients to test this new type of suction pile foundation on a largerscale.

According to D. Muir Wood [28], the skill in modelling is to spot the appropriate level of simpli�-cation and to recognise those features which are important and those which are unimportant. Thephysical model is designed to advance the con�dence in the theoretical model and to become awareof possibly neglected important processes. In that perspective one can see it as a re�ection orveri�cation of the predictions and hypotheses made in the theoretical model. When modelling ata certain scale, scale factors have to be applied in order to get a realistic picture of what happensin reality.

It is chosen to work with a relatively large model (scale 1:15) at earth's normal gravitationalacceleration (1g) and not in a geotechnical centrifuge, like other researchers did [2]. As shown insection 8.1.3, a geotechnical centrifuge and prototype soil stresses are not required to be able tomodel the considered processes correctly.

In order to avoid confusion, the scaled model is referred to as the "model" and the real suctionpile modelled by the model is referred to as the "prototype".

8.1.2. General

The theoretical analysis concluded that the installations of suction piles should be divided in twogroups: installation below and above the critical pressure. Because of this, the test set-up will betwofold: once with pressures above and once below the critical suction pressure (by adding moreself-weight). For both set-ups, the test will be done once with and once without a second top plate.

Chapter 8. Veri�cation 59


For both models the suction pressure versus the installation depth will be measured. The pressure- settlement curves resulting from these measurements will be used to con�rm or refute what ispredicted by the calculation model.

For the model tests with installation pressures below the critical pressure, the calculation modelpredicts that it is not possible for a conventional suction pile to get initial contact with the soil,because the erosion velocity will be too high. However, it is expected that a second top plate couldsolve this problem and that the suction pressures will increase signi�cantly once the second topplate touches the soil. At that moment the suction �ow Q is no longer a result of Qpenetration +Qsoil, in which Qpenetration is the discharge due to the installation velocity of the anchor, but onlyof Qsoil. This means that there must be a signi�cant increase in pressure. This should be visiblein the measurements of the installation pressures. As the critical gradient won't be exceeded, nosigni�cant plug heave will occur. This means that a gap due to subsidence of the soil plug is notto be expected.

For the model tests with installation pressures above the critical pressure, the calculation modelof this thesis can't be used. With an entirely lique�ed bed, erosion is not the measuring processcausing the gap between top plate and soil, but subsidence of the plug will occur once the pressuredrops. It is expected that in this case, the second top plate will "sink" in the lique�ed soil. Becausethe second top plate hinders the upward �ow, the �ow lines change direction and as the soil get"squeezed" underneath the second top plate, e�ective stress can mount up from the center of thesuction pile (see �gure 4.7).

The chosen test set-up, as shown in appendix B, gives no information about the bearing capacityof an installed pile, neither about the amount of erosion or the erosion velocity, because theseprocesses can be analysed, modelled and veri�ed by existing numerical models (Plaxis) or testsperformed by other researchers [23]. The test is only meant as a proof of concept, which makes ituseful and manageable in the context of this thesis.

The tests are performed at the geotechnical laboratories of the Technical University Delft in asand-�lled container. This test location is chosen because here a relatively large scaled model canbe built (the container has an inner diameter of 1900mm) and because the container is equippedwith a water in- and outlet. A sketch of the test set-up is provided in appendix B. The modelsare made of Perspex, so that there can be looked through the top plate and that it can be visuallyveri�ed if the predicted processes do occur.

A geotechnical model at 1g has certain limitations. The interpretation of such a small scalemodel strongly depends on the understanding of the relevant scaling laws. The in�uence of scalingon processes as seepage, erosion, soil stresses etc. has to be investigated before any meaningfulconclusions can be drawn from the model tests.

8.1.3. Scaling laws at earth's normal gravitational acceleration (1g) [22]

In order to investigate the di�erent relevant processes in the scaled model, some assumptions aremade. The model will be built at length scale nL (this means that the model is at scale 1 : nL).For the sand and the water of the model, the same material will be used as in the prototype. Withthese assumptions in mind, following scaling laws are valid:

Groundwater �ow (chapter 2.3)

q = k · i⇒ nq = nk · ni (8.1)



with

i =∆H

∆LnH = nL

⇒ ni =nHnL

⇒ ni =nLnL

⇒ ni = 1 (8.2)

and

nk = 1

⇒ nq = 1 (8.3)

The groundwater �ow depends on the applied gradient and on the permeability of the soil. Asmentioned above, the same sand is used in both model as prototype, which means that the per-meability doesn't scale. If the applied pressure head is at length scale, this means (according toequation 8.1) that the groundwater �ow (q, [m/s]) in both model and prototype is the same.

Erosion (chapter 3)

Q =1

4· π ·D2 · vinst + k · i ·A

⇒ nQ = n2L · nvinst

+ nk · ni · n2L

⇒ nQ = n2L · nvinst

+ 1 · 1 · n2L (8.4)

In wich vinst is the penetration velocity of the suction pile.

The total discharge of the pump depends on both the discharge through the soil and the installationvelocity (see equations 5.33 and 8.4). As explained in chapter 5.5, the discharge is linked with thepressure trough the pump characteristics. To scale this to a model test, a pump system has to bedesigned which is similar to what happens in reality. The installation velocity of the suction pileshould scale 1:1, otherwise the total discharge doesn't scale in an exact way (both terms of thesum in equation 8.4 should have the same scale). With the installation velocity at scale 1:1, thetotal discharge is at scale n2

L (equation 8.5). This means that now, the required discharge for themodel test is known and based on that the pump characteristics should be chosen in a way thatnot only the discharge but also the pressure scales in a correct way.

nvinst = 1

⇒ nQ = n2L (8.5)

With a test set up as in �gure 8.1 , where gravity is used to generate the required pressuredi�erence, the "pump characteristics" are determined by the �ow resistance of the tubes and theout�ow resistance of the nozzle. The curves of �gure 8.3 describe the relation between the pressureand the discharge for a certain tube-nozzle con�guration. By tweaking the out�ow-resistance,the factor α will change and the preferable curve can be approached. Depending on the requiredpressure and discharge (taking into account the scaling laws), an α-value for the model test canbe set. By decreasing the out�ow resistance during installation (ex. with a tap), α decreases andthe curve evolves from steep to shallow (from 1 to 3 in �gure 8.3). This way the pressure inside



Figure 8.1: Gravity controlled test set-up. Theout�ow nozzle can be tweaked.

Figure 8.2: Test set-up with a centrifugal pump.The out�ow nozzle can be tweaked.

the suction pile increases, while a relatively constant discharge (and so installation speed) can bemaintained without having to change the hydraulic head during the model test.

In case a pump (with constant rpm) is used, a similar graph as �gure 8.3 is valid. The pump systemwill have certain characteristics, resulting in a decreasing discharge with increasing pressure. Theout�ow nozzle of the pump system could also be tweaked to change the pump characteristics and tomaintain a relatively constant discharge (exactly as explained for the gravity based pump system,see �gures 8.1 and 8.2).

Based on the installation velocity, the scaling of the horizontal velocity can be determined. Ac-cording to equation 8.6, the horizontal velocity scales in the same way as the installation velocity,which means the scale factor is also 1:

Figure 8.3: Pressure characteristics of a gravitation driven pump system.



vhor =Q

π · r · d

⇒ vhor =14 · π ·D

2 · vinstπ · r · d

nvhor=

n2L · nvinst

n2L

⇒ nvhor= nvinst

(8.6)

With the installation velocity and the horizontal �ow velocity scaling in the same way, it shouldbe practical if the erosion velocity would also scale the same. Because the test set-up makes useof the same type of sand (nD50

= 1,nv = 1,n∆ = 1 and nD = 1) and because the test is conductedat 1g (ng = 1), the following is valid:

ve =1

1− n0 − cb

[0.00033D0.3

∗

(θ − θcrθcr

)1.5√g∆D − cbws

]

⇒ nve = n0.3D∗ · (ng · n∆ · nD) 0.5 + nws

with

D∗ = D50 ·(

∆ · gν2

)1/3

(8.7)

The settling velocity ws depends on the densities of �uid and particle, the radius of the particle,the gravitational acceleration and the dynamic viscosity of the �uid. All these parameters don'tscale in this physical model, so:

nws = 1

⇒ nve =

(nD50

·(ng · n∆

n2ν

)1/3)0.3

· (ng · n∆ · nD) 0.5

⇒ nve = 1 (8.8)

Which means that the erosion velocity and the horizontal �ow velocity scale in exactly the sameway [22].

E�ective stress (chapter 2)

σ′ = ρ · g · h⇒ nσ′ = nρ · ng · nh

with

nh = nL

nρ = 1

ng = 1

⇒ nσ′ = 1 · 1 · nL⇒ nσ′ = nL (8.9)



Assuming the model and the prototype are installed in the same soil, the e�ective stress is onlength scale, as it depends on the height of the soil column (see equation 8.9). The e�ective stressis needed to calculate the skirt friction of the suction pile.

Skirt friction (chapter 2)

τ = σ′ · tan(δ)

with

nδ = 1

⇒ nτ = nσ′ · 1⇒ nτ = nL (8.10)

Based on equation 8.10, the skirt friction scales the same as the e�ective stress. This is true sinceδ is dependent on the angle of internal friction φ, which is a constant for a given homogeneous soil.With the same soil in both prototype and model, the skirt friction scales on length scale.

Tip resistance (chapter 2)

The tip resistance can be predicted according to the formula of Brinch Hansen. Because a sandysoil is considered, the cohesion term can be ignored. This means that the "load term" and the"unit weight" term remain. The load term q consists of three di�erent terms, namely the unitweight of the surrounding soil, the resultant of the skirt friction and the excess pore pressure dueto the applied suction. The "unit weight" term consists of the soil density and the thickness of theskirt. In terms of scaling, this means:

p = c ·Nc + q ·Nq +1

2ρ · g · t ·Nγ (8.11)

With

Nq =1 + sinϕ

1− sinϕ· exp(π · tanϕ)

Nc = (Nq − 1) · cotϕNγ = 2 · (Nq − 1) · tanϕ

⇒ Nq,c,γ = 1

q = qe + qf + q∆p (8.12)

And

qe = ρ · g · h⇒ nqe = nρ · ng · nL⇒ nqe = nL

qf =FinA

=τs ·AsAs

⇒ nqf = nτs

⇒ nqf = nL

q∆p =1

2∆p

⇒ nq∆p = n∆p

⇒ nq∆p = nL

nq = nqe = nqf = nq∆p

⇒ nq = nL (8.13)



Now, with equations 8.12 and 8.13 combined in 8.11, this results in:

c = 0

⇒ p = q ·Nq +1

2ρ · g · t ·Nγ

⇒ np = nq = nρgt = nL (8.14)

Which means that also the tip resistance scales on length scale. Together with the skirt friction(also on length scale) this would mean that the soil resistance scales on length scale. However, thisis in contradiction with a CPT-based approach to calculate the soil resistance. The calculationmodel in this thesis uses a CPT-based approach, and as mentioned in �gure 5.3, the cone resistancedoesn't increase linearly with depth. This would mean that, if the soil resistance is calculated usingthis CPT-values, that a scaled pile will experience a relatively higher soil resistance compared tothe prototype. This nonlinearity can't be concluded from equations 8.11 and 8.10. In section 8.1.4this inconsistency is examined.

Time

t =L

v

⇒ nt =nLnv

⇒ nt = nL (8.15)

According to equation 8.15, the time scales on length scale as well. This means that if the modelgeometry is for example 10 times smaller than the prototype geometry, the installation will last afactor 10 shorter (which makes sense, because the speed doesn't scale). In table 8.1 all relevantparameters are summarized with their scaling factor.

Table 8.1: Summary of the scaling factors

Parameter Symbol Scale factor

Gradient i 1

Permeability k 1

Groundwater �ow q 1

Discharge Q n2L

Installation velocity vinst 1

Flow velocity vhor 1

Erosion velocity ve 1

E�ective stress σ′ nL

Skirt friction τ nL

Tip resistance p nL

Time t nL

8.1.4. Scaling e�ects

From table 8.1 it can be concluded that the scaling of the installation and erosion problem is ratherstraightforward. All velocities seem to scale in the same way and resistance-related terms are allon length scale. However, care should be taken regarding possible scaling e�ects that in�uence theresult of the model test. In this section possible scaling e�ects are summarized, so that their e�ecton the result can be taken into account in the interpretation phase of the model test.



A �rst scaling e�ect is the non-linearity of the cone resistance over depth. This e�ect is alreadymentioned above. It seems to be a contradiction that the skirt friction and the tip resistance scalelinearly, while the cone resistance of a homogeneous soil is not linear over depth. The predictionmethod of suction pile foundations is based on the cone resistance, which means that if a resistanceprediction is calculated for the prototype and the model, the scaling is not so straightforward asassumed in table 8.1.

This scaling e�ect can be explained because the CPT-approach is an empirical method. Theprediction of the cone resistance for a certain relative density is based on experience and takes alsoe�ects as compressibility of the grains into account. The theoretical formula for the tip resistance(Brinch Hansen) uses only parameters as e�ective stress and relative density of the soil. However,according to Lunne [15] the compressibility of the grains for example, can make a di�erence in coneresistance up to 200% for soils with low relative density. For sand with a higher relative densitythe e�ect of the compressibility is smaller, but still present. The cone resistance can be seen as atest load of the soil, and the results of such an in situ test are probably closer to reality than thetheoretical Brinch Hansen approach. Besides that, a CPT should have a certain depth in orderto avoid any in�uence of the so called "border e�ect": the entire shape of the failure mechanism(Prandtl 3D) should be inside the soil, which starts only at a certain depth. Nevertheless, if theawareness of this scaling e�ect is present, this can be taken into account once the test is interpreted.

A second scaling e�ect to take into account is the grain size compared to the gap between topplate and soil. The calculation model predicts erosion in case the top plate comes close to the soil.However, the gap scales on length scale, while the grain size in the model and the prototype isthe same. This means that if theoretically erosion is predicted at a gap of 2cm in the prototype,this is only 2mm in the model. This means that just a few grains are needed to close the gap andprevent further erosion.

Thirdly, the closed walls of the test tank will have their in�uence on the pressure distribution insidethe suction pile model. A prototype is installed in an in�netely open space, but the tank has alimited size. For the scaling of the geometry, this in�uence will be measuring and the size of thetank will determine the maximum size of the suction pile model. A maximum deviation of 10%of the pressure distribution inside the suction pile compared to an installation in an in�nitely bigtank is tolerated, as a zero tolerance would result in an even smaller model, which would enlargeother scaling e�ects.

Finally there is also a scaling e�ect in the roughness of the skirt, which is di�erent compared to theroughness in reality (because the grains are relatively bigger and the wall is relatively smoothercompared to the prototype). Because water will always take the route with the least resistance,this could result in piping close to the suction pile skirt in the model test.



8.1.5. The suction pile model

Now the scaling laws for this speci�c problem are known, it is time to determine the length scalenL of the model. It is preferable to make the model as big as possible, because with a biggermodel the scaling e�ects are minimal. This makes the size of the tank the limiting factor, becausethe wall of the tank should not in�uence the experiment which is conducted inside the tank. Thewall of the tank forms a closed bound, while in reality a suction pile is installed in an in�nite soilmass, which means that the boundaries in reality are open. The closed bound in the tank willmainly in�uence the pressure distribution due to the applied suction, so that's why this e�ect isinvestigated (see �gures 8.5 and 8.4).

