Numerical Modelling of Spudcan and Cone Penetration in Multi … · Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils by Jingbin Zheng B.Eng. This thesis is

Numerical Modelling of Spudcan and Cone

Penetration in Multi-Layer Soils

by

Jingbin Zheng

B.Eng.

This thesis is presented for the degree of

Doctor of Philosophy

of

Centre for Offshore Foundation Systems

School of Civil, Environmental and Mining Engineering

July 2015

Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils

I

ABSTRACT

Prior to any drilling operations, spudcan foundations supporting jack-up legs are

routinely preloaded through augmenting the weight of the rig by ballasting the hull. One

of the major geohazards related to spudcan installation is the potential for punch-

through failure, i.e. uncontrolled rapid leg penetration due to the reduction of soil

bearing capacity. This is a general concern for sites where stratified seabed comprises a

surface or interbedded strong layer overlying a soft layer, in particular with the move

towards heavier rigs and deeper waters.

In order to avoid unexpected punch-through failure, accurate rather than conservative

estimate of spudcan penetration resistance profile is required. However, current design

guidelines ISO standard 19905-1 recommend assessing the spudcan penetration

resistance by using a framework of conservative bearing capacity formulations, without

taking into account the true soil failure mechanisms associated with spudcan penetration

in multi-layer soils. The suggested ‘bottom-up approach’ combines the methods

developed for wished-in-place footings in single layer and two-layer soils (i.e.

squeezing for weak-over-strong layering system and punch-through for the reverse),

neglecting the influence of continuous spudcan penetration and trapped soil plug; and in

a strong-weak-strong layering system, the effect of the 3rd layer on the bearing capacity

in the 1st layer cannot be captured appropriately. It is a two-step approach in which soil

strength parameters are derived from the site specific soil investigation data for use in

bearing capacity models. Alternatively, for deeper water sites with the difficulty in

obtaining high-quality soil samples, the idea of correlating the spudcan penetration

resistance directly with the results from the in-situ cone penetration test (CPT) is

increasingly being considered. Thus far, correlations have been established only for

single layer soils.

The motivation for this study emanated directly from the ‘future needs’ identified by the

latest version of ISO standard 19905-1. The thesis presents the research on the bearing

response of spudcan foundation in multi-layer soils with the potential for punch-through.

Large deformation finite element (LDFE) methods were employed. The prime objective


II

was to develop rational and accurate design approaches for assessing spudcan

penetration resistance in multi-layer soils. The proposed design approaches can be

divided into two categories: (i) mechanism-based design approach with spudcan

penetration resistance calculated using soil parameters extracted from site investigation

data; and (ii) CPT-based design approach with spudcan penetration resistance calculated

directly from in-situ cone penetrometer tip resistance profile.

Four configurations of stratified deposit were considered, including (i) two-layer stiff-

over-soft clay, (ii) three-layer non-uniform clay with an interbedded stiff clay layer, (iii)

three-layer uniform stiff-soft-stiff clay, and (iv) clay-sand-clay deposits with and

without a 4th layer stiff clay. Clay layer was simulated using an elastic-perfectly plastic

Tresca soil model extended for strain softening and rate dependency of the undrained

shear strength, while sand layer was modelled using a modified Mohr-Coulomb model.

A number of analyses were performed with the aim of validating the numerical models

against existing data from centrifuge tests and case histories. Overall, satisfactory

agreement was obtained between the computed results and measured data, confirming

the capability and accuracy of the numerical models.

Parametric studies were then performed for spudcan and cone penetration to create a

database for the development of new mechanism-based and CPT-based design

approaches that rectify the deficiencies of the existing design methods. The new

mechanism-based design approaches account for the true soil failure mechanisms, and

strain softening and rate dependency of the undrained shear strength. Design formulas

were proposed to estimate the evolution of the soil plug height during spudcan

penetration and the corresponding influence on punch-through and squeezing.

Accordingly, CPT-based design approach was proposed by establishing direct

correlations between the penetration resistances of spudcan and cone for each

configuration of soil profile. In addition, adjustment factors were proposed for

improving the ISO suggested design methods and the design methods recently proposed

by other researchers.

The predicted profiles using the proposed design approaches were compared with the

data from centrifuge tests and case histories. The ISO bottom-up approach was also

adopted for comparison. Predictions using the new approaches were found to be in good

agreement with measured load-penetration profiles, while under most circumstances the


III

ISO bottom-up approach provided conservative estimation for the bearing capacity and

overestimation for the depth of triggering squeezing.


IV

DECLARATION

I hereby declare that, except where specific reference is duly made to the work of

others, the contents of this thesis are original and have not been submitted in whole or in

part to any other university.


V

ACKNOWLEDGEMENTS

First and foremost, I would like to express my heartfelt thanks to my supervisor Dr

Muhammad Shazzad Hossain for providing me with the opportunity to start this

fascinating and rewarding research journey. His guidance and support have inspired me

to begin and finish this research. Also thank you for putting up with my numerous

grammatical errors and typos when revising my papers and thesis, and in particular for

strongly supporting my ‘ISOPE Outstanding Student 2015’ award winning application.

Besides the research, do appreciate for the trip to Moore River, which made me realise

the great beauty of Western Australia.

Deepest gratitude also goes to my co-supervisor Dr Dong Wang, without whom I

would never finish my PhD. Many thanks to you for introducing me to the world of

LDFE methods, which was painful from the beginning to the end but accompanied with

strong sense of accomplishment. I am also grateful to you for the invitation to spend

each Spring Festival Eve with your family.

I am so grateful to my uncle Mr Shiquan Huang and his family, who helped me to

settle down in Perth. Thank you in particular for the fishes and crabs you caught and

shared with us. I also would like to extend my appreciation to my friends in Perth. I

would not have had such a happy and memorable time without your companionship.

Thanks also to my friends in China, who encouraged and helped me a lot.

I acknowledge the financial support from UWA SIRF and UIS scholarships, the ARC

Linkage Project LP110100174, the Convocation Postgraduate Research Travel Award

and Australia-China Natural Gas Technology Partnership Fund Scholarship. I also

gratefully appreciate all the administrative and IT support, especially from Mrs Monica

Mackman, Mr Kan Yu and Mr Keith Russell.

Finally, I am deeply indebted to my parents and my beloved wife, Linshan Hou. My

debts to you all could never be paid off. Your continuous support, love and dedication

are forever appreciated.


VI

TABLE OF CONTENTS

ABSTRACT ...................................................................................................................... I

DECLARATION ........................................................................................................... IV

ACKNOWLEDGEMENTS........................................................................................... V

TABLE OF CONTENTS.............................................................................................. VI

PUBLICATIONS ARISING FROM THIS RESEARCH .......................................... X

NOTATION ................................................................................................................. XII

CHAPTER 1. INTRODUCTION ............................................................................... 1-1

Jack-Up Rig and Spudcan Foundations .......................................................... 1-1

Jack-Up Evolution in Problematic Seabed Sediments .................................... 1-2

Punch-Through and Rapid Leg Run ............................................................... 1-2

ISO Suggested Design Methods ..................................................................... 1-3

1.4.1 Layering System a: Single Layer Clay .......................................... 1-4

1.4.2 Layering System b: Stiff-over-Soft Clay ....................................... 1-5

1.4.3 Layering System b: Sand-over-Clay .............................................. 1-6

1.4.4 Layering System c: Soft Clay Overlying Strong Layer ................. 1-7

1.4.5 Spudcan Penetration in Multi-Layer Soils ..................................... 1-7

Alternative Cone Penetrometer-Based Direct Design Approach .................... 1-8

Objectives and Structure of the Thesis ........................................................... 1-8

Reference ................................................................................................................ 1-11

Figures .................................................................................................................... 1-15

CHAPTER 2. LARGE DEFORMATION FINITE ELEMENT METHODS ........ 2-1

Introduction ..................................................................................................... 2-1

Theoretical Background of CEL and ALE ..................................................... 2-2

2.2.1 CEL Approach ............................................................................... 2-3

2.2.2 ALE Approach ............................................................................... 2-5

Numerical Model ............................................................................................ 2-7

2.3.1 Model Details ................................................................................. 2-7

2.3.2 Constitutive Models ....................................................................... 2-9

Validation ...................................................................................................... 2-14

Reference ................................................................................................................ 2-16

Tables ..................................................................................................................... 2-20

Figures .................................................................................................................... 2-22

CHAPTER 3. CONE IN SINGLE LAYER CLAY AND SAND ............................. 3-1

Introduction ..................................................................................................... 3-1

Literature Review ............................................................................................ 3-1

3.2.1 CPT in Clays .................................................................................. 3-2


VII

3.2.2 CPT in Sands .................................................................................. 3-3

Numerical Analysis ......................................................................................... 3-3

Results and Discussion: Clay .......................................................................... 3-4

3.4.1 Penetration in Non-Softening, Rate-Independent Clay .................. 3-5

3.4.2 Penetration in Strain-Softening, Rate-Dependent Clay ................. 3-5

Results and Discussion: Sand ......................................................................... 3-7

3.5.1 Simulation of Centrifuge Test ........................................................ 3-9

3.5.2 Results of Parametric Study ......................................................... 3-10

3.5.3 Formula for Cone Tip Resistance in Silica Sand ......................... 3-11

Concluding Remarks ..................................................................................... 3-11

Reference ................................................................................................................ 3-13

Tables ..................................................................................................................... 3-16

Figures .................................................................................................................... 3-17

CHAPTER 4. SPUDCAN IN STIFF-OVER-SOFT CLAY ..................................... 4-1

Introduction ..................................................................................................... 4-1

Literature Review ............................................................................................ 4-2


4.3.1 Simulation of Centrifuge Tests ...................................................... 4-4

4.3.2 Results and Discussion ................................................................... 4-5

New Mechanism-Based Design Approach ..................................................... 4-7

4.4.1 Peak Resistance .............................................................................. 4-7

4.4.2 Resistance at Layer Interface ....................................................... 4-10

4.4.3 Deep Bearing Capacity Factor Ncd ............................................... 4-10

4.4.4 Summary Design Procedure ......................................................... 4-11

New CPT-Based Design Approach ............................................................... 4-11

4.5.1 Peak Resistance ............................................................................ 4-13

4.5.2 Resistance at Layer Interface ....................................................... 4-14

4.5.3 Deep Penetration Resistance in Soft Clay .................................... 4-14

4.5.4 Summary Design Procedure ......................................................... 4-14

Application .................................................................................................... 4-15


Reference ................................................................................................................ 4-17

Tables ..................................................................................................................... 4-19

Figures .................................................................................................................... 4-22

CHAPTER 5. SPUDCAN IN NON-UNIFORM CLAY WITH AN INTERBEDDED

STIFF CLAY LAYER ................................................................................................. 5-1

Introduction ..................................................................................................... 5-1


5.2.1 Validation of Numerical Model ..................................................... 5-2

5.2.2 Soil Flow Mechanisms ................................................................... 5-4

5.2.3 Parametric Study ............................................................................ 5-4



VIII

5.3.1 Limiting Cavity Depth ................................................................... 5-7

5.3.2 Simplified Penetration Resistance Profile ...................................... 5-7

5.3.3 Punch-through ................................................................................ 5-8

5.3.4 Bearing Capacity in 1st Layer ....................................................... 5-10

5.3.5 Points 3 and 4 ............................................................................... 5-11

5.3.6 Bearing Capacity in Bottom Layer .............................................. 5-12

5.3.7 Summary Design Procedure......................................................... 5-13

New CPT-Based Design Approach............................................................... 5-13

5.4.1 Simplified Penetration Resistance Profiles .................................. 5-14

5.4.2 Single Layer Response: Stages (1) and (5) .................................. 5-15

5.4.3 Squeezing: Point 2 ....................................................................... 5-16

5.4.4 Peak Resistance: Point 3 .............................................................. 5-16


Application .................................................................................................... 5-17

5.5.1 Centrifuge Tests ........................................................................... 5-17

5.5.2 Case History ................................................................................. 5-19

Conluding Remarks ...................................................................................... 5-19

Reference ................................................................................................................ 5-21

Tables ...................................................................................................................... 5-23

Figures .................................................................................................................... 5-24

CHAPTER 6. SPUDCAN IN UNIFORM STIFF-SOFT-STIFF CLAY ................. 6-1

Introduction ..................................................................................................... 6-1


6.2.1 Validation of Numerical Model ..................................................... 6-2

6.2.2 Soil Flow Mechanisms ................................................................... 6-3

6.2.3 Parametric Study ............................................................................ 6-3


6.3.1 Limiting Cavity Depth ................................................................... 6-5

6.3.2 Simplified Penetration Resistance Profile ...................................... 6-6

6.3.3 Bearing Capacity in 1st Layer ......................................................... 6-8

6.3.4 Bearing Capacity in 2nd Layer ........................................................ 6-9

6.3.5 Bearing Capacity in 3rd Layer ...................................................... 6-10


New CPT-Based design Approach ............................................................... 6-12

6.4.1 Simplified Penetration Resistance Profiles .................................. 6-12

6.4.2 Bearing Capacity in 1st Layer ....................................................... 6-13

6.4.3 Bearing Capacity in 2nd Layer ...................................................... 6-14

6.4.4 Bearing Capacity in 3rd Layer ...................................................... 6-15


Application .................................................................................................... 6-16

6.5.1 Centrifuge Test ............................................................................. 6-16

6.5.2 Case History ................................................................................. 6-17


IX


Reference ................................................................................................................ 6-20

Tables ..................................................................................................................... 6-21

Figures .................................................................................................................... 6-22

CHAPTER 7. SPUDCAN IN MULTI-LAYER SOILS WITH AN INTERBEDDED

SAND LAYER .............................................................................................................. 7-1

Introduction ..................................................................................................... 7-1

Design Methods .............................................................................................. 7-1


Numerical Results and Discussion .................................................................. 7-4

7.4.1 Simulation of Centrifuge Tests ...................................................... 7-4

7.4.2 Effect of 1st Layer Clay .................................................................. 7-5

7.4.3 Effect of 2nd Layer Sand ................................................................. 7-6

7.4.4 Effect of 3rd Layer Clay.................................................................. 7-7

Suggested Improvements ................................................................................ 7-9

7.5.1 Peak Resistance in Sand Layer ...................................................... 7-9

7.5.2 Limiting Squeezing Depth ........................................................... 7-10

Overall Performance of Design Methods ...................................................... 7-11

7.6.1 Peak Resistance in Sand Layer .................................................... 7-11

7.6.2 Bearing Capacity in Clay Layer ................................................... 7-12

7.6.3 Limiting Squeezing Depth ........................................................... 7-13

CPT-Based Design Approach ....................................................................... 7-13


Reference ................................................................................................................ 7-16

Tables ..................................................................................................................... 7-18

Figures .................................................................................................................... 7-22

CHAPTER 8. CONCLUDING REMARKS .............................................................. 8-1

Introduction ..................................................................................................... 8-1

Key Contributions and Findings ..................................................................... 8-2

8.2.1 Implementation of Advanced Soil Models .................................... 8-2

8.2.2 Cone Penetration in Single Layer Clay and Sand Deposits ........... 8-2

8.2.3 Spudcan Penetration in Layered Deposits ..................................... 8-3

Recommendations for Future Research .......................................................... 8-6

8.3.1 LDFE Analyses Covering Broader Range of Parameters .............. 8-6

8.3.2 Advanced Sand Models.................................................................. 8-6

8.3.3 Generalisation of Design Methods ................................................. 8-7

8.3.4 Consolidation and Extraction Problems ......................................... 8-7

Reference .................................................................................................................. 8-8


X

PUBLICATIONS ARISING FROM THIS RESEARCH

JOURNAL PAPERS

1. Zheng, J., Hossain, M. S. & Wang, D. (2014). Numerical modeling of spudcan

deep penetration in three-layer clays. International Journal of Geomechanics,

ASCE, 10.1061/(ASCE)GM.1943-5622.0000439, 04014089.

2. Zheng, J., Hossain, M. S. & Wang, D. (2015). New design approach for spudcan

penetration in nonuniform clay with an interbedded stiff layer. Journal of

Geotechnical and Geoenvironmental Engineering, ASCE 141, No. 4, 04015003.

3. Zheng, J., Hossain, M. S. & Wang, D. (2015). Estimating spudcan penetration

resistance in stiff-soft-stiff clay. Journal of Geotechnical and Geoenvironmental

Engineering, ASCE, Submitted June 2015.

4. Zheng, J., Hossain, M. S. & Wang, D. (2015). Prediction of spudcan penetration

resistance profile in stiff-over-soft clays. Canadian Geotechnical Journal,

Submitted July 2015.

5. Zheng, J., Hossain, M. S. & Wang, D. (2015). Numerical investigation of

spudcan penetration in multi-layer deposits with an interbedded sand layer.

Under preparation.

CONFERENCE PAPERS

1. Zheng, J., Hossain, M. S. & Wang, D. (2012). 3D large deformation FE analysis

of circular footing and spudcan on clay using CEL approach. Proc. 2nd

International Symposium on Constitutive Modelling of Geomaterials, Beijing,

803-810.

2. Zheng, J., Hossain, M. S. & Wang, D. (2013). 3D large deformation FE analysis

of spudcan and cone penetration on three-layer clays. Proc. 23rd International

Offshore and Polar Engineering Conference, Anchorage, ISOPE-I-13-241.

3. Zheng, J., Hossain, M. S. & Wang, D. (2014). Large deformation finite element

analysis of cone penetration on strain softening, rate dependent non-

homogeneous clay. Proc. 3rd International Symposium on Cone Penetration

Testing, Las Vegas, Nevada.


XI

4. Zheng, J., Hossain, M. S. & Wang, D. (2014). CPT based direct design approach

for spudcan penetration in non-uniform clay with an interbedded stiff layer.

Proc. 14th International Conference of the International Association for

Computer Methods and Advances in Geomechanics, Kyoto, 895-900.


XII

NOTATION

A spudcan plan area at largest section

C1~C5 coefficients for estimating cone tip resistance

D spudcan diameter at largest section

Dc cone diameter at largest section

DF distribution factor

d penetration depth of spudcan or cone at lowest point of largest section

dd penetration depth of dummy spudcan base (bottom of soil plug)

dH penetration depth of soil backflow

dint depth of stiff-soft or sand-clay layer interface

dkt steady state depth

dp penetration depth of peak resistance

dr penetration depth of establishing single layer response

dsq penetration depth of triggering squeezing

dtip penetration depth of cone tip

E Young’s modulus

f1, f2 coefficients for estimating soil plug thickness during penetration

Hcav open cavity depth after spudcan installation

Hplug total soil plug thickness

Hplug,i soil plug thickness in ith layer soil

Hs thickness of sand layer

hP-T punch-through distance


XIII

hsq limiting squeezing depth

ID relative density of sand

IR dilatancy index

Ir rigidity index

K0 coefficient of lateral earth pressure at rest

Ks punching shear coefficient

k rate of increase of undrained shear strength of bottom layer soil

ki rate of increase of undrained shear strength of ith layer soil

Nc bearing capacity factor

Nc,int bearing capacity factor at layer interface of two-layer system

Ncd deep bearing capacity factor of spudcan

Ncr shallow bearing capacity factor for rough-based spudcan

Nkt deep bearing capacity factor of cone

Nkt,s shallow bearing capacity factor of cone

ns load spread factor

P total vertical reaction force

Ppeak total vertical reaction force at peak

p mean effective stress

p0 effective overburden pressure of soil at depth d

Qv gross penetration resistance = Aqv

Qv,peak gross penetration resistance at peak

q deviatoric stress

q0 surcharge on sand layer surface

qc measured cone tip resistance


XIV

qD/2,comp computed penetration resistance at D/2 below sand-clay layer interface

qD/2,est estimated penetration resistance at D/2 below sand-clay layer interface

qD/2,meas measured penetration resistance at D/2 below sand-clay layer interface

qD,comp computed penetration resistance at 1D below sand-clay layer interface

qD,est estimated penetration resistance at 1D below sand-clay layer interface

qD,meas measured penetration resistance at 1D below sand-clay layer interface

qint net penetration resistance at layer interface of stiff-over-soft clay deposit

qnet net penetration resistance of spudcan according to Equation 4.1

qnet,c net penetration resistance of cone

qnet,c0 net cone tip resistance at spudcan base level

qnet,c1b net cone tip resistance at bottom of 1st layer soil

qnet,cbs net cone tip resistance at surface of bottom layer soil

qnet,ci net cone tip resistance of ith layer soil

qnet,cis net cone tip resistance at surface of ith layer soil

qnet,ct net cone tip resistance of top layer soil

qnet,sp net penetration resistance of spudcan according to Equation 4.8

qnets net penetration resistance of spudcan at seabed surface

qpeak penetration resistance of spudcan at peak

qpeak,comp computed peak resistance in sand layer

qpeak,est estimated peak resistance in sand layer

qpeak,meas measured peak resistance in sand layer

qt total cone tip resistance after correction for unequal pore pressure

qu total penetration resistance

qu,c total penetration resistance of cone


XV

qu,sp total penetration resistance of spudcan

qv gross penetration resistance

Rb rate coefficient

Rsp-c penetration resistance ratio

St soil sensitivity

su intact undrained shear strength of clay

su,int intact undrained shear strength of clay at sand-clay layer interface

su0 intact undrained shear strength at penetration depth d

su2e equivalent undrained shear strength of 2nd layer soil in stiff-soft-stiff clay

sub intact undrained shear strength of bottom layer soil

sub0 intact undrained shear strength at penetration depth d in bottom layer

subs intact undrained shear strength at surface of bottom layer soil

suc undrained shear strength of clay after strain softening and rate effects

sud0 intact local undrained shear strength at dummy spudcan base level dd

sues equivalent undrained shear strength at sand-clay layer interface

sui intact undrained shear strength of ith layer soil

suib intact undrained shear strength at bottom of ith layer soil

suip average undrained shear strength around soil plug periphery in ith layer

suis intact undrained shear strength at surface of ith layer soil

sum intact undrained shear strength at mudline (i.e. z = 0)

sut intact undrained shear strength of top layer soil

T distance between spudcan base and layer interface in two-layer system

T equivalent thickness of soil plug (upper layer soil) in lower layer

t thickness of top layer soil


XVI

ti thickness of ith layer

Vp intended preload for spudcan installation

Vsp volume of spudcan submerged by soil

vfield penetration velocity in the field

z depth below soil surface

cone area ratio

effective unit weight of soil

b effective unit weight of bottom layer soil

c effective unit weight of clay

i effective unit weight of ith layer soil

s effective unit weight of sand

t effective unit weight of top layer soil

maximum shear strain rate

b average maximum shear strain rate in deep penetration

ref reference shear strain rate at which su is assessed

d incremental penetration depth during each time step

p

ije incremental deviatoric plastic strain tensor

, increment of maximum, minimum principal strain

p

1 , p

3 increment of maximum, minimum principal plastic strain

rem remoulded ratio (inverse of sensitivity)

ep cumulative equivalent plastic strain

ep

crit cumulative equivalent plastic strain required to achieve critical state


XVII

ep

p cumulative equivalent plastic strain corresponding to peak friction angle

stress ratio

adjustment factor considering strain softening and rate effects

post-peak gradient of penetration resistance profile

factor for estimating bearing capacity at soft-stiff layer interface

adjustment factor considering presence of 4th layer stiff clay

rate parameter

cumulative absolute plastic shear strain

95 softening parameter

b average cumulative plastic shear strain in deep penetration

rate of increase of net cone tip resistance in bottom layer soil

i rate of increase of net cone tip resistance in ith layer soil

v0 total overburden stress

1, 3 maximum, minimum effective principal stress

m geostatic mean effective stress

effective friction angle

crit critical state friction angle

i initial effective friction angle

p peak effective friction angle

* reduced friction angle

dilation angle

p peak dilation angle

Chapter 1. Introduction

1-1

CHAPTER 1. INTRODUCTION

JACK-UP RIG AND SPUDCAN FOUNDATIONS

Mobile jack-up rigs are used widely in the offshore oil and gas industry for installing

small platforms, maintenance work and drilling and even for production for fields of

limited life. Today’s jack-ups typically consist of a buoyant triangular platform

supported by three independent vertically retractable K-lattice legs, each resting on a

spudcan (Figure 1.1). Spudcans are generally circular or polygonal in plan, with a

shallow conical underside sometimes incorporating a central spigot to provide improved

sliding resistance, as illustrated schematically in Figure 1.2a. Spudcans may also be

with 3 or 4 cutouts (Figure 1.2b) and with a short skirt around the periphery (Figure

1.2c). The typical area equivalent diameter of spudcan ranges from 10 to 20 m.

Prior to commencing jack-up operations, spudcans are routinely proof loaded by static

vertical preloading (either sequentially or simultaneously) to increase the size of the

yield envelope in vertical, horizontal and moment load space, and thus ensure they have

sufficient reserve capacity in any extreme storm design event (ISO, 2012). Typically,

preloading is accomplished by pumping seawater into holding tanks within the hull,

once the legs are pinned to the seabed under the rig’s self-weight and an air gap has

been created between the underside of the hull and the sea surface. Each spudcan is

preloaded to between 50 and 100% above normal operating conditions (ISO, 2012). The

preload is generally maintained for 2 to 4 hours. This causes the spudcan foundations to

penetrate into the seabed until the load on the spudcan is equilibrated by the resistance

of the underlying soil. The preload is then dumped and the hull is elevated further to

provide an adequate air gap for subsequent operations. During this preloading stage,

assuming calm weather, the foundations of a jack-up unit are subjected to essentially

vertical loading. The preload bearing pressure usually ranges from 150 to 500 kPa

(Menzies & Roper, 2008; Menzies & Lopez, 2011; Hossain et al., 2014).