10 20 30 40 50 60 70

20

40

60

0

0.2

0.4

0.6

0.8

10 20 30 40 50 60

20

40

60

0

0.2

0.4

0.6

0.8

5 10 15 20 25

20

40

60

0

0.2

0.4

0.6

0.8

Figure 8.4: Pressure distribution for di�erent Rsp/Rt ratio's. The picture in the middle represents thesituation of the model test (Rsp/Rt = 0.33). The top �gure has an Rsp/Rt-ratio of 0.2 while the bottom

one has a ratio of 0.8.

First the pressure distribution is calculated for a suction pile with a radius of 4m with an openboundary (�xed gradient, Dirichlet). In �gure 8.5 this line is plotted in red and called "open



0 2 4 6 8 10 12 14 16 18 20 22 240

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Radius of the tank (= Rt [m])

Pressure

headatpiletiplevel[%

ofapplied

pressure] r/R = 0.80

r/R = 0.66

r/R = 0.57

r/R = 0.50

r/R = 0.44

r/R = 0.40

r/R = 0.36

r/R = 0.33

r/R = 0.31

r/R = 0.29

r/R = 0.27Open bound

10%-line

Radius of the suction pile (Rsp)

Figure 8.5: Required distance of the boundary to minimize its in�uence on the model test.

bound"'. The curves indicate the pressures at pile tip level in a range from the center of the pileto the boundary of the computer model. The "Open bound"-line shows the pressure distributionwhich is most similar to the pressure distribution in reality. The other lines plotted in this �gureshow pressure distributions for a model with a closed bound (no �ow, Neumann). The di�erencebetween these lines is their Rsp/Rt-ratio. The top line has the highest ratio, which means that theradius of the suction pile (Rsp) is large compared to the radius of the tank (Rt).

It is clear that for small Rsp/Rt-ratio's the best approach of the prototype's pressure distribution isfound. However, it is preferable to have a large model to minimize other scaling e�ects, so on thispoint some concession is made. The dashed line di�ers 10% from the "Open bound"-line and ischosen to be the upper limit for the deviation of the model compared to the prototype. A deviationof 10% is acceptable because this di�erence can be taken into account during interpretation of themodel test.

Because mainly the pressure at pile tip level inside the suction pile is important, an Rsp/Rt-ratio ischosen below this upper bound: Rsp/Rt = 0.33, which is the black thick line on �gure 8.5. Becausethe tank has a radius of 90cm, the model will have a radius of 30cm. If the prototype has a radiusof 3m, this means the model is at length scale 1 : 10. Technical drawings of the model are includedin appendix B.

In �gure 8.4, the same principle as in �gure 8.5 is shown: the chosen radius of the suction pilemodel (the picture in the middle) is compared to a bigger and a smaller model. It is clear thatthe in�uence of the boundary on the pressure distribution is huge in case of bigger Rsp/Rt- ratio's(the �gures are radial symmetric, with the left side of the �gures is the center of the suction pile,the white line shows the skirt and the right side is modelled as a closed boundary, exactly as inthe tank which will be used for the model test).



8.1.6. The tank

The tank in the geotechnical laboratory of the TUDelft has a diameter of 1900mm and an e�ectiveheight of 2300mm (see �gure 8.6). The tank is �lled with sand. In its most loosely packed state,the height of the sand packet is around 1900mm, which results in a height of the water (Zw) of40mm. The tank is equipped with two vibrators, which can be used to vibrate the entire tank.This vibration results in a higher density and so a decrease in volume of the sand in the tank.

Figure 8.6: A sketch of the tank which is used for the model. A technical drawing is included inappendix B

The tank has an in�ow and an over�ow at the top and an out�ow at the bottom. This designallows to �ll the tank from the top, or with a �uidisation system at the bottom of the tank. Thisway an up- and downward �ow can be generated. The �uidisation system is used to bring the sandin its loosest state. This is done before each test to get equal boundary conditions for all di�erenttests. During the test itself, the �uidisation system isn't used. To maintain a constant water levelduring suction, a water in�ow at the top of the tank makes sure that the over�ow is permanentlyworking.

8.1.7. The sand

8.1.7.1. Initial boundary conditions

All tests have been conducted on one single type of uniformly distributed �ne sand. For this sand,two sieve curves are made. One with sand taken from the surface of the tank, and one with sandtaken from a greater depth. This because the tank has been �uidized several times, so all the �nesare transported to the surface of the tank. In �gure 8.7 both curves are shown, and it is clear thatthe top layer of the sand contains more �nes than the rest of the tank. It is assumed that thistop layer is relatively thin compared to the rest of the tank, so a D50 of 0.25mm is used in thecalculations. In order to calculate the permeability, the D10 of the soil is relevant, because mainlythe smaller particles in�uence the groundwater �ow. A. Hazen [17] proposed following empiricalequation, which is used as a rough estimation for the permeability of the sand in the tank:



k = 100 ·D210 (8.16)

With D10 is the grain size in cm and k the permeability coe�cient in cm/sec. D10 equals 0.018cm(see �gure 8.7), so the �rst estimation of the permeability is 3.24 · 10−4 [m/s]. It should be clearthat this is a rough estimation, as the permeability is not solely related to grain size but also tofactors as grain distribution, density, etc. This formula is only used to verify the order of magnitudewhich is measured with the falling head test through the tank.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.2

0.4

0.6

0.8

1

Sieve size [mm]

Percentagepassed

through[-]

Sample at higher depthSample at the surface

Figure 8.7: Sieve curves of the soil inside the model test tank.

Broere [6] did several tests in the same tank to determine the relative density in relation with thevibration time. To do so, he measured the e�ective reduction in volume of the sand inside the tank,for di�erent periods of vibration. As an example: for the sand used by Broere, the initial relativedensity (in the loosest state) was 0.182. 30 seconds of vibrations resulted in a relative density of0.311. With this increase in relative density in mind, it is expected that the soil resistance fora suction pile installation in "30 seconds vibrated sand" should be signi�cantly higher than foran installation in not vibrated sand. However, �gure 8.8 shows more or less the opposite. Thevibrated tests results in less soil resistance than the test conducted on not vibrated sand.

0 2 4 6 8 10

0

0.1

0.2

0.3

0.4

0.5


Penetrationdepth

[m]

test 1 - 0s vibratedtest 2 - 30s vibrated

Figure 8.8: The suction pressures for two model tests in a sand bed prepared with two di�erentvibration periods.

The compaction of sand requires out�ow of water, and because the vibrating is done with a closedout�ow at the bottom of the tank, the water should �ow upward to leave the pores (which is



necessary to get volume reduction). This means that, as long as the bottom layer in the tankisn't fully compacted yet, water will �ow upward trough the soil, resulting in a lique�ed bed. Thevolume will decrease, but compaction will initially start at the bottom of the tank. A measurementof the total volume of soil inside the tank gives than a measure of the average density of the soil.However, for the tests performed in the context of this thesis, it is not useful to know the averagerelative density inside the tank, but it should be possible to densify the top layer (as the experimenthappens in this speci�c part). A simple groundwater �ow calculation is executed to estimate therequired vibrating time to get compaction at the top of the tank.

According to van der Schrieck, [22], the maximum porosity of a typical Dutch sand with D50 equalto 0.25mm can be estimated at 43% (see �gure 8.9). This porosity is present at the loosest state ofthe sand. The minimum porosity, at the most dense packing of the sand, is about 34%. As the soilis assumed to be completely saturated, this means that 9% of the total volume should �ow out toget it in the densest state. Because it is not likely to get the entire tank in its densest state (Broere[6] reached a maximum relative density of 0.80), it is assumed that 7% of the volume should �owout.

Figure 8.9: Permeability k as a function of porosity n for several Dutch sand types [22].

Not only the porosity, but also the permeability can be estimated from �gure 8.9. In its looseststate, the permeability should be around 5.5 · 10−4. Assuming that the compaction starts in asmall layer at the bottom of the tank and that the grains slowly settle to end up in a denser state,this could be seen as a progressive phenomenon of a settlement-front going upward in the tank. Itis assumed that the soil above this settlement-front has during the entire process a permeabilityequal to the initial permeability. Once the settlement-front reaches the top of the tank, the entiretank is compacted. The system is driven by the gradient due to the excess pore pressure:

ρs − ρwρw

≈ 1 (8.17)

And the out�ow discharge is calculated using Darcy's law q = ki. With i = 1 the �ow q becomesequal to k, which is for this soil 5.5 · 10−4[m/s]. The total discharge is equal to q ·A, the height ofthe soil plug is initially 1.85m and the time required for the settlement front to reach the top ofthe tank is now calculated as follows:

Vwater = h · r2 · π · 0.07

= 0.367[m3]

= t · q ·A⇒ t = 4min (8.18)



So a continuous vibration should last around 4 min to densify the entire tank. It is expected thatthe end of compaction should be visual at the soil bed: during compaction the bed is expected tobe lique�ed, a process that should stop once the grains at the bed are settled in their denser state.It should be noted that this calculation is just a rough estimation to get an idea of the requiredvibration time. The calculation indicates the minimal required vibration time to get a 7% volumereduction of the soil volume. The weakness of this method is that it is not exactly known what thedensity of the sand at the bottom will be. If the sand gets in a denser state than expected, morewater will have to �ow up and it will probably last longer before the top of the tank will reach it'srequired density.

8.1.7.2. In situ veri�cation of the assumed soil parameters

The permeability is in the above calculations estimated from the grain size and �gure 8.9. Toverify this estimation with a simple check, the time needed to lower the water level in the tank tobed-level is measured. This "falling-head" test is done before and after compacting the sand andthe resulting permeability is compared to the values estimated above.

The driving force for this downward groundwater �ow is the gradient between the top and thebottom of the tank, which decreases as the water level of the tank lowers. The lowering of thewater table in time is measured and Darcy is used again to get the permeability:

q =Vwater

A

t

k =q

i(8.19)

This is done for small time intervals. For every interval, the time, the lost volume and the gradientis calculated, resulting in a value for the permeability for every interval. This values should be thesame for every interval, so the mean value is taken to get the overall permeability of the tank (seeappendix C). The result of this calculation is shown in table 8.2. The calculation is done for thecompacted and the not-compacted soil and compared with the values estimated from �gure 8.9and equation 8.16.

Table 8.2: Permeability of the soil inside the tank (D50 is 0.25mm, D10 is 0.18mm).

Method Not compacted Compacted

Reference Sand Types (Figure 8.9) 5.5 · 10−4 1.5 · 10−4

Hazen Formula (Equation 8.16) 3.24 · 10−4 3.24 · 10−4

Falling Head Test (Equation 8.19) 2.0 · 10−4 1.2 · 10−4

It should be noted that the in situ measurement of the permeability of the not compacted sandis signi�cantly lower than estimated. This could be explained because the water on the soil bedcontained lots of �ne particles during the measurement (which was not the case for the test in thecompacted sand). During the test the water �ows through the sand in the tank. Fine particlessettle on the soil bed and a �lter cake of �ne material is formed which is less permeable than therest of the soil. Because of this phenomenon, only the measurement of the �rst two intervals areused, as the cake is not fully present at this moment. With only one measurement, this valueshould be treated with care. For the compacted sand, the value (1.2 · 10−4) is a lot more reliable,as all 7 intervals showed about the same value.

From table 8.2 and 8.9 it is concluded that the soil was in a very dense state after 8 minutes ofvibrating (assumed: Dr = 0.80), as the combination of the measured permeability (1.2 · 10−4) andthe 0.25mm line on the graph result in a porosity close to the minimal porosity of the referencesoil. For the loosest state the measured permeability is not reliable, but due to the test procedure(the tank is always lique�ed before each test), it is expected that the porosity will be close to themaximum porosity of the soil (assumed: Dr = 0.20).



The strength parameters Because the availability of the geotechnical laboratory is limited, itis not possible to perform an extensive soil investigation to determine the exact angle of internalfriction and relative density for each test. It is also not possible to do CPT-tests inside the tank,so basically the information about the soil is limited. These preconditions lead to some creativesolutions to get a feeling for the desired input parameters of the calculation model. It is alreadydescribed above how the relative density of the soil is estimated using an empirical graph and afalling head test. The strength of the soil is now estimated with a self-made CPT-like device: thepenetration depth of a certain weight on a pile with a diameter of 24.5mm is measured. In �gure8.10, a result of this test is shown for the suction pile installation in dense sand.

0 0.5 1 1.5 2 2.5 3

0

0.1

0.2

0.3

0.4

0.5

Bearing Capacity [MPa]

Depth

[m]

Before installationAfter installation

Figure 8.10: The reduction in relative density (and so in bearing capacity) of the soil plug, due to plugloosening.

The measurement is done, inside the suction pile, before and after installation of the pile, to con�rmif the dense soil plug loosened during installation. It is clear that the bearing capacity of the soildecreases signi�cantly during installation, which means that the critical gradient is exceeded andplug loosening was clearly the case. The measurement is done in the center of the pile and closeto the skirt to verify if the entire plug loosens and not only locally at the skirt. Both penetrationtests had exactly the same result and showed an equal reduction in relative density over the entireplug. These measurements are not very accurate and only meant to give an idea of what happens.In chapter 9.2, a recommendation is included to improve this part for further research.

8.1.8. Test results

8.1.8.1. Low relative density

Repeated tests in loose sand are performed. A low relative density is used to be sure that theinstallation pressures are below the critical suction pressure. This is necessary because erosion istested and a stable bed is required to verify if the gap is formed as predicted by the erosion-ratemodel.

Erosion of the bed: Part of the test set-up was to test if the behaviour of a conventional suctionpile without a second top plate was as it is expected to be. In engineering practice a gap remainsbetween top plate and soil, so the �rst tests are executed to see if this is also the case for the scaled



model. At �rst stage the tests are executed without any measuring sensors, as the presence of thegap can be veri�ed by lifting up the top plate after installation.

The gap is, theoretically, a result of erosion of the bed (for suction pressures below critical suction).Depending on the installation velocity of the suction pile and the permeability of the soil, thedischarge changes. A higher discharge means higher �ow velocities on the bed and this results inhigher erosion velocities. In chapter 8.1.3 is shown that the erosion velocity of the model scales1:1 compared to the erosion velocity of the prototype. This means that if the �ow velocity of themodel test is measured, that the erosion of a prototype with similar �ow velocities should be thesame.

It is expected that the limiting factor of the installation will be the suction of sand due to theerosion. As soon as large amounts of sand are pumped out, this could damage the pump and theinstallation should be stopped. Once this is the case, the remaining gap is measured. As the modelis on length scale, the expected prototype's gap is a factor nL bigger than the measured gap in themodel. It could be argued that the prototype's pumps are better resistant against the pumping ofsand, which could make it in reality possible to continue pumping when erosion already started.This is indeed true, but if the initiation of erosion could be con�rmed by the model test, this couldvalidate the calculation model also for continuously pumping once erosion already started.

Figure 8.11: Gap remaining after installation ofa conventional suction pile in the lab.

Figure 8.12: Mark of the second top plate.Contact between the second top plate and the soil

seems possible.

Figure 8.13: Initial penetration of the suctionpile, the top has to be installed.

Figure 8.14: The top plate "sinks" in the soil incase of critical suction.

All tests are stopped due to the transport of sand particles by the pump. The measured gapbetween top plate and soil was for all three tests between 2.5 and 3 cm at the skirt, and around 3.5cm in the center of the pile. The size of the gap is at length scale, so this means that the expectedgap at prototype scale is between 25 cm at the skirt and 35 cm in the center. The exact shape of



the gap as predicted in �gure 5.17 couldn't be con�rmed, as pumping of the sand particles damagedthe pump. Better results can be obtained with a less sensitive pump. However, it is con�rmed thaterosion occurs inside a conventional suction pile, and it is con�rmed that it starts at a distance ofabout 3.5 cm (35cm on prototype scale) (see �gure 8.11).

The erosion is also tested for a suction pile equipped with a second top plate. The tests con�rm thatfor the same circumstances (a loosely packed soil, installation below the critical suction pressure)initial contact between top plate and soil is feasible in this case (see �gure 8.12).

Suction pressure: The required suction pressure is predicted with the installation resistanceand bearing capacity model. A relative density of 0.20 is chosen and the calculation is done usingFeld's method. The result is plotted in �gure 8.15. The measured suction pressure shows goodagreement with the predictions, for all three tests performed in loose sand. Two tests with a secondtop plate ((1) and (2)) and one conventional suction pile (3) are shown.

0 1 2 3 4 5 6 7 8 9 10

0

5 · 10−2

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5


Depth

[m]

Feld - Upper boundFeld - Lower bound

With second top (0s vibrated) (1)

With second top (30s vibrated)(2)

Without second top (0s vibrated)(3)Critical suction pressure

2nd top plate touches the soil

(1)

(2)

(3)

Figure 8.15: Measured suction pressures compared to the predicted suction pressure for tests in looselypacked sand.

It should be noted that for one of the two tests with a second top plate, No. (2), the pressuresensor didn't register an increase in suction pressure after contact between the second top plate andthe soil, while for installation (1) a clear increase in pressure is measured. This can be explainedbecause for test (2) the tank was vibrated during 30 seconds. As explained above, this short periodof vibrating can cause the upper part of the tank to liquefy, which probably happened here. Thetop plate sinks in the soil and no increase in resistance occurs after touch down. This would alsoexplain the relatively low suction pressures measured for this test.

The fast increase in suction pressure the moment the pressure is started, is due to the initialpenetration of the pile. In reality the suction piles penetrate due to self-weight, but in these modeltests the weight of the suction pile was not scaled correctly. Because of that, an initial penetrationwas set with an additional load before penetration started (see �gure 8.13). This load is thanremoved, so the suction pressure should �rst increase until the actual soil resistance at the "initialpenetration depth" is reached.



The peak in the measurements for test (3), between 0.2 and 0.25m penetration, is due to problemswith the out�ow of the pump and should be ignored.

8.1.8.2. High relative density

Due to the limited availability of the geotechnical laboratory, only one test in dense sand is per-formed (see �gure 8.16). However, this one set of data shows some interesting elements:

Erosion of the bed: In terms of erosion, this test can't be used to conclude anything aboutthe possibility of initial contact between top plate and soil, because critical suction is exceededand plug loosening occured. The second top plate seems to sink in the soil, which is squeezedunderneath the top plate and ends up on top of it. In �gure 8.14 is shown that the top plate isentirely �lled with soil after installation.

It is recommended (see chapter 9.2) to repeat the test without exceeding the critical gradient inorder to verify the erosion of the bed as it is predicted by the erosion-rate model.

Suction pressure: In �gure 8.16 it is clearly visible that the critical gradient is exceeded. Thisis the case because the weight of the suction pile is relatively low. Besides that, it seems thatthe suction pressures are higher than expected. The band predicted by Feld doesn't show goodagreement with the measured data. This could be the case due to underestimation of the relativedensity in the model or due to the uncertain behaviour of soils at these low stress levels. However,the main reason is probably the crossing of the critical suction line. It is clear from the graph thatthe moment the critical suction is exceeded, no more extra reduction is expected (as reductionis already at its maximum), which results in a fast increase of the required suction pressure. Inthis model test the critical suction is exceeded immediately, due to the initial penetration in thesoil. Probably a more gradual installation of a heavier pile would give better agreement withthe predicted pressures, as the reduction will smoothly increase and not immediately be at itsmaximum.

Once the second top plate touches the soil, a slight increase in resistance is measured. Due to theloosend plug, this increase is comparable with the increase measured in test (3) in loose sand. Theincrease in case of sub-critical suction in dense sand should still be investigated in further research.

8.2. Analysis of existing projects

8.2.1. Introduction

In order to verify the ideas and conclusions made in this thesis, a physical model test is executed,which is described above. Besides that, two existing installation projects are analysed. Bothprojects are heavy weight platforms installed on a sandy, permeable soil and for both projects theproblem of the gap between top plate and soil was present. The installation data are available,which makes it possible to use the proposed calculation model and to verify it with reality. Thepenetration resistance is already calculated in chapter 6.1, here the results of this calculation areveri�ed using the actual measured data. Not only the penetration resistance is veri�ed, but alsothe expected plug loosening is checked.

8.2.2. Installation resistance and bearing capacity model

The scattered points on the graph show the actual measured installation pressures for the di�erentsuction piles of the respective platforms. The line of the critical suction pressure is plotted as thedotted line. With all this data combined in one graph, many conclusions made in this thesis canbe con�rmed.



0 2 4 6 8 10 12 14

0

5 · 10−2

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5


Depth

[m]

Feld - Upper boundFeld - Lower bound

With second top (8 min vibrated)Critical suction pressure

2nd top plate touches the soil

Figure 8.16: Measured suction pressures compared to the predicted suction pressure for tests in denselypacked sand.

The �rst thing to notice is that the penetration due to self-weight is for both projects about a factor2 higher than expected. Besides that, it seems that the boundaries predicted by the DNV-methodare rather conservative, as the upper bound predicts pressures which are almost a factor 2 higherthan the actual measured pressures. The suction pressure predicted with Feld's method gives amore narrow band, as the �nal pressure at maximum depth remains well between both thin lines.

8.2.3. Erosion-rate model and plug loosening

It is clear that for both installations the critical suction pressure is exceeded. According to theanalysis made in this thesis, this would mean that the inner plug lique�ed and that a volumeincrease should be measured once the critical suction pressure is exceeded. For the �rst project,the critical suction is exceeded at -4.5m, while the installation pressures of the second projectcrosses the critical suction line between -9 and -10. Because of the plug loosening, it is for bothprojects expected that the echo sounder measures a gap once the suction is stopped. This isanalysed in the following paragraph.

A �rst conclusion in the analysis of both projects is that the rough data of project 1 are manipulatedin a way that they are useless for further research. This because the depth is recorded using theecho sounder inside the suction pile instead of a reference at the outside. This makes it impossibleto analyse the gap, as this can only be done by comparing the inner and outer measurement (see�gure 8.19):

Ptogo = Zref − Zoutloosening = Ptogo − Zecho (8.20)



0 50 100 150 200 250 300 350 400 450

0

1

2

3

4

5

6

7


Dep

th [m

]

Required suction: Feld versus SPT method

Feld − Lower boundFeld − Upper boundDNV − Most probableDNV − Highest expectedSkid1Skid2Skid3Critical suction

Figure 8.17: Project 1, actual installation data compared to the predicted installation pressures.

0 50 100 150 200 250 300 350 400 450 500

0

2

4

6

8

10

12

14


Dep

th [m

]

Required suction: Feld versus SPT method

Feld − Lower boundFeld − Upper boundDNV − Most probableDNV − Highest expectedSkid1Skid2Critical suction

Figure 8.18: Project 2, actual installation data compared to the predicted installation pressures.

with Ptogo is the penetration to go. Zref and Zout are measured using pressure sensors. Zref isused to be able to compensate for waves and tides.

Luckily the rough data of the second project are not manipulated and can be used to verify thegap between top plate and soil. It was already concluded from �gure 8.18 that the critical pressureis exceeded between -9 and -10m. Analysis of the echo-sounder's data compared with the depthmeasurement of di�erent skids (see �gures 8.20 and 8.21), show almost exactly the expected plug



Figure 8.19: Depth measurements of a suction pile, schematized.

loosening: starting from a depth of around -10m, the echo-sounder measures higher depths thanthe reference measurement outside the suction pile. The di�erence between both measurementsgradually increases until full penetration is reached. Here the di�erence (and so the loosened plug)is at its maximum (almost 1 meter volume increase). The measurements also show that once thesuction is stopped, the di�erence between both measurements decreases again, with a remaininggap of around 30cm.

For this project the desired depth was 12m. From both �gures 8.20 and 8.21 it can be concludedthat this depth is reached. To do so, the pile had to be made 12.5m long, to give room to the plugloosening and still reach the desired depth. The measurements of project 1 give the impression thatthe desired depth of 7m is not reached (see �gure 8.17, suction stops at -6m). The �nal penetrationdepth of -6m led to the conclusion that the outer sensor was wrongly calibrated (as it was expectedto end up at -7m), so the echo-sounder was used to measure the depth. An ROV-robot was usedin this case to con�rm the penetration depth of -7m.

8.2.4. Conclusion

The analysis of the second project con�rms several aspects brought up by this thesis. It should benoted that only one project is analysed, so it is recommended to do further research on this topicon other past and future projects.

Firstly it can be concluded that the DNV-method, which is used in engineering practice, results inrelatively high demands on the structural strength of the suction pile, as it seems to overestimatethe required suction pressures. For both analysed projects, the more theoretically method proposedby Feld [12] seems to give a better approach of the actual pressures.

Secondly, the second project shows that no or limited plug heave occurs before the critical suctionis exceeded. Once critical suction is exceeded, there is a clear di�erence between the inner andouter measurements.

Finally it is con�rmed that a gap remains after installation. Just before suction is stopped, thevolume increase of the soil plug is maximal and once suction is stopped, the volume decreasesagain. A gap and a permanent expansion of the soil plug remain present.



0 200 400 600 800 1,000 1,200 1,400 1,600 1,800

0

2

4

6

8

10

Time

Penetrationto

go[m]

Measurement echosounderMeasurement outside pile

Figure 8.20: Penetration depth: echo sounder compared with depth sensor, plug heave starts with 2.5mto go.

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800

0

2

4

6

8

10

Time

Penetrationto

go[m]

Measurement echosounderMeasurement outside pile

Figure 8.21: Penetration depth: echo sounder compared with depth sensor, plug heave starts with 2mto go.



8.3. Design considerations and procedure for the new

calculation model

The calculation model developed in this thesis can be used for the entire design phase of a suctionpile foundation in permeable soil. In this section the procedure is described which should be fol-lowed once using the model in engineering practice. This chapter can also be used by a programmerto develop a graphic user interface in order to make the code more user friendly.

Input of the soil parameters: In engineering practice the soil parameters usually come froman in-situ soil investigation as a CPT and/or boring. These values can be used as input. However,in case of a tender without the availability of soil data, it is also possible to make an estimationusing the Brinch-Hansen calculation model with an estimated φ and σ′v.

Input of the geometry of the suction pile: Depending on the required bearing capacity,an initial geometry should be chosen. This geometry can be adapted in a later stage in order tooptimize the design.

Prediction of the required installation pressures and the critical pressures: Once thesoil parameters and the geometry are set, the calculation model basically shows everything youshould know. The required installation pressures are predicted and the critical suction pressureover depth is displayed. Based on the output of this calculation phase, new design decisions shouldbe made, based on the result for the required installation pressure and its position relative to thecritical pressure.

If the critical pressure is exceeded by the installation pressure, plug loosening will occur. This is inall cases undesirable, because plug loosening results in a decrease in end bearing. So at �rst stagean attempt is made to prevent plug loosening. This can be achieved by decreasing the L/D ratio:a bigger diameter results in a lower required suction pressure. Another possibility is to increasethe weight of the suction pile, as the weight of the pile is also a driving force for the installation.

Nevertheless, it is possible that due to limitations of the client or price considerations, the decisionis made to install the pile using higher pressures than the critical suction pressure. This is notinherently problematic, because it is still possible to install the pile with a lique�ed soil plug.However, it should be noted that the reduction in soil friction as well as the limited amountof bearing capacity of the top plate should be included in the decision making. It could beeconomically advantageous in certain situations to enlarge the diameter of the pile and reduce thelength in a way that the critical pressure won't be exceeded. This way a higher inner friction willbe achieved and the top plate will require less settlement before fully plugged behaviour is reached.

Once the decision is made between installation below or above the critical suction pressure, the topplate can be designed. The top plate doesn't in�uence the installation, but could have a big impacton the settlement and the bearing capacity of the suction pile in the "as-installed" situation.

Situation A: installation pressure stays below the critical suction pressure: For instal-lations below the critical suction pressure, a second top plate as in �gure 4.1 could be used. Inthis case, the above presented erosion model should be used to verify if it is possible to get initialcontact between top plate and soil. For this type of installations, the horizontal �ow velocity andthe erosion of the bed are the determining factors. In case the model indicates that the erosionvelocity is negligible compared to the installation velocity, than it should be possible to get initialcontact between soil and top plate. In case of a densely packed soil (as on most platform locationson the North Sea), it is expected that contact between soil and top plate results in a vast increasein bearing capacity. Because the soil plug isn't loosened during this type of installation, the secondtop plate theoretically solves the problem of the gap. This should be veri�ed by model tests.



In case the second top plate doesn't reduce the �ow velocity su�ciently, a perforated top platecould be used. This way the horizontal �ow velocity is limited to a minimum because the watercan directly �ow upward. Because no liquefaction and no erosion will occur in this case, it is notneeded to use any kind of �lter material. This should also be con�rmed by model tests.

The second top plate is not only a solution to the gap between top plate and soil, it can also beused to pre-stress the soil. The idea is to keep the pressure on once the top plate touches the soil.Because the second top plate is smaller than the original top plate (over which the di�erentialpressure works), a downward force will start pushing on the soil plug. However, the presence of thegradient also in�uences the behaviour of the plug. As shown in �gures 8.22 and 8.23, the gradientinside the soil increases signi�cantly around the edges of the second top plate. This will result inliquefaction in this area and a local reduction in relative density. This is not favourable for thebearing capacity of the second top plate, so is advised not to try to pre-stress the soil in case thecritical stress wasn't exceeded during installation.

Situation B: installation pressures above the critical suction pressure: If it turned outto be impossible to install the suction pile without exceeding the critical suction pressure, the topplate should be adapted to the fact that the plug will loosen during installation. The soil willbecome in its loosest state and a second top plate as in �gure 4.1 will "sink" in the lique�ed soil.The soil underneath this second top plate will be squeezed out and initially no or little increase inbearing capacity is expected. However, if penetration continues, contact between the second topplate and the soil will cause the �owlines to change direction and bearing capacity can built upstarting in the center of the suction pile (see �gures 8.22 and 8.23).

Calculation of the bearing capacity: Once the type of top plate is chosen using the erosionmodel, the exact design should be optimized to reach the highest possible bearing capacity. Theway this should be done is explained in chapter 7.



10 20 30 40 50 60 70

10

20

30

40

50

60

70

Radius of the model [cm]

Penetrationdepth

ofthemodel[cm]

0

0.2

0.4

0.6

0.8

Figure 8.22: Pressure distribution inside the model before contact between second top plate and soil.

10 20 30 40 50 60 70

10

20

30

40

50

60

70

Radius of the model [cm]

Penetrationdepth

ofthemodel[cm]

0

0.2

0.4

0.6

0.8

Figure 8.23: Pressure distribution once the top plate touches the soil. The top plate is modelled as ano-�ow boundary.





9 | Conclusion and recommendations

9.1. Conclusion

The main objective of this research is to investigate the feasibility of initial top plate bearing afterinstallation of a suction pile in permeable soils. In practice, ithout any measures, a gap remainsbetween top plate and soil, which is normally �lled with a grout mixture. The presence of a gapbetween top plate and soil plug is undesirable, as settlements could occur once the foundation isloaded with the top structure and "plugged" behaviour is needed to meet the foundation's bearingcapacity requirements. The conventional solution of grouting the gap is an expensive o�shoreoperation and is, because of its uncontrollability, an undesired measure for many clients. Hence,the o�shore industry is eager to �nd a solution which overcomes this unintended phenomenon.