There has been continual evolution of rig operations into new regions and greater water

depths, and today independent-legged jack-up rigs are used for most offshore drilling

operations in water depths up to around 150 m. With the move towards heavier rigs in


1-2

deeper water, appraisal of the performance and safety of jack-up rigs have become

increasingly important. A crucial aspect is to improve the understanding of the

mechanisms of soil flow around spudcan foundations undergoing continuous large

penetration, and to assess the likelihood of a sudden penetration of the spudcan and its

degree of severity.

JACK-UP EVOLUTION IN PROBLEMATIC SEABED SEDIMENTS

Depletion of known reserves in the shallow waters of traditional hydrocarbon regions is

resulting in exploration in deeper, unexplored and undeveloped environments, which are

exhibiting more complex soil conditions at the seabed. The Sunda Shelf, offshore

Malaysia, Australia’s Bass Strait and North-West Shelf, Gulf of Thailand, South China

Sea, offshore India and Arabian Gulf are particularly problematic in terms of

stratigraphy and soil types (see Figure 1.3). Layered deposits are also encountered in the

Gulf of Mexico (Menzies & Lopez, 2011). Layered soil profiles result from various

geological processes, including previous crustal desiccation, sand channelling and

evolving depositional environments associated with changing sea level (Castleberry II

& Prebaharan, 1985; Paisley & Chan, 2006).

PUNCH-THROUGH AND RAPID LEG RUN

Jack-up installation in stratified deposits, where a surface or an interbedded strong layer

overlies a weaker layer, has always been a challenge. A sudden decrease of soil bearing

capacity, which occurs when the spudcan punches a block of soil from the strong layer

into the underlying weaker layer, leads to rapid leg penetration. In the oil and gas

industry, this is termed either ‘rapid leg run’, which is controllable by jacking capacity,

or ‘punch-through’ failure, which signifies the uncontrollable penetration over a

significant depth (see Figure 1.4). Geotechnically and in general, the term ‘punch-

through’ is defined for a negative post peak gradient of the penetration resistance, < 0,

and ‘rapid leg run’ for essentially no increases in penetration resistance (i.e. 0).

Although the potential hazard of crustal features is well documented (SNAME, 2002),

jack-ups continue to suffer failures at an increasing rate (increased by a factor of five


1-3

over the last eight years; Jack et al., 2013). These events can result in loss of drilling

time (jack-up rigs’ average daily rate from $68,000 to $180,000; www.rigzone.com),

and sometimes may even lead to buckling of the leg, effectively decommissioning the

platform, or toppling of the unit (McClelland et al., 1982; Aust, 1997; Maung & Ahmad,

2000; Brennan et al., 2006; Kostelnik et al., 2007; Chan et al., 2008). The consequential

cost is estimated to be between $5 and $50 million per incident (Jack et al., 2013).

ISO SUGGESTED DESIGN METHODS

The recently finalised version of ISO standard 19905-1 (ISO, 2012; Wong et al., 2012)

is an improvement of the existing guidelines in SNAME (2002) for the jack-up industry,

based on the industry and academic publications then available. The design methods for

assessing spudcan penetration resistance are recommended for three configurations of

soil layering system: (a) single layer soils; (b) punch-through criterion for strong-over-

weak layering system; and (c) squeezing criterion for weak-over-strong layering system.

Owing to the lack of investigation on more general multi-layer deposits, no

recommendation is given apart from concisely noting that a so-called ‘bottom-up

approach’ can be used combining the squeezing and punch-through criteria for two-

layer systems.

In this section, for each configuration of soil profile (layering system a, b or c), the

design formulas recommended by ISO (2012) and their deficiencies are first briefly

discussed. The design approaches proposed by recent investigations, which will be used

in other chapters for comparison with the results from this study, are then highlighted.

Layering system a can generally be divided as single layer clay and single layer sand

deposits. For single layer sand, spudcans barely penetrate up to the full diameter, which

is beyond the scope of this thesis, and hence only the discussion on single layer clay is

included. Discussion on layering system b is further divided into two categories: stiff-

over-soft clay and sand overlying clay as commonly encountered in the field.

To calculate the penetration resistance profile of spudcans of various shapes and

geometries, ISO (2012) recommends using a simplified flat- (Skempton method;

Skempton, 1951) or conical-based (Houlsby-Martin method; Houlsby & Martin, 2003)

circular foundation with area equivalent diameter, Deq. This concept is illustrated in

http://www.rigzone.com/


1-4

Figure 1.5. Analysing field data, centrifuge test data and numerical results, Hossain et al.

(2015) broadly confirmed the accuracy of these assumptions for assessing spudcan

penetration resistance. As such, no further attention is given on the effect of spudcan

geometry in this study.

1.4.1 Layering System a: Single Layer Clay

For single layer clay deposit under undrained conditions (friction angle = 0), the

calculation of bearing capacity profile adopts the bearing capacity factors reported by

Prandtl (1921) for a surface strip footing on homogeneous clay, with adjustment of

shape and depth factors after Skempton (1951). The penetration resistance of a spudcan

foundation of diameter D and maximum bearing area A, at a certain depth d, then is

expressed as

(1.1)

where Qv is the gross penetration resistance with an open cavity above the foundation

(i.e. assuming no soil backfill), Nc = Min[6(1 + 0.2d/D), 9.0] is the bearing capacity

factor, su is the undrained shear strength of the (uniform) clay deposit, and p0 is the

effective overburden pressure of soils above spudcan base level. For non-uniform clay

deposits, this bearing capacity factor is significantly affected by the gradient of shear

strength with depth. Based on field experience (Young et al., 1984), it is recommended

that for typical Gulf of Mexico shear strength gradients (k = 1.0~2.5 kPa/m) and

spudcan dimensions (Deq = 10.6~19.8 m; Menzies & Roper, 2008; Hossain et al., 2014),

an average su over a depth of D/2 (or Deq/2) below the spudcan base level can be used.

Alternatively, Houlsby & Martin (2003) presented lower bound solutions for a conical

footing embedded in non-uniform clay of shear strength increasing linearly with depth.

The tables in Annex E of ISO standard 19905-1 provide the bearing capacity factors as

a function of cone angle, cone roughness, embedment ratio, and shear strength gradient.

More recently, Hossain et al. (2005, 2006) and Hossain & Randolph (2009a, 2009b)

carried out centrifuge tests and large deformation finite element (LDFE) analyses for

continuous spudcan penetration in single layer clay deposits. The observed soil flow

patterns revealed three distinct mechanisms of soil flow around the advancing spudcan:

(i) shallow failure with outward and upward flow leading to surface heave and

v c u 0Q A N s p


1-5

formation of a cavity above the spudcan (Figure 1.6a); (ii) gradual backflow into the

cavity (Figure 1.6b); and (iii) deep failure mechanism with fully localised flow around

the embedded spudcan and the unchanged cavity (Figure 1.6c). Hossain & Randolph

(2009b) and Hossain et al. (2014) proposed a mechanism-based design approach that

accounts for the evolving failure mechanisms during spudcan penetration and the effects

of strain softening and rate dependency of the undrained shear strength of clays.

1.4.2 Layering System b: Stiff-over-Soft Clay

For calculating spudcan penetration resistance on stiff-over-soft clay deposits, ISO

(2012) recommends using Brown & Meyerhof’s (1969) factor, but adjusted for

embedment depth by applying a constant depth factor following Skempton (1951). For

spudcan penetrating in a stiff clay layer of undrained shear strength sut overlying a soft

clay layer of undrained shear strength sub, the penetration resistance is calculated as

(1.2)

where Nc,int = Min[6(1 + 0.2dint/D), 9.0] is the bearing capacity factor at the depth dint of

the stiff-soft layer interface and T is the thickness of the top layer beneath the base of

the advancing spudcan. The corresponding punching shear model is delineated in Figure

1.7. The 1st bracketed term is the contribution from the end bearing capacity at the base

of the plug. The 2nd term of the equation represents the shear resistance along the

vertical shear planes in the strong layer by assuming a cylindrical soil plug and

mobilised shear strength at the plug-adjacent soil interface as 0.75sut. The key

deficiency of the ISO method is that the soil plug base is assumed to be fixed at the

stiff-soft layer interface regardless of the spudcan penetration. As such, the soil plug

carried down with the spudcan from the stiff layer into the soft layer, and corresponding

contribution to the penetration resistance, are neglected. Additionally, the effects of

strain softening and rate dependency of clays are not explicitly considered although a

factor of 0.75 is applied on intact sut.

Recent development of design methods for spudcan penetration in stiff-over-soft clay

includes: (i) Edwards-Potts method (Edwards & Potts, 2004), which was proposed

based on small strain finite element (FE) analyses for a surface circular footing; (ii)

mechanism-based Hossain-Randolph method (Hossain & Randolph, 2009c), developed

v c,int ub 0 ut c ut 0

4ATQ A N s p 0.75s A N s p

D


1-6

based on LDFE analyses, but modelling the clays as non-softening, rate-independent

materials; and (iii) Dean method (Hossain & Randolph, 2011), which incorporated the

effect of an unchanged plug (with height equal to the thickness of the stiff clay layer) in

the punching shear model.

1.4.3 Layering System b: Sand-over-Clay

For sand-over-clay deposits, ISO (2012) recommends calculating penetration resistance

according to the load spread method (also known as projected area method) and

alternatively the punching shear method. In the load spread model (Figure 1.8), the

bearing capacity of the spudcan in the sand layer is assumed equal to that of a fictitious

footing resting at the surface of the underlying clay layer without considering the shear

resistance from the sand layer, which is expressed as

(1.3)

where ns is the load spread factor determining the diameter of the fictitious footing. It is

recommended that, for silica sand, ns in the range of 3 to 5 be used.

The punching shear model is consistent with the one considered for stiff-over-soft clay

(Figure 1.7), and the shear resistance along the vertical shear planes in the sand layer is

now calculated based on lateral earth pressure as

(1.4)

where Ks is the punching shear coefficient and is the effective friction angle of sand.

A design chart is provided for Ks.

However, the observations from centrifuge tests of spudcan penetration in a surface

sand layer overlying clay indicate significantly different failure mechanisms (Craig &

Chua, 1990; Teh et al., 2008). According to the observed failure mechanisms, new

conceptual models for calculating the peak resistance in the sand layer and bearing

capacity factors in the clay layer were proposed by Teh et al. (2009), Lee et al. (2013a,

b), and Hu et al. (2014a, 2014b, 2015) based on the results from centrifuge tests and

LDFE analyses.

2

v c,int ub 0

s

TQ 0.25 D 2 N s p

n

v c,int ub 0 0 s

2ATQ A N s p T 2p K tan

D


1-7

1.4.4 Layering System c: Soft Clay Overlying Strong Layer

For spudcan penetration in soft clay overlying a strong layer (sand or stiff clay), ISO

(2012) recommends calculating the bearing capacity resulting from squeezing as

v c ut 0 c ut 0 v,int

DQ Max A N 1 s p ,A N s p Q

3T

(1.5)

where Qv,int is the gross penetration resistance at the weak-strong layer interface. The

equation is taken from Meyerhof & Chaplin (1953), but adjusted for shape and depth

factors following Skempton (1951). It is recommended that squeezing occurs when

sqhT 1

D D 3.45 1 1.025d / D

for d/D ≤ 2.5 (1.6)

where hsq is the limiting squeezing depth, that is the distance between the spudcan base

and the surface of the strong layer, within which the penetration resistance increases

sharply due to the influence of the underlying strong layer. Equation 1.6 indicates that

the limiting squeezing depth is only a function of penetration depth. However, for

spudcan penetration in strong-weak-strong deposits, Hossain et al. (2011) and Hossain

(2014) noted that the soil plug trapped at the base of the advancing spudcan from the

overlying strong layer would augment the limiting squeezing depth significantly.

Equation 1.5 was theoretically derived based on the assumption that the cylindrical clay

block between parallel rigid plates is squeezed out completely. As such, for spudcan

penetration in a soft clay layer overlying a relatively stronger layer, it is assumed that all

soft soil beneath the spudcan will be squeezed out and the layer interface will not

deform. However, from the observations in centrifuge tests, Hossain et al. (2011) and

Hossain (2014) highlighted that the soft clay may be trapped at the base of the spudcan

as it penetrates into the underlying strong layer.

1.4.5 Spudcan Penetration in Multi-Layer Soils

For the bottom-up approach suggested by ISO (2012), first the bearing capacity of a

spudcan on the top of the lowest two layers is computed. These two layers are then

treated as one (lower) layer in a subsequent two-layer system analysis involving the

immediate upper layer. However, no detailed instruction is given.


1-8

Most recently, centrifuge tests were carried out by Hossain et al. (2011) and Hossain

(2014) modelling spudcan penetration in multi-layer soils of up to six layers. These tests

have revealed the significant effect of the accumulated soil plug from the upper layers

carried down by the advancing spudcan on squeezing and punch-through. Based on the

observed soil failure mechanisms, Hossain (2014) proposed some useful suggestions

that can be taken into account for predicting punch-through and squeezing behaviours of

spudcan penetrating in multi-layer soils.

ALTERNATIVE CONE PENETROMETER-BASED DIRECT DESIGN APPROACH

The design methods suggested by ISO (2012) are based on classical bearing capacity

models plugging in the shear strength parameters gleaned mostly from laboratory test

data. Alternatively, InSafeJIP (2011) recommends using a direct correlation between the

penetration resistance profiles of spudcan and penetrometers if high-quality, almost

continuous, penetration testing data are available [typically from cone or piezocone

penetration test (CPT or CPTu), but alternatively from T-bar or ball penetrometer].

Although estimating spudcan penetration resistance directly from CPT data is

increasingly being considered, design formula is only given for single layer clay deposit

by InSafeJIP (2011). A small number of researches have been published regarding

penetrometer-based assessment of spudcan penetration resistance (Erbrich, 2005; Lee &

Randolph, 2011; Cassidy, 2012; Pucker et al., 2013). Erbrich (2005) and Cassidy (2012)

have worked on carbonate soils. Lee & Randolph (2011) established a correlation model

between spudcan and penetrometers under different consolidation conditions. A

consolidation index was induced to calculate the penetration resistance ratio. For

spudcan penetration in silica sand, a CPT-based predictive method was proposed by

Pucker et al. (2013) based on a database comprising results from centrifuge model tests

and LDFE analyses. However, to date no research has been published for a direct

correlation between spudcan and cone penetration resistances in layered deposits.

OBJECTIVES AND STRUCTURE OF THE THESIS

The motivation and goals of this study emanate directly from the ‘future needs’

identified by the recently finalised version of ISO standard 19905-1, i.e. from the lack


1-9

of predictive methods for multi-layer soils as just noted. LDFE methods were adopted to

simulate continuous spudcan and cone penetration using the Coupled Eulerian-

Lagrangian (CEL) approach and the Arbitrary Lagrangian-Eulerian (ALE) approach,

respectively. Distinguishing from previous researches, which concentrated on spudcan

penetration in single- or two-layer soils, four configurations of soil profile were

considered including: (i) stiff-over-soft clay deposit; (ii) non-uniform clay with an

interbedded stiff clay layer; (iii) uniform stiff-soft-stiff clay; and (iv) clay-sand-clay

deposits with and without a 4th layer stiff clay.

The results were validated against centrifuge test data from previous studies and field

data from case histories. Parametric studies were then performed with the aim of

creating a database leading to the development of new mechanism-based and CPT-

based design approaches that rectify the deficiencies of the current design methods.

The proposed design approaches incorporate the combined effect of strain softening and

rate dependency of the undrained shear strength of clays. For surface or interbedded

strong-over-weak layering system, expressions were proposed to estimate the height of

the trapped soil plug, and the corresponding contribution to the penetration resistance

was considered.

The outline of this thesis is listed as follows

CHAPTER 2 details the theoretical background and implementation of the LDFE

approaches and describes the numerical models used for spudcan and cone penetration

analyses.

CHAPTER 3 reports the results from LDFE analyses of cone penetration in clay and

sand deposits. Design formulas are proposed to correlate cone penetration resistance

with the undrained shear strength of clay and relative density of sand.

CHAPTER 4 presents the results from LDFE analyses of spudcan penetration in stiff-

over-soft clay deposit. New mechanism-based and CPT-based design approaches are

developed to predict the peak resistance and deep bearing capacity in the stiff and soft

layers, respectively. An improved ISO method is also proposed for estimating the peak

resistance, incorporating the influence of the soil plug below the stiff-soft layer interface

on penetration resistance. This chapter was documented in Zheng et al. (2015d).


1-10

CHAPTER 5 presents the LDFE results for spudcan penetration in non-uniform clay

with an interbedded stiff clay layer. New mechanism-based and CPT-based design

approaches are proposed. For spudcan penetration in the 1st layer soft clay, a consistent

limiting squeezing depth is suggested. Considering the local deformation, the bearing

capacity at the soft-stiff layer interface is calculated as a fraction of that estimated for a

spudcan resting at the interface. This chapter was documented in Zheng et al. (2014,

2015b).

CHAPTER 6 presents the LDFE results for spudcan penetration in stiff-soft-stiff clay

and develops new mechanism-based and CPT-based design approaches. The effect of

the 3rd layer stiff clay on the bearing capacity in the 1st layer is considered in the

proposed approaches. An iterative approach is proposed to estimate the limiting

squeezing depth in the 2nd layer soft clay considering the effect of the soil plug from the

1st layer. This chapter was documented in Zheng et al. (2015a).

CHAPTER 7 presents the results from LDFE analyses of spudcan penetration in clay-

sand-clay deposits with and without a 4th stiff layer. The limiting squeezing depth is

suggested for a clean spudcan (without any trapped soil) penetrating surface soft clay

layer overlying sand. The influence of the presence of a 4th layer stiff clay on the

bearing response is also highlighted, with design formulas proposed to estimate the

increase of peak resistance and limiting squeezing depth. CPT-based correlations for

peak resistance in the sand layer and deep penetration resistance in the underlying clay

layer are also established. This chapter was documented in Zheng et al. (2015c).

CHAPTER 8 summarises the conclusions and suggests areas that require future study.


1-11

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1-12

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1-13

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1-14

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1-15

FIGURES

Figure 1.1 Jack-up rig and spudcan foundation

SpudcanD = 10~20 m

~170 m

Water surface

Truss-work leg

Platform


1-16

Plan View

Elevation View

1.2(a) Marathon LeToumeau Design, Class 224-C (Super Gorilla)


1-17

Plan View

Elevation View

1.2(b) Marathon LeToumeau Design, Class 116-C


1-18

1.2(c) Skirted spudcan (unit: mm)

Figure 1.2 Spudcan geometries and dimensions (after Menzies & Roper, 2008;

Hossain et al., 2015)

10.90

60.00

6.9

0 0.80

8.0

0

14.70

77°

13°

13°


1-19

1.3(a) Uniform stiff-soft-stiff clay

0

2

4

6

8

10

12

14

16

18

20

0 30 60 90 120 150D

ep

th b

elo

w m

ud

lin

e,

z:

m

Undrained shear strength, su: kPa

InSafeJIP (2011)

Chan et al. (2008)


1-20

1.3(b) Non-uniform clay with an interbedded stiff layer

Figure 1.3 Typical idealised shear strength profiles of three-layer clay with

potential for punch-through

0

2

4

6

8

10

12

14

16

18

20

0 30 60 90 120 150

De

pth

be

low

mu

dli

ne

, z:

m

Undrained shear strength, su: kPa

InSafeJIP (2011)

Handidjaja et al. (2004)


1-21

Figure 1.4 Penetration resistance profiles of punch-through and rapid leg run

1

Penetration resistance

0Rapid legrun

Pen

etr

ati

on

dep

th Strong

Weak

Punch-throughdistance, hP-T

< 0Punch-through


1-22

1.5(a) Flat-based circular plate (Skempton, 1951)

1.5(b) Conical-based circular footing (Houlsby & Martin, 2003)

Figure 1.5 Simplified equivalent spudcans (ISO, 2012)


1-23

Figure 1.6 Soil failure mechanisms during spudcan penetration in single layer clay

(after Hossain et al., 2014)

Figure 1.7 Punching shear model for spudcan penetration in strong layer overlying

soft clay

(a) Surface heave mechanism (b) Onset of backflow mechanism

(c) Fully localised flow mechanism

Spudcan

Sand or Stiff clay

Soft clay

6(1+0.2dint/D)sub

Shear resistance

Soil plug

T

d

dint

D


1-24

Figure 1.8 Load spread model for spudcan penetration in sand overlying clay

Spudcan

Sand

6[1+0.2dint/(D+2T/ns)]sub

Clay

1

ns

1

nsT

d

dint

D

D 2T/ns

Chapter 2. Large Deformation Finite Element Methods

2-1

CHAPTER 2. LARGE DEFORMATION FINITE

ELEMENT METHODS

INTRODUCTION

Many applications in offshore engineering involve large movements of foundation or

anchoring elements relative to the seabed. These include penetration of spudcan

foundations for mobile drilling platforms, partial embedment and lateral motion of

pipelines, interpretation of penetrometer tests and pullout of anchors. Numerical

analysis requires techniques that allow simulation of large strains and deformations

within the soil, with the ability to track changes in originally horizontal strength

contours, and also changes in strength due to gradual remoulding (Randolph et al.,

2008). Over the last decade, large deformation finite element analysis (LDFE) methods

that avoid extreme mesh distortion through mesh adjustment of nodal positions or mesh

generation have been applied to a variety of offshore design problems.

A number of investigations have been carried out on the continuous penetration of

spudcan and cone through various LDFE methods, mostly limited to the penetration in

single- and two-layer soil profiles (Wang & Carter, 2002; Lu et al., 2004; Huang et al.,

2004; Walker & Yu, 2006; Hossain & Randolph, 2009a, 2009b; Liyanapathirana, 2009;

Hossain & Randolph, 2010b; Qiu et al., 2011; Qiu & Henke, 2011; Tolooiyan & Gavin,

2011; Qiu & Grabe, 2012; Yu et al., 2012; Kouretzis et al., 2014; Pucker et al., 2013).

Recently, Walker & Yu (2010) and Ma et al. (2015) explored cone penetration in three-

layer clay deposits. The used LDFE methods can be divided into two categories: (i) the

Coupled Eulerian-Lagrangian (CEL) approach and (ii) the classic Arbitrary Lagrangian-

Eulerian (ALE) approach.

In this study, continuous penetration of spudcan was simulated using the CEL approach

and that of cone using the ALE approach. All the numerical analyses were performed in

the commercial finite element (FE) package Abaqus/Explicit (DSS, 2010). As such, this

chapter introduces the theoretical basis and implementation of the CEL and ALE

approaches and tabulates the parameters of cases used for validation.


2-2

THEORETICAL BACKGROUND OF CEL AND ALE

According to continuum mechanics, the deformation or motion of a continuum is

usually described as a function of coordinates and time using either Lagrangian

description or Eulerian description. In FE methods, the continuum is discretised with

elements. As for Lagrangian description, the detailed history of material deformation is

represented by the movement of mesh. In contrast, for Eulerian description, the mesh is

fixed and the materials pass through the mesh. Correspondingly, the FE methods can be

formulated as pure Lagrangian approach, pure Eulerian approach, and as an in-between

approach, according to the relative movement of the mesh and materials.

PURE LAGRANGIAN APPROACH: The elements move exactly with the material

so that the motion of the material can be inferred from the mesh directly. The

advantages of this approach are that the governing equations are satisfied naturally in

each element, and that the boundary and contact of materials can be precisely tracked

and defined. However, for geotechnical problems with considerable deformation, the

elements may become seriously distorted.

PURE EULERIAN APPROACH: The FE Eulerian mesh is retained and fixed in the

space, while the materials flow through elements that do not deform. The elements may

be partially void. The advantage of this approach is that all elements remain the original

shape and do not incur any numerical instability due to element distortion. However, it

is difficult to track the moving boundary, material interface, and hence interaction

between materials, especially when an element is filled with more than one material.

The application of the Eulerian approaches in solid mechanics is very limited.

IN-BETWEEN APPROACH: The in-between approach combines the features of pure

Lagrangian approach and pure Eulerian approach. The governing equations of this

approach are derived by substituting the relationship between the material time

derivative and spatial time derivative into the Lagrangian expression of governing

equations. This substitution gives rise to convective terms that account for the transport

of materials through the Eulerian mesh. The equations that couple the material

deformation and convective effects can be solved simultaneously. Alternatively, most

in-between approaches are based on the operator split technique (Gadala, 2004). This


2-3

technique decouples the equations so that the material deformation and convective

effects are treated separately.

The CEL and ALE approaches essentially fall within the framework of the in-between

approach. Both approaches adopt the computationally efficient operator split technique,

dividing each incremental time step into a Lagrangian phase and an Eulerian phase. In

the Lagrangian phase, the solution of governing equations, the same as that in a pure

Lagrangian analysis, is advanced in time. An explicit integration scheme – the central

difference method – is adopted. In the subsequent Eulerian phase, the solutions are

mapped from the old mesh onto the new mesh (also termed ‘advection’) as follows

(Benson, 1992; Wang et al., 2015)

1. A new mesh is generated (remeshing). The usual strategy is either to adjust the

nodal positions but maintain the topology in an ALE analysis, or to retain the

original mesh that is fixed in space in a CEL analysis.

2. The field variables, including stresses (either total stresses or effective stresses

depending on the type of analysis) and material properties at integration points

together with the velocities and accelerations at nodes, are mapped following a

certain advection algorithm.

The implementation of the CEL and ALE approaches differs in element type, contact,

remeshing strategy, and advection algorithms. The detailed algorithms and formulations

of each method are introduced below (DSS, 2010).

2.2.1 CEL Approach

The current CEL function in Abaqus/Explicit is only for three-dimensional (3D)

elements. Both Lagrangian body and Eulerian materials can be included in the model,

with the former usually discretised using solid elements and the latter using Eulerian

elements. The Eulerian mesh is fixed, while the Eulerian materials ‘flow’ through the

Eulerian elements. A schematic example of Eulerian elements before and after

remeshing is shown in Figure 2.1.