In this thesis a calculation model is developed which describes the known processes occurringduring a conventional suction pile installation in a permeable soil. The alleged causes of the gapbetween the top plate and the soil plug are included as well, resulting in an entire mathematicaldescription of the model. This model is veri�ed using existing models, measurements from practiceand various scaled model tests in a laboratory.

After validating the calculation model for conventional suction piles, new measures could be im-plemented and the results of this investigation are compared to the old situation. Next, the mostpromising solution is highlighted and further investigated. A physical model is built to compare theconventional suction pile design with a design equipped with a second top plate, which is slightlysmaller than the original top plate. The most important conclusions resulting from this researchare listed below.

1. The calculation model used in engineering practice uses empirical values to calculate thereduction in soil resistance which occurs during suction pile installation. These values ap-pear to be rather conservative. This research shows, mainly supported by �eld data, thata prediction with theoretically derived reduction factors approaches the predicted suctionpressures a lot better (see chapters 6 and 8).

2. The behaviour of sandy soils during installation of a suction pile depends on the height ofthe required suction pressure. Depending on the applied suction pressure, a certain thresholdvalue can be exceeded. This threshold value is called the "critical suction pressure" and isde�ned as the pressure at which the critical gradient (γ′/γw) inside the soil plug is exceeded.In the design of suction pile foundations the distinction should be made between critical andsub-critical suction pile installations. It is important to notice that installation is possiblefor both situations, although the soil will behave di�erently.

3. The developed calculation model con�rms the presence of the gap, both for critical as sub-critical suction installations of conventional suction piles. For subcritical suction the gaporiginates from an erosion driven system, while installations above the critical pressure showa gap which originates from plug loosening and compacting of the soil once the gradient isremoved. Plug loosening is not likely in case the critical suction pressure is not exceeded.This is con�rmed by both model tests and analysis of �eld data.

4. The calculation model shows that, for subcritical suction, contact between a second top plateand the soil seems to be feasible. The horizontal �ow velocities on the bed are su�cientlyreduced to eliminate erosion of the bed. This is con�rmed by laboratory tests, however theincrease in bearing capacity is not con�rmed yet (see recommendations).

Chapter 9. Conclusion and recommendations 85


5. For higher suction pressures, above the critical threshold value, the second top plate willsink into the loosely packed soil, resulting in no or little increase in bearing capacity. Initialcontact between top plate and soil is possible, but the soil is quasi squeezed underneath thesecond top plate. This is also con�rmed by the model tests. However, some installationsin extremely loosely packed conditions showed an increase in soil resistance after contactbetween soil and top plate. This indicates an increase in e�ective stress underneath the topplate, which probably originates from a change of the �ow lines in the plug.

6. Pre-stressing of the soil using the second top plate is unlikely to contribute to a higher bearingcapacity, as the soil will locally liquefy rather than compact. This should be con�rmed bylaboratory tests in densely packed sands (see recommendations).

The developed calculation model and the performed laboratory tests gave more insight in thefeasibility of initial top plate bearing. The results of the performed model tests are promising, butmore research is required to be a 100 percent certain that the injection of grout becomes completelysuper�uous.

The above conclusions are based on a theoretical calculation model which is (i.a.) validated usinglaboratory tests. However, in the context of this master thesis, the availability of the facilitiesin the geotechnical laboratory were limited, which made it impossible to su�ciently repeat thedi�erent test set-ups. That's why in the following section (9.2) some extra laboratory research isrecommended.

9.2. Recommendations

The theoretical approach and the experimental work has shown that a second top plate could beused to overcome the problem of the gap between top plate and soil. However, many improvementscan still be made and many aspects of the installation remain unclear. In this section somesuggestions for further research are summarised:

1. As mentioned above, further research is required to get a better understanding of the processthat causes the soil plug to loosen in case of a critical gradient. It is common geotechnicalpractice that if a critical gradient in a soil plug is exceeded, the entire plug is lifted up andthe grains "rain" down at the bottom of the plug to end up in a looser state. However,Tran [21] investigated the loosening of the plug inside a suction pile, and he didn't seethis phenomenon. He reports, for homogeneous sands, a more gradually loosening of theplug instead of instantaneous plug loosening and no compaction once the suction pressure isstopped. This is in contradiction with experience and measurements from practice. Furtherinvestigation on this topic is required.

2. The behaviour of the soil just before the (second) top plate touches the soil remains uncertain.In this research it is assumed that the small gap resulting in erosion is negligible comparedto the roughness and relief of the sea bed, but this should be investigated in detail.

3. The behaviour of a loosened soil plug in the use phase remains unclear. Further research isrecommended to see if any densi�cation of the soil plug occurs due to vibrations etc. in theuse phase.

4. The behaviour of a (dense) soil plug after "touch down" of the second top plate should beinvestigated further as well. The groundwater �ow model developed in this thesis predictsan increase in gradient at the edges of the second top plate and an increased erosion on thislocation. More research is required to quantify the e�ect of these processes on the bearingcapacity of the soil plug.

5. Related to recommendation 4, The possibility to pre-stress the soil plug during the installationphase requires more research. Theoretically, if the second top plate touches the soil, suction



can continue and the second top plate will be pushed down on the soil bed. This will resultin increased e�ective stresses in the plug and can be seen as "pre-stressing" of the plug.However, at the same time the opposite happens: the suction pressure used to push the piledown, results in an increase of the upward gradient. This gradient reduces the e�ective stressagain. Further research is recommended to investigate the feasibility of pre-stressing the soilplug.

It is recommended to perform additional model tests and use a similar test set up as the one usedin this thesis to prove or refute the statements and theories presented above. Small adjustmentsare su�cient to improve the test and get insight in some of the unknown processes:

1. Measurements of plug loosening during and after installation of the pile: by measuring therelative density of the plug during and after installation (for example with CPT's inside thesuction pile), a better understanding of the behaviour of the plug during suction can beobtained.

2. Implementation of a load on the suction pile after installation: this way the bearing capacityof the suction pile can be measured and compared for both the conventional suction pile andthe suction pile with second top plate. With a jack and a press box the load-displacementcurves for di�erent designs can be obtained.

3. Simulation of vibrations and cyclic loads due to waves: this is useful to test for suction pileswith a loosened soil plug due to the installation pressures. With a perspex suction pile modelthe compaction of the plug in the use phase can be quanti�ed.

4. The possibility of pre-stressing the soil: the e�ectiveness of this idea can also be checkedusing a static load on an installed suction pile model. In one test suction should be stoppedimmediately after contact between top plate and soil, while in the comparative test the soilshould be pre-stressed by continuing to pump.

It is recommended to perform the tests mentioned above for di�erent relative densities and not onlywith the top plate design as used in this thesis. A perforated top plate or strip bearing elementsare equally promising solutions and are worth investigating as well.

Even if more research is recommended, the results of this primary investigation on initial bearingcapacity of a top plate gave a promising outcome and resulted in a patent connecting this knowledgeto SPT O�shore. This means that the o�shore industry is highly interested in this new technology,which is encouraging in view of the conduct of the recommended additional research.





A | Calculation models

A.1. Calculation model based on homogeneous soil and

cone resistance

1 %Simon Lembrechts%1386549%MSc Thes i s : I n i t i a l top p l a t e bear ing o f a suc t i on p i l e

c l e a r a l l ; c l c ;6

%% INPUT

H = input ( ' S i z e o f one g r id element ( square ) , H = f . e . 0 . 2 [m] ' ) ;x = input ( 'Amount o f e lements in x d i r e c t i o n (MAX 100 ! ) ' ) ;

11 d i sp l ay (H∗x ) ;y = input ( 'Amount o f e lements in y d i r e c t i o n (MAX 100 ! ) ' ) ;d i sp l ay (H∗y ) ;x1 = input ( ' Radius o f the suc t i on p i l e [# elements ] ' ) ;d i sp l ay (H∗x1 ) ;

16 y1 = input ( ' Considered depth o f the suc t i on p i l e [# elements ] ' ) ;d i sp l ay (H∗y1 ) ;L = input ( ' Total l ength o f the suc t i on p i l e [m] ' ) ;

%% PARAMETERS21

% Diameter o f the suc t i on p i l e [m]% Wal l th i ckness o f the suc t i on p i l e [m]% Submerged weight anchor [ kN ]D = 2∗x1∗H;

26 twa l l = 0 . 0 4 ;Gsub = 1000 ;

% Grain s i z e [m]% Sand from 0.002m − 0.000063m

31 % Unit weight water [ kN/m3]% Unit weight g r a i n s [ kN/m3]% Kinematic v i s c o s i t y [m2/ s ] at 5 degree s% Gravity [m/ s2 ]% Waterdepth [m]

36 d15 = 0 . 0002 ;d50 = 0 . 0002 ;gamma_w = 10 . 2 5 ;gamma_s = 26 . 5 0 ;nu = 1.519∗10^−6;

41 g = 9 . 8 1 ;H_w = 40 ;

% Area o f the suc t i on p i l e top p l a t e [m2]% Radius o f the suc t i on p i l e [m]

46 % Gr id s i z e [m x m]% Depth i n t e r v a l s [− ]Area = 0.25∗D^2∗ pi ;r = x1∗H;g r i d s i z e = [ x∗y x∗y ] ;

51 z = l i n s p a c e (0 , y1∗H, ( y1+1) ) ;

A = ze ro s ( g r i d s i z e ) ;

%% GEOTECHNICAL INFORMATION56

% Poros i ty ( c a l c u l a t i o n w i l l be executed f o r n1 d i f f e r e n t dry

Appendix A. Calculation models 89


% den s i t i e s between 0 .29 and 0 . 5 . These are the minimal and maximal% dry dens i ty f o r sphe r i c a l , uniform gra in s )n1 = 10 ;

61 n = l i n s p a c e ( 0 . 2 9 , 0 . 5 , n1 ) ;%n = 0 . 4 ;

% Minimum and maximum dry dens i ty o f the bulk mate r i a lgamma_D = (1−n) ∗(gamma_s) ;

66 gamma_D_min = (1−0.5) ∗(gamma_s) ;gamma_D_max = (1−0.29)∗gamma_s ;

% Re la t i v e dens i tyDr = ((1/gamma_D_min) . . .

71 −(1./gamma_D) ) . / . . .( (1/gamma_D_min) . . .−(1/gamma_D_max) ) ;

% Relat ion between r e l a t i v e dens i ty and i n t e r n a l f r i c t i o n :76 % Fundamentals o f g e o t e chn i c a l eng in e e r i ng ( th i rd ed i t i on , Braja M. Das )

phi = ones ( l ength (Dr) ,1 ) ;phi (Dr>0.8) = 45 ;phi (Dr<0.8) = 40 ;phi (Dr<0.6) = 35 ;

81 phi (Dr<0.4) = 30 ;phi (Dr<0.2) = 25 ;phi = ( phi /180∗ pi ) ' ;

% K_0 [− ]86 % Wet dens i ty o f the mate r i a l

% Ve r t i c a l e f f e c t i v e s t r e s s [ kPa ]K0 = 1− s i n ( phi ) ;gamma_W = gamma_D + n∗gamma_w;sigma_tot = z '∗gamma_W + H_w∗gamma_w;

91 sigma_v_eff = ( z ' ∗ (gamma_W − gamma_w) ) ;gamma_eff = gamma_W − gamma_w;

% Relat ion between cone r e s i s t a n c e and e f f e c t i v e s t r e s s /% l a t e r a l earth p r e s su r e (Non−con so l i da t ed sand ) (Lunne et al , Cone

96 % penet ra t i on t e s t i n g in Geotechn ica l p r a c t i c e )

qc = 157∗( sigma_v_eff . ^0 . 5 5 ) . ∗ ( exp (2 . 41∗ ones ( y1+1 ,1)∗Dr) ) ;

% Conso l idated sand101 % sigma_m = ( sigma_v_eff . ∗ . . .

% (1+2∗( ones ( y1+1 ,1)∗K0) ) ) /3 ;% qc = (181∗ ( sigma_m) .^0 . 5 5 ) . ∗ . . .% ( ones ( y1+1 ,1)∗exp (2 . 61∗Dr) ) ;

106 %% RELATIVE DENSITY VS CONE RESISTANCE% Compare t h i s p l o t with the p l o t from the Canadian Geotechn ica l journa l ,% page 12% Plot o f the cone r e s i s t a n c e vs v e r t i c a l e f f e c t i v e s t r e s s , a f t e r% Jamiolkowski

111 f i g u r e (1 ) ;c l f ;p l o t (0 . 001∗ qc , sigma_v_eff ) ;x l ab e l ( 'Cone r e s i s t a n c e qc [MPa] ' ) ;y l ab e l ( ' V e r t i c a l e f f e c t i v e s t r e s s [ kPa ] ' ) ;

116 s e t ( gca , 'YDir ' , ' r e v e r s e ' ) ;% Create legend f o r d i f f e r e n t l i n e s% %.2 f g i v e s the amount o f decimals , a{ i i } i s the i i ' th element o f a ,% has to be f i l l e d with the i i ' th element o f Dra = c e l l (1 , n1 ) ;

121 f o r i i =1:n1 ,a{ i i } = s p r i n t f ( '%.2 f ' ,Dr( i i ) ) ;

end ;

l egh = legend (a , ' l o c a t i o n ' , ' EastOutside ' ) ;126 v = get ( legh , ' t i t l e ' ) ;

s e t (v , ' s t r i n g ' , ' Re l a t i v e dens i ty ' ) ;



matlab2t ikz ( ' c o n e r e s i s t a n c e_ e f f e c t i v e s t r e s s . tex ' ) ;

% Plot o f the cone r e s i s t a n c e vs the depth131 f i g u r e (2 ) ;

p l o t (0 . 001∗ qc , z ) ;x l ab e l ( 'Cone r e s i s t a n c e qc [MPa] ' ) ;y l ab e l ( 'Depth [m] ' ) ;s e t ( gca , 'YDir ' , ' r e v e r s e ' ) ;

136

a = c e l l (1 , n1 ) ;f o r i i =1:n1 ,

a{ i i } = s p r i n t f ( '%.2 f ' ,Dr( i i ) ) ;end ;

141 l egh = legend (a , ' l o c a t i o n ' , ' EastOutside ' ) ;v = get ( legh , ' t i t l e ' ) ;s e t (v , ' s t r i n g ' , ' Re l a t i v e dens i ty ' ) ;mat lab2t ikz ( ' coneres i s tance_depth . tex ' ) ;

146 % Plot o f the v e r t i c a l e f f e c t i v e s t r e s s vs the depthf i g u r e (3 ) ;p l o t ( sigma_v_eff , z ) ;x l ab e l ( ' V e r t i c a l e f f e c t i v e s t r e s s [ kPa ] ' ) ;y l ab e l ( 'Depth [m] ' ) ;

151 s e t ( gca , 'YDIR ' , ' r e v e r s e ' ) ;

a = c e l l (1 , n1 ) ;f o r i i =1:n1 ,

a{ i i } = s p r i n t f ( '%.2 f ' ,Dr( i i ) ) ;156 end ;

l egh = legend (a , ' l o c a t i o n ' , ' EastOutside ' ) ;v = get ( legh , ' t i t l e ' ) ;s e t (v , ' s t r i n g ' , ' Re l a t i v e dens i ty ' ) ;mat lab2t ikz ( ' v e r t i c a l s t r e s s_dep th . tex ' ) ;