Contact algorithm

Two contact algorithms termed ‘contact pair’ and ‘general contact’ are available in

Abaqus/Explicit. However, the contact in CEL analysis must be defined using general


2-4

contact. There are two types of contact defined by the general contact in the CEL

analysis – the Eulerian-to-Eulerian contact and the Eulerian-Lagrangian contact. The

Eulerian-to-Eulerian contact occurs automatically when Eulerian materials come into

interaction, while the properties of Eulerian-Lagrangian contact between Eulerian

materials and Lagrangian body should be defined in the settings of general contact.

For Eulerian-to-Eulerian contact, the material boundaries are computed through the

volume fraction of each material within an element and the interface reconstruction

algorithm. The strain at the integration point of each Eulerian element is unique for all

materials accommodated by the element. Mean strain rate mixture theory is used to

calculate the contact force in each element. At the interfaces of Eulerian-to-Eulerian

contact, tensile stress can be transmitted and no slip occurs.

The Eulerian-Lagrangian contact formulation is based on an enhanced immersed

boundary method. The contact constraints are enforced using the penalty method. The

contact algorithm automatically computes and tracks the interface between the

Lagrangian body and the Eulerian materials. During the analysis, The Lagrangian body

and Eulerian materials cannot occupy the same space. The Lagrangian body pushes

Eulerian materials out of the space that it passes through, while Eulerian materials

cannot flow into the space that is already occupied by the Lagrangian body.

Remeshing strategy

At the end of the Lagrangian phase of each time increment, a small tolerance is used to

determine which Eulerian elements are ‘excessively’ deformed. These elements will be

moved to the original configuration during the Eulerian phase, while the others remain

inactive. The tolerance is so minimal that the mesh appears to be ‘fixed’ in the space.

Advection method

The field variables are mapped to the new mesh in the Eulerian phase. Two advection

algorithms are available in Abaqus/Explicit, i.e. the default second-order method

developed by Van Leer (1977) and a first-order method based on the donor cell

differencing. The second-order method was used.

The second-order advection method maps the variables from the old mesh to the new

mesh by first determining a linear distribution of the variable in each old element. The


2-5

linear distribution in the middle element depends on the values in the adjacent elements.

Figure 2.2 illustrates the procedure for a simple one-dimensional mesh:

1. A quadratic interpolation is constructed within the values of the variable at the

integration points of the middle element and its adjacent elements;

2. The quadratic function is differentiated at the integration point of the middle

element to calculate the trial linear distribution;

3. The slope of the trial linear distribution in the middle element is reduced until its

minimum and maximum values are within the range of the original constant

values in the adjacent elements.

Once the linear distributions are determined for all elements in the old mesh, these

distributions are integrated over each new element.

2.2.2 ALE Approach

The ALE function is available for two-dimensional (2D) and 3D solid elements.

Remeshing, which is also referred to as ALE adaptive meshing in Abaqus

documentations (DSS, 2010), can be applied to an entire FE model or to individual parts

of a model. The domain of remeshing allows the elements to move independently of the

material, but does not alter the topology of the mesh. Unlike the CEL approach, the

elements in the ALE approach after remeshing and advection are always 100% full of a

single material. An example of elements with and without ALE adaptive meshing is

shown in Figure 2.3.

Contact algorithm

The contact pair algorithm is usually used in the ALE analysis because the general

contact algorithm in Abaqus/Explicit places more restrictions on the ALE adaptive

meshing. For example, the nodes in a general contact domain cannot be defined as

adaptive. Therefore, the contact pair algorithm was adopted and corresponding contact

formulations are introduced below.

For a given contact pair, either the pure master-slave algorithm or the balanced master-

slave algorithm can be used through specifying a weighting factor for the contact

surface. Kinematic or penalty method can be used to enforce the contact constraints. For


2-6

relative motion of the two surfaces forming a contact pair, there are three sliding

formulations – finite sliding, small sliding, and infinitesimal sliding.

As the cone penetrometer is much more rigid than the soils, the contact in all analyses

was established using the pure master-slave algorithm. The cone was modelled using an

analytical rigid surface, which was selected as the master surface. The soil surfaces

were designated as slave surface.

For contact constraints, kinematic enforcement method was used. In each increment of

the analysis, Abaqus/Explicit first predicts the positions of the master and slave surfaces

without considering the contact conditions. On the slave surfaces, the slave nodes that

penetrate into the master surfaces are then found. The penetration depth of each slave

node, the mass associated with the node, and the time increment are used to calculate

the resisting force required to oppose the penetration. For the hard contact used in this

study, this resisting force would make the slave nodes revert to contacting the master

surface exactly. However, the nodes on the master surface are still likely to penetrate

coarsely discretised slave surfaces, as shown in Figure 2.4.

To account for the relative motion between the master and slave surfaces, the finite

sliding formulation was adopted, which allows for arbitrary separation, sliding, and

rotation of the surfaces. The relative motion is tracked by using a global search at the

beginning of each step, and then a hierarchical global/local search algorithm for the

subsequent increments. For a given contact pair, the global search searches the master

nodes and tracks the one that is nearest to each slave node, as shown in Figure 2.5a. By

contrast, for each slave node, the local search first searches the master surface facets

that are attached to the previously tracked master node. Among these facets, the nearest

one to the considered slave node is determined. Abaqus/Explicit then determines which

node on that nearest master surface facet is closest to the slave node and updates this

master node as the currently tracked master node. If this updated master node is not the

same as the previously tracked master node, another iteration of the local search is

performed, as shown in Figure 2.5b.

Remeshing strategy

The domain of the ALE adaptive meshing is remeshed at an interval of certain

increments. The increment in which the ALE adaptive meshing is performed is referred


2-7

to as an adaptive meshing increment. The number of time increments between two

adaptive meshing increments can be specified. During the adaptive meshing increment,

an improved mesh is created by sweeping iteratively over the adaptive mesh domain

and adjusting the positions of the nodes to reduce the element distortion. The number of

sweeps in an adaptive meshing increment can also be specified.

There are three remeshing methods for the ALE approach in Abaqus/Explicit. These

include the volume smoothing, Laplacian smoothing, and equipotential smoothing. A

combination of these methods can also be defined by specifying the weight of each

method. The default method, volume smoothing, was used, which relocates a node by

computing a volume-weighted average of the element centres in the elements

surrounding the node. In Figure 2.6, the new position of node M is determined by a

volume-weighted average of the positions of the element centres of elements C1~C4.

The volume weighting tends to move node M away from element centre C1 and toward

element centre C3, which reduces the element distortion.

Advection method

In an adaptive meshing increment, the same methods as those in the CEL approach are

available to map the field variables from the old to new integration points after

remeshing. The second-order method was also adopted in the ALE analysis to ensure

computational accuracy.

NUMERICAL MODEL

2.3.1 Model Details

As mentioned previously, the continuous penetration of spudcan in stratified deposits

was simulated using the CEL approach. The 2D ALE approach was employed to

simulate cone penetration, and the analyses were only performed for cone penetration in

single layer soils rather than in layered profiles. The reasons are clarified as follows:

1. The current CEL function is only for 3D elements and explicit integration

scheme. Due to the significant difference in diameter (e.g. D = 10~20 m for

commonly used spudcans vs. Dc = 0.0357 m for the standard cone commonly

used for site investigation), the computational cost is unaffordable to perform


2-8

analysis using the CEL approach for cone penetration in the same multi-layer

soil profile with penetration depth similar to the spudcan (e.g. 3D spudcan

penetration depth vs. 840~1681Dc cone penetration depth).

2. The maximum thickness of the transitional zones as the cone penetrates from

one layer to another is usually < 10Dc (~0.36 m), and the maximum depth

required for mobilising the full cone tip resistance is usually < 20Dc (~0.71 m;

Walker & Yu, 2010; Ma et al., 2015). These are negligible compared to the

minimum layer thickness considered for spudcan penetration analysis, which is

usually larger than the spudcan tip height of 2.3~3.5 m (i.e. 64~98Dc, see Figure

1.2; Menzies & Roper, 2008).

It is therefore sufficient to combine cone tip resistance profiles for single layer soils to

obtain the simplified complete profile for the multi-layer soil.

On the other hand, the geometry of spudcan is more complex than the cone (see Figure

2.7). For the soil domain that interacts with the spudcan, the remeshing techniques used

by the ALE approach are unable to prevent the elements from becoming distorted.

Therefore, it is impractical to simulate spudcan penetration using the ALE approach,

especially for stratified soils.

Relevant nomenclatures used in this study are illustrated in Figure 2.7 for an example of

non-uniform clay with an interbedded stiff clay layer. The penetration depth d is

measured from the seabed to the spudcan base (lowest point of largest plan area).

Symbols including ti, sui, i, and ki, respectively, represent the layer thickness, intact

undrained shear strength, effective unit weight, and shear strength gradient of the ith

layer soil. suis and suib are the undrained shear strengths of the ith layer at the top and

bottom layer interfaces, respectively. The symbols used for each particular

configuration of soil profile are also introduced in the corresponding chapter.

For spudcan penetration, analyses of parametric studies were undertaken for a circular

spudcan with a 13° shallow conical underside profile (included angle of 154°) and a 76°

protruding spigot of height 0.14D. The spudcan shape is similar to the spudcans of the

“Marathon LeTourneau Design, Class 82-SDC” jack-up rig illustrated by Menzies &

Roper (2008). The spudcan diameter in the parametric studies was taken as D = 6 m and

12 m for Chapters 4 and 7 and Chapters 5 and 6, respectively. In contrast, analyses were


2-9

undertaken for standard cones of Dc = 25.2~43.7 mm, with a 60 tip-apex angle, as

shown schematically in Figure 2.7.

Both cone and spudcan were simulated as rigid. The soil-cone interface was defined as

smooth for clay (Walker & Yu, 2006, 2010), and frictional with a roughness factor of

0.5 for sand (Kouretzis et al., 2014). The spudcan base was modelled as rough in order

to maintain the soil plug thickness trapped by the advancing spudcan, which played a

major role in developing the penetration resistance. In addition, the friction resistance

between spudcan-clay interactions that depends on the relative roughness of the spudcan

base appears to have little influence on the spudcan penetration resistance for

penetration in layered clay profiles (Hossain & Randolph, 2010b; also see Figure 4.5a).

These contact conditions were adopted unless otherwise stated.

Typical numerical models for spudcan and cone penetration in clay deposits are shown

in Figure 2.8. In spudcan penetration analysis, the soil domain was chosen as 6.25D in

width and 11.7D in depth unless otherwise stated, while the axisymmetric soil domain

in cone penetration analysis was chosen as 23~40Dc in radius and 34~60Dc in depth.

The soil domain size were selected deliberately to avoid boundary effects during the

process of penetration. For the simulation of spudcan penetration, a full spudcan was

simulated and only a quarter sector of the soil domain was involved in the analyses

accounting for the inherent symmetry. The soil layers were discretised using Eulerian

elements of type EC3D8R, and they underlain an initially ‘void’ layer to accommodate

the soil heave resulting from spudcan penetration. The soil domain in the analysis of

cone penetration was discretised using solid elements. The boundary of the soil domain

along the axis of symmetry was offset outwards by 0.003Dc in radial direction to avoid

distortion of the mesh beneath the advancing cone. A smooth rigid cylindrical surface

was then fixed along the offset boundary to prevent inward movement of the adjacent

soil. This technique has been used in investigating various geotechnical problems, with

the details presented by Mahutka et al. (2006) and Yi et al. (2012) among others.

2.3.2 Constitutive Models

Clay layer

The clay layer was modelled as an elastic-perfectly plastic material obeying the Tresca

yield criterion, but extending to capture strain rate and strain softening effects. The


2-10

undrained shear strength at each integration point was modified at the beginning of each

time step, based on the shear strain rate over the last time step and the current

accumulated absolute plastic shear strain , following Einav & Randolph (2005) as

95

ref 3ξ /ξ

uc rem rem u

ref

Max ,s 1 μlog δ 1 δ e s

(2.1)

where suc is the undrained shear strength after considering rate dependency and strain

softening and su is the intact undrained shear strength measured at the reference shear

strain rate prior to any softening. The value of of each time step is calculated as

1 3

fieldd / v

(2.2)

where and are the increments of maximum and minimum principal strains,

respectively, d is the incremental penetration depth of spudcan and cone during each

time step in the numerical analysis, and vfield is the penetration velocity of spudcan and

cone in the field. The accumulated absolute plastic shear strain is defined as

p p

1 3 (2.3)

where p

1 and p

3 are the increments of maximum and minimum principal plastic

strains, respectively.

The first bracketed term of Equation 2.1 augments the strength according to the shear

strain rate relative to a reference value ref , which may vary from 1 to 4%/h for triaxial

tests and up to 20%/h for direct simple shear tests (Erbrich, 2005; Lunne et al., 2006).

The augment of shear strength follows a logarithmic law with rate parameter taken in

the range of 0.05~0.2 (Hossain & Randolph, 2009a). The spudcan penetration rate in the

field mostly varies between 0.36~2 m/hour (Hossain et al., 2014), while that of cone is

20 5 mm/s.

The second part of Equation 2.1 models the degradation of strength according to an

exponential function of , from the intact condition to a fully remoulded ratio rem (=

1/St, i.e. inverse of sensitivity St). The relative ductility is controlled by the parameter


2-11

95, which represents the cumulative plastic shear strain required for 95% remoulding.

Typical values of 95 were estimated as 10~25 by matching degradation curves from

cyclic penetration and extraction tests of T-bar and ball penetrometers (Randolph, 2004).

For the parametric studies of spudcan penetration, the parameters in Equation 2.1 were

calibrated against a number of centrifuge tests and field case histories. The value of ref

was selected so that the normalised penetration rate vfield/(D ref ) = 11.11 (Hossain &

Randolph, 2009a; Hossain et al., 2014). The rate parameter was assumed as 0.1 for

“circular” spudcan foundations (Low et al., 2008). rem = 0.3~0.36 was adopted to

represent the most prevalent sensitivity in the field with the value of 95 = 12. The same

strain rate and strain softening parameters were adopted throughout the clay layers.

These parameters were considered for analyses unless otherwise stated. For the

parametric study of cone penetration, the parameters in Equation 2.1 were varied as

tabulated in Table 3.1.

For the simulation of spudcan penetration, the elastic parameters for clay were

considered independent of stresses and a uniform ratio of E/suc = 200 (where E is the

Young’s modulus) was taken throughout the clay profile. The ratio is within the range

commonly adopted for soft clays, but the precise value has negligible effect on spudcan

penetration resistance. The effect of rigidity index Ir on cone penetration resistance was

investigated separately, with Ir = 67~500. Considering the relatively fast penetration of

cone (20 5 mm/s) and spudcan (0.36~2 m/h) and the large diameter of spudcan

foundations (10~20 m) in the field, all the analyses simulated undrained conditions and

adopted a Poisson’s ratio of 0.49 (sufficiently high to give minimal volumetric strains,

while maintaining numerical stability). The geostatic stress conditions were modelled

with coefficient of lateral earth pressure of K0 = 1, as the stable penetration resistance

was found to be nearly unaffected by the coefficient (Zhou & Randolph, 2009).

Sand layer

The stress-strain response and volumetric behaviour of silica sand are affected by the

relative density ID of sand and the stress level during shearing. Typical results of

drained triaxial and plane strain tests on silica sand are shown in Figure 2.9. This study

has considered medium dense to very dense sands of ID = 44~90%. During spudcan


2-12

penetration, the mean stress p observed at the integration points of the interbedded sand

layer are mostly ≤ 150 kPa (White et al., 2008; Hu et al., 2015). Comparing the

magnitudes of relative density and mean stress level with those in Figure 2.9, the stress-

strain relationship of the sands was assumed as hardening followed by strain softening.

The classic Mohr-Coulomb model was modified to allow the effects of strain hardening

and softening, following Potts et al. (1990). In this modified Mohr-Coulomb (MMC)

model, the strength parameter – effective friction angle was assumed to vary linearly

as a function of the accumulated equivalent plastic strain ep. For sands exhibiting strain

hardening followed by strain softening, as shown in Figure 2.10, the internal effective

friction angle is expressed as

epep ep

i p i pep

p

ep ep

p ep ep ep

p p crit p critep ep

crit p

ep ep

crit crit

for

for

for

(2.4)

where the subscripts i, p and crit represent initial, peak and critical state values,

respectively. The accumulated equivalent plastic strain, ep, is computed according to

ep p p

ij ij

2e e

3 (2.5)

where p

ije is the incremental deviatoric plastic strain tensor.

The parameters ep

p and ep

crit were selected based on a wide range of literature review on

stress-strain responses of silica sand from laboratory tests. It has been found that, for

most tests, ep

p = 2~5% and ep

crit = 10~20%. Therefore, ep

p = 4% and ep

crit = 10% were

adopted in all analyses, as were considered by Hu et al. (2015).

The initial and peak friction angles were selected based on the theories as follows. For

triaxial compression condition of 1 > 2 = 3, the deviatoric stress q = (1 3),

and the mean effective stress p = (1 + 23)/3. The Mohr-Coulomb criterion with the


2-13

intercept at the origin can then be written in terms of stress ratio = q/p, and effective

friction angle , as

1 3

1 3

3sin

6

(2.6)

At initial geostatic condition of 2 = 3 = K01, Equation 2.6 can be rewritten in terms

of K0 to calculate the initial friction angle as

3 1 0i

3 1 0

1 / 1 Ksin

1 / 1 K

(2.7)

The coefficient of lateral earth pressure of K0 = (1 sincrit) was selected according to

the Jaky’s (1944) expression as a function of the critical state friction angle crit.

The peak friction angle p was determined according to Bolton’s (1986) formulas

correlating friction angle with relative density and stress level as

R DI I 10 ln p 1 (2.8)

p crit RmI (2.9)

where IR is the dilatancy index in the unit of degree, and m is a coefficient equal to 5 for

plane strain conditions and 3 for triaxial strain conditions. Therefore, m = 3 was adopted.

As noted previously, the mean effective stress p for conical footings in sand is usually

≤ 150 kPa. As such, the recommendation by Bolton (1987) that the term ln(p) = 5 for p

≤ 150 kPa was considered. The critical state angle for most silica sands was suggested

as crit = 31 ~ 34 (Bolton, 1986; O’loughlin & Lehane, 2003; Randolph et al., 2004)

and hence a value of crit = 34 was adopted to be consistent with Hossain (2014).

The dilation angle = 0 was considered for ep < 1% and ep > ep

crit = 10%. It

increases sharply from 0 to the peak value p as ep increases from 1% to 1.2% and

then remains constant until ep = ep

p , followed by a linear decrease for ep between ep

p

and ep

crit . The peak dilation angle, p was also calculated after Bolton (1986) who

suggested for plane strain conditions


2-14

p crit p0.8 (2.10)

It has been proved (Vermeer & de Borst, 1984; Bolton, 1986; Schanz & Vermeer, 1996)

that the dilation angle is independent of strain path (i.e. consistent value of IR or in

plane strain and triaxial strain conditions). As such, according to Equation 2.9, the

difference of (p crit) for plane strain conditions is 5/3 times higher than that for

triaxial strain conditions. The peak dilation angle p for triaxial strain conditions then

can be obtained from Equation 2.10 as

p p crit / 0.48 (2.11)

For elastic parameters, the Young’s modulus E, was considered constant along the depth

of sand layer, with E = 25 MPa for ID = 45% and E = 50 MPa for ID = 90%. For ID

between 45 and 90%, the value of E was estimated through linear interpolation. The

Poisson’s ratio was taken as 0.3 for all analyses.

VALIDATION

In order to validate the numerical model of spudcan penetration, analyses were

performed replicating centrifuge tests and case histories. All the analyses of spudcan

penetration carried out for validation are assembled in Table 2.1. For spudcan

penetration in single layer clay, some of the results are demonstrated in Figure 2.11,

while the others are presented by Hossain et al. (2014). In Figure 2.11b, numerical

results for spudcan foundation shapes matching either the real geometry (including cut-

outs, see Figure 1.2b) or an area equivalent circular foundation (idealised spudcan, see

Figure 2.8b) are included. The results for spudcan penetration in layered soil profiles are

presented in the relevant chapters for the particular configuration of soil profile. Figure

2.11 shows that, for spudcan penetration in single layer non-uniform clay, the

penetration resistance profiles predicted by the numerical model agree reasonably well

with those recorded in the centrifuge test and case histories.

The validation of the numerical model for cone penetration in clay was undertaken by

simulating cone penetration in single layer clay with an extensive range of soil

parameters of practical interest (see Chapter 3). The computed cone factors have a range

of 11.3~16, which falls within the band of 8.61~17.39 recommended by Low et al.


2-15

(2010) who assembled a worldwide, high-quality database of lightly overconsolidated

clays and correlated net cone tip resistance with undrained shear strength deduced from

laboratory tests (triaxial compression test and the average of triaxial compression,

simple shear and triaxial extension tests). Comparisons were also made between the

cone factors from this study and those proposed by previous researches for cone

penetration in ideal non-softening rate-independent clay, and between numerical and

experimental results of cone penetration in silica sand, which are presented in Chapter 3.


2-16

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Barden, L., Ismail, H. & Tong, P. (1969). Plane strain deformation of granular material

at low and high pressures. Géotechnique 19, No. 4, 441-452.

Benson, D. J. (1992). Computational methods in Lagrangian and Eulerian hydrocodes.

Computer Methods in Applied Mechanics and Engineering 99, No. 2-3, 235-394.

Bolton, M. D. (1986). The strength and dilatancy of sands. Géotechnique 36, No. 1, 65-

78.

Bolton, M. D. (1987). Discussion on ‘The strength and dilatancy of sands’.

Géotechnique 37, No. 2, 219-226.

DSS (Dassault Systèmes Simula Corp.) (2010). Abaqus 6.10 online documentation.

Providence, RI, USA: Dassault Systèmes Simula Corp..

Einav, I. & Randolph, M. F. (2005). Combining upper bound and strain path methods

for evaluating penetration resistance. International Journal for Numerical

Methods in Engineering 63, No. 14, 1991-2016.

Erbrich, C. T. (2005). Australian frontiers – spudcans on the edge. Proc. 1st

International Symposium on Frontiers in Offshore Geotechnics, ISFOG, Perth,

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Gadala, M. S. (2004). Recent trends in ALE formulation and its applications in solid

mechanics. Computer Methods in Applied Mechanics and Engineering 193, No.

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Hossain, M. S. & Randolph, M. F. (2010a). Deep-penetrating spudcan foundations on

layered clays: centrifuge tests. Géotechnique 60, No. 3, 157-170.

Hossain, M. S. & Randolph, M. F. (2010b). Deep-penetrating spudcan foundations on

layered clays: numerical analysis. Géotechnique 60, No. 3, 171-184.




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Hossain, M. S., Cassidy, M. J., Baker, R. & Randolph, M. F. (2011a). Optimization of

perforation drilling for mitigating punch-through in multi-layered clays. Canadian

Geotechnical Journal 48, 1658-1673.

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2-20

TABLES

Table 2.1 Summary of spudcan penetration analyses performed for validation

Case

No.

D:

m

Layer 1 Layer 2 Layer 3

Remarks su1:

kPa

t1:

m

su2: kPa or

ID: %

t2:

m

su3:

kPa

t3:

m

Cen

trif

uge

test

CT1 12 0.9 +

1.95z 50 - - - -

Single layer

non-uniform

clay; Hossain et

al. (2015)

CT2 3 24 1.5 2.3 +

1.34(z – t1) 10.5 - - Stiff-over-soft

clay; Hossain &

Randolph

(2010a) CT3 6 47 4.5 9.2 +

1.23(z – t1) 7.5 - -

CT4 8 10 2.5 40 2.4 10 9.9 Soft-stiff-soft

clay; Hossain et

al. (2011a,

2011b)

CT5 8 10 2 40 4 10 10.4

CT6 12 2 +

0.6z 4.5 23 6.9

2 +

0.6z 14.6

CT7 12 21 5 8.5 6 35.5 13

Stiff-soft-stiff

clay; Hossain et

al. (2011b)

CT8# 12 9 3 44 6 9 11.5

Clay-sand-clay-

clay; Hossain

(2014)

CT9 6 0.5 +

0.75z 3.7 89 1.5

0.5 +

0.75z 20.8

Clay-sand-clay;

Hossain (2014) CT10 6

0.5 +

0.75z 3.7 89 2

0.5 +

0.75z 20.3

CT11 6 0.5 +

0.75z 3.7 89 4

0.5 +

0.75z 18.3

Case

his

tory

CH1 13.5 2.4 +

1.35z 42.7 - - - -

Single layer

clay; Hossain et

al. (2014)

CH2 13.5 2.4 +

1.59z 48.2 - - - -

CH3 13.7 2.4 +

1.43z 43.6 - - - -

CH4 12 15.6 +

1.24z 24.1 - - - -

CH5 13.5 10.5 +

2.55z 19.5 - - - -


2-21

Case

No.

D:

m

Layer 1 Layer 2 Layer 3

Remarks su1:

kPa

t1:

m

su2: kPa or

ID: %

t2:

m

su3:

kPa

t3:

m

CH6 13.7 0.27 +

1.33z 43.0 - - - -

CH7 16.3 6.75 +

1.16z 49.8 - - - -

CH8 13.7 1 +

1.05z 3.8 40.5 2.1

14 +

2.55z -

Soft-stiff-soft

clay; InSafeJIP

(2011) # Layer 4: su4 = 36 kPa, t4 = 4 m.