161

%% FRICTION, BASED ON qc , BEST ESTIMATE

% Most probable s k i r t pene t ra t i on f a c t o r − FRICTION(DNV '92)% Most probable s k i r t pene t ra t i on f a c t o r − END BEARING (DNV '92)

166 kf = 0 . 0 0 1 ;kp = 0 . 3 ;

% Highest expected s k i r t pene t ra t i on f a c t o r − FRICTION(DNV '92)% Highest expected s k i r t pene t ra t i on f a c t o r − END BEARING (DNV '92)

171 % kf = 0 . 0 0 3 ;% kp = 0 . 6 ;

% Inner f r i c t i o n per depth i n t e r v a l [ kPa ]% Total inne r f r i c t i o n at a c e r t a i n depth , without reduct i on [ kPa ]

176 f r i c t i o n_ i n = (D−2∗ twa l l ) ∗ pi .∗ kf .∗ qc∗H;

f o r i = 1 : y1+1,f o r j = 1 : n1 ,

Fr i c t ion_in ( i , j ) = sum( f r i c t i o n_ i n ( 1 : i , j ) ) ;181 end

end

% Outer f r i c t i o n per depth i n t e r v a l [ kPa ]% Total outer f r i c t i o n at a c e r t a i n depth , without reduct i on [ kPa ]

186 f r i c t i on_out = D∗ pi .∗ kf .∗ qc∗H;

f o r i = 1 : y1+1,f o r j = 1 : n1

Fr ict ion_out ( i , j ) = sum( f r i c t i on_out ( 1 : i , j ) ) ;191 end

end

% Tip bear ing without reduct i on [ kPa ]t ip_bear ing = twa l l ∗(D−twa l l ) ∗ pi ∗kp∗qc ;

196



%% ITERATIVE PROCESS TO CALCULATE THE REQUIRED PRESSURE ACCORDING TO SPT

% Extra f a c t o r s f o r inner and outer f r i c t i o n / t i p bear ing ( in case201 % the p i l e has a d i f f e r e n t layout and has more su r f a c e on the i n s i d e )

A_1 = 1 ;A_2 = 1 ;A_3 = 1 ;

206 % Total s o i l r e s i s t a n c e without f r i c t i o n reduct i on [ kPa ]% Submerged weight o f the ca i s s on [ kPa ]tsr_SPT = A_1∗Fr ic t ion_in+A_2∗Frict ion_out+A_3∗ t ip_bear ing ;W_sub = ones ( y1+1,n1 ) ∗Gsub ;

211 % Routine to f i nd the suc t i on pr e s su r e accord ing to SPT−o f f s ho r e ' s% i n s t a l l a t i o n method . Two loops are necessary , because the% t r a n s i t i o n zone between suc t i on and no suc t i on i s not c l e a r us ing t h i s% method . This because the reduct i on f a c t o r s are emp i r i c a l% and do not depend on the app l i ed p r e s su r e .

216 suction_pressure_SPT = ( tsr_SPT − W_sub) /Area ;temp2 = suction_pressure_SPT ;temp2 ( temp2<=0) = 1 ;temp2 ( temp2~=1) = 0 ;

221 tsr_SPT = . . .temp2 . ∗ (A_1∗Fr ic t ion_in ) + . . .( ( temp2+0.5)−0.5∗temp2 ) . ∗ (A_3∗ t ip_bear ing ) + . . .A_2∗Frict ion_out ;

226 suction_pressure_SPT_A = (tsr_SPT − W_sub) /Area ;suction_pressure_SPT_A ( suction_pressure_SPT_A<0) = 0 ;

%% ITERATIVE PROCESS TO CALCULATE THE REQUIRED PRESSURE ACCORDING TO FELD231

% Cr i t i c a l suc t i on p r e s su r e accord ing to f e l d f o r d i f f e r e n t d e n s i t i e sf e l d = 1 . 32∗ ( ( z ' /D) .^0 . 7 5 ) ∗D∗gamma_eff ;

% Total s o i l r e s i s t a n c e without f r i c t i o n reduct i on [ kPa ]236 % Submerged weight o f the ca i s s on [ kPa ]

t s r_ f e l d = A_1∗Fr ic t ion_in + . . .A_2∗Frict ion_out+A_3∗ t ip_bear ing ;

W_sub = ones ( y1+1,n1 ) ∗Gsub ;

241 % I n i t i a l va lue s to s t a r t c a l c u l a t i o nsuct ion_pres sure_fe ld = ones ( y1+1,n1 ) ;temp1 = ones ( y1+1,n1 ) ;counter = 0 ;

246 % Routine to c a l c u l a t e the reduced t o t a l s o i l r e s i s t a n c ewhi l e any ( any ( abs ( t s r_ f e l d − W_sub − . . .

suc t ion_pres sure_fe ld ∗Area ) >0.0001) ) && counter <50000

suct ion_pres sure_fe ld = ( t s r_ f e l d − W_sub) /Area ;251 temp1 = ( . 9 . ∗ temp1+.1.∗ suct ion_pres sure_fe ld ) ;

s e l = ( temp1>=f e l d ) ;% temp1 ( s e l )=f e l d ( s e l ) ;% temp1 ( temp1<=0) = 0 ;% Makes a l l va lue s sma l l e r than 0 in suct ion_pres sure_fe ld equal to 0

256 % This makes f e l d (1−temp1 . / f e l d ) equal to 1 in t h i s ca s e st s r_ f e l d = . . .

(1−(temp1 . / f e l d ) ) . ∗ . . .(A_1∗Fr ic t ion_in+A_3∗ t ip_bear ing ) + . . .A_2∗Frict ion_out ;

261 % Make a l l NaN va lue s equal to 0 , because o f d i v i d i ng by 0t s r_ f e l d ( i snan ( t s r_ f e l d ) )= 0 ;counter = counter+1;

endf p r i n t f (1 , 'Number o f i t e r a t i o n s %.0 f \n ' , counter ) ;

266

suct ion_pres sure_fe ld = ( t s r_ f e l d − W_sub) /Area ;



suct ion_pres sure_fe ld ( suct ion_pressure_fe ld <0)=0;

271 %% THE GROUNDWATER FLOW: A RADIAL SYMMETRIC PROBLEMt i c ;

% FACTORS TO MAKE THE PROBLEM RADIAL SYMMETRIC

276 % Factor f o r the c e l l to the l e f t o f the cons ide r ed c e l lC1 = 1 − ( 1 . / ( 2 .∗ ( 0 : ( x−1) ) ) ) ' ;

% Factor f o r the c e l l to the r i g h t o f the cons ide r ed c e l lC2 = 1+(1 . / ( 2 .∗ ( 0 : ( x−1) ) ) ) ' ;

281

% The f i r s t row ( at x = 0) has no reduct ion , so f a c t o r equa l s 1C1( i s i n f (C1) ) = 1 ;C2( i s i n f (C2) ) = 1 ;

286 % The r i gh t boundary i s model led as c l o s ed (dh/dr = 0)C1(x , 1 ) = 1 ;

% Transforms C1 in a r e p e t i t i v e vec to r with s i z e x∗yC1 = repmat (C1 , y , 1 ) ;

291 C2 = repmat (C2 , y , 1 ) ;

% The c e l l s in the s k i r t don ' t have the reduct ion , as dh/dr = 0k = 0 : ( y1−1) ;C1(k .∗ x+x1 , 1 ) = 1 ;

296 C2(k .∗ x+x1+1 ,1) = 1 ;

% C1 i s a f a c t o r f o r the "−1 d iagona l " , which has l ength D0−1% C2 i s a f a c t o r f o r the "+1 d iagona l " , which has l ength D0−1C1 = C1 ( 2 : end ) ;

301 C2 = C2 ( 1 : end−1) ;

%% THE GROUNDWATER FLOW: BUILDING THE BAND MATRIX

% D0 − Main d iagona l306 D0 = diag (A)−4; % In normal c i r cumstances the main diag i s −4

k = 1 : x ; % Top boundary as a f i x ed po t e n t i a lD0(k , 1 ) = −1;

311

% D1 − F i r s t band , below the diagonal , c e l l s to the l e f t o f the cons ide r ed% c e l lD1 = diag (A,−1)+1; % In normal c i rcumstances , t h i s band equa l s 1

316 k = 0 : ( y1−1) ;D1(k .∗ x+x1 , 1 ) = 0 ; % This c e l l has to be 0 to model the s k i r tD1(k .∗ x+x1−1 ,1) = 2 ;

k = 1 : ( y−1) ; % Ce l l s to be zero in order to remove the321 D1(k .∗ x , 1 ) = 0 ; % l i n k between the l a s t and the f i r s t column

k = 1 : y ; % Right boundary model led as a f i x edD1(k .∗ x−1) = 0 ; % po t en t i a l ( D i r i c h l e t ) , a l s o p o s s i b l e to

% model as a c l o s ed bound (Neumann)326

k = 1 : x−1; % Top boundary as a f i x ed po t e n t i a lD1(k , 1 ) = 0 ;

D1( end−x+1:end ) = 0 ;331

% D2 − Second band , above the diagonal , c e l l s to the r i g h t o f the% cons ide r ed c e l lD2 = diag (A, 1 ) +1; % In normal c i rcumstances , t h i s band equa l s 1

336

k = 0 : ( y1−1) ;



D2(k .∗ x+x1 , 1 ) = 0 ; % This c e l l has to be 0 to model the s k i r tD2(k .∗ x+x1+1) = 2 ;

341 k = 0 : ( y−1) ; % Ce l l s to compensate f o r the l e f t boundaryD2(k .∗ x+1 ,1) = 2 ; % This va lue i s 2 , because to c a l c u l a t e

% the po t e n t i a l in column one , you can take% 1/4∗( twice column two + row above +% row below ) as i t i s r a d i a l symmetric

346

k = 1 : ( y−1) ; % Ce l l s to be zero in order to remove theD2(k .∗ x , 1 ) = 0 ; % l i n k between the f i r s t and the l a s t column

D2( end−x+1:end ) = 0 ;351


356 % D3 − Third band , below the diagonal , c e l l s above the cons ide r ed c e l lD3 = diag (A,−x )+1; % Bottom boundary model led as a c l o s edD3( end−x+1:end ) = 2 ; % bound (Neumann) , a l s o p o s s i b l e to apply a

% c e r t a i n po t e n t i a l ( D i r i c h l e t )

361 D3( end−x+1:end ) = 0 ;

k = 1 : ( y−1) ;D3(k∗x ) = 0 ; % Right bound modelled as a D i r i c h l e t bound

366

% D4 − Fourth band , above the diagonal , c e l l s below the cons ide r ed c e l lD4 = diag (A, x )+1;

k = 1 : ( y−1) ;371 D4(k∗x ) = 0 ; % Right bound modelled as a D i r i c h l e t bound


376 %% ADDING THE FACTORS TO MAKE IT A CYLINDRICAL PROBLEM

% Band D1 and D2 are the bands used to l i n k the cons ide r ed c e l l to% the c e l l b e f o r e and the c e l l a f t e r i t s e l f . So these d i agona l s% should have the reduct i on f a c t o r s

381 D1 = D1.∗C1 ; % This i n c l ud e s the f a c t o r s f o r theD2 = D2.∗C2 ; % c y l i n d r i c a l c oo rd ina t e s

%% SOLVING THE PROBLEM

386 % Matrix AA = diag (D0) + diag (D1,−1) + diag (D2 , 1 ) . . .

+ diag (D3,−x ) + diag (D4 , x ) ;

% Fixed node matrix B, This matrix i n c l ud e s the p o t e n t i a l s in the391 % f i x ed nodes , in t h i s case the p r e s su r e i n s i d e the suc t i on p i l e

B = ze ro s ( x∗y , 1 ) ;k = 1 : x1 ;

% This va lue i s the app l i ed p r e s su r e i n s i d e the suc t i on p i l e396 B(k , 1 ) = −1;

% Equation to be so lved to generate a vec to r with l ength x∗yY = A\B;

401 % We want to have a matrix with y rows and x columnsr e s u l t = ze ro s (x , y ) ;f o r i = 1 : y ,

r e s u l t ( : , i ) = Y(((−1+ i ) ∗x+1) : ( i ∗x ) ) ;end

406

% Get the geometry r i g h t



r e s u l t = transpose ( r e s u l t ) ;

toc ;411

% r e s u l t ( 1 : y1 , ( x1+1) ) = NaN;

%% PLOTTING THE SOLUTION416

% Plot the r e s u l t in p i x e l s% imagesc ( r e s u l t ) ;

% Plot the r e s u l t smoothly421 f i g u r e (4 ) ;

contour f ( r e su l t , 1 1 ) ;colormap ( f l i p ud ( colormap ) ) ;s e t ( gca , 'YDir ' , ' rev ' ) ;c o l o rba r ;

426 hold on ;r e c t ang l e ( ' Po s i t i on ' , [ x1 , 0 , 1 , y1+1] , ' FaceColor ' , 'w ' ) ;hold on ;l i n e ( [ 0 x1 ] , [ y1+1 y1+1] , ' LineWidth ' ,3 , ' Color ' , 'w ' ) ;hold o f f ;

431

% Calcu la te the pore p r e s su r e at the p i l e t i p ( compared to the app l i ed% pre s su r er a t i o = ( y1 /(2∗ ( x1−1) ) ) ;d i sp l ay ( r a t i o ) ;

436

%% AVERAGE PRESSURE AT PILE TIP LEVEL

% To c a l c u l a t e the t o t a l i n f l ow o f water , the average p r e s su r e at the% p i l e t i p i s c a l c u l a t ed . As i t i s a c y l i n d r i c a l problem , the p r e s su r e s are

441 % f i r s t mu l t i p l i e d by a " su r f a c e f a c t o r " , b e f o r e the average i s taken .k = 1 : x1 ;f a c t o r = (2∗k−1)∗H^2∗ pi ;f a c t o r = f a c t o r /sum( f a c t o r ) ;pres s_t ip = r e s u l t ( y1+1 ,1: x1 ) .∗ f a c t o r ;

446 press_t ip = sum( press_t ip ) ;d i sp l ay ( pres s_t ip ) ;

pore_press_pi le_tip = ( r e s u l t ( y1+1,x1 )+r e s u l t ( y1+1,x1+1) ) /2 ;d i sp l ay ( pore_press_pi le_tip ) ;

451

%% PLOTS OF THE REQUIRED SUCTION PRESSURES

% C r i t i c a l g rad i en ti c r i t = (gamma_W−gamma_w)/gamma_w;

456 % Cr i t i c a l p r e s su r ep c r i t = ( l i n s p a c e (0 , 1 , l ength ( z ) ) ' ) ∗( sigma_v_eff ( end , 1 : end ) . / . . .

(1−press_t ip ) ) ;

f i g u r e (7 ) ;461 p lo t ( pc r i t , z ' , '−− ' ) ;

hold onp lo t ( f e l d , z ' ) ;hold o f f

466 f i g u r e (5 ) ;c l f ;p l o t ( suct ion_pressure_fe ld , z ) ;x l ab e l ( ' Required suc t i on pr e s su r e [ kPa ] ' ) ;y l ab e l ( 'Depth [m] ' ) ;

471 t i t l e ( ' Required suc t i on : Feld ver sus SPT method ' ) ;s e t ( gca , 'YDir ' , ' r e v e r s e ' ) ;% hold on% p lo t ( suction_pressure_SPT_A , z , ' l inewidth ' , 2 ) ;hold on

476 p lo t ( pc r i t , z , '−− ' ) ;hold o f f



% plo t ( suction_pressure_SPT_A_he , z , ' l inewidth ' , 3 ) ;

%% PRESSURE GRADIENT INSIDE THE SUCTION PILE481

% Gradient = ( app l i ed p r e s su r e ∗ p r e s s u r e d i f f ) / l engthp r e s s u r e d i f f = 1 − press_t ip ;% Gradient i n s i d e the suc t i on p i l eg rad i en t = ( suct ion_pres sure_fe ld ( end , 1 : n1 ) . . .

486 .∗ p r e s s u r e d i f f ) . / ( ( y1+1)∗H) ;

% Flow i n s i d e the suc t i on p i l e% Permeab i l i ty o f the s o i l ( den Adel , 1987)

491 k = ( g∗d15^2.∗n .^3) . / ( ( 160∗ nu) .∗(1−n) .^2) ;d i sp l ay (k ) ;

% Discharge through the s o i l [m3/h ]Q = ( grad i en t .∗ k . ∗ ( Area/gamma_w) ) ∗60∗60;

496 d i sp l ay (Q) ;

%% PUMP CURVES% I t i s assumed that a pump i s used which has a f l e x i b l e power input . With% th i s type o f pumps a r e l a t i v e l y constant d i s cha rge can be maintained .

501 % This means that an i n i t i t a l d i s cha rge i s s e t up , r e s u l t i n g in an i n i t i a l% v e l o c i t y . Once the r e s i s t a n c e i n c r e a s e s , the p r e s su r e should i n c r e a s e and% the d i s cha rge should stay approximately the same . This by i n c r e a s i n g the% rounds per minute o f the used c e n t r i f u g a l pump .

506 p_feld = suct ion_pres sure_fe ld ( end , 1 : n1 ) /10 ;i n i t i a l _ i n s t a l l s p e e d = 1 ; % [m/h ]Qtotaal = Area ∗ i n i t i a l _ i n s t a l l s p e e d ; % [m3/h ]

i f any (Q>Qtotaal ) ,511 e r r o r ( 'SOIL TOO PERMEABLE TO INSTALL ' ) ;

end

%I n s t a l l a t i o n speed when the p i l e i s at depth y [m/ s ]

516 i n s t a l l s p e e d = ( Qtotaal − Q) . / ( Area ∗60∗60) ;d i sp l ay ( i n s t a l l s p e e d ) ;

%% FLOW ON THE BED INSIDE THE SUCTION PILE

521 % Discharge at a c e r t a i n l o c a t i o n i s de f ined by t h i s formula , each row o f% the d i s cha rge matrix shows the d i s cha rge at a c e r t a i n l o c a t i o n in the% suc t i on p i l ei = l i n s p a c e (0 , r , 1 00 ) ;d i s cha rge = (1− i .^2/ r ^2) '∗ ( Qtotaal . / (60∗60 ) ) ;

526

% Hor i zonta l speed at a c e r t a i n l o c a t i o n on the bed [m/ s ]s u r f a c e = 2∗ pi ∗(L−y1∗H) ∗ i ;speed = bsxfun ( @rdivide , d i scharge , su r face ' ) ;

531

% Plotsf i g u r e (6 ) ;subplot ( 2 , 1 , 1 ) ;p l o t ( i /( x1∗H) , speed ' ) ;

536 x l ab e l ( ' r /R [− ] ' ) ;y l ab e l ( ' Hor i zonta l f low speed [m/ s ] ' ) ;ax i s ( [ 0 . 1 1 0 0 . 0 5 ] ) ;hold on ;

541 subplot ( 2 , 1 , 2 ) ;p l o t ( i /( x1∗H) , d i scharge ' ) ;x l ab e l ( ' r /R [− ] ' ) ;y l ab e l ( ' Discharge [m3/ s ] ' ) ;hold o f f ;

546 matlab2t ikz ( ' ve l oc i tynosecondtop . tex ' ) ;



% Ver t i c a l speed i n s i d e the s o i lf l owspeed = (Q/(60∗60) ) . / ( n∗Area ) ;d i sp l ay ( f lowspeed ) ;

551

% The p lo t o f the d i s cha rge in the cent e r o f the suc t i on p i l e ( so the t o t a l% d i s cha rge )% f i g u r e (8 ) ;% p lo t (Dr , d i s cha rge ( 1 , 1 : n1 ) ) ;

556 % x lab e l ( ' Re l a t i v e dens i ty [ − ] ' ) ;% y l ab e l ( ' Total d i s cha rge [m^3/ s ] ' ) ;

%% EROSION561

% Sp e c i f i c weight s o i ld e l t a = (gamma_s−gamma_w)/gamma_w;

% Shie lds ' parameter566 theta = ( speed .^2) . / ( g∗ de l t a ∗d50 ) ∗ ones (1 , l ength (n) ) ;

% Reynolds numberRp = ( d50∗ s q r t ( d e l t a ∗g∗d50 ) ) /nu ;

571 % Cr i t i c a l Shie ld ' s parametertheta_c = 0.22∗Rp^−0.6 + 0.06∗ exp (−17.77∗Rp^−0.6) ;

% Exit g rad i en t ( seepage )i 1 = grad i en t . /gamma_w;

576

A = 1 . 7 ; %1/(1−n0 )cb = 0 ;ws = 1 ;

581 % Cr i t i c a l Shie ld ' s parameter i n c l ud ing the g rad i en ttheta_c1= ones ( l ength ( i ) , 1 ) ∗( theta_c .∗(1−A. ∗ ( i 1 . / de l t a ) ) ) ;

% Dimens ion les s p a r t i c l e diameterD_star = d50 ∗ ( ( d e l t a ∗g ) /(nu^2) ) ^(1/3) ;

586

% Pick−up func t i onphi_p = 0.00033∗ ( D_star ^0 .3) . ∗ ( ( theta−theta_c1 ) . / theta_c1 ) . ^ 1 . 5 ;

% Eros ion v e l o c i t y591 ve = ones ( l ength ( i ) , 1 ) ∗(1./(1−n−cb ) ) . ∗ . . .

( phi_p .∗ s q r t ( g∗ de l t a ∗d50 )−(cb∗ws) ) ;ve ( ve<0) = 0 ;ve ( i snan ( ve ) ) = 0 ;

596 % Plot o f the e r o s i on v e l o c i t y ver sus the i n s t a l l a t i o n v e l o c i t yf i g u r e (9 ) ;p l o t ( i , ve ) ;x l ab e l ( ' Radius [m] ' ) ;y l ab e l ( ' Eros ion v e l o c i t y [m/ s ] ' ) ;

601 a = c e l l (1 , n1 ) ;f o r i i =1:n1 ,

a{ i i } = s p r i n t f ( '%.2 f ' ,Dr( i i ) ) ;end ;l egh = legend (a , ' l o c a t i o n ' , ' EastOutside ' ) ;

606 v = get ( legh , ' t i t l e ' ) ;s e t (v , ' s t r i n g ' , ' Re l a t i v e dens i ty ' ) ;ax i s ( [ 0 x1∗H 0 0 . 0 0 0 5 ] ) ;hold on ;p l o t ( i , ones ( l ength ( i ) , 1 ) ∗ i n s t a l l s p e e d , '−− ' ) ;

611 hold o f f ;

s t r = ' Distance between top p l a t e and s o i l ' ;num = L−y1∗H;f i g u r e (10) ;

616 p lo t ( i , ve . / ( ones ( l ength ( i ) , 1 ) ∗ i n s t a l l s p e e d ) )x l ab e l ( ' Radius [m] ' ) ;



y l ab e l ( ' Eros ion / i n s t a l l a t i o n v e l o c i t y [− ] ' ) ;t i t l e ( [ s t r ' : ' num2str (num) ' [m] ' ] ) ;a = c e l l (1 , n1 ) ;

621 f o r i i =1:n1 ,a{ i i } = s p r i n t f ( '%.2 f ' ,Dr( i i ) ) ;

end ;l egh = legend (a , ' l o c a t i o n ' , ' EastOutside ' ) ;v = get ( legh , ' t i t l e ' ) ;

626 s e t (v , ' s t r i n g ' , ' Re l a t i v e dens i ty ' ) ;ax i s ( [ 0 . 1 x1∗H 0 1 ] ) ;mat lab2t ikz ( ' nosecondtop . tex ' ) ;

Combined_�le_v3.m

A.2. Calculation model based on non-homogeneous soil and

cone resistance

A.2.1. Parameters Project 1

% This model i s used to c a l c u l a t e the r equ i r ed suc t i on pr e s su r e to i n s t a l l2 % a suc t i on p i l e in r e a l i t y , g iven a c e r t a i n CPT p r o f i l e

c l e a r a l l ; c l c ;

% PROJECT 1 : D = 10m, H = 7m, twa l l = 30mm, Gsub = 3205kN%__________________________________________________________________________

7

% GENERAL PARAMETERS

% Gridx = input ( 'Amount o f e lements in x d i r e c t i o n (MAX 100 ! ) ' ) ;

12 y = input ( 'Amount o f e lements in y d i r e c t i o n (MAX 100 ! ) ' ) ;

% P i l ex1 = input ( ' Radius o f the suc t i on p i l e [# elements , 1 element = Hm] ' ) ;y1 = input ( 'Depth o f the suc t i on p i l e [# elements , 1 element = Hm] ' ) ;

17 H = input ( ' S i z e o f one g r id element ( square ) , H = f . e . 0 . 1 [m] ' ) ;

D = 2∗( x1 ) ∗H; % Diameter o f the suc t i on p i l etwa l l = 0 . 0 3 ;Gsub = 3205 ; % Submerged weight anchor [ kN ]

22 A = 0.25∗D^2∗ pi ; % Area o f the suc t i on p i l e top p l a t e

A_1 = 1 ; % Extra f a c t o r f o r inne r f r i c t i o nA_2 = 1 . 4 1 ; % Extra f a c t o r f o r outer f r i c t i o nA_3 = 1 . 2 ; % Extra f a c t o r f o r t i p bear ing

27

% Othergamma_w = 10 . 2 5 ; % Unit weight water [ kN/m3]H_w = 38 ; % Waterdepth [m]

32 % ________________________________________________________________________% GEO% FILL IN THE RESULTS OF THE CONE PENETRATION TEST. ATTENTION: ALL VECTORS% SHOULD HAVE THE SAME LENGTH!

37 gamma_s = 26 . 5 0 ; % Unit weight sandgamma_eff = 10 ; % Dry dens i ty bulk mater ia l , min and max

top_layer = [0 2 11 .5 13 .5 2 0 ] ' ; % Layer ing o f the s o i l42 bottom_layer = [2 11 .5 13 .5 20 2 0 ] ' ;

qc_top_layer = [0 27 43 43 0 ] ' ; % CPT per l ay e rqc_bottom_layer = [27 43 43 20 0 ] ' ;

Ithaca_jacky.m



A.2.2. Parameters Project 2

% Simon Lembrechts% 1386549% MSc Thes i s : I n i t i a l top p l a t e bear ing o f a suc t i on p i l e

4

% This model i s used to c a l c u l a t e the r equ i r ed suc t i on pr e s su r e to i n s t a l l% a suc t i on p i l e in r e a l i t y , g iven a c e r t a i n CPT p r o f i l ec l e a r a l l ; c l c ;

9 % PROJECT 2 : D = 15m, H = 12m, twa l l = 40mm, Gsub = 9042kN

%% PARAMETERS

14 % Gridx = input ( 'Amount o f e lements in x d i r e c t i o n (MAX 100 ! ) ' ) ;y = input ( 'Amount o f e lements in y d i r e c t i o n (MAX 100 ! ) ' ) ;

% P i l e19 x1 = input . . .

( ' Radius o f the suc t i on p i l e [# elements , 1 element = Hm] ' ) ;y1 = input . . .

( 'Depth o f the suc t i on p i l e [# elements , 1 element = Hm] ' ) ;H = input . . .

24 ( ' S i z e o f one g r id element ( square ) , H = f . e . 0 . 1 [m] ' ) ;

D = 2∗x1∗H; % Diameter o f the suc t i on p i l etwa l l = 0 . 0 4 ;Gsub = 9042 ; % Submerged weight anchor [ kN ]

29 A = 0.25∗D^2∗ pi ; % Area o f the suc t i on p i l e top p l a t e

% Extra f a c t o r s f o r inner f r i c t i o n , outer f r i c t i o n and% t i p bear ing ( in case the p i l e has a d i f f e r e n t layout% and has more su r f a c e on the i n s i d e )

34 A_1 = 1 ;A_2 = 1 ;A_3 = 1 ;

% Other39 gamma_w = 10 . 2 5 ; % Unit weight water [ kN/m3]

H_w = 40 ; % Waterdepth [m]

%% GEOTECHNICAL INFORMATION44 % FILL IN THE RESULTS OF THE CONE PENETRATION TEST. ATTENTION: ALL VECTORS

% SHOULD HAVE THE SAME LENGTH!

gamma_s = 26 . 5 0 ; % Unit weight sandgamma_eff = 10 ; % E f f e c t i v e weight bulk mate r i a l

49

top_layer = [0 0 .3 6 9 1 0 ] ' ; % Layer ing o f the s o i lbottom_layer = [ 0 . 3 6 9 10 1 5 . 8 ] ' ;qc_top_layer = [0 0 .2 50 35 6 0 ] ' ; % CPT per l ay e rqc_bottom_layer = [ 0 . 2 50 35 60 6 0 ] ' ;

54

% Layer th i c kne s sl aye r_th i ckne s s = bottom_layer−top_layer ;% In− or dec r ea se in cone r e s i s t a n c e per meterdelta_qc = ( qc_bottom_layer − . . .

59 qc_top_layer ) . / l aye r_th i cknes s ;% NaN numbers become 0delta_qc ( i snan ( delta_qc ) ) = 0 ;

% Depth i n t e r v a l s64 z = l i n s p a c e (0 , y1∗H, ( y1+1) ) ;

% In− or dec r ea se in cone r e s i s t a n c e f o r a depth−s tepdqc = ze ro s ( l ength ( z ) , 1 ) ;dqc ( z>bottom_layer ( end ) ) = delta_qc ( end ) ;



69

f o r x = 1 : ( l ength ( delta_qc )−1) ,dqc ( z<bottom_layer ( end−x ) ) = delta_qc ( end−x ) ;

end

74 dqc = [0 dqc ( 1 : end−1) ' ] ;qc = dqc '∗H;

f o r x = 1 : ( l ength ( qc )−1) ,qc ( x+1 ,1) = qc (x+1)+qc (x ) ;

79 end

qc = 1000 ∗ qc ; % From MPa to kPa

Venture_project.m

The model continues at rule 162 of the calculation model which is included in apendix A.1.