2-22

FIGURES

Figure 2.1 Deformation and remeshing of Eulerian elements in a time increment

After Lagrangian phase

After Eulerain phase


2-23

Figure 2.2 Illustration of second-order advection in Abaqus/Explicit (after DSS,

2010)

Valu

e o

f vari

ab

leQuadratic

Trial

Limited

Element 2 Element 3Element 1

Constant


2-24

Figure 2.3 ALE adaptive meshing for a bulk forming simulation (after DSS, 2010)

Figure 2.4 Illustration of kinematic enforcement method (after DSS, 2010)

Without ALE adaptive meshing

With ALE adaptive meshing

Rigid die

Axis

of sym

me

try

GapMaster node can

penetrate slave segment

Slave surface

Penetration

Slave nodes cannot penetratemaster segments

Master surface


2-25

2.5(a) Global search

2.5(b) Local search

Figure 2.5 Schematic diagram of global search and local search (after DSS, 2010)

Location of tracked master node

Searched master facets

Master surface

Slave surface

Considered slave node

Location of previously tracked master node

Location of currently tracked master node

Motion of slave surface

Master surface

Slave surface

Considered slave node


2-26

Figure 2.6 Illustration of volume smoothing method (after DSS, 2010)

Figure 2.7 Schematic diagram of embedded cone penetrometer and spudcan

foundation in non-uniform clay with an interbedded stiff clay layer

C1

C4C3

C2

M

d

Hcav

z

Spudcan

Cavity

K-lattice leg

D

Cone t1

t2

Dc

su1, 1

su2, 2

su3, 3

su1s su

k1

su1b

su3s

k3


2-27

2.8(a) Cone penetration

Offset bounday

Axis of symmetryCone tip

1 m

1.5

m


2-28

2.8(b) Spudcan penetration

Figure 2.8 Numerical models for spudcan and cone penetration in clay deposits

Void layerSpudcan

1st soil layer

2nd soil layer

3rd soil layer11.7D


2-29

2.9(a) Triaxial tests (after Yamamoto et al., 2009)

De

via

tori

c s

tres

s:

kP

a

Shear strain: %

IDLine

8%

21%

47%

73%

99%

CID testsToyoura siliceous sand

Confining pressure = 100 kPa


2-30

2.9(b) Triaxial tests (after Muir Wood et al., 1994)

0

0.5

1

1.5

2

0 5 10 15 20

Str

ess

rati

o,

Triaxial shear strain: %

1

3

2

1: dense sand at low stress level2: dense sand at medium stress level3: loose sand at low stress level

-10

-5

0

5

10

0 5 10 15 20

Vo

lum

etr

ic s

tra

in:

%

Triaxial shear strain: %

1

3

2


2-31

2.9(c) Plane strain test (after Barden et al., 1969)

Figure 2.9 Stress-strain response and volumetric behaviour of silica sands

0

1

2

3

4

5

6

0 2 4 6 8 10

Str

ess

rati

o,

Axial strain: %

138 kPa

2068 kPa

5861 kPa

3

Plane strain testsRiver Welland sandRelative density, ID = 68%

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 2 4 6 8 10

Vo

lum

etr

ic s

tra

in:

%

Axial strain: %


2-32

Figure 2.10 Variation of friction and dilation angles of MMC model

Eff

ecti

ve f

ricti

on

an

gle

, :

, o

r

dilati

on

an

gle

,

:

Equivalent plastic strain, ep: %

p

crit

i

i = crit = 0

p

1

1.2

crit = 34

4 10


2-33

2.11(a) Centrifuge test (CT1, Table 2.1)

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500N

orm

ali

se

d p

en

etr

ati

on

de

pth

, d

/D

Bearing pressure: kPa

Centrifuge test

Numerical analysis


2-34

2.11(b) Case histories (CH1 and CH4, Table 2.1)

Figure 2.11 Validation of numerical model for spudcan penetration in single layer

clay

0

0.5

1

1.5

2

2.5

3

0 100 200 300 400 500 600

No

rmalised

pen

etr

ati

on

dep

th,

d/D

Bearing pressure: kPa

Numerical analysis

Numerical analysis

Port

Bow

Starboard

CH4

CH1

Idealisedspudcan

Spudcan withcut-outs

Idealisedspudcan

Spudcan withcut-outs

Chapter 3. Cone in Single Layer Clay and Sand

3-1

CHAPTER 3. CONE IN SINGLE LAYER CLAY AND

SAND

INTRODUCTION

One of the key objectives of this research is to establish direct correlations between

spudcan and cone penetration resistances in multi-layer soils. To achieve this, an

extensive database of spudcan and cone penetration resistance profiles in the same soil

profiles is required. For spudcan, parametric studies for different configurations of soil

profile of up to four layers consisting of clay and sand layers were carried out using the

3D Coupled Eulerian-Lagrangian (CEL) approach. For cone, as clarified in Chapter 2,

instead of simulating cone penetration in multi-layer soils using the CEL approach,

analyses of cone penetration in single layer soils were carried out using the 2D

axisymmetric Arbitrary Lagrangian-Eulerian (ALE) approach.

This chapter reports the results from large deformation finite element (LDFE) analyses

of cone penetration in single layer clay and sand deposits. The effects of soil rigidity

index, sensitivity, ductility, strength non-homogeneity and rate dependency of the

undrained shear strength of clay, and relative density (and overburden stress) of sand

were explored. Based on the results from these parametric studies, design formulas were

proposed for cone factors in clay deposits as a function of rigidity index and strain

softening and rate parameters, and for predicting cone resistance profile in sand deposits

as a function of its relative density and effective stress level.

LITERATURE REVIEW

Currently, the most commonly adopted in-situ test in offshore site investigations is the

cone penetration test (CPT) or piezocone penetration test (CPTu). Parameters measured

during a piezocone test include (i) cone tip resistance, qc; (ii) sleeve friction, fs; and (iii)

pore water pressure at the shoulder of the cone, u2, while the former two during a cone

penetration test. The continuous or semi-continuous profiles of these parameters are

used for soil layer identification, soil classification, and estimation of soil properties.


3-2

Figure 3.1 shows the conventional terminology and inner structure of a typical cone

penetrometer used in the field. The bearing area of the standard cone penetrometer

commonly used in offshore site investigations is 1000 mm2 (i.e. cone diameter Dc

35.7 mm) with a 60 tip angle. Cone penetrometers with bearing areas of 1500 mm2 and

500 mm2 (Dc 43.7 mm and 25.2 mm, respectively) are also used (Lunne et al., 1997).

The penetration tests are carried out at a standard rate of 20 5 mm/s (ISSMGE IRTP,

1999; ASTM, 2007). Generally, this velocity ensures undrained conditions for clay

deposits and drained conditions for sand deposits (Lunne et al., 1997).

The penetration resistance measured by the CPTu must first be corrected for the effects

of unequal pore pressure (see Figure 3.1b). The measured cone tip resistance qc is

corrected to total cone resistance qt using the following relationship (Lunne et al., 1997)

t c 2q q u 1 (3.1)

where is the net area ratio (i.e. ratio of the cross-sectional area of the load cell divided

by the bearing area of the cone; see Figure 3.1b). Typical values of range from 0.59 to

0.85. Note, this correction was not necessary for the computed cone resistances from

LDFE analyses as the cone was simulated with a solid shaft (see Figure 3.2; i.e. qt = qc).

A vast number of studies have been conducted investigating the relationship between

the measured parameters and various soil properties (e.g. unit weight, sensitivity,

different moduli, shear strength, relative density etc.). Nevertheless, this section only

reviews those that investigated the relationship between cone tip resistance and soil

strength characteristics in accordance with the objective of this study.

3.2.1 CPT in Clays

For CPT test in clay deposit, the undrained shear strength su can be derived using

t v0u

kt

qs

N

(3.2)

where v0 is the total overburden stress at the cone shoulder and Nkt is the bearing

capacity factor of cone (or cone factor). The value of Nkt is affected by a number of

factors including rigidity index Ir = G/su (where G is the shear modulus), in-situ stress

anisotropy, cone roughness, and soil strength anisotropy.


3-3

A number of analytical, numerical and experimental investigations have been carried

out on cone penetration. The bearing capacity factor of cone in clay has been explored

through strain path method, hybrid strain path method, cavity expansion method and

conventional small strain finite element (FE) analysis (Baligh, 1985; Teh & Houlsby,

1991; Yu, 2000). Recently, this problem has been addressed through LDFE analysis

(van den Berg, 1994; Lu et al., 2004; Walker & Yu 2006; Liyanapathirana, 2009). The

results from part of these studies will be compared with the LDFE results presented

later.

To evaluate the in-situ undrained shear strength profile, the conventional practice is to

use a constant cone factor Nkt, which is determined by correlating the net cone tip

resistance with the undrained shear strengths measured from element tests on boring

core samples (e.g. Chan et al., 2008; Ozkul et al., 2013). Low et al. (2010) correlated the

cone tip resistances from a worldwide high-quality database of lightly overconsolidated

clays with typical laboratory test (such as triaxial tests and simple shear test) data,

giving a range of Nkt from 8.61~17.39.

3.2.2 CPT in Sands

For assessing spudcan penetration resistance in sand, effective friction angle of sand

is used considering drained conditions. Numerous methods have been published for

evaluating from cone tip resistance. The methods can be divided into three categories

(Lunne et al., 1997): (i) empirical or semi-empirical correlations using other parameters

that can be derived from CPT data, such as relative density and state parameter (Baldi et

al., 1986; Been et al., 1986); (ii) bearing capacity theory (Janbu & Senneset, 1974;

Lunne & Christoffersen, 1983; Cassidy & Houlsby, 2002); and (iii) cavity expansion

theory (Vesic, 1972; Baligh, 1975). More recently, with the development of LDFE

method, Tolooiyan & Gavin (2011) and Kouretzis et al. (2014) simulated cone

penetration in sand using advanced constitutive models with the soil parameters back-

calculated from existing test data, and obtained satisfactory agreement.

NUMERICAL ANALYSIS

In the numerical analysis, a cone penetrometer of diameter Dc is penetrated into a single

layer clay or sand deposit, as illustrated in Figure 3.2. For single layer clay deposit, a


3-4

non-uniform intact undrained shear strength su was considered, increasing linearly with

depth with a gradient k and equalled to sum at the mudline. To be consistent with the

CPT test in the field, the diameter of cone was varied as Dc = 25.2, 35.7 and 43.7 mm

with a 60 tip angle, penetrating at velocities of vfield = 15~25 mm/s. The selected

parameters, together with the parameters for the constitutive model, are summarised in

Table 3.1. For single layer sand deposit, parametric study was performed for a range of

relative density ID = 45~90% with the critical state friction angle crit = 34. The sand

was simulated using the modified Mohr-Coulomb model as illustrated in Figure 2.10.

The relevant parameters for the model, including initial friction angle and peak friction

and dilation angles, were calculated based on ID and crit as described in Chapter 2. As

an interbedded sand layer was considered in the spudcan penetration analysis (Chapter

7), a range of overburden pressure q0/(Dc) from 0 to 252.1 was applied on the surface

of the sand domain to consider the effect of the overlying clay layer.

Further details of the numerical analysis, such as the set-up for the numerical model,

constitutive model, and relevant elastic and plastic parameters, have been introduced in

Chapter 2, and hence are not reiterated here.

RESULTS AND DISCUSSION: CLAY

A typical load-penetration response for cone penetration in strain-softening, rate-

dependent non-uniform clay is illustrated in Figure 3.3. The load-penetration response is

presented in terms of shallow cone factor (Nkt,s) or deep cone factor (Nkt) as a function

of the normalised cone tip depth dtip/D (see Figure 3.2). The profile is divided by the

steady state depth dkt into two parts – shallow penetration response before the steady

state and deep penetration response with a stabilised cone factor. For cone penetration in

non-uniform clay, the value of cone factor Nkt,s or Nkt from numerical analysis is

calculated using

net,c u,c

kt,s kt

u0 u0

q q dN or N

s s

(3.3)

where qu,c is the total cone tip resistance, is the effective unit weight of soil, and su0 is

the intact undrained shear strength at the depth d of the cone shoulder (see Figure 3.2).


3-5

3.4.1 Penetration in Non-Softening, Rate-Independent Clay

To explore the effect of soil rigidity index Ir (= G/su; where G is the shear modulus),

analyses were undertaken for cone penetration on non-softening, rate-independent non-

uniform clay with Ir = 67, 150, 300 and 500 (Group I, Table 3.1). The corresponding

values of deep cone factor Nkt are plotted in Figure 3.4 as a function of Ir, together with

those calculated using the expressions proposed by Baligh (1985), Teh & Houlsby

(1991), Lu et al. (2004), Walker & Yu (2006) and Liyanapathirana (2009). The results

from this study are very close to those presented by Baligh (1985) and fall close to the

line proposed by Lu et al. (2004). The close agreement confirms the capability of the

numerical model. The relationship between the deep cone factor Nkt and rigidity index Ir

can be expressed as

kt rN 0.33 2.2ln I (3.4)

3.4.2 Penetration in Strain-Softening, Rate-Dependent Clay

Clays exhibit strain rate dependency and soften as they are sheared and remoulded. In

order to explore these effects, a parametric study was conducted simulating CPT test on

strain-softening, rate-dependent clay varying related parameters (Groups III~VI, Table

3.1). Additional analyses were also performed to investigate the effects of rigidity index

Ir (Group II, Table 3.1) and soil strength non-homogeneity, kDc/sum (Group VII, Table

3.1). In the following subsections, discussions are made in regards to the effects of the

various parameters on shallow and deep penetration responses.

Shallow penetration response

To illustrate the effect of the degree of non-homogeneity on the form of the penetration

resistance profile at shallow depths (dtip/Dc ≤ dkt/Dc) prior to establishing the steady

penetration response, cone factors from analyses of various values of kDc/sum =

0~10.7110-2 (Group VII, Table 3.1) are presented in Figure 3.5. Due to the small size

of cone penetrometer and hence the small values of kDc/sum, the range of non-

homogeneity factors explored has negligible effect on the shallow penetration response.

All shallow cone factor profiles are within a narrow band with a consistent normalised

steady state depth of dkt/D = ~8.4. For all the analyses (Table 3.1) performed, it is found


3-6

that the steady state depth dkt/Dc varies only as a function of Ir. For the range of Ir =

67~500, dkt/D can be estimated using a linear expression as

ktr

c

d0.016I 7.35

D for 67 ≤ Ir ≤ 500 (3.5)

Interestingly, if the shallow cone factor Nkt,s is normalised by the deep cone factor Nkt,

and expressed as a function of the normalised tip penetration depth dtip/dkt, a somewhat

unified form of load-penetration response can be obtained. Figure 3.6 shows the

Nkt,s/Nkt profiles obtained from all numerical analyses (Table 3.1). A best fit curve is

also included in the figure to represent the profiles with the expression given by

tip kt5.3d /dkt,s

kt

N1 e

N

for 0 ≤ dtip/dkt ≤ 1 (3.6)

The undrained shear strength of clay for dtip/Dc ≤ dkt/Dc can thus be interpreted using

Equations 3.5 and 3.6 with Nkt given by Equation 3.7 proposed in the next section.

Deep penetration response

The effect of strain softening and rate dependency on the value of Nkt is also

investigated through Figure 3.4. The deep cone factor is increased by about 30% when

the combined effect of strength degradation and rate dependency (Group II, Table 3.1)

is incorporated, confirming the dominance of rate dependency for cone penetration. In

addition, consistent with the finding for the shallow cone factor, the degree of soil

strength non-homogeneity also has minimal effect on the profiles of deep cone factor

Nkt, as shown in Figure 3.5.

The deep cone factors obtained from analyses (Groups III~VI, Table 3.1) for different

combination of parameters related to strain softening and rate dependency are plotted in

Figure 3.7. The deep cone factor tends to increase with increasing parameters ,

log(vfield/Dcref), rem and 95 (these parameters are defined in Equation 2.1).

As expected, the effect of the rate parameter appears to be the most significant. Figure

3.7a shows that, as increases from 0 to 0.2, the deep cone factor is increased by

around 75% and 79% for rem = 0.25 and 1.0, respectively. For a typical combination of

soil parameters (Group VII, Table 3.1), the deep cone factor is proportional to the


3-7

normalised penetration velocity log(vfield/Dcref), with Nkt increasing from 13.32 to 14.5

for an increase of log(vfield/Dcref) from 3.8 to 5.55 (Figure 3.7b).

By contrast, parameters related to strength degradation have trivial influence on the

deep cone factor Nkt. As shown in Figure 3.7c, the value of Nkt increases by 7.2~7.4%

as the remoulded ratio rem increases from 0.1 to 1 (or sensitivity St decreases from 10 to

1). The effect of the ductility parameter 95 is shown in Figure 3.7d, which is

insignificant, with an increase of Nkt by 2.8~3.3% as 95 increases from 12 to 24.

A simple expression can be derived to fit Nkt factors for all the analyses in Table 3.1

b 953 /bkt rem rem r

ref

N 1 log 1 e 0.33 2.2ln I

(3.7)

where b = 0.06vfield/Dc and b = 0.3 are the average maximum shear strain rate and

average cumulative plastic shear strain around a deeply penetrated cone penetrometer,

respectively; and the 3rd bracketed term is from Equation 3.4 representing Nkt factor for

a cone penetrating in ideal non-softening, rate-independent clay. The lines predicted by

Equation 3.7 are also included in Figure 3.7, showing an error less than 3%.

For soft clay sediments commonly encountered in offshore site investigation, the

sensitivity St varies between 2 and 10 (i.e. rem = 0.1~0.5) with typical values of rate

parameter = 0.1 and soil ductility 95 = 12. Considering a practical range of stiffness

ratio of E/su = 200~500 (i.e. Ir = 67~168), standard CPT test procedure (i.e. Dc =

25.2~43.7 mm and v = 20 5 mm/s) and typical strain rates of laboratory test (i.e. ref

=

1~20%/h), Equation 3.7 gives a range of Nkt = 11.3~16. Assembling a worldwide, high-

quality database of lightly overconsolidated clays, Low et al. (2010) reported a range of

Nkt factor as 8.61~17.39 correlating cone tip resistance with undrained shear strength

deduced from laboratory tests (triaxial compression test and the average of triaxial

compression, simple shear and triaxial extension tests). The Nkt factors from this study

fall within the range recommended by Low et al. (2010), which confirms the accuracy

of the numerical model and the proposed design formula.

RESULTS AND DISCUSSION: SAND


3-8

Similar to cone penetration in clay deposits, the penetration resistance profile for a cone

penetrometer penetrating in a single layer sand deposit was also found to have two

penetration phases corresponding to shallow and deep failure mechanisms. Based on the

data from calibration chamber tests and shallow offshore cone tests, Puech & Foray

(2002) recognised the influence of the change from shallow to deep failure mechanism

on the measured cone resistance. For shallow failure mechanism, the soil deformation

was shown to direct upward to the soil surface adjacent to the cone shaft, while for deep

failure mechanism, the soil deformation concentrated around the cone tip (similar to the

cavity expansion mechanism). To predict the penetration resistance profile consisting of

shallow and deep penetration responses, Senders (2010) established a relationship

between the total cone tip resistance qu,c and the relative density and mean effective

stress of the silica sand as

C53 m

2C4

c DD

CdCD 100I2.93Im

u,c 1 mq C e 1 e100

(3.8)

where m is the geostatic mean effective stress expressed as

v0 0

m

1 2K

3

(3.9)

Senders (2010) adopted a constant value of K0 = 0.8.

The first bracketed term of Equation 3.8 is the expression commonly used to predict the

cone resistance in sand deposit (e.g. Lunne & Christoffersen, 1983; Jamiolkowski et al.,

1988), while the second part determines the form of the cone resistance profile for

shallow failure mechanism. For deep penetration response only, the second part can be

omitted, with qu,c expressed as

2

D

C

2.93Imu,c 1 mq C e

100

(3.10)

Senders (2008) carried out centrifuge tests (g level: 1~150 g) in single layer silica sand

using model cone penetrometer of diameter of 7 and 10 mm (0.007~1.5 m in prototype).

For most of the tests, the deep penetration response was not achieved due to the limited

depth of the testing strongbox. Equation 3.8 was calibrated against the results, leading to


3-9

coefficients of C1 = 22.5, C2 = C5 = 0.5, C3 = 0.095 and C4 = 2 that best predict the

shallow penetration resistances up to a depth of 30Dc.

However, for the interbedded sand layer with an overlying clay layer of thickness 3 m

investigated in this study (see Chapter 7), the cone resistance profile corresponding to

the deep failure mechanism is of particular interest as the penetration depth of the

standard cone (Dc = 35.7 mm) is significantly greater than 30Dc. As such, LDFE

analyses were carried out for the standard cone penetrometer penetrating in single layer

sand deposit, with the computed penetration resistance profiles used to calibrate

Equation 3.8.

3.5.1 Simulation of Centrifuge Test

Numerical analysis was first performed to simulate two centrifuge tests (50 g) carried

out by Chow et al. (2015) at the University of Western Australia. Both tests were

conducted using a cone penetrometer of Dc = 0.01m (model scale) penetrating saturated

silica sand of effective unit weight s = 6.87 kN/m3 and relative density ID = 70%.

Figure 3.8 compares the measured and computed penetration resistance profiles. The

penetration depths of the measured profiles are corrected considering the non-linear

stress variation along depth caused by the radial acceleration field in the centrifuge

(Schofield, 1980; Bolton et al., 1999). The predicted penetration resistance profiles with

and without considering the shallow penetration response (Equations 3.8 and 3.10,

respectively) are also included in the figure. Two values of K0 are used, with K0 = 0.44

estimated following Jaky (1944) and K0 = 0.8 to be consistent with the value used by

Senders (2010) for calibrating Equation 3.8.

The numerical result, the lower penetration resistance profile from the centrifuge test

and the profile predicted by Equation 3.8 with K0 = 0.8 agree well with each other.

Generally, the predictions using Equation 3.10 overestimate the centrifuge test data,

while the profile by Equation 3.8 with K0 = 0.44 provides a conservative estimate.

Nevertheless, the value of K0 is a function of sand properties and hence it is more

rational to adopt the K0 value estimated following Jaky’s (1944) formula. As such, a

parametric study was carried out varying the relative density ID and the overburden

pressure q0 applied on the surface of the soil domain. Based on the results, the values of

C1~C5 are calibrated with K0 estimated following Jaky (1944).


3-10

3.5.2 Results of Parametric Study

Effect of normalised overburden stress q0/(Dc)

To explore the effect of overburden stress on the cone penetration resistance in sand, the

load-penetration responses obtained from numerical analyses for relative densities of ID

= 45 and 90% are plotted in Figure 3.9, with q0/(Dc) varying between 0 and 252.1. The

predictions according to Equation 3.8 are also included for comparison.

All penetration resistance profiles of the same relative density tend to merge into one

line, achieving stabilised penetration resistances of ~7000 and ~20000 kPa for ID = 45

and 90%, respectively. The depth of attaining stabilised penetration resistance reduces

with increasing overburden stress.

For the penetration resistance profiles for q0/(Dc) = 0, the estimated profiles using

Equation 3.8 provide an excellent prediction at shallow depths (up to a depth of ~28Dc),

followed by underestimation and overestimation for ID = 45 and 90%, respectively. For

q0/(Dc) > 0, shallow penetration resistance profiles for ID = 45% are still reasonably

estimated by Equation 3.8, while conservative estimation is given for ID = 90%. For

deep penetration, the stabilised penetration resistance cannot be captured by Equation

3.8, with the degree of overestimation increasing with increasing overburden stress.

However, this study investigates soil profiles consisting of an sand layer that is overlain

by a thick clay layer ( 3 m or 84Dc; Chapter 7), and hence, the deep penetration

resistance for q0/(Dc) > 0 is crucial.

Effect of relative density ID

To demonstrate the effect of relative density on the form of shallow and deep

penetration resistance profiles, the results of ID = 45, 60, 75 and 90% are plotted in

Figures 3.10a and 3.10b, with overburden stress q0/(Dc) = 0 and 252.1, respectively.

As anticipated, the penetration resistance increases with increasing ID.

The penetration resistance profiles estimated using Equation 3.8 are also included for

comparison. For q0/(Dc) = 0, the estimated profiles agree reasonably for the depths

correspond to shallow and transitional failure mechanisms for all relative densities.

Overall, the penetration resistance profile is underestimated for lower ID and


3-11

overestimated for higher ID, especially for d/Dc > 28. For q0/(Dc) = 252.1, with the

mobilisation of deep failure mechanism and stable penetration resistance, Equation 3.8

tends to overestimate the penetration resistance for all cases. The discrepancy between

computed and estimated profiles becomes more profound for denser sand deposit.

3.5.3 Formula for Cone Tip Resistance in Silica Sand

The penetration resistance profiles for q0/(Dc) = 0 and 252.1 are used to calibrate the

coefficients in Equation 3.8, best fitting both shallow and deep penetration resistances.

As the coefficients after Senders (2010) already provides reasonable predictions for

shallow penetration resistance profiles, the same values of C3 = 0.095 and C4 = 2 are

adopted. In addition, it is assumed that C2 = C5 following Senders (2010).

The calibrated values of C1, C2 and C5 are plotted in Figure 3.11 as a function of relative

density. As ID increases, the value of C1 decreases from 21.7 to 16.6, while those of C2

= C5 increase slightly from 0.72 to 0.79. To simplify the formula and considering that

C2 = C5 vary within a narrow range, an average value of C2 = C5 = 0.75 is selected, with

the corresponding values of C1 (also plotted in Figure 3.11) expressed as

D4.8I

1C 21.4 0.07e (3.11)

Substituting the calibrated values for C1~C5 in Equation 3.8, the modified formula for

standard cone penetrometer of Dc = 0.0357 m is expressed as

0.75m

2DD D

d 0.0950.750.0357 100I4.8I 2.93Im

u,c mq 21.4 0.07e e 1 e100

(3.12)

The estimated cone resistance profiles using Equation 3.12 for the cases in Figure 3.10

are also included in the figure for comparison. Overall, improved predictions are given

by the proposed formula compared to Equation 3.8 in terms of shallow and deep

penetration resistances.