A.3. Calculation model based on Brinch-Hansen

c l e a r a l lc l c

3

time = x l s r ead ( 'Withoutsecondtop1 ' , ' t e s t 1 ' , 'C5 : C1977 ' ) ;pressure_out = x l s r e ad ( 'Withoutsecondtop1 ' , ' t e s t 1 ' , 'E5 : E1977 ' ) ;pressure_in = x l s r e ad ( 'Withoutsecondtop1 ' , ' t e s t 1 ' , 'F5 : F1977 ' ) ;

8 d i f f_ suc t i on = pressure_out−pressure_in ;

i n s t a l l t im e = 1850−258;l ength1 = 0 . 5 ;i n s t a l l s p e e d 1 = length1 /( i n s t a l l t im e /60/60) ;

13 d i sp l ay ( i n s t a l l s p e e d 1 ) ;

l e n g t h s c a l e = ( time (258 :1850)−258)/ i n s t a l l t im e ∗ l ength1 ;o f f s e t = mean( pressure_out ( 1 : 5 0 ) )−mean( pressure_in ( 1 : 5 0 ) ) ;

18 %% PARAMETERS

parami . gamma=8.5;parami . Di=0.6 ;parami .K=0.8;

23 parami . d=(1/12)∗ pi ;parami . Fi=1;

paramo .gamma=8.5;paramo .Do=0.61;

28 paramo .K=0.8;paramo . d=(1/12)∗ pi ;paramo . Fo=1;

phi = (1/6) ∗ pi ;33 twa l l = 0 . 0 1 ;

% S i z e o f one g r id elementH = 0 . 0 2 ;% Elements in x d i r e c t i o n

38 x = 75 ;% Elements in y d i r e c t i o ny = 75 ;% Radius o f the suc t i on p i l ex1 = parami . Di/2/H;

43 % Considered depth o f the suc t i on p i l ey1 = 30 ;% Total l ength o f the suc t i on p i l eL = 0 . 6 5 ;% Submerged weight suc t i on p i l e

48 Gsub = 0 . 2 ;% Pressure due to submerged weight



pressure_sub= Gsub/( x1^2∗ pi ) ;

53 % Grain s i z e [m]% Sand from 0.002m − 0.000063m% Unit weight water [ kN/m3]% Unit weight g r a i n s [ kN/m3]% Kinematic v i s c o s i t y [m2/ s ] at 5 degree s

58 % Gravity [m/ s2 ]% Waterdepth [m]d15 = 0 . 0002 ;d50 = 0 . 0002 ;gamma_w = 10 . 2 5 ;

63 gamma_s = 26 . 5 0 ;nu = 1.519∗10^−6;g = 9 . 8 1 ;H_w = 40 ;

68 % Diameter o f the suc t i on p i l e% Area o f the suc t i on p i l e top p l a t e [m2]% Radius o f the suc t i on p i l e [m]% Gr id s i z e [m x m]% Depth i n t e r v a l s [− ]

73 D = x1∗H∗2 ;Area = 0.25∗D^2∗ pi ;r = x1∗H;g r i d s i z e = [ x∗y x∗y ] ;z = l i n s p a c e (0 , y1∗H, ( y1+1) ) ;

78

A = ze ro s ( g r i d s i z e ) ;

y1step = l i n s p a c e (1 , y1 , y1 ) ;s ig i_deep1 = ones ( y1 , 1 ) ;

83 s i g i 1 = ones ( y1 , 1 ) ;s i g o1 = ones ( y1 , 1 ) ;i n t e g r aa l_s i g i d e ep1 = ones ( y1 , 1 ) ;i n t e g r a a l_ s i g i 1 = ones ( y1 , 1 ) ;i n t eg r aa l_s i go1 = ones ( y1 , 1 ) ;

88

% Fol lowing loop i s used because the ode45so lve r chooses i t ' s own time% st ep s . Because inner and outer f r i c t i o n should be c a l c u l a t ed at the same% depth to c a l c u l a t e the t o t a l s o i l r e s i s t an c e , the loop i s made and% c a l c u l a t e s the t o t a l s o i l r e s i s t a n c e at p i l e t i p f o r d i f f e r e n t

93 % penet ra t i on l eng th s . The r e s u l t i n g vec to r g i v e s the inner and outer% f r i c t i o n f o r equal s t ep s .f o r a = 1 : l ength ( y1step ) ,

%% SOLVER OF THE DIFFERENTIAL PROBLEM98 s ig i_0=0;

sigo_0=0;z1span =[0 .01 , a∗H] ;z2span =[0 .01 , a∗H] ;[ z1 , s i g i ]=ode45 (@func , z1span , s ig i_0 , [ ] , parami ) ;

103 [ z2 , s i g o ]=ode45 (@func2 , z2span , sigo_0 , [ ] , paramo ) ;

ga=10;Da=10;Ka=0.8;

108 da=(1/6)∗ pi ;

%% PLOT OF THE SOLLUTION% f i g u r e (1 ) ;

113 % plo t ( s i g i , z1 , ' l inewidth ' , 2 , ' co lo r ' , ' r ' ) ;% hold on ;% p lo t ( s igo , z2 , ' l inewidth ' , 2 ) ;% % hold on ;% % plo t ( s ig3 , t ) ;

118 % legend ( ' E f f e c t i v e s t r e s s i n s i d e p i l e ' , ' E f f e c t i v e s t r e s s ou t s id e p i l e ' , . . .% ' l o ca t i on ' , ' northeast ' ) ;



% x lab e l ( ' S t r e s s [ kPa ] ' ) ;% y l ab e l ( ' Depth [m] ' ) ;% s e t ( gca , ' YDir ' , ' r eve r s e ' ) ;

123 % matlab2t ikz ( ' br inchhansen1 . tex ' ) ;

Zideep = parami . Di /(4∗ parami .K∗ tan ( parami . d) ) ;s ig i_deep = parami . gamma∗Zideep ∗( exp ( z1/Zideep )−1) ;i n t e g r aa l_s i g i d e ep = parami . gamma . . .

128 ∗Zideep ^2∗( exp ( z1/Zideep )−1−(z1/Zideep ) ) ;

i n t e g r a a l_ s i g i=ones ( l ength ( z1−1) ,1 ) ;s t a r t = 0 ;

133 f o r i =1: l ength ( z1 )−1,i n t e g r a a l_ s i g i ( i )=(z1 ( i +1)−z1 ( i ) ) ∗( s i g i ( i +1)+s i g i ( i ) )/2+ s t a r t ;s t a r t = i n t e g r a a l_ s i g i ( i ) ;

end

138 f o r i =1: l ength ( z1 ) ,i f z1 ( i )<parami . Fi∗parami . Di /2 ,

i n t e g r a a l_ s i g i ( i )=i n t e g r a a l_ s i g i ( i ) ;e l s e

i n t e g r a a l_ s i g i ( i )=i n t e g r a a l_ s i g i ( i −1)+( i n t e g r aa l_s i g i d e ep ( i ) . . .143 − i n t e g r aa l_s i g i d e ep ( i −1) ) ;

endend

in t e g r aa l_s i g o=ones ( l ength ( z2−1) ,1 ) ;148 s t a r t = 0 ;

f o r i =1: l ength ( z2 )−1,i n t e g r aa l_s i g o ( i )=(z2 ( i +1)−z2 ( i ) ) ∗( s i g o ( i +1)+s i g o ( i ) )/2+ s t a r t ;s t a r t = in t eg r aa l_s i g o ( i ) ;

end153

s i g i 1 ( a ) = s i g i ( end ) ;s i g o1 ( a ) = s i g o ( end ) ;s ig i_deep1 ( a ) = s ig i_deep ( end ) ;i n t e g r aa l_s i g i d e ep1 ( a ) = in t e g r aa l_s i g i d e ep ( end ) ;

158 i n t e g r a a l_ s i g i 1 ( a ) = i n t e g r a a l_ s i g i ( end−1) ;i n t eg r aa l_s i go1 ( a ) = in t eg r aa l_s i g o ( end−1) ;end

f o r i =1: l ength ( z1 ) ,163 i f z1 ( i )<parami . Fi∗parami . Di /2 ,

s i g i ( i ) = s i g i ( i ) ;e l s e

s i g i ( i ) = s i g i ( i −1)+(s ig i_deep ( i )−s ig i_deep ( i −1) ) ;end

168 end

f i g u r e (1 ) ;p l o t ( s i g i , z1 , ' l i n ew id th ' ,2 , ' c o l o r ' , ' r ' ) ;hold on ;

173 p lo t ( s igo , z2 , ' l i n ew id th ' , 2 ) ;% hold on ;% p lo t ( s ig3 , t ) ;l egend ( ' E f f e c t i v e s t r e s s i n s i d e p i l e ' , ' E f f e c t i v e s t r e s s ou t s id e p i l e ' , . . .

' l o c a t i o n ' , ' no r theas t ' ) ;178 x l ab e l ( ' S t r e s s [ kPa ] ' ) ;

y l ab e l ( 'Depth [m] ' ) ;s e t ( gca , 'YDir ' , ' r e v e r s e ' ) ;mat lab2t ikz ( ' br inchhansen1 . tex ' ) ;

183 %% FRICTION IN

% fr ic t ion_in_deep = in t e g r aa l_s i g i d e ep ∗parami .K∗ tan ( parami . d) ∗ pi ∗parami . Di ;f r i c t i o n_ i n = i n t e g r a a l_ s i g i 1 ∗parami .K∗ tan ( parami . d) ∗ pi ∗parami . Di ;

188 % f r i c t i o n_ i n = ones ( l ength ( z1 ) ,1 ) ;% f o r i = 1 : l ength ( z1 ) ,



% i f z1 ( i )<parami . Fi∗parami . Di /2 ,% f r i c t i o n_ i n ( i )=f r i c t i o n_ in sha l l ow ( i ) ;% e l s e

193 % f r i c t i o n_ i n ( i )=f r i c t i o n_ i n ( i −1)+( f r i c t ion_in_deep ( i ) ) ;% end% end

198 %% FRICTION OUT

f r i c t i on_out=in t eg raa l_s i go1 ∗paramo .K∗ tan ( paramo . d) ∗ pi ∗paramo .Do ;

203 %% TIP BEARINGNq = (1+ s in ( phi ) ) /(1− s i n ( phi ) ) ∗exp ( p i ∗ tan ( phi ) ) ;Ngamma = 2∗(Nq−1)∗ tan ( phi ) ;alpha = s i g i 1−s i g o1 ;

208 % t1 = x −−> ( see paper houlsby )t1 = alpha< 2∗ twa l l ∗Ngamma/Nq ;t1 = t1 . ∗ ( twa l l /2 + alpha ∗Nq/(4∗ parami . gamma∗Ngamma) ) ;

sig_end = s i go1 ∗Nq+paramo .gamma. ∗ ( twal l −2∗t1 .^2/ twa l l ) .∗Ngamma;213

end_bearing = sig_end∗ pi ∗parami . Di∗ twa l l ;

z1 = l i n s p a c e (0 , y1∗H, y1 ) ;

218 %% TOTAL SOIL RESISTANCEt s r=( f r i c t i o n_ i n+f r i c t i on_out+end_bearing ) ;

f i g u r e (2 ) ,p l o t ( t s r , z1 , ' l i n ew id th ' ,2 , ' c o l o r ' , ' r ' ) ;

223 ax i s ( [ 0 t s r ( end−2)+0.5 0 z1 ( end−2) ] ) ;l egend ( ' Total s o i l r e s i s t a n c e ' , ' l o c a t i o n ' , ' nor theas t ' ) ;x l ab e l ( ' S o i l r e s i s t a n c e [ kPa ] ' ) ;y l ab e l ( 'Depth [m] ' ) ;s e t ( gca , 'YDir ' , ' r e v e r s e ' ) ;

228 matlab2t ikz ( ' br inchhansen2 . tex ' ) ;

%% THE GROUNDWATER FLOW: A RADIAL SYMMETRIC PROBLEMt i c ;

233 % FACTORS TO MAKE THE PROBLEM RADIAL SYMMETRIC

% Factor f o r the c e l l to the l e f t o f the cons ide r ed c e l lC1 = 1 − ( 1 . / ( 2 .∗ ( 0 : ( x−1) ) ) ) ' ;

238 % Factor f o r the c e l l to the r i g h t o f the cons ide r ed c e l lC2 = 1+(1 . / ( 2 .∗ ( 0 : ( x−1) ) ) ) ' ;

% The f i r s t row ( at x = 0) has no reduct ion , so f a c t o r equa l s 1C1( i s i n f (C1) ) = 1 ;

243 C2( i s i n f (C2) ) = 1 ;

% The r i gh t boundary i s model led as c l o s ed (dh/dr = 0)C1(x , 1 ) = 1 ;

248 % Transforms C1 in a r e p e t i t i v e vec to r with s i z e x∗yC1 = repmat (C1 , y , 1 ) ;C2 = repmat (C2 , y , 1 ) ;

% The c e l l s in the s k i r t don ' t have the reduct ion , as dh/dr = 0253 k = 0 : ( y1−1) ;

C1(k .∗ x+x1 , 1 ) = 1 ;C2(k .∗ x+x1+1 ,1) = 1 ;

% C1 i s a f a c t o r f o r the "−1 d iagona l " , which has l ength D0−1258 % C2 i s a f a c t o r f o r the "+1 d iagona l " , which has l ength D0−1

C1 = C1 ( 2 : end ) ;



C2 = C2 ( 1 : end−1) ;

263 %% THE GROUNDWATER FLOW: BUILDING THE BAND MATRIX

% D0 − Main d iagona lD0 = diag (A)−4; % In normal c i r cumstances the main diag i s −4

268 k = 1 : x ; % Top boundary as a f i x ed po t e n t i a lD0(k , 1 ) = −1;

% D1 − F i r s t band , below the diagonal , c e l l s to the l e f t o f the cons ide r ed273 % c e l l

D1 = diag (A,−1)+1; % In normal c i rcumstances , t h i s band equa l s 1

k = 0 : ( y1−1) ;D1(k .∗ x+x1 , 1 ) = 0 ; % This c e l l has to be 0 to model the s k i r t

278 D1(k .∗ x+x1−1 ,1) = 2 ;

k = 1 : ( y−1) ; % Ce l l s to be zero in order to remove theD1(k .∗ x , 1 ) = 0 ; % l i n k between the l a s t and the f i r s t column

283 k = 1 : y ; % Right boundary model led as a f i x edD1(k .∗ x−1) = 0 ; % po t en t i a l ( D i r i c h l e t ) , a l s o p o s s i b l e to

% model as a c l o s ed bound (Neumann)

k = 1 : x−1; % Top boundary as a f i x ed po t e n t i a l288 D1(k , 1 ) = 0 ;

D1( end−x+1:end ) = 0 ;

293 % D2 − Second band , above the diagonal , c e l l s to the r i g h t o f the% cons ide r ed c e l lD2 = diag (A, 1 ) +1; % In normal c i rcumstances , t h i s band equa l s 1

k = 0 : ( y1−1) ;298 D2(k .∗ x+x1 , 1 ) = 0 ; % This c e l l has to be 0 to model the s k i r t

D2(k .∗ x+x1+1) = 2 ;

k = 0 : ( y−1) ; % Ce l l s to compensate f o r the l e f t boundaryD2(k .∗ x+1 ,1) = 2 ; % This va lue i s 2 , because to c a l c u l a t e

303 % the po t e n t i a l in column one , you can take% 1/4∗( twice column two + row above +% row below ) as i t i s r a d i a l symmetric

k = 1 : ( y−1) ; % Ce l l s to be zero in order to remove the308 D2(k .∗ x , 1 ) = 0 ; % l i n k between the f i r s t and the l a s t column

D2( end−x+1:end ) = 0 ;

k = 1 : x−1; % Top boundary as a f i x ed po t e n t i a l313 D2(k , 1 ) = 0 ;

% D3 − Third band , below the diagonal , c e l l s above the cons ide r ed c e l lD3 = diag (A,−x )+1; % Bottom boundary model led as a c l o s ed

318 D3( end−x+1:end ) = 2 ; % bound (Neumann) , a l s o p o s s i b l e to apply a% c e r t a i n po t e n t i a l ( D i r i c h l e t )

D3( end−x+1:end ) = 0 ;

323 k = 1 : ( y−1) ;D3(k∗x ) = 0 ; % Right bound modelled as a D i r i c h l e t bound

% D4 − Fourth band , above the diagonal , c e l l s below the cons ide r ed c e l l328 D4 = diag (A, x )+1;



k = 1 : ( y−1) ;D4(k∗x ) = 0 ; % Right bound modelled as a D i r i c h l e t bound

333 k = 1 : x−1; % Top boundary as a f i x ed po t e n t i a lD4(k , 1 ) = 0 ;

%% ADDING THE FACTORS TO MAKE IT A CYLINDRICAL PROBLEM338

% Band D1 and D2 are the bands used to l i n k the cons ide r ed c e l l to% the c e l l b e f o r e and the c e l l a f t e r i t s e l f . So these d i agona l s% should have the reduct i on f a c t o r sD1 = D1.∗C1 ; % This i n c l ud e s the f a c t o r s f o r the

343 D2 = D2.∗C2 ; % c y l i n d r i c a l c oo rd ina t e s

%% SOLVING THE PROBLEM

348 % Matrix AA = diag (D0) + diag (D1,−1) + diag (D2 , 1 ) . . .