CONCLUDING REMARKS

This chapter has reported results of numerical analyses for cone penetrometers

penetrating in single layer non-uniform clay and uniform sand deposits. All analyse


3-12

were carried out using the ALE approach coupled with the commercial FE package

Abaqus/Explicit. Parametric studies were undertaken to explore the correlations

between the cone tip resistance and the strength parameters of clay and sand. The

effects of soil rigidity index, degree of soil strength non-homogeneity and strain rate and

softening parameters of clay; and relative density and effective stress level of sand, on

cone tip resistance were investigated.

For clay deposit, the effect of soil strength non-homogeneity on the shallow and deep

cone factors was negligible. The depth dkt of attaining the steady state penetration

resistance increased with increasing rigidity index. For shallow penetration response,

profiles of the normalised cone factor Nkt,s/Nkt showed a somewhat unique trend, which

increased with the normalised cone tip penetration depth dtip/dkt. Expressions were

proposed for estimating the depth dkt and shallow cone factor Nkt,s. For deep penetration

response, the deep cone factor Nkt increased with strain softening and rate parameters ,

log(vfield/Dc ref), rem and 95, with the rate parameter μ identified as the most

influencing factor. An expression was also proposed for estimating Nkt factors as a

function of rigidity index and strain softening and rate parameters. For a range of soil

parameters commonly encountered in offshore site investigation, the proposed design

expression for Nkt provided a range of cone factors that fell within the range that was

suggested based on a worldwide, high-quality database.

For cone penetration in sand deposit, the design formula proposed by Senders (2010)

was modified with new values for the coefficients calibrated against the numerical

results. The modified design formula was shown to provide improved predictions in

terms of both shallow and deep penetration resistances.


3-13

REFERENCE

ASTM (2007). Standard test method for electronic friction cone and piezocone

penetration testing of soils, ASTM-D 5778. West Conshohocken: ASTM

International.

Baldi, G., Bellotti, R., Ghionna, V., Jamiolkowski, M. & Pasqualini, E. (1986).

Interpretation of CPTs and CPTUs; Part 2: drained penetration of sands. Proc. 4th

International Geotechnical Seminar, Singapore, 143-156.

Baligh, M. M. (1975). Theory of deep site static cone penetration resistance.

Massachusetts Institute of Technology, Department of Civil Engineering,

Cambridge, Mass., Publication No. R75-56.

Baligh, M. M. (1985). Strain path method. Journal of Geotechnical Engineering, ASCE

111, No. 9, 1108-1136.

Been, K., Crooks, J. H. A., Becker, D. E. & Jefferies, M. G. (1986). The cone

penetration test in sands: Part I, state parameter interpretation. Géotechnique 36,

No. 2, 239-249.

Bolton, M. D., Gui, M. W., Garnier, J., Corte, J. F., Bagge, G., Laue, J. & Renzi, R.

(1999). Centrifuge cone penetration tests in sand. Géotechnique 49, No. 4, 543-

552.

Cassidy, M. J. & Houlsby, G. T. (2002). Vertical bearing capacity factors for conical

footings on sand. Géotechnique 52, No. 9, 687-692.

Chan, N. H. C., Paisley, J. M. & Holloway, G. L. (2008). Characterization of soils

affected by rig emplacement and Swiss cheese operations - Natuna Sea, Indonesia,

a case study. Proc. 2nd Jack-up Asia Conference and Exhibition, Singapore.

Chow, S. H., O’Loughlin, C. D. & Gaudin, C. (2015). GeoWAVE D3.4: centrifuge

testing report. Centre for Offshore Foundation Systems, Perth, Australia.

ISSMGE IRTP (1999). International reference test procedure for the cone penetration

test (CPT) and the cone penetration test with pore pressure (CPTU). Report of the

ISSMGE Technical Committee 16 on Ground Property Characterization from In

Situ Testing, 1999 (corrected 2001). London: International Society of Soil

Mechanics and Geotechnical Engineering.

Jaky, J. (1944). The coefficient of earth pressure at rest. In Hungarian (A nyugalmi

nyomas tenyezoje). J. Soc. Hung. Eng. Arch. (Magyar Mernok es Epitesz-Egylet

Kozlonye), 355-358.


3-14

Jamiolkowski, M., Ghionna, V. N., Lancellotta, R. & Pasqualini, E. (1988). New

correlations of penetration tests for design practice. Proc. 1st International

Symposium on Penetration Testing, 1, 263-296.

Janbu, N. & Senneset, K. (1974). Effective stress interpretation of in situ static

penetration tests. Proc. the European Symposium on Penetration Testing, ESOPT,

Stockholm, 181-193.

Kouretzis, G. P., Sheng, D. & Wang, D. (2014). Numerical simulation of cone

penetration testing using a new critical state constitutive model for sand.


Liyanapathirana, D. S. (2009). Arbitrary Lagrangian Eulerian based finite element

analysis of cone penetration in soft clay. Computers and Geotechnics 36, No.5,

851-860.

Low, H. E., Lunne, T., Andersen, K. H., Sjursen, M. A., Li, X. & Randolph, M. F.

(2010). Estimation of intact and remoulded undrained shear strengths from

penetration tests in soft clays. Géotechnique 60, No. 11, 843-859.

Lu, Q., Randolph, M. F., Hu, Y. & Bugarski, I. C. (2004). A numerical study of cone

penetration in clay. Géotechnique 54, No. 4, 257-267.

Lunne, T. & Christoffersen, H. P. (1983). Interpretation of cone penetrometer data for

offshore sands. Proc. Offshore Technology Conference, Houston, OTC 4464.

Lunne, T., Robertson, P. K. & Powell, J. J. M. (1997). Cone penetration test in

geotechnical practice. London: Blackie Academic & Professional.

Ozkul, Z. H., Bik, M. & Remmes, B. (2013). Piezocone profiling of a deepwater clay

site in the Gulf of Guinea. Proc. Offshore Technology Conference, Houston, OTC

24136.

Puech, A. & Foray, P. (2002). Refined model for interpreting shallow penetration CPTs

in sands. Proc. Offshore Technology Conference, Houston, OTC 18268.

Schofield, A. N. (1980). Rankine lecture: Cambridge University geotechnical centrifuge

operations. Géotechnique 30, No. 3, 227-268.

Senders, M. (2008). Suction caissons in sand as tripod foundation for offshore wind

turbines. PhD thesis, The University of Western Australia, Perth.

Senders, M. (2010). Cone resistance profiles for laboratory tests in sand. Proc. 2nd

International Symposium on Cone Penetration Testing, Huntington Beach, paper

no. 2-08.

Teh, C. I. & Houlsby, G. T. (1991). An analytical study of the cone penetration test in

clay. Géotechnique 41, No. 1, 17-34.


3-15

Tolooiyan, A. & Gavin, K. (2011). Modelling the cone penetration test in sand using

cavity expansion and arbitrary Lagrangian Eulerian finite element methods.

Computers and Geotechnics 38, No. 4, 482-490.

van den Berg, P. (1994). Analysis of soil penetration. Delft: Delft University Press.

Vesic, A. S. (1972). Expansion of cavities in infinite soil mass. Journal of the Soil

Mechanics and Foundations Division, ASCE 98, No. 3, 265-290.

Walker, J. & Yu, H. S. (2006). Adaptive finite element analysis of cone penetration in

clay. Acta Geotechnica 1, No.1, 43-57.



Yu, H. S. (2000). Cavity expansion methods in geomechanics. Rotterdam: Balkema.


3-16

TABLES

Table 3.1 Summary of LDFE analyses performed for cone penetration in clay

Group kDc/sum

(10-2) log(vfield/Dc

ref) Ir 95 rem Notes

I 3.57 -

67, 150,

300 and

500

0 - 1.0

Effect of Ir on

non-softening,

rate-independent

clay

II 3.57 5.13

67, 150,

300 and

500

0.1 12 0.25

Effect of Ir on

strain-softening,

rate-dependent

clay

III 3.57 5.13 150 0.1 and

0.2 12

0.1,

0.25,

0.5 and

1.0

Effect of rem

IV 3.57 5.13 150 0, 0.1

and 0.2 12

0.25

and 1.0 Effect of

V 3.57 5.13 150 0.1 and

0.2

12, 18

and

24

0.25 Effect of 95

VI 3.57 3.8, 4.4, 5.13

and 5.55 150 0.1 12 0.25

Effect of

log(vfield/Dcref)

VII

0,0.36,

1.43,

3.57,

5.36 and

10.71

5.13 150 0.1 12 0.25 Effect of kDc/sum


3-17

FIGURES

3.1(a) Terminology for cone penetrometers

3.1(b) Pore water pressure effects on measured parameters

Figure 3.1 Schematic diagram of a typical cone penetrometer (after Lunne et al.,

1997)

Pore pressure filter location

Friction sleeve

Cone penetrometer

Coneu1

u2

u3

Bearing area of cone

u2

u3

u2

Cross-sectional area of load cell


3-18

Figure 3.2 Schematic diagram of cone penetrometer in single layer soil

d

z

Cone

dtip

z

Clay Sand

ID (crit)

Dc

q0 q0

sum su

k

1

su0


3-19

Figure 3.3 Typical load-penetration response of cone penetration in clay (Ir = 150;

Group II, Table 3.1)

0

4

8

12

16

20

0 3 6 9 12 15 18

No

rmalised

tip

pen

etr

ati

on

dep

th,

dti

p/D

c

Cone factor, Nkt,s or Nkt

Steady state depth, dkt/Dc

Shallow penetrationresponse, Nkt,s

Deep penetrationresponse, Nkt


3-20

Figure 3.4 Comparison of Nkt factors from this study and previous researches

(Groups I and II, Table 3.1)

0

2

4

6

8

10

12

14

16

18

20

1 10 100 1000

De

ep

co

ne

fa

cto

r, N

kt

Rigidity index, Ir

Baligh (1985)

Teh & Houlsby (1991)

Lu et al. (2004)

Walker & Yu (2006)

Liyanapathirana (2009)

This study

Non-softening, rate-indepenent clay

Strain-softening, rate-depenent clay


3-21

Figure 3.5 Cone factor profiles for non-homogeneous clays (Group VII, Table 3.1)

0

4

8

12

16

20

0 3 6 9 12 15 18

No

rma

lis

ed

tip

pe

ne

tra

tio

n d

ep

th,

dti

p/D

c

Cone factor, Nkt,s or Nkt

Steady state depth, dkt/Dc

Shallow penetrationresponse, Nkt,s

Deep penetrationresponse, Nkt

kDc/sum =

0~10.71 10-2


3-22

Figure 3.6 Variation of normalised shallow cone factor Nkt,s/Nkt with normalised

cone tip penetration depth dtip/dkt (Groups I~VII, Table 3.1)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

No

rmalis

ed

tip

pen

etr

ati

on

dep

th,

dti

p/d

kt

Normalised shallow cone factor, Nkt,s/Nkt

tip kt5.3d /dkt,s

kt

N1 e

N


3-23

3.7(a) Effect of

3.7(b) Effect of log(vfield/Dcref)

10

12

14

16

18

20

22

0 0.05 0.1 0.15 0.2

De

ep

co

ne

fa

cto

r, N

kt

Equation 3.7

rem = 1

rem = 0.25

8

10

12

14

16

18

20

3.2 3.9 4.6 5.3 6

De

ep

co

ne

fa

cto

r, N

kt

log(vfield/Dcref)

Equation 3.7

.


3-24

3.7(c) Effect of rem

3.7(d) Effect of 95

Figure 3.7 Effect of strain softening and rate parameters on Nkt factors (Groups

III~VI, Table 3.1)

8

10

12

14

16

18

0 0.2 0.4 0.6 0.8 1

De

ep

co

ne

fa

cto

r, N

kt

rem

Equation 3.7

= 0.1

= 0

8

10

12

14

16

18

6 10 14 18 22 26 30

De

ep

co

ne

fa

cto

r, N

kt

95

Equation 3.7

= 0.1

= 0


3-25

Figure 3.8 Predicted, measured and computed penetration resistance profiles for

cone penetration in silica sand

0

3

6

9

12

15

0 2000 4000 6000 8000 10000 12000

No

rmalised

pen

etr

ati

on

dep

th,

d/D

c

Cone penetration resistance, qu,c: kPa

K0 = 0.8Equation 3.10

K0 = 0.44Equation 3.10

Numerical analysis

K0 = 0.44 Equation 3.8

K0 = 0.8 Equation 3.8 Centrifuge

tests


3-26

3.9(a) ID = 45%

0

10

20

30

40

50

60

70

80

90

0 1500 3000 4500 6000 7500 9000

No

rmalised

pen

etr

ati

on

dep

th,

d/D

cCone penetration resistance, qu,c: kPa

Numerical analysis

Equation 3.8

q0/(Dc) = 0, 42, 84, 126.1, 168.1, 210.1 and 252.1


3-27

3.9(b) ID = 90%

Figure 3.9 Effect of overburden stress (q0) on cone penetration resistance in sand

0

10

20

30

40

50

60

70

80

90

0 5000 10000 15000 20000 25000 30000 35000

No

rma

lis

ed

pe

ne

tra

tio

n d

ep

th,

d/D

c


q0/(Dc) = 0, 42, 84, 126.1, 168.1, 210.1 and 252.1

Numerical analysis

Equation 3.8


3-28

3.10(a) q0/(Dc) = 0

0

10

20

30

40

50

60

70

80

90

100

0 4000 8000 12000 16000 20000

No

rmalised

pen

etr

ati

on

dep

th,

d/D

cCone penetration resistance, qu,c: kPa

Numerical analysis

Equation 3.8

Equation 3.12

ID = 45% 60% 75%90%


3-29

3.10(b) q0/(Dc) = 252.1

Figure 3.10 Effect of relative density of sand (ID) on cone penetration resistance

0

15

30

45

60

75

90

105

120

0 6000 12000 18000 24000 30000 36000N

orm

alised

pen

etr

ati

on

dep

th,

d/D

c


Equation 3.8Numerical analysis

Equation 3.12

ID = 45% 60% 75% 90%


3-30

Figure 3.11 Effect of relative density on coefficients C1, C2 and C5

0

0.4

0.8

1.2

1.6

2

0

5

10

15

20

25

0 20 40 60 80 100

Co

eff

icie

nts

C2

an

d C

5

Co

eff

icie

nt

C1

Relative density, ID: %

C1: best fit

C1: best fit for C2 = C5 = 0.75

C2 and C5: best fit

Chapter 4. Spudcan in Stiff-over-Soft Clay

4-1

CHAPTER 4. SPUDCAN IN STIFF-OVER-SOFT CLAY

INTRODUCTION

Punch-through incident occurs in stratified soil conditions with a surface or interbedded

strong layer overlying a weak layer. Recently, design approaches for spudcan

penetration in sand-over-clay deposits have been reported by Teh et al. (2009), Lee et

al. (2013a, 2013b), and Hu et al. (2014a, 2014b, 2015). This chapter addresses the gap

by developing new mechanism-based and CPT-based design approaches for spudcan

penetration in stiff-over-soft clay deposits with the potential for punch-through (see

Figure 4.1). A database comprising experimental and numerical data is used to calibrate

the proposed design approaches.

The experimental data are from the centrifuge tests reported by Hossain & Randolph

(2010a) for spudcan penetration in stiff-over-soft clays, which are assembled in Table

4.1. The undrained shear strengths in these tests were measured using T-bar

penetrometer test and the calculation framework at that time with a deep bearing

capacity factor of 10.5. However, recent studies have highlighted two issues for

characterising stiff-over-soft clay deposits (White et al., 2010; Zhou et al., 2013; Lee et

al., 2013a): (i) for the thin top stiff layer relative to the penetrometer diameter, the full

(i.e. stable) penetration resistance of that layer may not be mobilised; and (ii) in the

underlying soft layer, a soil plug may be brought down by the penetrometer from the top

layer and hence the mobilised resistance may be higher compared with the actual

resistance of that layer. Adjustments are therefore required. This is particularly critical

for the T-bar penetrometer of 0.5 m (prototype) diameter used in centrifuge tests

reported by Hossain & Randolph (2010a). As such, the strength values are corrected

through trial and error by simulating T-bar penetration in stiff-over-soft clays, which is

discussed in Section 4.3.1 on ‘Simulation of Centrifuge Tests’.

A numerical parametric study for spudcan penetration (Groups II-IV, Table 4.2) using

large deformation finite element (LDFE) method was carried out to complement the

centrifuge test data. The effects of strain softening and rate dependency of the undrained

shear strength of clay were incorporated.


4-2

Based on the database (Table 4.1 and Groups II-IV, Table 4.2), this chapter aims to (i)

present an extensive LDFE parametric study for spudcan penetration in stiff-over-soft

clay with strain softening and rate dependency; and (ii) propose new design approaches

to predict the depth and magnitude of the peak resistance in the top layer, the resistance

at the stiff-soft layer interface and the penetration resistance profile in the bottom layer.

The outcomes presented in this chapter have been documented in Zheng et al. (2015).

LITERATURE REVIEW

The design formula Equation 1.2 recommended in the current design guidelines ISO

19905-1 (ISO method; ISO, 2012) follows the Brown & Meyerhof’s (1969) factor, but

is adjusted for embedment depth by applying a constant depth factor, following the

semi-empirical approach of Skempton (1951). The deficiencies of the ISO method have

been introduced in Chapter 1, and hence are not reiterated here.

To improve the ISO method, a number of investigations have been conducted on the

bearing response of foundations in stiff-over-soft clays. Wang & Carter (2002)

simulated continuous penetration of a circular footing in two-layer clay deposits, using a

LDFE method. Small strain finite element (FE) analyses of surface footings on uniform-

over-uniform clays were undertaken by Edwards & Potts (2004) and Merifield &

Nguyen (2006). The results from centrifuge model tests and LDFE analyses for spudcan

penetration in stiff-over-soft clays were reported by Hossain & Randolph (2010a,

2010b). Based on the results from LDFE analyses, Hossain & Randolph (2009)

proposed a mechanism-based design approach for predicting the spudcan penetration

resistance profile in stiff-over-soft clays. However, the clay was modelled as a non-

softening plastic material in the simulation. Therefore, the form of the penetration

resistance profile, including the depth and value of peak resistance, was not simulated

accurately and the penetration resistance profiles were consistently overestimated.

Edwards & Potts (2004) summarised the results from their small strain FE analyses and

proposed a new design approach for spudcan penetration in uniform stiff-over-soft clays.

For spudcan in the top layer, the contribution to the penetration resistance from the

upper stiff layer is considered as a proportion of the difference between the bearing

capacities of stiff layer and soft layer. The value of the proportion is estimated from the


4-3

proposed formula as a function of strength ratio between clay layers and thickness ratio

of the stiff layer. For spudcan penetration in the bottom layer, the conventional single

layer approach following Skempton (1951) is recommended.

Based on the centrifuge test data of spudcan penetration in uniform-over-uniform clay

reported by Hossain & Randolph (2010a), Dean proposed an improvement of the ISO

method (Dean method) in the discussion with Hossain & Randolph (2011). In the Dean

method, the thickness of the soil plug, equal to the top layer thickness, is assumed to be

unchanged during the spudcan penetration so that the bearing resistance from the

periphery and base of the soil plug in the underlying soft layer can be calculated. For the

calculation of spudcan penetration resistance in the top layer, adjustment coefficients

were back-calculated for the terms of shear resistance and end bearing capacity. No

recommendations were given for the calculation of the bottom layer. Hossain &

Randolph (2011) supplemented the data with those from additional centrifuge tests and

LDFE analyses for spudcan penetration in uniform-over-non-uniform clay, with slightly

different adjustment coefficients obtained from the best fit.

The performance of the design approach proposed in this chapter is compared with the

ISO method, Edwards-Potts method (Edwards & Potts, 2004) and Dean method

(Hossain & Randolph, 2011).

NUMERICAL ANALYSIS

This chapter has considered a circular spudcan of diameter D, penetrating into a two-

layer clay deposit as illustrated schematically in Figure 4.1, where the top stiff layer

with uniform undrained shear strength sut, effective unit weight t, and thickness t is

underlain by the bottom soft layer of non-uniform undrained shear strength sub = subs +

k(z – t), and effective unit weight b. subs is the undrained shear strength of the bottom

soft layer at the stiff-soft layer interface.

The numerical model was first validated against centrifuge test data (Group I, Table 4.2).

A series of parametric analyses (Groups II~IV, Table 4.2) were then performed. The

thickness of the top layer t was varied relative to the spudcan diameter as 0.25D~1D,

with nominally infinite thickness of the bottom layer. A thickness ratio of t/D > 1 was

not considered in the numerical parametric study, as the spudcan does not penetrate


4-4

through such thick strong layers during jack-up installation. The strength ratio at the

interface between the bottom and top layers, subs/sut, was varied as 0.25~0.75. For

convenience, the effective unit weight of the deposit was considered to be constant and

was taken as = 8 kN/m3. The normalised strength of the bottom layer at the interface

was subs/D = 0.31, with the degree of non-homogeneity kD/subs = 0~3.

Further details of the numerical analysis, such as the set-up for the numerical model,

constitutive model, and relevant elastic and plastic parameters, have been introduced in

Chapter 2, and hence are not reiterated here.

4.3.1 Simulation of Centrifuge Tests

As discussed previously, the undrained shear strengths reported by Hossain & Randolph

(2010a) for the centrifuge tests may have been misinterpreted using a constant T-bar

factor of 10.5. As such, CEL analyses were first undertaken simulating T-bar

penetration for centrifuge tests in Table 4.1 in an effort to explore the actual values of

undrained shear strengths. The accuracy of the numerical model has already been

verified through validation against measured data, as presented in Chapters 2 and 3. The

computed results for T-bar penetration in tests E2UNU-I-T 3 and E2UNU-II-T 5 are

presented in Figure 4.2 in terms of total bearing pressure qu as a function of the

penetration depth of the T-bar invert. Two sets of undrained shear strength profiles were

used, including one suggested by Hossain & Randolph (2010a) and the other corrected

through trial and error.

Figure 4.2 indicates that a thickness of t = 4.5 m relative to the T-bar diameter of 0.5 m

is not thick enough to establish the full T-bar penetration resistance in the top layer due

to the influence of the bottom soft layer. For the T-bar penetration in the bottom layer,

the difference between numerical results and centrifuge test data is believed to be

caused by the stiff soil plug brought down by the T-bar from the top layer. The bearing

pressure profiles from numerical analyses using corrected undrained shear strengths, by

contrast, agree well with the centrifuge test data.

Numerical analyses were also performed simulating spudcan penetration for tests

E2UNU-I-T 3 and E2UNU-II-T 5 using the corrected undrained shear strengths. Figure

4.3 compares the experimental and numerical results. The computed penetration


4-5

resistance profiles agree reasonably well with the measured data, confirming the

correctness of using the corrected values of undrained shear strengths. Therefore,

corrected undrained shear strengths obtained through trial and error, listed in Table 4.1,

were used to propose the new design approach.

4.3.2 Results and Discussion

The load-penetration responses are presented in terms of the normalised net bearing

pressure, qnet/sub0, as a function of the normalised penetration depth, (d – t)/D, with qnet

calculated as

net

P Vq γ

A A (4.1)

where P is the total vertical reaction force, A is the maximum bearing area of the

spudcan and V is the volume of the embedded spudcan including shaft. sub0 = subs +

Max[k(d t), 0] is the undrained shear strength at the spudcan base level d for d t (see

Figure 4.1), with sub0 = subs for d < t.

The soil failure mechanisms and hence the penetration resistance profile of spudcan

foundation on stiff-over-soft clays are affected by a number of factors, including the

strength ratio subs/sut, the thickness of the top layer relative to the spudcan diameter t/D,

and the strength non-homogeneity factor of the bottom layer kD/subs. The effects of

these factors on the depth dp and value qpeak of the peak resistance in the top layer and

the bearing capacity factor in the bottom layer are briefly discussed below. This will

lead to the development of the new design approach.

Effect of strength ratio subs/sut

To investigate the effect of the strength ratio subs/sut on the penetration resistance profile,

Figure 4.4 is plotted for strength ratio subs/sut = 0.25, 0.3, 0.4, 0.5 and 0.75 with t/D =

0.75, subs/D = 0.31 and kD/subs = 0.5 (Group II, Table 4.2). It can be seen that the

normalised depth of peak resistance dp/D increases from ~0.17 to ~0.72 with increasing

subs/sut from 0.25 to 0.75.

The load-penetration response in the bottom layer is also affected by subs/sut. The

normalised resistance close to the interface is higher for a lower strength ratio. This

discrepancy diminishes gradually as the spudcan penetrates deeper. This is caused by


4-6

the soil plug carried down by the advancing spudcan from the stiff layer and

corresponding additional resistance: a lower strength ratio enables a thicker soil plug to

be forced down (see insets in Figure 4.4). The soil plug height diminishes gradually

with the initiation of soil backflow and the increasing strength in the bottom layer.

Effect of thickness ratio t/D

The penetration resistance profiles from analyses of t/D = 0.25, 0.5, 0.75 and 1.0 are

plotted in Figures 4.5a and 4.5b for subs/sut = 0.25 and 0.5, respectively, with subs/D =

0.31 and kD/subs = 0 (Group III, Table 4.2). As t/D increases, dp/D becomes deeper,

which is more profound for higher strength ratio subs/sut.

In the bottom layer, the effect of the soil plug is more profound for subs/sut = 0.25, with

thicker stiff layer leading to a higher normalised penetration resistance. In contrast, for

higher strength ratio of subs/sut = 0.5, all the profiles form a unique line after (d – t)/D =

~0.6, with Ncd = qnet/sub0 = ~11.4.

Effect of strength non-homogeneity kD/subs

The effect of soil strength non-homogeneity, indicated by kD/subs, on the bearing

response of spudcan is specifically focused through Figures 4.6a and 4.6b. The

penetration resistance profiles are from analyses for kD/subs = 0, 0.25, 0.5 and 3.0, with

identical subs/D = 0.31 and subs/sut = 0.25, but for thickness ratios of t/D = 0.5 and 1.0,

respectively (Group IV, Table 4.2). It can be seen that the depth of peak resistance dp/D

increases as kD/subs increases.

The effect of kD/subs on the bearing response in the bottom layer is significant

particularly close to the layer interface. For high non-homogeneity factor of kD/subs =

3.0, the normalised penetration resistance is higher at the layer interface, but it reduces

rapidly with penetration depth and finally stabilises at a depth of (d – t)/D = ~1.0. In

contrast, for lower non-homogeneity of kD/subs = 0, the normalised penetration

resistance is lower over the early penetration in the bottom layer. However, the profile

reduces at a lower rate, due to the presence of the soil plug that diminishes slower (see

insets in Figure 4.6), leading to higher normalised penetration resistance over deep

penetration.


4-7

Effect of Sensitivity St

The above parametric study was undertaken for a consistent value of sensitivity, St =

2.8. In order to examine the effect of sensitivity on the penetration resistance, additional

analyses were carried out with St = 1 (rate-dependent soil without strain softening) and

5 for a representative case (subs/sut = 0.5, t/D = 1.0, kD/subs = 0.5 and subs/D = 0.31,

Group V, Table 4.2).

The penetration resistance profiles for different sensitivities are plotted in Figure 4.7. As

St increases from 1 to the practical value of 2.8, the depth and value of the peak

resistance is considerably affected. The values of dp/D and qpeak/subs decrease from 1.0 to

0.58 and from 19.2 to 16.2, respectively, whereas the penetration resistance in the

bottom layer is reduced by ~25%. This is close to the suggestion by Menzies & Roper

(2008) and Hossain et al. (2014) who recommended a 20% reduction to be applied to

the numerical modelling results of spudcan penetration in single layer non-softening,

rate-independent clay. With further increase of St from 2.8 to 5, the depth and value of

the peak resistance decrease marginally, while the deep penetration resistance is reduced

further by about 10%.

NEW MECHANISM-BASED DESIGN APPROACH

Based on the results from centrifuge tests reported by Hossain & Randolph (2010a), as

tabulated in Table 4.1, and parametric LDFE analyses performed in this study (Groups

II~IV, Table 4.2), a new mechanism-based design approach is developed for predicting

the penetration resistance profile of spudcan in stiff-over-soft clay deposit. The new

design approach predicts the position and magnitude of the peak resistance (dp, qpeak) in

the top layer, the bearing capacity at the stiff-soft layer interface (dint, qint), and the deep

bearing capacity factor Ncd. For the prediction of qpeak, two design methods are

proposed, including the semi-empirical method and the improved ISO method.

4.4.1 Peak Resistance

Depth of peak resistance dp

According to the previous discussion, the depth of peak resistance relative to the

spudcan diameter, dp/D, varies as a function of normalised parameters, subs/sut, t/D and


4-8

kD/subs. The trend is shown in Figure 4.8 plotting the values from centrifuge tests and

parametric study, which can be expressed as

1.5 0.5

p ubs

ut ubs

d s t kD t1.3 1

D s D s D

(4.2)

Once dp/D is determined, the corresponding penetration resistance at the peak can be

calculated using either the semi-empirical method or the improved ISO method, as

introduced below.

Magnitude of peak resistance qpeak

Semi-empirical method

The net peak resistance qpeak normalised by subs can be estimated according to

0.771 0.50.75

peak ubs nets

ubs ut ubs ubs

q s qt kD6.35 5 1

s s D s s

(4.3)

where qnets is the net penetration resistance at the top of the stiff layer, which can be

calculated using the ISO method (Equation 1.2). The relationship between Equation 4.3

and values of qpeak/subs obtained from centrifuge tests and numerical analyses is shown

in Figure 4.9a, while Figure 4.9b shows that the design formula predicts the peak

resistance mostly within an error of 10%.

Improved ISO method

The ISO method for punch-through is expressed as Equation 1.2, with the

corresponding punch-through model delineated in Figure 4.10. As illustrated in Chapter

1, Equation 1.2 consists of the end bearing capacity for a fictitious footing at the stiff-

soft layer interface assuming a general shear failure and the shear resistance along the

shear planes in the stiff layer. The key deficiency of the ISO method is that the soil plug

base is assumed to be fixed at the layer interface regardless of the spudcan penetration,

and hence the corresponding resistance from the soil plug in the soft clay is neglected.

As such, the improved ISO method for predicting peak resistance is proposed as

follows. The depth of punch-through is assumed as identical to dp obtained from

Equation 4.2. The gross penetration resistance at the peak Qv,peak is then calculated for


4-9

all cases (Table 4.1 and Groups II-IV, Table 4.2) using Equation 1.2 with d = dp but

adding a plug (of height T) in the soft layer and shifting the fictitious footing position

to the base of the added plug, as illustrated in Figure 4.10. A factor of 0.75 is applied to

the shear resistance around the soil plug in the soft layer to be consistent with the

calculation in the stiff layer. Adding the additional resistance (4.2ATsubs/D: 3ATsubs/D

from the shear resistance around the soil plug and 1.2ATsubs/D from the end bearing

capacity) provided by the plug in the soft layer to Equation 1.2, the improved punch-

through criterion for spudcan penetration in uniform stiff-over-soft clay deposit (sub =

subs) is therefore expressed as

v,peak c,int ub 0 ut ubs

AT ATQ A N s p 3 s 4.2 s

D D

(4.4)

where Nc,int = Min[6(1 + 0.2dint/D), 9.0] is the bearing capacity factor at the depth of the

stiff-soft layer interface, p0 is the effective overburden pressure of soils above spudcan

base level and T is the thickness of the stiff layer between the base of the advancing

spudcan and the initial layer interface.

To keep a simple form of the formula, Equation 4.4 is also used to predict the peak

resistance for spudcan penetration in uniform-over-non-uniform deposit (i.e. k > 0),

taking sub in Equation 4.4 as the average strength over the depth of D/2 below the layer

interface. Calibration of the calculated values of Qv,peak against the measured and

computed data provides the values of T. All the normalised values of T/t are plotted in

Figure 4.11a with the approximation given as

t0.5

0.5 21 D

ubs

ut ubs

sT t kD0.53 3 1.5

t s D s

for kD/subs ≤ 3 (4.5)

It can be seen in Figure 4.11b that the proposed method predicts qpeak within an error of

10% for all cases except one centrifuge test with low peak resistance. Note, high

values of T/t (e.g. 6.8 for Test E2UNU-I-T 2) are associated with thin stiff layer and

very weak soft layer.

For undrained shear strength profile where non-homogeneity factor kD/subs > 3, due

care should be taken when selecting T. This is because the empirical undrained shear


4-10

strength sub (average shear strength over a depth of D/2 below the layer interface) in

Equation 1.2 could already be an overestimate for the average shear strength that is

actually mobilised by the spudcan for these cases. Therefore, high value of kD/subs may

lead to an unsafe prediction of the penetration resistance using Equation 4.4.

The improved ISO method explicitly considers the effect of the soil plug in the

underlying soft layer in the calculation of the bearing capacity at punch-through. The

method modifies the original formula in a pithy way without changing the framework of

bearing capacity calculation recommended by ISO standard 19905-1 (ISO, 2012).

4.4.2 Resistance at Layer Interface

The severity of punch-through failure or the degree of reduction of bearing capacity can

be indicated by connecting spudcan resistances at punch-through (dp, qpeak) and at stiff-

soft layer interface (dint, qint). As such, the normalised bearing capacities, qint/subs, at the

layer interface are plotted in Figure 4.12, which are best fitted by

0.850.5 0.250.25

peakint ubs

ubs ut ubs ubs

qq s t kD10.2 1

s s D s s

(4.6)

4.4.3 Deep Bearing Capacity Factor Ncd

For spudcan penetration resistance in the bottom layer, a simplified single layer

approach is used, which implicitly incorporates the effect of the soil plug and

corresponding additional resistance into the deep bearing capacity factor Ncd. To

explore the value of Ncd, all profiles of qnet/sub0 as a function of (d t)/D from numerical

analyses and centrifuge tests are plotted in Figure 4.13. The corresponding stabilised

values of Ncd are plotted in Figure 4.14, with the best fit linear line expressed as

1 10.5

ubscd

ut ubs

s t kDN 9.8 1.3 Min ,1.0 1 15.5

s D s

(4.7)

For the range of soil properties and layer geometries explored in this study, Equation 4.7

predicts the value of Ncd mostly within an error of 1.0.


4-11

4.4.4 Summary Design Procedure

The design procedure is summarised as follows:

1. Predict the depth of peak resistance dp in the top layer using Equation 4.2, and

corresponding peak resistance qpeak using Equation 4.3 according to the semi-

empirical method or Qv,peak using Equation 4.4 combined with Equation 4.5

according to the improved ISO method;

2. Calculate the total vertical reaction force Ppeak at d = dp by adding the buoyancy

Vsp to Aqpeak, or by adding the buoyancy Vsp to Qv,peak and then deducting the

weight of the backfill soil above the spudcan;

3. Compare Ppeak with the intended preload Vp. If Ppeak ≤ Vp, punch-through failure

would not occur and the spudcan would rest at a depth ≤ dp (although in practice,

a safety factor should be applied, e.g. Vp ≤ ~0.75Ppeak);

4. Otherwise, estimate the penetration resistances at the layer interface, (Aqint +

Vsp), and in the bottom layer, (ANcdsub0 + Vsp), with qint and Ncd calculated

using Equations 4.6 and 4.7, respectively, and determine the punch-through

distance hP-T;

5. Compare (ANcdsub0 + Vsp) with Vp to determine final spudcan-resting depth.

If a complete penetration resistance profile is required, straight lines can be used to

connect the penetration resistances at the surface of the stiff layer, at d = dp and at d =

dint, and the penetration resistance profile in the bottom layer (see Figure 4.18). The

bearing capacity at the surface of the stiff layer can be calculated using Equation 1.2.

The proposed design approach generally applies to stiff-over-soft clay deposits of a

practical range of soil parameters with kD/subs ≤ 3. However, it should be noted that for

spudcan penetration in soils of high sensitivity (e.g. St 5), the depth and value of the

peak resistance will be slightly decreased, and at least a 10% reduction is suggested to

be applied on the estimated penetration resistance profile in the soft clay layer.

NEW CPT-BASED DESIGN APPROACH

Depletion of known reserves in the shallow waters of traditional hydrocarbon regions is

resulting in exploration in deeper, unexplored and undeveloped environments. The


4-12

difficulty in obtaining high-quality soil samples from these sites for laboratory

determination of soil properties has placed increasing reliance on results from in-situ

testing. As such, to supplement the ‘two-step’ mechanism-based design approaches, a

new CPT-based design approach is proposed in this section establishing direct

correlations between spudcan and cone tip resistances in stiff-over-soft clay. To be

consistent with practice, the correlations are established between net penetration

resistance profiles of spudcan (qnet,sp) and cone (qnet,c), which are calculated from the

corresponding total penetration resistances qu,sp and qu,c according to

sp

net,sp u,sp cav

Vq q Min d,H

A

for shallow bearing response (4.8a)

sp

net,sp u,sp

Vq q

A for deep bearing response (4.8b)

net,c kt u u,cq N s q d (4.8c)

where subscripts net, u, sp and c represent net bearing pressure, total bearing pressure,

spudcan and cone, respectively. Nkt is the bearing capacity factor of cone in clay, which

is assumed as a constant value throughout the soil profile for design purpose, and is

calculated according to Equation 3.7. Note, qnet,sp is different from qnet in Equation 4.1

where only the buoyancy (V/A) of the embedded spudcan in soil is negated from the

total penetration resistance.

As noted previously in Chapter 2, the distance of transition of the cone penetration

resistance profile when the cone penetrates from one layer to another is negligible

compared with the layer thickness considered in spudcan penetration design (Walker &

Yu, 2010; Ma et al., 2015). Therefore, the CPT profile is simplified by combining the

profile in each layer (calculated using Equations 3.7 and 4.8) and neglecting the

transitional zones, which is similar to the form of the undrained shear strength profile.

As such, the normalised limiting cavity depths Hcav/D observed in the numerical

analyses (Groups II~IV, Table 4.2), as plotted in Figure 4.15, can be expressed as a

function of the cone tip resistances from the simplified CPT profile and cone factor as

0.50.5

net,ctcav

kt b net,cbs

qH t D0.95 1

D N D D q

(4.9)


4-13

where qnet,ct is the net cone tip resistance in the top (stiff) clay layer, is the gradient of

the net cone tip resistance in the bottom (soft) clay layer and qnet,cbs is the net cone tip

resistance of the bottom (soft) clay layer at the layer interface. The limiting cavity

depths measured in the centrifuge tests (Table 4.1) where stable cavity could be

observed are also plotted in Figure 4.15, showing reasonable agreement with the

proposed formula.

The relationship between net spudcan and cone tip penetration resistances at any depth

is expressed by the penetration resistance ratio Rsp-c, which correlates qnet,sp and qnet,c as

net,sp sp c net,cq R q (4.10)

Similar to the two-step mechanism-based design approach proposed in the last section,

correlations are established for the peak resistance in the stiff clay layer, the resistance

at the stiff-soft layer interface and the deep penetration resistance in the soft clay layer.

4.5.1 Peak Resistance

Equation 4.2 was proposed in Section 4.4.1 to predict the depth of peak resistance dp

and can be transformed as a function of cone penetration resistances as

1.5 0.5

p net,cbs

net,ct net,cbs

d q t D t1.3 1

D q D q D

(4.11)

The penetration resistance ratio Rsp-c at d = dp then can be obtained by dividing the

value of qnet,sp at the peak from centrifuge tests (Table 4.1) and numerical analyses

(Groups II~IV, Table 4.2) by the corresponding value of qnet,ct. The cone factors used in

the calculation are 10.5 (Watson et al., 2000) for centrifuge tests and 12.7 (i.e. rigidity

index Ir = 67) for numerical analyses. All the calculated penetration resistance ratios are

plotted in Figure 4.16, and are best fitted by

net,sp 0.15

sp c

net,ct kt

0.50.5

net,cbs

net,ct net,cbs

q 12.7R 1.7x 1

q N

q t Dwhere x 1

q D q

for d = dp (4.12)


4-14

The first term of the equation is proposed for the numerical data with Ir = 67. As the

magnitude of the rigidity index has negligible effect on the spudcan penetration

resistance but affects the cone tip resistance significantly, the second term of Equation

4.12 is adopted to consider the effect of Ir.

4.5.2 Resistance at Layer Interface

For the penetration resistance ratio at the stiff-soft layer interface, the following

equation can be used

net,sp 0.65

sp c

net,cbs kt

0.5 0.50.25

net,cbs

net,ct net,cbs

q 12.7R 0.75x

q N

q t Dwhere x 1

q D q

for d = dint (4.13)

The penetration resistance ratio from Equation 4.13 should be limited by that from

Equation 4.12. The relationship between the estimated Rsp-c using Equation 4.13 and

corresponding measured or computed values is illustrated in Figure 4.17.

4.5.3 Deep Penetration Resistance in Soft Clay

A deep bearing capacity factor Ncd was proposed for the mechanism-based design

approach, assuming a localised soil flow mechanism. As such, the penetration resistance

ratio in the bottom (soft) clay layer can be evaluated as Rsp-c = Ncd/Nkt, with Ncd

expressed as a function of cone resistances:

1 10.5

net,cbs

cd

net,ct net,cbs

q t DN 9.8 1.3 Min ,1.0 1 15.5

q D q

(4.14)


The proposed CPT-based design approach estimates the penetration resistances of

spudcan at the peak in the stiff layer, at the stiff-soft layer interface and in the bottom

soft layer. The summary of the design procedure is provided below:

1. Obtain design parameters from the CPT test results, such as qnet,ct, qnet,cbs, , t

and ;


4-15

2. Estimate the depth of peak resistance in the stiff clay layer using Equation 4.11

and calculate the corresponding penetration resistance ratio using Equation 4.12;

3. Calculate the penetration resistance ratio at the stiff-soft layer interface using

Equation 4.13;

4. Evaluate the penetration resistance ratios in the bottom layer according to Rsp-c =

Ncd/Nkt, with Ncd estimated using Equation 4.14;

5. Plot the total penetration resistance profile according to Equations 4.8 and 4.10,

with the limiting cavity depth estimated using Equation 4.9.

APPLICATION

As shown in Figure 4.18, the proposed design approaches are used to predict the data

from centrifuge tests E1UU-I-T 3 and E2UNU-II-T 5 in Table 4.1. The predictions from

the ISO, Edwards-Potts and Dean methods are also included for comparison. As the ISO

and Edwards-Potts methods are proposed for uniform clays, the strength of the bottom

layer non-uniform clay is taken as the average over the depth of D/2 below the layer

interface. For the application of the Dean method, adjustment coefficients from Hossain

& Randolph (2011) for uniform-over-non-uniform clay profiles were used.

Figure 4.18 shows that the depth of peak resistance dp predicted by Equation 4.2 or 4.11

is with an error < 0.2D, while the other methods indicate the peak resistance at the top

surface of the stiff layer. Compared with the centrifuge test data, the corresponding peak

resistances from the semi-empirical method, improved ISO method and CPT-based

design approach are, respectively, 5.6, 5.8 and 6.0% higher for test E1UU-I-T 3, and

0.5% lower, 2.3% higher and 3.2% lower for test E2UNU-II-T 5. In contrast, those from

the ISO, Edwards-Potts and Dean methods are, respectively, 13.5 and 13.4% lower and

0.3% higher than the centrifuge test data for test E1UU-I-T 3, and 21.1, 0.7 and 6.6%

lower for test E2UNU-II-T 5. The magnitude of the peak resistance is better predicted

by the proposed methods due to the fact that the methods were proposed based on the

experimental and numerical studies of continuous spudcan penetration, and the

contribution from the soil plug in the bottom layer to the bearing capacity is considered.

For penetration resistance in the bottom layer, the bearing capacity factors for circular

footing on single layer uniform clay reported by Skempton (1951) are recommended by


4-16

ISO (2012), without considering the effect of the trapped soil plug. In the calculation for

non-uniform clay, the average strength over a depth of D/2 below the spudcan base is

considered. It can be seen in Figure 4.18 that for test E1UU-I-T 3, the deep penetration

resistance predicted by the ISO method is approximately 20.5% lower than the

centrifuge test, while the predictions from the proposed approaches are very close to the

centrifuge test data. For test E2UNU-II-T 5, the proposed approaches reasonably

estimate centrifuge test data with an underestimate of about 4%, while the penetration

resistance profile from the ISO method is overall ~15% lower.

CONCLUDING REMARKS

This chapter has reported LDFE analyses of spudcan penetration in stiff-over-soft clay

deposits with the effect of strain softening and rate dependency of undrained shear

strength. The existing data from centrifuge model tests were accumulated. Based on the

centrifuge test data and LDFE results, new mechanism-based and CPT-based design

approaches were proposed for predicting spudcan penetration in stiff-over-soft clay

deposits. The approaches provide estimates of (i) the peak penetration resistance and its

depth in the stiff layer, (ii) the resistance at the stiff-soft layer interface, and (iii) the

penetration resistance profile in the soft layer. The design formula suggested by ISO for

punch-through was also improved to predict the peak penetration resistance in the stiff

layer. Comparison between the predictions using the ISO method, recently developed

methods and proposed approaches, and the measured data from centrifuge tests

demonstrated the improvement by the proposed approaches.


4-17

REFERENCE



Foundation Engineering, Mexico 2, 45-51.

Edwards, D. H. & Potts, D. M. (2004). The bearing capacity of circular footing under

“punch-through” failure. Proc. 9th International Symposium on Numerical Models

in Geomechanics, Ottawa, 493-498.

Hossain, M. S. & Randolph, M. F. (2009). New mechanism-based design approach for







Hossain, M. S. & Randolph, M. F. (2011). Discussion on ‘Deep-penetrating spudcan

foundations on layered clays: centrifuge tests’. Géotechnique 61, No. 1, 85-87.









Journal 51, No 10, 1151-1164.







overlying clay soils: experimental and finite-element investigation of potential



4-18



1285-1297.






Merifield, R. S. & Nguyen, V. Q. (2006). Two- and three-dimensional bearing capacity

solutions for footing on two-layered clays. Geomechanics and Geoengineering 1,

No. 2, 151-162.


London, 1, 180-189.

Teh, K. L., Leung, C. F., Chow, Y. K. & Handidjaja, P. (2009). Prediction of punch-

through for spudcan penetration in sand overlying clay. Proc. Offshore

Technology Conference, Houston, OTC 20060.



Wang, C. X. & Carter, J. P. (2002). Deep penetration of strip and circular footings into

layered clays. International Journal of Geomechanics, ASCE 2, No 2, 205-232.

Watson, P. G., Suemasa, N. & Randolph, M. F. (2000). Evaluating undrained shear

strength using the vane shear apparatus. Proc. 10th International Offshore and

Polar Engineering Conference, Seattle, 2, 485-493.

White, D. J., Gaudin, C., Boylan, N. & Zhou, H. (2010). Interpretation of T-bar

penetrometer tests at shallow embedment and in very soft soils. Canadian

Geotechnical Journal 47, No. 2, 218-229.

Zheng, J., Hossain, M. S. & Wang, D. (2015). Prediction of spudcan penetration



Zhou, M., Hossain, M. S., Hu, Y. & Liu, H. (2013). Behaviour of ball penetrometer in

uniform single- and double-layer clays. Géotechnique 63, No.8, 682-694.


4-19

TABLES

Table 4.1 Summary of centrifuge tests (after Hossain & Randolph, 2010a)

Specimen Test D:

m

t:

m t/D

t(avg):

kN/m3

b(avg):

kN/m3

sut:

kPa

subs:

kPa

k:

kPa/m

Even

t – 1

(E

1U

U)

I

T 1 6

1.5

0.25

7.2 7

14

(12.3)#

10

(11) # 0.26

T 2 6 0.25

T 3 3 0.5 12

(10.2) #

8.5

(9.35) # 0.37

II

T 4 6

4.5

0.75

7.35 7.15

21.3

(20.3) #

11

(13) # 0

T 5 6 0.75

T 6 3 1.5 17

(16.6) #

11.2

(12.5) # 0

III

T 7 6

6

1

7.5 7.3

20

(20) #

11

(12.3) # 0

T 8 6 1

T 9 3 2 15

(15) #

11

(11.7) # 0

IV

T 10 6

7.5

1.25

7.5 7.3

20

(20) #

12.2

(13.6) # 0

T 11 6 1.25

T 12 3 2.5 17.5

(17.5) #

11.4

(12.7) # 0

Even

t – 2

(E

2U

U)

I

T 1 6

1.5

0.25

8.0 7.35

34

(26) #

11

(13.7) # 0

T 2 6 0.25

T 3 3 0.5 23.8

(18.3) #

11.6

(13.7) # 0

II

T 4 6

4.5

0.75

8.03 7.43

41

(38.3) #

9

(11) # 0

T 5 6 0.75

T 6 3 1.5 25.5

(24.2) #

9.9

(12.4) # 0

III

T 7 6

6

1

8.11 7.5

42.7

(42.7) #

12.1

(13.5) # 0

T 8 6 1

T 9 3 2 26.6

(26.6) #

12.3

(13.7) # 0

IV

T 10 6

7.5

1.25

8.13 7.75

47.3

(47.3) #

14

(14.7) # 0

T 11 6 1.25

T 12 3 2.5 27.5

(27.5) #

15.3

(17) # 0


4-20

Specimen Test D:

m

t:

m t/D

t(avg):

kN/m3

b(avg):

kN/m3

sut:

kPa

subs:

kPa

k:

kPa/m

Even

t – 1

(E

1U

NU

)

I

T 1 6

1.5

0.25

7.5 7.25

16.2

(12.5) #

3.6

(5.8) # 1.55

T 2 6 0.25

T 3 3 0.5 13

(10) #

3.8

(5.8) # 1.55

II

T 4 6

4.5

0.75

7.5 7.25

21.4

(20.5) #

7.5

(8.3) # 2.6

T 5 6 0.75

T 6 3 1.5 14

(13.4) #

7

(8) # 2

Even

t – 2

(E

2U

NU

)

I

T 1 6

1.5

0.25

7.85 7. 2

29.5

(17.3) #

3

(3.5) # 1.26

T 2 6 0.25

T 3 3 0.5 24

(12.3) #

2.3

(2.5) # 1.34

II

T 4 6

4.5

0.75

8.1 7.5

47

(41) #

9.2

(11.5) # 1.23

T 5 6 0.75

T 6 3 1.5 31

(27) #

6.8

(7.5) # 1.54

# Original undrained shear strength measured using T-bar with a T-bar factor of 10.5


4-21

Table 4.2 Summary of LDFE analyses performed for spudcan penetration

Group subs/sut t/D kD/subs subs/γbD St Remarks

I

0.096 0.5 1.75 0.11 2.8 Comparison with

centrifuge test data

from Hossain &

Randolph (2010a) 0.2 0.75 0.8 0.2 2.8

II 0.25~0.75 0.75 0.5 0.31 2.8 Effect of subs/sut

III 0.25 and

0.5 0.25~1.0 0 0.31 2.8 Effect of t/D

IV 0.25 0.5 and

1.0 0~3.0 0.31 2.8 Efffect of kD/subs

V 0.5 1.0 0.5 0.31 1, 2.8

and 5 Effect of St


4-22

FIGURES

d

hP

-T

dp

din

t

qnet

qpeak

d

Hcav

z

Sp

ud

ca

n

Cavity

K-lattic

e le

g

D

t S

tiff

cla

y

sut, t

subs 1

k

Soft

cla

y

sub,

b

su

sut

sub0

Fig

ure

4.1

Sch

em

ati

c d

iagra

m o

f em

bed

ded

sp

ud

can

fou

nd

ati

on

in

sti

ff-o

ver

-soft

cla

y s

how

ing i

dea

lise

d o

pen

cavit

y

an

d c

orr

esp

on

din

g p

enet

rati

on

res

ista

nce

pro

file


4-23

Figure 4.2 Comparison between experimental and numerical results of T-bar

penetration in stiff-over-soft clay

0

2

4

6

8

10

12

0 100 200 300 400 500

Pen

etr

ati

on

dep

th o

f T

-bar

invert

: m

Bearing pressure, qu: kPa

Stiff

Soft

E2UNU-II-T 5

E2UNU-I-T 3

LDFE, corrected su

Centrifuge test

LDFE, without correctionof su


4-24

Figure 4.3 Comparison between experimental and numerical results of spudcan

penetration in stiff-over-soft clay (Group I, Table 4.2)