+ diag (D3,−x ) + diag (D4 , x ) ;

% Fixed node matrix B, This matrix i n c l ud e s the p o t e n t i a l s in the353 % f i x ed nodes , in t h i s case the p r e s su r e i n s i d e the suc t i on p i l e

B = ze ro s ( x∗y , 1 ) ;k = 1 : x1 ;

% This va lue i s the app l i ed p r e s su r e i n s i d e the suc t i on p i l e358 B(k , 1 ) = −1;

% Equation to be so lved to generate a vec to r with l ength x∗yY = A\B;

363 % We want to have a matrix with y rows and x columnsr e s u l t = ze ro s (x , y ) ;f o r i = 1 : y ,

r e s u l t ( : , i ) = Y(((−1+ i ) ∗x+1) : ( i ∗x ) ) ;end

368

% Get the geometry r i g h tr e s u l t = transpose ( r e s u l t ) ;

toc ;373

% r e s u l t ( 1 : y1 , ( x1+1) ) = NaN;

%% PLOTTING THE SOLUTION378

% Plot the r e s u l t in p i x e l s% imagesc ( r e s u l t ) ;

% Plot the r e s u l t smoothly383 f i g u r e (3 ) ;

contour f ( r e su l t , 1 1 ) ;colormap ( f l i p ud ( colormap ) ) ;s e t ( gca , 'YDir ' , ' rev ' ) ;c o l o rba r ;

388 hold on ;r e c t ang l e ( ' Po s i t i on ' , [ x1 , 0 , 1 , y1+1] , ' FaceColor ' , 'w ' ) ;hold on ;l i n e ( [ 0 x1 ] , [ y1+1 y1+1] , ' LineWidth ' ,3 , ' Color ' , 'w ' ) ;hold o f f ;

393

% Calcu la te the pore p r e s su r e at the p i l e t i p ( compared to the app l i ed% pre s su r er a t i o = ( y1 /(2∗ ( x1−1) ) ) ;d i sp l ay ( r a t i o ) ;

398



%% AVERAGE PRESSURE AT PILE TIP LEVEL

% To c a l c u l a t e the t o t a l i n f l ow o f water , the average p r e s su r e at the403 % p i l e t i p i s c a l c u l a t ed . As i t i s a c y l i n d r i c a l problem , the p r e s su r e s are

% f i r s t mu l t i p l i e d by a " su r f a c e f a c t o r " , b e f o r e the average i s taken .k = 1 : x1 ;f a c t o r = (2∗k−1)∗H^2∗ pi ;f a c t o r = f a c t o r /sum( f a c t o r ) ;

408 press_t ip = r e s u l t ( y1+1 ,1: x1 ) .∗ f a c t o r ;pres s_t ip = sum( press_t ip ) ;d i sp l ay ( pres s_t ip ) ;

pore_press_pi le_tip = ( r e s u l t ( y1+1,x1 )+r e s u l t ( y1+1,x1+1) ) /2 ;413 d i sp l ay ( pore_press_pi le_tip ) ;

%% SUCTION ASSISTED PENETRATION% Cr i t i c a l suc t i on p r e s su r e accord ing to f e l d f o r d i f f e r e n t d e n s i t i e s

418 f e l d = 1 . 32∗ ( ( z1/D) .^0 . 7 5 ) ∗D∗parami . gamma;

% Total s o i l r e s i s t a n c e without f r i c t i o n reduct i on [ kPa ]% Submerged weight o f the ca i s s on [ kPa ]W_sub = ones ( l ength ( z1 ) ,1 ) ∗Gsub ;

423

% I n i t i a l va lue s to s t a r t c a l c u l a t i o nsuct ion_pres sure = ones ( l ength ( z1 ) ,1 ) ;temp1 = ones ( l ength ( z1 ) ,1 ) ;counter = 0 ;

428

% Routine to c a l c u l a t e the reduced t o t a l s o i l r e s i s t a n c ewhi l e any ( any ( abs ( t s r − W_sub − . . .

suc t ion_pres sure ∗Area ) >0.0001) ) && counter <50000

433 suct ion_pres sure = ( t s r − W_sub) /Area ;temp1 = ( . 9 . ∗ temp1+.1.∗ suct ion_pres sure ) ;s e l = ( temp1>=fe ld ' ) ;% temp1 ( s e l )=f e l d ( s e l ) ;% temp1 ( temp1<=0) = 0 ;

438 % Makes a l l va lue s sma l l e r than 0 in suct ion_pres sure_fe ld equal to 0% This makes f e l d (1−temp1 . / f e l d ) equal to 1 in t h i s ca s e st s r = . . .

(1−(temp1 . / f e l d ' ) ) . ∗ . . .( f r i c t i o n_ i n+end_bearing ) + . . .

443 (1+(temp1 . / f e l d ' ) ) .∗ f r i c t i on_out ;% Make a l l NaN va lue s equal to 0 , because o f d i v i d i ng by 0t s r ( i snan ( t s r ) )= 0 ;counter = counter+1;

end448 f p r i n t f (1 , 'Number o f i t e r a t i o n s %.0 f \n ' , counter ) ;

suct ion_pres sure = ( t s r − W_sub) /Area ;suct ion_pres sure ( suct ion_pressure <0)=0;

453

%% PLOTS OF THE REQUIRED SUCTION PRESSURES

f i g u r e (5 ) ;c l f ;

458 p lo t ( suct ion_pressure , z1 ) ;x l ab e l ( ' Required suc t i on pr e s su r e [ kPa ] ' ) ;y l ab e l ( 'Depth [m] ' ) ;ax i s ( [ 0 f e l d ( end ) 0 z1 ( end−2) ] ) ;s e t ( gca , 'YDir ' , ' r e v e r s e ' ) ;

463 hold onp lo t ( f e l d , z1 , ' r−− ' ) ;hold onp lo t ( d i f f_ suc t i on (258 :1850)−o f f s e t , l e n g t h s c a l e +0.1 , ' l i n ew id th ' , 2 ) ;hold o f f

468 l egend ( ' Required suc t i on pr e s su r e ' , ' C r i t i c a l p r e s su r e ' , . . .' l o c a t i o n ' , ' no r theas t ' ) ;



matlab2t ikz ( ' br inchhansen3 . tex ' ) ;

brinchhansen.m

Some parameters need to be adapted, but in general the model continues at rule 271 of thecalculation model which is included in apendix A.1.

A.4. Strength parameters of the soil during the model tests

c l e a r a l lc l c

4 % gamma_eff should be somewhere between the minimal and maximal r e l a t i v e% dens i tygamma_eff = l i n s p a c e (8 ,13 ,100) ;K = 0 . 8 ;phi = (1/7) ∗ pi ;

9 de l t a = (2/3) ∗phi ;Do = 0 . 6 4 ;Di = 0 . 6 2 ;D = 0 . 6 3 ;t = 0 . 0 1 ;

14 h = 0 . 2 0 ;gamma = gamma_eff + 10 ;

Nq = (1+ s in ( phi ) ) /(1− s i n ( phi ) ) ∗exp ( p i ∗ tan ( phi ) ) ;Ngamma = 2∗(Nq−1)∗ tan ( phi ) ;

19

% V = the measured s o i l r e s i s t a n c e in [ kN ]V = 0 . 6 1 ;% Brinch = the bear ing capac i ty accord ing to Brinch Hansen [kN ]Brinch = ( ( gamma_eff∗h^2) /2) ∗(K∗ tan ( de l t a ) ) ∗( p i ∗Do) . . .

24 +((gamma_eff∗h^2) /2) ∗(K∗ tan ( de l t a ) ) ∗( p i ∗Di ) . . .+(gamma_eff∗h∗Nq+gamma∗ t /2∗Ngamma) ∗( p i ∗D∗ t ) ;

% The p lo t i s used to f i nd at which gamma_eff Brinch Hansen equal i s to% the measured s o i l r e s i s t a n c e

29 p lo t ( gamma_eff , Brinch ) ;hold on ;p l o t ( gamma_eff ,V∗ ones (1 , l ength ( Brinch ) ) ) ;hold o f f ;

34 % As the bear ing capac i ty i s de f ined by a combination o f phi and gamma_eff ,% f o l l ow i n g tab l e i s used to es t imate phi :% Fundamentals o f g e o t e chn i c a l eng in e e r i ng ( th i rd ed i t i on , Braja M. Das )% phi = ones ( l ength (Dr) ,1 ) ;% phi (Dr>0.8) = 45 ;

39 % phi (Dr<0.8) = 40 ;% phi (Dr<0.6) = 35 ;% phi (Dr<0.4) = 30 ;% phi (Dr<0.2) = 25 ;% phi = ( phi /180∗ pi ) ' ;

checkmaterial.m





B | Technical drawings of the model

B.1. The tank

Figure B.1: Technical drawing of the tank [6]

Appendix B. Technical drawings of the model 109


B.2. The procedure

Figure B.2: Installation of the pile.

Figure B.3: Test 1, without second top plate.



Figure B.4: Test 2, with second top plate.



B.3. Views of the di�erent test set-ups

Figure B.5: Side view of test 1.

Figure B.6: Top view of test 1.



Figure B.7: Side view of test 2.

Figure B.8: Top view of test 2.





C | Soil characterization model test

C.1. Permeability

Table C.1: Falling head test for vibrated sand, in a loose state

Count h A V T Q q i k

[-] [m] [m2] [m3] [s] [10−3m3/s] [10−3m/s] [−] [10−4m/s]

1 0.1 2.833 0.283 383 0.74 0.2611 1.184 2.2112 0.055 2.833 0.156 335 0.465 0.164 1.154 1.423

TOT 0.155 2.833 0.439 718 0.612 0.216 1.054 2.051

Table C.2: Falling head test for vibrated sand, in a dense state

Count h A V T Q q i k

[-] [m] [m2] [m3] [s] [10−3m3/s] [10−3m/s] [−] [10−4m/s]

1 0.04 2.833 0.113 280 0.405 0.143 1.29 1.1112 0.05 2.833 0.142 328 0.432 0.152 1.26 1.2133 0.04 2.833 0.113 312 0.363 0.128 1.23 1.0394 0.075 2.833 0.213 459 0.463 0.163 1.20 1.3725 0.055 2.833 0.156 484 0.322 0.114 1.16 0.9806 0.05 2.833 0.142 340 0.417 0.147 1.13 1.3007 0.045 2.833 0.128 344 0.371 0.131 1.11 1.183

TOT 0.355 2.833 1.006 2547 0.395 0.139 1.20 1.166

Appendix C. Soil characterization model test 115


Appendix C. Soil characterization model test 116


Bibliography

[1] C.G. Aldwinkle and Junaideen. The installation of o�shore plated foundations for oil Rig.PhD thesis, Department of Engineering Science, Oxford University, 1994.

[2] H.B.G. Allersma. Simulation of suction pile installation in sand in a geocentrifuge. ISOPE97Conference, Honolulu, 1:761�766, 1997.

[3] APPC. Appendix c - properties of soils. http://www.scribd.com/doc/120546245/APPC-Soil-Properties-pdf, January 2013.

[4] G. Baldi, V. Belloti, N. Ghionn, M. Jamiolkowski, and E. Pasqualini. Interpretation of cpt'sand cptu's. 4th International Geotechnical Seminar Field Instrumentation and In-Situ Mea-surements, pages 143�156, 1986.

[5] F.B.J. Barends and G.J.M. U�nk. Groundwater Mechanics, �ow and transport. TUDelft,1997.

[6] W. Broere. Tunnel Face Stability & New CPT Applications. PhD thesis, Delft University ofTechnology, 2001.

[7] G.A. Bruggeman. Analytical solutions of geohydrological problems. Elsevier, 1999.

[8] B.W. Byrne. Investigations of Suction Caissons in Dense Sand. PhD thesis, University ofOxford, 2000.

[9] Braja M. Das. Principles of Geotechnical Engineering. Cengage Learning inc., 2010.

[10] DNV. Foundations, classi�cation notes No 30.4. Hovik, 1992.

[11] C.T. Erbrich and T.I. Tjelta. Installation of bucket foundations and suction caissons in sand:geotechnical performance. O�shore Technology Conference, Houston, Texas, 1999.

[12] T. Feld. Suction buckets, a new innovative foundation concept, applied to o�shore wind tur-bines. PhD thesis, Aalborg University, 2001.

[13] G.T. Houlsby and B.W. Byrne. Design procedures for installation of suction caissons in clayand other materials. Geotechnical Engineering, 158(2):75�82, 2005.

[14] M.B. Jamiolkowski, V. Ghionna, and R. Lancellotta. New correlations of penetration testsfor design practice. Proceedings of the international symposium on penetration testing., 1988.

[15] T. Lunne, P. Robertson, and J. Powell. Cone penetration testing in geotechnical practice.1997.

[16] M. Senders. Suction caissons in sand as tripod foundations for o�shore wind turbines. PhDthesis, The University of Western Australia, School of Civil and Resource Engineering, August2008.

[17] K. Terzaghi, R.B. Peck, and G. Mesri. Soil Mechanics in Engineering Practice. 1995.

[18] T.I. Tjelta. Geotechnical aspects of bucket foundations replacing piles for europipe 16/11-eproject. Proc O�shore Technology Conference (OTC 7379), 1994.

[19] T.I. Tjelta, T.R. Guttormsen, and J. Hermstad. Large scale penetration test at a deepwatersite. Proc O�shore Technology Converence, Houston, Texas, USA, 1986.

Bibliography 117


[20] Manh Ngoc Tran. Installation of suction caissons in dense sand and the in�uence of silt andcemented layers. PhD thesis, The University of Sydney, October 2005.

[21] M.N. Tran, M.F. Randolph, and D.W. Airey. Study of seepage �ow and sand plug looseningin installation of suction caissons in sand. 2005.

[22] G.L.M. van der Schrieck. Dredging Technology, Guest lecture notes CIE5300. 2012.

[23] C. van Rhee. Sediment entrainment at high �ow velocity. Journal of hydraulic engineering,pages 572�582, 2010.

[24] C. van Rhee and A. van Bezuijen. In�uence of seepage on the stability of a sandy slope.Journal of Geotechnical Engineering, 118(8):1236�1240, 1992.

[25] L. C. van Rijn. Sediment pick-up functions. Journal of Hydraulic Engineering, 110(10):1494�1502, 1984.

[26] A. Verruijt and S. van Baars. Soil Mechanics. VSSD, 2007.

[27] D.J. White, H.K. Sidhu, T.C.R. Finlay, M.D. Bolton, and T. Nagayama. Press-in piling:the in�uence of plugging on driveability. International Conference on the Deep FoundationInstitute, New York, 8:299�310, 2000.

[28] D. Muir Wood. Geotechnical Modelling. Spon Press, 2004.

Bibliography 118

Documents

Initial top plate bearing of a suction pile