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250

No

rma

lis

ed

pe

ne

tra

tio

n d

ep

th,

d/D


Stiff

Soft

E2UNU-I-T 3E2UNU-II-T 5

Centrifuge test

LDFE, corrected su


4-25

Figure 4.4 Effect of strength ratio (subs/sut) on spudcan penetration resistance

(kD/subs = 0.5, t/D = 0.75, subs/D = 0.31, rem = 1/St = 0.36; Group II, Table 4.2)

-1

-0.5

0

0.5

1

1.5

2

0 5 10 15 20 25N

orm

ali

se

d p

en

etr

ati

on

de

pth

, (d

t)

/D

Normalised bearing pressure, qnet/sub0

Stiff

Soft

subs/sut = 0.25, 0.3, 0.4, 0.5 and 0.75

subs/sut = 0.25

(d t)/D = 0.2

Seabed

subs/sut = 0.75

(d t)/D = 0.2


4-26

4.5(a) subs/sut = 0.25

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 5 10 15 20 25

No

rmali

sed

pen

etr

ati

on

dep

th, (d

t)

/DNormalised bearing pressure, qnet/sub0

t/D = 0.25, 0.5, 0.75 and 1.0

Stiff

Soft

(d t)/D = 0.4

t/D = 0.25 t/D = 1.0

(d t)/D = 0.4

Seabed

t/D = 0.5smooth-based spudcan


4-27

4.5(b) subs/sut = 0.5

Figure 4.5 Effect of thickness ratio (t/D) on spudcan penetration resistance (kD/subs

= 0, subs/D = 0.31, rem = 1/St = 0.36; Group III, Table 4.2)

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 3 6 9 12 15 18N

orm

ali

se

d p

en

etr

ati

on

de

pth

, (d

t)

/D


t/D = 0.25, 0.5, 0.75 and 1.0

Stiff

Soft

(d t)/D = 0

t/D = 0.25 t/D = 1.0

(d t)/D = 0

Seabed


4-28

4.6(a) t/D = 0.5

-1

-0.5

0

0.5

1

1.5

2

0 5 10 15 20 25

No

rmalised

pen

etr

ati

on

dep

th,

(d

t)/D


kD/subs = 0, 0.25, 0.5 and 3.0

Stiff

Soft

kD/subs = 0kD/subs = 3.0

(d t)/D = 0.4

Seabed

(d t)/D = 0.4


4-29

4.6(b) t/D = 1.0

Figure 4.6 Effect of strength non-homogeneity (kD/subs) of bottom layer on spudcan

penetration resistance (subs/sut = 0.25, subs/D = 0.31, rem = 1/St = 0.36; Group IV,

Table 4.2)

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 5 10 15 20 25 30N

orm

alised

pen

etr

ati

on

dep

th,

(d

t)/D


kD/subs = 0, 0.25, 0.5 and 3.0

Stiff

Soft

(d t)/D = 0.4

kD/subs = 0

Seabed

kD/subs = 3.0

(d t)/D = 0.4


4-30

Figure 4.7 Effect of sensitivity (St) on spudcan penetration resistance (subs/sut = 0.5,

t/D = 1.0, kD/subs = 0.5, subs/D = 0.31; Group V, Table 4.2)

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 5 10 15 20 25

No

rmalised

pen

etr

ati

on

dep

th,

(d

t)/D


Stiff

Soft

St = 5, 2.8 and 1

Seabed


4-31

Figure 4.8 Design chart for normalised depth of peak resistance (dp/D) for spudcan


0

0.4

0.8

1.2

1.6

2

0 0.3 0.6 0.9 1.2 1.5N

orm

ali

se

d d

ep

th o

f p

ea

k r

es

ista

nc

e,

dp/D

Numerical analysis

Centrifuge test

1.5 0.5

p ubs

ut ubs

d s t kD t1.3 1

D s D s D

1.5 0.5

ubs

ut ubs

s t kD1

s D s


4-32

4.9(a) Design chart for normalised peak resistance (qpeak/subs) for spudcan


6

12

18

24

30

36

42

0 2 4 6 8 10 12

No

rma

lis

ed

pe

ak

re

sis

tan

ce

, q

peak/s

ub

s

Numerical analysis

Centrifuge test

0.771 0.50.75

peak ubs

ubs ut ubs

q s t kD6.35 5 1

s s D s

1 0.50.75

ubs

ut ubs

s t kD1

s D s


4-33

4.9(b) Ratio between predicted and measured or computed qpeak

Figure 4.9 Relationship between predicted and measured or computed data of

peak resistance using semi-empirical method

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

0 100 200 300 400 500

Ra

tio

be

twe

en

pre

dic

ted

an

d m

ea

su

red

or

co

mp

ute

d q

peak

Measured or computed qpeak: kPa

Numerical analysis

Centrifuge test


4-34

Figure 4.10 Conceptual model for spudcan at punch-through in stiff-over-soft clay

Spudcan

Stiff

Soft

T

6(1+0.2dint/D)sub

Shear resistance3Tsut/D

TBack-calculated soil plug in the soft layer

Soil plug in the stiff layer

Shear resistance

3Tsub/D

6[1+0.2(dint+T)/D]sub

d

dint


4-35

4.11(a) Design chart for thickness of equivalent soil plug (T) in soft clay

0

1

2

3

4

5

6

7

8

0 3 6 9 12 15

No

rma

lis

ed

eq

uiv

ale

nt

plu

g t

hic

kn

es

s,

T/t

Numerical analysis

Centrifuge test

t0.5

0.5 21 D

ubs

ut ubs

sT t kD0.53 3 1.5

t s D s

t0.50.5 21 D

ubs

ut ubs

s t kD3 1.5

s D s


4-36

4.11(b) Ratio between predicted and measured or computed qpeak

Figure 4.11 Relationship between predicted and measured or computed data of

peak resistance using improved ISO method

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0 100 200 300 400 500

Ra

tio

be

twe

en

pre

dic

ted

an

d m

ea

su

red

or

co

mp

ute

d q

peak

Measured or computed qpeak: kPa

Numerical analysis

Centrifuge test


4-37

Figure 4.12 Design chart for normalised bearing capacity at layer interface

(qint/subs) for spudcan penetration in stiff-over-soft clay

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5

No

rma

lis

ed

be

ari

ng

pre

ss

ure

at

laye

r in

terf

ac

e,

qin

t/s

ub

s

Numerical analysis

Centrifuge test

0.5 0.250.25

ubs

ut ubs

s t kD1

s D s

0.850.5 0.250.25

int ubs

ubs ut ubs

q s t kD10.2 1

s s D s


4-38

Figure 4.13 Normalised penetration resistance profiles during spudcan penetration

in bottom layer soft clay

0

0.4

0.8

1.2

1.6

2

0 5 10 15 20 25 30

No

rma

lise

d p

en

etr

ati

on

dep

th,

(d

t)/D


Upper bound, Ncd = 15.5

Lower bound,Ncd = 9.8


4-39

Figure 4.14 Design chart for deep bearing capacity factor (Ncd) for spudcan


6

7.5

9

10.5

12

13.5

15

16.5

18

0 1 2 3 4 5 6

De

ep

be

ari

ng

ca

pa

cit

y f

ac

tor,

Ncd

Numerical analysis

Centrifuge test

1.0

1.0

1 10.5

ubs

ut ubs

s t kDMin ,1.0 1

s D s

1 10.5

ubscd

ut ubs

s t kDN 9.8 1.3 Min ,1.0 1 15.5

s D s


4-40

Figure 4.15 Design chart for limiting cavity depth (Hcav) for spudcan penetration in

stiff-over-soft clay

0

0.2

0.4

0.6

0.8

1

1.2

0 0.3 0.6 0.9 1.2 1.5

No

rmalised

lim

itin

g c

avit

y d

ep

th,

Hcav/D

Numerical analysis

Centrifuge test

0.50.5

net,ctcav

kt b net,cbs

qH t D0.95 1

D N D D q

0.5

net,ct

kt b net,cbs

q t D1

N D D q


4-41

Figure 4.16 Design chart for penetration resistance ratio Rsp-c at d = dp for spudcan


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1 1.2

Pe

ne

tra

tio

n r

es

ista

nc

e r

ati

o,

Rsp

-c

Numerical analysis

Centrifuge test

Equation 4.12:Nkt = 10.5 and 12.7

0.50.5

net,cbs

net,ct net,cbs

q t D1

q D q


4-42

Figure 4.17 Design chart for penetration resistance ratio Rsp-c at stiff-soft layer

interface

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6

Pe

ne

tra

tio

n r

es

ista

nc

e r

ati

o,

Rsp

-c

Numerical analysis

Centrifuge test

Equation 4.13:Nkt = 10.5 and Nkt = 12.7

0.5 0.50.25

net,cbs

net,ct net,cbs

q t D1

q D q


4-43

Figure 4.18 Comparison between centrifuge test data and estimated penetration

resistance profiles for spudcan penetration in stiff-over-soft clay

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250N

orm

alised

pen

etr

ati

on

dep

th,

d/D


Centrifuge test

ISO method

Dean method

Edwards-Potts method

Semi-empirical method

Improved ISO method

CPT-based design approach

Stiff

Soft

E2UNU-II-T 5

E1UU-I-T 3

Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer

5-1

CHAPTER 5. SPUDCAN IN NON-UNIFORM CLAY

WITH AN INTERBEDDED STIFF CLAY LAYER

INTRODUCTION

This chapter focuses on spudcan penetration in three-layer non-uniform clay with an

interbedded stiff clay layer (see Figure 5.1). As noted in Chapter 1, the ISO standard

19905-1 (ISO, 2012) recommends using the bottom-up approach combining the

squeezing (for strong-over-weak layering system) and punch-through (for the reverse)

criteria for two-layer systems. For the soil profile in this chapter, the bottom-up

approach includes (a) Skempton’s (1951) or Houlsby & Martin’s (2003) method for

single layer clay (calculation for the 3rd layer); (b) Brown & Meyerhof’s (1969)

punching shear method for the 2nd-3rd layer system (calculation for the 2nd layer); and

(c) Meyerhof & Chaplin’s (1953) squeezing method for the 1st-2nd layer system

(calculation for the 1st layer). Details of these design methods can be found in Chapter 1.

However, these predictive methods were developed for a surface or pre-embedded (i.e.

wished in place) footing. As such, for a continuously penetrating spudcan in non-

uniform clay with an interbedded stiff layer, several deficiencies in these methods can

be identified (Zheng et al., 2015): (i) for the squeezing method in the 1st-2nd soft-over-

stiff layering system, the underlying layer is assumed as a rigid boundary, and hence the

true squeezing is exaggerated and the local deformation of the underlying layer interface

is neglected; (ii) for the punching shear method in the 2nd-3rd stiff-over-soft layering

system, the movement of the soil plug trapped at the base of the spudcan from the 1st

(soft) layer and the local deformation of the underlying 2nd-3rd layer interface are

neglected; and (iii) the effects of strain softening and rate dependency of the undrained

shear strength are not considered explicitly.

This chapter emanates from an extensive study of large deformation finite element

(LDFE) analyses on continuous spudcan and cone penetration in non-uniform clay with

an interbedded stiff clay layer. Strain softening and rate dependency of the undrained

shear strength are accounted for. The aim is to rectify the perceived deficiencies in the


5-2

ISO (2012) design approaches. Results obtained from the numerical modelling of

spudcan penetration are presented first in terms of load-penetration responses, while

those from analyses of cone penetration in clay are reported in Chapter 3. Based on the

computed results, a new mechanism-based approach is developed, accounting for the

true soil failure mechanisms, soil strength non-homogeneity, and strain softening and

rate dependency of the undrained shear strength. Additionally, a new CPT-based design

approach is developed, giving design formulas for the ratio between spudcan and cone

penetration resistances at critical depths. The outcomes presented in this chapter have

been documented in Zheng et al. (2014a, 2015).

NUMERICAL ANALYSIS

This chapter has considered a circular spudcan of diameter D, penetrating into a three-

layer clay deposit as illustrated schematically in Figure 5.1, where the 2nd (stiff) clay

layer with uniform undrained shear strength su2 and thickness t2 is sandwiched by the 1st

layer clay of non-uniform undrained shear strength su1 = su1s + k1z, thickness t1, and

interface strength su1b = su1s + k1t1; and the 3rd layer clay of non-uniform undrained shear

strength su3 = su3s + k3(z t1 t2). The symbol su0 represents the undrained shear

strength at the spudcan base level.

The selected parameters for this study are assembled in Table 5.1. Along with the

simulation of centrifuge model tests and a case history (Groups I and II, Table 5.1), a

series of parametric analyses (Group III, Table 5.1) were carried out encompassing a

range of parameters of practical interest. For convenience, the effective unit weight was

considered to be constant (= 8 kN/m3) throughout the soil profile. Further details of

the numerical analysis, such as the set-up for the numerical model, constitutive model,

and relevant elastic and plastic parameters, can be found in Chapter 2.

5.2.1 Validation of Numerical Model

Centrifuge tests

Hossain et al. (2011a, 2011b) reported data from centrifuge model tests carried out for

spudcan foundations (D = 8 m, Tests T1 and T2; Hossain et al., 2011a) penetrating

through four-layer uniform soft-stiff-soft-stiff clays (su1 = su3 = 10 kPa, su2 = 40 kPa,


5-3

t1/D = 0.31, t2/D = 0.3, rem = 1/St = 0.36 for Test T1; and su1 = su3 = 10 kPa, su2 = 40

kPa, t1/D = 0.25, t2/D = 0.5, rem = 1/St = 0.36 for Test T2; Group I, Table 5.1); and a

spudcan (D = 12 m, Test T6; Hossain et al., 2011b) penetrating through non-uniform

clay with an interbedded stiff clay layer (su1 = su3 = 2 + 0.6z kPa, su2 = 23 kPa, t1/D =

0.38, t2/D = 0.58, rem = 1/St = 0.36; Group I, Table 5.1). The thickness of the 3rd layer

for Tests T1 and T2 reported by Hossain et al. (2011a) on four-layer deposit is 1.24D

and 1.3D, respectively, which are considered as thick enough to eliminate the effect of

the 4th layer stiff clay on spudcan penetration in the 2nd layer. As such, only the first

three layers were considered in the numerical simulations, as it is relevant to the

stratification considered in this chapter.

Figures 5.2a~c compare the experimental and numerical results in terms of total bearing

pressure, qu, as a function of the normalised penetration depth, d/D. The difference

between penetration resistance profiles from LDFE analyses and centrifuge tests is

mostly less than 5% over the full penetration depths in the upper two layers and early

penetration in the 3rd layer. Key features are also well captured in terms of squeezing,

the depth of triggering punch-through or rapid leg run, and the magnitude of peak

penetration resistance. For Tests T1 and T2 (Hossain et al., 2011a), the bearing pressure

profile after the depth, from which the penetration resistance starts increasing in the 3rd

layer due to the influence of the stiff 4th layer, is omitted. For Test T6 reported by

Hossain et al. (2011b), the divergence of profiles after a penetration depth of about 1.1D

is probably caused by the effect of the bottom boundary of the testing strong box in the

centrifuge test (with the total sample thickness of ~2.2D).

Case history

InSafeJIP (2011) reported a case history where a spudcan of D = 13.7 m penetrated in

non-uniform clay with an interbedded stiff clay layer. The undrained shear strength

profile can be idealised as su1 = 1 + 1.05z kPa, su2 = 40.5 kPa, su3 = 29 + 2.55(z – t1 – t2)

kPa, t1/D = 0.28 and t2/D = 0.15, with rem = 1/St = 0.3 (Group II, Table 5.1). The

recorded load-penetration profiles are plotted in Figure 5.2d, together with the result

from the LDFE simulation. It is seen that reasonable agreement is obtained between the

computed and measured data for all three legs.


5-4

5.2.2 Soil Flow Mechanisms

In general, with the progress of the spudcan penetration in soft non-uniform clay with

an interbedded stiff clay layer, four interesting features of soil flow can be identified (as

can be seen e.g. in Figure 5.3 for su1 = 2 + 2z kPa, su2 = 40 kPa, su3 = 30 + (z – t1 – t2)

kPa, t1/D = 0.25, t2/D = 0.5, rem = 1/St = 0.3; Group III, Table 5.1): (i) soil squeezing

out during penetration in the 1st (soft) layer sensing the underlying stiff clay layer

(Figure 5.3a); (ii) soil backflow above the spudcan, and deformation of the 1st-2nd layer

interface (Figure 5.3b); (iii) the spudcan in the 2nd (stiff) layer with a trapped softer

layer at the base and the soil deformation beneath the advancing spudcan mainly

towards the lower layer, with temporary pausing in soil backflow (Figure 5.3c); (iv) the

soil plug at the base of the spudcan consisting of soils from the 1st and 2nd layers during

and after triggering punch-through or rapid leg run in the 2nd layer (Figure 5.3d).

5.2.3 Parametric Study

Spudcan penetration resistance profiles in clays with and without considering strain

softening and rate dependency were compared by Zheng et al. (2014b). The comparison

highlighted the necessity for incorporating the combined effect of strain softening and

rate dependency in simulating spudcan penetration in layered clay deposits, especially

in respect to the accurate prediction of the likelihood and severity of punch-through and

the deep penetration resistance. A parametric study was therefore conducted simulating

spudcan penetration in strain-softening, rate-dependent non-uniform clay with an

interbedded stiff clay layer, varying strengths (su1 and su2), thickness ratios (t1/D and

t2/D), and the non-homogeneity factor of the 3rd layer clay (k3D/su3s). The ranges of

parameters considered in the parametric study are assembled in Group III, Table 5.1.

The corresponding results are presented in terms of normalised penetration resistance

qnet/su3s or qnet/su0, with qnet calculated according to Equation 4.1.

The discussions in this chapter are limited to the aspects related to the development of

the new design approaches, starting with the evaluation of the effects of various critical

factors that are related to layer geometries and soil strengths. The detailed discussion on

the effects of various parameters on the form of the load-penetration response and the

depth of soil backflow were noted in Zheng et al. (2014b).


5-5

Effect of 2nd layer strength (su2) or strength ratios su1b/su2 and su2/su3s

The strength of the 2nd layer clay su2 is critical for spudcan penetration in three-layer

soft-stiff-soft clay deposits, as it determines the increase of bearing pressure due to

squeezing in the 1st (soft) layer, and the likelihood and severity of punch-through in the

2nd and 3rd layers. To explore the effect of su2 on spudcan penetration resistance, the

results for strength ratios su2/su3s = 1.33 and 2.5 are plotted in Figure 5.4 with thickness

ratios t1/D = 0.25 and t2/D = 0.25 or 0.5. The strength non-homogeneity factors for the

top and bottom layers are k1D/su1s = 12 and k3D/su3s = 0.4, respectively [i.e. su1 = 2 + 2z

kPa and su3 = 30 + 1(z – t1 – t2) kPa].

It is seen that the limiting squeezing depth in the 1st (soft) layer is not affected by the

strength ratio su1b/su2 (for this range of strength ratio). The distance from the depth of

punch-through to the 2nd-3rd layer interface and the magnitude of peak resistance both

increase with increasing su2 (or decreasing su1b/su2 and increasing su2/su3s). The trend is

more obvious for a thicker 2nd layer. As su2 increases from 40 to 75 kPa, the normalised

peak resistance qpeak/su3s increases from 10.8 to 12.8 and from 11.8 to 15.0 for t2/D =

0.25 and 0.5, respectively; while the normalised depth of peak resistance dp/D decreases

from 0.5 (i.e. at the 2nd-3rd layer interface for the case without the potential for punch-

through) to 0.41 for t2/D = 0.25, and from 0.61 to 0.41 for t2/D = 0.5.

In the 3rd layer, the bearing pressure remains higher for higher su2 (or higher su2/su3s) at

early penetration. The discrepancy diminishes gradually as the penetration depth

increases. This is caused by the soil plug carried down by the spudcan from the 1st and

2nd layers, which is thicker and stronger for higher strength ratio su2/su3s. A single layer

response with minimal influence of the soil plug (i.e. the soil plug reaches its minimum

thickness) is established at a certain depth of dr/D in the 3rd layer, with the penetration

resistance increasing at a constant rate. Therefore, a deeper depth of dr/D is necessary

for a higher strength ratio su2/su3s. For instance, as the undrained shear strength su2

increases from 40 to 75 kPa (or su2/su3s from 1.33 to 2.5), dr/D increases from 0.86 to

1.03 for t2/D = 0.25, and from 1.0 to 1.3 for t2/D = 0.5.

Effect of thickness ratio (t2/D)

To demonstrate the effect of the relative thickness of the 2nd layer, penetration resistance

profiles are plotted in Figure 5.5 for a range of t2/D from 0.25 to 0.75, but with identical


5-6

1st layer thickness t1/D = 0.25 and non-homogeneity factor k1D/su1s = 12, strength ratio

su2/su3s = 2.5, and bottom layer non-homogeneity factor k3D/su3s = 0.4. It can be seen

that the proximity of the peak resistance to the 2nd-3rd layer interface reduces

significantly with increasing t2/D.

Figure 5.5b shows the penetration resistance profiles in the bottom layer, as a function

of the normalised penetration depth, (d – t1 – t2)/D. The penetration resistance is

normalised by the local undrained shear strength su0 at the spudcan base level, giving

the deep bearing capacity factor. It can be seen that the bearing pressure at early

penetration in the 3rd layer increases significantly as t2/D increases from 0.25 to 0.5.

However, further increase of t2/D from 0.5 to 0.75 only leads to a marginal increase of

bearing pressure. This discrepancy of bearing pressures is caused by the soil plug

brought down by the spudcan – higher t2/D leads to a thicker soil plug at the base of the

advancing spudcan. However, the discrepancy diminishes gradually with penetration

depth. Once the soil plug attains its minimum thickness, the penetration resistance

profiles merge together, with a deep bearing capacity factor of ~10.4.

Effect of non-homogeneity factor of bottom layer (k3D/su3s)

Analyses were performed for spudcan penetration in clay profiles with k3D/su3s ranging

between 0 and 1.2 in an effort to investigate the effect of the bottom layer non-

homogeneity. The other parameters were kept identical for the analyses – the top layer

of t1/D = 0.5 and su1 = 5 + 3z kPa, was underlain by the middle layer of t2/D = 0.75 and

su2 = 75 kPa, with the strength ratio at the 2nd-3rd layer interface su2/su3s = 2.5. This range

of parameters was chosen deliberately to illustrate the effect of the bottom layer strength

gradient on the severity of punch-through. The results are shown in Figure 5.6.

The load-penetration profiles show that the squeezing resistance at the 1st-2nd layer

interface increases slightly with increasing bottom layer non-homogeneity. Punch-

through occurred for all cases in the 2nd layer stiff clay at a depth of dp/D ranging

between 0.71 and 0.74, on which the effect of the bottom layer non-homogeneity was

found to be minimal (at least for the selected parameters).

The corresponding penetration resistance profiles in the bottom layer are plotted in

Figure 5.6b. For a higher non-homogeneity factor, the normalised bearing pressure at

the 2nd-3rd layer interface is higher, especially for an increase of k3D/su3s from 0 to 0.4.


5-7

However, as the spudcan penetrates deeper, the bearing capacity factor for k3D/su3s =

1.2 decreases rapidly and forms the lower bound, while the bearing capacity factors for

lower values of k3D/su3s become higher. This also reflects the effect of the trapped soil

plug, which is thicker and diminishes more slowly in a bottom layer with lower strength

gradient. At a depth of about 0.8D below the 2nd-3rd layer interface, all the bearing

pressure profiles stabilise at a unique deep bearing capacity factor of ~10.5.


Based on the results from the parametric study, a new mechanism-based design

approach is proposed. Design formulas are developed to estimate the limiting cavity

depth, variation of soil plug thickness, maximum penetration resistance during

squeezing in the 1st (soft) layer, penetration resistances at punch-through and at soil

backflow, and penetration resistance profile in the bottom layer.

5.3.1 Limiting Cavity Depth

As discussed previously, the soil downward deformation after a punch-through or rapid

leg run in the 2nd (stiff) layer provides a temporary pause in soil backflow above the

spudcan (Figure 5.3c). At a certain stage of penetration, soil backflow resumes and the

continual backflow gradually provides a seal above the spudcan and limits the cavity

depth. In all the numerical analyses, the spudcan was penetrated deep enough so that a

stable cavity was observed. The normalised limiting cavity depth, Hcav/D, obtained from

the parametric LDFE analyses (Group III, Table 5.1), is a function of normalised soil

parameters and layer geometries as plotted in Figure 5.7, which can be expressed as

0.51 12

cav u1b u3s 31 2

u2 u3s

H s s k Dt t0.25 1 1

D D s D D s

(5.1)

5.3.2 Simplified Penetration Resistance Profile

A typical penetration resistance profile with the potential for punch-through [su1 = 5 +

3z kPa, su2 = 75 kPa, su3 = 30 + (z – t1 – t2) kPa, t1/D = 0.25, t2/D = 0.75, rem = 1/St =

0.3; Group III, Table 5.1] is shown in Figure 5.8. Six transitional stages are marked

using Points 1, 2, 3, 4 and 5 on the profile including: (1) single layer response before


5-8

squeezing; (2) squeezing in the 1st layer; (3) gradual increase in penetration resistance in

the 2nd layer until the peak; (4) post-peak reduction or a plateau in penetration resistance;

(5) further reduction due to soil backflow; and (6) establishing single layer penetration

response in the 3rd layer. For the proposed design approach, the locations of Points 1~5

are predicted and then connected by straight lines, as shown in Figure 5.8.

A conceptual model delineated in Figure 5.9 has been established based on the observed

soil failure mechanisms illustrated in Figure 5.3 to quantify the penetration resistances.

The formulas based on this conceptual model are proposed in the following subsections

for the gross penetration resistance qv to be consistent with ISO (2012). The total

penetration resistance qu is calculated by deducting the submerged weight of the backfill

soil and accounting for the buoyancy of the embedded spudcan according to

sp

u v cav

Vq q Max d H ,0

A

for shallow bearing response (5.2a)

sp

u v

Vq q

A

for deep bearing response (5.2b)

where Vsp is the volume of the embedded spudcan including shaft, and A is the largest

plan area of the spudcan.

5.3.3 Punch-through

Based on the conceptual model in Figure 5.9, an improved punch-through criterion is

proposed accounting for the soil plug below the 2nd-3rd layer interface and

corresponding influences on the end bearing capacity and peripheral frictional resistance:

plug,2 u2p plug,3 u3p

v cr ud0 0 cr u0 0 1 cav

4 (H s H s )q N s p N s p for t d H

D

(5.3)

where p0 is the effective overburden pressure of soils above spudcan base level.

For the first term, an adjustment factor is incorporated considering the effects of strain

rate and strain softening after Hossain & Randolph (2009a) and Hossain et al. (2014),

which is similar to Equation 2.1 and expressed as

b 953 /ξb

t

t

1 R μ1 S 1 e

S

(5.4)


5-9

where Rb and b represent the effects of average relative strain rate and accumulated

plastic strain around a deep penetrating spudcan, respectively. Hossain et al. (2014)

suggested Rb = 0.77 and 1.47, respectively, for lower (0.36 m/h) and upper (2 m/h)

bounds of spudcan penetration rate during preloading relative to the reference strain rate

refγ = 1%/h, while b = 2.4 for a deeply embedded spudcan in single layer clay. For the

field penetration rate ~2 m/h and similar reference strain rate considered in this study, a

consistent value of Rb = 1.47 and a lower value (accounting for the influence of the soft

soils trapped from the 1st layer) of b = 1.5 are adopted compared to those suggested by

Hossain & Randolph (2009a).

The total soil plug thickness Hplug = Hplug,2 + Hplug,3 decays gradually with increasing

penetration depth in the 2nd and 3rd layers (i.e. d t1), which comprises the soil plug

thickness in the 2nd layer, Hplug,2, and that in the 3rd layer, Hplug,3. Nevertheless, a small

amount of soil plug from the upper layers can still be observed for d > 3D [see also

Hossain et al. (2015)]. Therefore, the expression proposed by Hossain & Randolph

(2009c) for ideal stiff-over-soft clay is improved accounting for a faster rate of decay

and a minimum value of the thickness of the soil plug as

12

d tf

plug plug,2D

1

2 2

H HMax f e 1,0.1,

t t

for d t1 (5.5a)

where the coefficients f1 and f2 are expressed as

1 1

u3s 21

u2

s tf 2 0.01

s D

(5.5b)

0.5

u3s 3 22

u2 u1b u3s

s k D tf 0.2 0.5 1

s s s D

(5.5c)

For example, Figure 5.10 demonstrates the variation of the soil plug thickness from one

of the analyses [su1 = 2 + 2z kPa, su2 = 75 kPa, su3 = 30 + (z – t1 – t2) kPa, t1/D = 0.25,

t2/D = 0.5, rem = 1/St = 0.3; Group III, Table 5.1] along with the prediction from

Equation 5.5. The plug thicknesses in different layers then can be calculated as Hplug,2 =

Max(t1 + t2 – d, 0) and Hplug,3 = Hplug – Hplug,2 for d t1.


5-10

For the second term in Equation 5.3, the shallow bearing capacity factors reported by

Hossain & Randolph (2009b) for rough-based spudcan in non-homogeneous clay are

used in combination with the shear strength sud0 at the base of the dummy spudcan (i.e.

soil plug base; see Figure 5.9). The effects of strain softening and rate dependency are

not considered in this term as only a small amount of plastic strain was observed in the

bottom layer at this stage of penetration. The shallow bearing capacity factor Ncr is

reported by Hossain & Randolph (2009b) as (originally proposed for single layer clay

with the penetration depth d at the base of the spudcan, but here d is replaced by the

penetration depth at the base of the soil plug or dummy spudcan, i.e. dd = d + Hplug)

0.8 1.5

d d 3 dcr

ud0

plugd

d d k D dN 6.05 1 1 0.191 / 1

0.22D 3.65D s D

d Hdfor Min ,1.825

D D

(5.6)

5.3.4 Bearing Capacity in 1st Layer

The position of Point 1 indicates the depth after which squeezing dominates the spudcan

penetration response sensing the influence of the underlying stiff clay layer. For

spudcan penetration before the depth of Point 1 [i.e. Stage (1)], the penetration

resistance can be estimated using a single layer bearing capacity formula (e.g. Skempton,

1951). The distance from Point 1 to the soft-stiff layer interface is defined as the

limiting squeezing depth, hsq, which is taken as 0.18D [a range of 0.17~0.2D observed

in the centrifuge tests by Hossain et al. (2011b) and Hossain (2014)].

From the results of the numerical analyses and centrifuge tests, it is found that the gross

penetration resistance qv at Point 2 is a fraction of that estimated for a spudcan resting

on the surface of the 2nd layer. As such, the bearing pressure at Point 2 can be expressed

as 1

v d tq

, where

1v d t

q

is estimated using Equations 5.3~5.6 assuming d = t1 and is

the reduction factor that considers the local deformation of the layer interface and varies

as a function of normalised soil properties:

11

u1b u3 3 u3s2

u2 u3s

0.71

s s k D st1

s D s D

(5.7)


5-11

The comparison between 1

v d tq

calculated using proposed formulas and qv obtained

from numerical analyses (Groups III, Table 5.1) and centrifuge tests used for validation

is illustrated in Figure 5.11. As a result, the gross penetration resistance in the 1st layer

can be calculated as

v cr u0 0q N s p for d ≤ t1 0.18D (5.8a)

1v v d t

q q

for d = t1 (5.8b)

where Ncr is from Equation 5.6 but replacing k3, sud0 and dd by k1, su0 and d,

respectively; and and 1

v d tq

are from Equations 5.7 and 5.3, respectively.

5.3.5 Points 3 and 4

As discussed previously, the normalised distance, (t1 + t2 dp)/D, from the depth dp of

occurring punch-through or rapid leg run, to the 2nd-3rd layer interface, is found to vary

as a function of strength ratio and thickness ratio as shown in Figure 5.12 for numerical

analyses (Groups III, Table 5.1) and centrifuge tests, and can be presented by

2t

D1 2 p u3s 2

u2 u1b

t t d s 0.9tMin Max ln 0.1 ,0 ,

D s s D

(5.9)

The lower bound for (t1 + t2 dp)/D is zero, representing cases without any potential for

punch-through or rapid leg run in the 2nd (stiff) layer. The upper bound is 0.9t2/D since

the depth of triggering punch-through or rapid leg run is always marginally below the

surface of the stiff layer, as indicated by the measured and computed data (Hossain &

Randolph, 2010a, 2010b; Hossain et al., 2011a, 2011b).

It is assumed that the punching shear mechanism dominates the bearing response at d =

dp. The penetration resistance at Point 3, p

v d dq

can now be estimated using a

combination of Equations 5.3~5.6 with d = dp. For the depth dH of Point 4, it may be

assumed that the depth of soil backflow is equal to the average limiting cavity depth,

Hcav, which can be evaluated using Equation 5.1. However, it has been found that the

stable cavity depth after deep spudcan penetration in multi-layer soils is actually


5-12

shallower than the depth of backflow. For a more accurate prediction of dH, the iterative

approach (Hossain & Randolph, 2009b) suggested by ISO (2012) can be used. Similar

to the penetration resistance at Point 3, the penetration resistance H

v d dq

at Point 4 can

be computed using a combination of Equations 5.3~5.6 and d = Max(dp, dH) assuming

that the punching shear mechanism still dominates the bearing response. To ensure a

conservative design, the estimated value of H

v d dq

should be ≤

pv d d

q

5.3.6 Bearing Capacity in Bottom Layer

For the simplified penetration resistance profile in the bottom layer (Figure 5.8), the

bearing pressure only needs to be predicted at Point 5 and onwards [i.e. for Stage (6)].

The depth of Point 5, dr (i.e. depth of establishing the single layer penetration response

of the 3rd layer) is assumed to be the depth where the thickness of the total soil plug

attains to a minimum value of Hplug/t2 = 0.1 in the 3rd layer. As such, dr can be calculated

by inversing Equation 5.5a as

r 1 1 2

2 1

d t t t1 1.1Max ln ,

D D f f D

(5.10)

In order to explore the accuracy of Equation 5.10, a comparison between predicted and

measured or computed values of dr/D is plotted in Figure 5.13, with the error of the

predicted dr/D being mostly less than 0.1D.

The gross bearing pressure at and after Point 5 (i.e. d dr) then can be estimated by

assuming a fully localised failure mechanism (Hossain & Randolph, 2009b) as

2 u3p

v cd ud0

0.4t sq N s

D

for d dr (5.11)

where Ncd is the deep bearing capacity factor proposed by Hossain & Randolph (2009b)

2cd

d 0.1tN Min 10 1 0.065 ,11.3

D

(5.12)

For simplicity, the small amount of soil trapped underneath the spudcan can also be

neglected (i.e. t2 = 0 in Equations 5.11 and 5.12).


5-13


The following is a summary of the design procedure for estimating the penetration

resistance profile of spudcan in non-uniform clay with an interbedded stiff clay layer:

1. Determine representative values of the soil properties, layer thicknesses and

spudcan geometries su1s, k1, su2, su3s, k3, , St, t1, t2, D and Vsp;

2. Plot the gross penetration resistance profile in the 1st layer according to Equation

5.8 in combination with Equations 5.3~5.7;

3. Estimate the depths dp of Point 3 and dH of Point 4 (with dH dp) using

Equations 5.9 and 5.1, respectively, and then calculate the gross penetration

resistance at these depths using Equation 5.3 in combination with Equations

5.4~5.6;

4. Evaluate the depth dr of Point 5 using Equation 5.10 together with Equations

5.5b and 5.5c, and then plot the gross penetration resistance at Point 5 and

onwards using Equations 5.11 and 5.12;

5. Connect Points 1, 2, 3, 4 and 5, meanwhile estimate limiting cavity depth Hcav

using Equation 5.1, and then update the gross penetration resistance profile to

total penetration resistance profile using Equation 5.2.

For assessing spudcan penetration resistance in the field, the proposed approach can be

used for a practical range of soil parameters of three-layer (uniform or non-uniform i.e.

regardless of values of k1 and k3) sediments with an interbedded stronger layer.


A CPT-based design approach that establishes direct correlations between spudcan and

cone penetration resistances in non-uniform clay with an interbedded stiff clay layer is

proposed in this section. The results from numerical analyses of spudcan and cone

penetration are used to calibrate the correlations. The spudcan and cone (net) tip

resistance profiles are first simplified. A constant cone factor Nkt is assumed throughout

the soil profile, and is calculated according to Equation 3.7. Design formulas are then

proposed to estimate the values of penetration resistance ratio Rsp-c at critical penetration

depths of the simplified profiles. The other design formulas are transformed from those


5-14

for the proposed mechanism-based design approach, but expressed as a function of net

cone tip resistances and cone factor.

5.4.1 Simplified Penetration Resistance Profiles

For spudcan penetration in non-uniform clay with an interbedded stiff clay layer, a

typical penetration resistance profile with the potential for punch-through (su1 = 1 + 1z

kPa, su2 = 75 kPa, su3 = 30 + (z – t1 – t2)z kPa, t1/D = 0.5, t2/D = 0.75, rem = 1/St = 0.3;

Group III, Table 5.1) is shown in Figure 5.14, together with the simplified CPT profile.

Both profiles are presented in terms of net bearing pressure as a function of the

normalised penetration depth d/D.

As justified in Chapter 2, the distance of transition of the cone penetration resistance

profile when the cone penetrates from one layer to another is negligible compared with

the layer thickness considered in spudcan penetration design (Walker & Yu, 2010; Ma

et al., 2015). Therefore, the CPT profile is simplified by combining the profile in each

layer and neglecting the transitional zones.

Five transitional stages are marked on a typical spudcan penetration resistance profile

using Points 1, 2, 3 and 4 (see Figure 5.14). These include: (1) single layer response

before squeezing; (2) squeezing in the 1st layer; (3) gradual increase in penetration

resistance in the 2nd layer until the peak; (4) post-peak reduction or a plateau (note, as

the alternative approach focuses on predicting the potential for punch-through and

punch-through distance, the stage of further reduction of bearing capacity due to soil

backflow is omitted for simplification); and (5) establishing single layer penetration

response in the 3rd layer. In the simplified profile for Stages (2), (3) and (4), it is

sufficient to predict the locations of Points 1~4 and connect them by straight lines.

With the simplified cone tip resistance profile, the design formula, Equation 5.1, for

assessing the limiting cavity depth after deep spudcan penetration, can be transformed

as a function of cone resistances and cone factor:

0.51 12

net,c1b net,c3scav 31 2

kt net,c2 net,c3s

q qH Dt t0.25 1 1

D N D q D D q

(5.13)


5-15

where qnet,c1b, qnet,c2, and qnet,c3s are the net bearing pressures of cone at different depths,

and 3 is the bearing pressure gradient in the 3rd layer, as illustrated in Figure 5.14.

5.4.2 Single Layer Response: Stages (1) and (5)

Positions of Points 1 and 4

Identical to the mechanism-based design approach presented in Section 5.3.4, a unique

value of the limiting squeezing depth hsq = 0.18D is adopted for the CPT-based

approach. Therefore, the depth of Point 1 is d = Max(t1 – 0.18D, 0). For the depth of

Point 4, dr, expressions proposed in Section 5.3.6 can be re-arranged as a function of

cone resistances and layer thicknesses as

r 1 1 2

2 1

d t t t1 1.1Max ln ,

D D f f D

(5.14a)

1 1

net,c3s 21

net,c2

q tf 2 0.01

q D

(5.14b)

0.5

net,c3s 3 22

net,c2 net,c1b net,c3s

q D tf 0.2 0.5 1

q q q D

(5.14c)

Correlation for single layer response

For undrained penetration considered in this study, the penetration resistance ratio Rsp-c

before Point 1 and after Point 4 can be evaluated as Ncr/Nkt [for d Max(t1 – 0.18D, 0)]

and Ncd/Nkt (for d dr), respectively, where Ncr and Ncd are the bearing capacity

factors reported by Hossain & Randolph (2009b) for spudcan penetration in single layer

clay. Considering a consistent cone factor throughout the soil profile and neglecting the

small amount of trapped soil in deep penetration, Ncr and Ncd can be expressed as a

function of spudcan penetration depth and cone resistances, as

0.8 1.5

1cr

net,c0

Dd d dN 6.05 1 1 0.191 / 1

0.22D 3.65D q D

d dfor Min ,1.825

D D

(5.15a)


5-16

cd

dN Min 10 1 0.065 ,11.3

D

(5.15b)

where 1 is the gradient of net cone tip resistance in the 1st layer, and qnet,c0 is the net

cone tip resistance at spudcan base level.

5.4.3 Squeezing: Point 2

Based on the results from parametric studies of spudcan and cone penetration, the

penetration resistance ratio Rsp-c at Point 2 (d = t1) can be expressed as

2

net,sp 3.3

sp c

net,c2 kt

t1

Dnet,c1b net,c3s

net,c2

q 12.7R 0.28 0.2x

q N

q qwhere x

q

for d = t1 (5.16)

The penetration resistance ratio predicted using Equation 5.16 should be limited by the

value given by Equation 5.18 for the peak resistance.

As the rigidity index Ir of clay has negligible effect on the spudcan penetration

resistance, but significant influence on the cone factor Nkt, it is of interest to investigate

the effect of Ir on the ratio Rsp-c at Point 2. Figure 5.15 shows that the values of Rsp-c,

decrease with increasing Nkt. For the range of soil parameters explored, a typical range

of Rsp-c between 0.22 and 0.5 at Point 2 can be obtained.

5.4.4 Peak Resistance: Point 3

Equation 5.9 proposed in Section 5.3.5 to predict the depth of peak resistance can be

transformed as a function of cone penetration resistances:

2t

D1 2 p net,c3s 2

net,c1b net,c2

t t d q 0.9tMin Max ln 0.1 ,0 ,

D q q D

(5.17)

The corresponding penetration resistance ratio Rsp-c at d = dp is expressed as


5-17

net,sp x

sp c

net,c2 kt

0.5 0.5

net,c3s 3 1 2

net,c2 net,c3s

q 12.7R 0.8 0.8e

q N

q D t twhere x 1 1 1

q q D D

for d = dp (5.18)

Similar to Point 2, Figure 5.16 is plotted to demonstrate the relationship between the

penetration resistance ratio and cone factor. It can be seen that, for the range of soil

parameters explored, Rsp-c ranges between 0.26~0.68 at the peak.


The new CPT-based design approach estimates spudcan penetration resistance

(simplified) profile from the mudline to the bottom layer of three-layer sediments. A

detailed procedure for employing the CPT-based approach is introduced below:

1. Simplify the cone tip resistance (continuous) profile and pick design parameters,

such as qnet,c1b, qnet,c2, qnet,c3s, 1, 3, t1, t2 and ;

2. Determine the depth of Point 1 and calculate the penetration resistance ratio

before Point 1, d ≤ Max(t1 – 0.18D, 0), according to Rsp-c = Ncr/Nkt;

3. Estimate the penetration resistance ratio at the 1st-2nd layer (Point 2) interface

using Equation 5.16 or Figure 5.15;

4. Evaluate the depth of Point 3 (peak penetration resistance), dp, using Equation

5.17, and then estimate the corresponding penetration resistance ratio Rsp-c using

Equation 5.18 or Figure 5.16;

5. Determine the depth of Point 4, dr, using Equation 5.14, and calculate the

penetration resistance ratio for d dr according to Rsp-c = Ncd/Nkt;

6. Plot the full penetration resistance profile according to Equations 4.8 and 4.10,


APPLICATION

5.5.1 Centrifuge Tests

For the centrifuge tests used for validation in Section 5.2.1, the estimated profiles using

the proposed approaches are now included in Figures 5.2a~c. The required soil


5-18

parameters and layer geometries can be found in Section 5.2.1 and Table 5.1. In absence

of the cone penetration data for the centrifuge tests, it is assumed that the net cone

resistance follows the T-bar resistance closely during penetration in kaolin clay (Watson

et al., 2000). As such, the net cone penetration resistances are back-calculated according

to the undrained shear strength deduced from T-bar penetration data using qnet,c = 10.5su

(as su was calculated using a T-bar factor of 10.5). For example, the undrained shear

strength profile (su1 = su3 = 2 + 0.6z kPa, su2 = 23 kPa, t1/D = 0.38, t2/D = 0.58) for the

centrifuge test in Figure 5.2c implies that the corresponding net cone penetration

resistances input in the formulas are qnet,c1b = 49.35 kPa, qnet,c2 = 241.5 kPa, qnet,c3s =

92.82 kPa and 1 = 3 = 6.3 kPa/m.

The proposed mechanism-based approach estimates the penetration resistance profiles

with an error of mostly less than 5% at most depths. However, the estimation provides

lower penetration resistance in the 3rd layer, owing to the effect of the bottom boundary

of the testing strongbox or the 4th layer stiff clay.

The proposed CPT-based design approach estimates similar penetration resistance

profiles to those predicted using the new mechanism-based approach apart from the

post-peak behaviour. However, the penetration resistance profiles from the CPT-based

design approach agree reasonably well with the centrifuge test data in terms of

squeezing in the top soft layer, peak resistance in the stiff layer and deep penetration

resistance profile in the bottom layer. It is capable of assessing the likelihood and

severity of punch-through by comparing the penetration resistance profile with the

intended full preload. As such, the CPT-based design approach is an effective

alternative approach for estimating the spudcan penetration resistance.

The ISO (2012) bottom-up approach provides a similar estimation for the bearing

pressure in the 1st layer. However, in the 2nd layer with the potential for punch-through,

the predicted peak resistance rests at the 1st-2nd layer interface for all centrifuge tests.

Moreover, the predicted penetration resistance profiles using the ISO approach are

about 15~30% lower than the recorded centrifuge test data, i.e. providing a conservative

estimation. For the 3rd layer, the ISO approach applies single layer response once the

spudcan penetration exceeds the 2nd-3rd interface. This results in increasing penetration

resistance from the surface of the 3rd layer due to the increasing depth factor (for d/D <

2.5). However, for the bottom layer, the profile would keep reducing (due to the effect


5-19

of diminishing the trapped soil plug) or level off, as reported by Hossain & Randolph

(2010a, 2010b) and Hossain et al. (2011a, 2011b). This part of the profile is reasonably

estimated using the proposed approaches.

The centrifuge test data from spudcan penetration in a soft-stiff-soft-stiff clay deposit (D

= 12 m, su1 = 8.5 kPa, su2 = 25 kPa, su3 = 10 kPa, t1/D = 0.25, t2/D = 0.5, rem = 1/St =

0.36) reported by Hossain (2014) is also compared with the estimated profiles. The

thickness of the 3rd layer soft clay is 0.96D, which is considered as thick enough to

eliminate the effect from the 4th stiff layer on spudcan penetration in the 2nd layer. The

estimated profiles and measured data are presented in Figure 5.17. In the 1st layer, the

estimated profiles using the proposed approaches and the ISO bottom-up approach are

consistent, and show good agreement with the centrifuge test data. However, in the 2nd

layer, the bearing pressure profiles from the proposed approaches agree well with the

measured data, with an error of less than 5%, while the ISO approach provides a

conservative estimate of the penetration resistance.

5.5.2 Case History

The proposed design approaches are also used to predict the case history used for

validation, as shown in Figure 5.2d. The layer geometries and strength parameters can

be found in Section 5.2.1. The simplified cone penetration resistance profile for the case

history shows qnet,c1b = 100 kPa, qnet,c2 = 810 kPa, qnet,c3s = 580 kPa and 3 = 50.9 kPa/m

with a cone factor of Nkt = 20.

The proposed design approaches and the ISO bottom-up approach all give reasonable

predictions compared with the measured load-penetration responses, with an error of

5~10% for the final penetration depth. The bottom-up approach provides a similar

prediction to that estimated by the proposed approach. This is because the 2nd (stiff)

layer is so thin (t2/D = 0.15) that the effect of the trapped soil plug is minimal.

CONLUDING REMARKS

This chapter has developed new mechanism-based and CPT-based design approaches

for assessing the penetration resistance of spudcan in non-uniform clay with an

interbedded stiff clay layer, based on the results from a series of LDFE analyses.


5-20

For the mechanism-based design approach, the evolving soil failure patterns with the

progress of spudcan penetration and the combined effect of strain softening and rate

dependency of the undrained shear strength were accounted for. Guidelines were also

provided to apply the design approach.

For the CPT-based design approach, the formulas for penetration resistance ratio Rsp-c in

different penetration stages were developed as a function of cone resistances and cone

factor. The ranges of Rsp-c, indicated by the proposed formulas with soil parameters and

layer geometries varying in a range of practical interest, have been given for the critical

depths in the practice of spudcan penetration design for soft-stiff-soft clay deposits, i.e.

at the depths of soft-stiff layer interface and peak resistance.

The predicted profiles using these two approaches have been compared with data from

centrifuge tests and a case history. The bottom-up approach recommended in the ISO

standard 19905-1 was also adopted for comparison. Predictions using the proposed

approaches were found to be in good agreement with measured load-penetration

profiles, with underestimation or overestimation in terms of penetration resistance or

penetration depth at critical points being mostly less than 5 %. The peak penetration

resistance at punch-through (if any), the depth of triggering punch-through and the

likelihood and severity of punch-through were also well predicted. The ISO bottom-up

approach provided a relatively less accurate estimation of the penetration resistance

profile, with underestimation of the bearing capacity (or overestimation of penetration

depth) and inaccurate identification of the likelihood and severity of punch-through.


5-21

REFERENCE










Hossain, M. S. & Randolph, M. F. (2009c). New mechanism-based design approach for









Hossain, M. S., Cassidy, M. J., Baker, R. & Randolph, M. F. (2011a). Optimization of

perforation drilling for mitigating punch-through in multi-layered clays. Canadian

Geotechnical Journal 48, 1658-1673.

Hossain, M. S., Randolph, M. F. & Saunier, Y. N. (2011b). Spudcan deep penetration in






Hossain, M. S., Zheng, J., Safinus, S., Kim, Y., Won, J., Park, J. S. & Jun, M. J. (2015).

Installation of spudcan foundations in layered soils: centrifuge test and numerical

analysis. Proc. 25th International Offshore and Polar Engineering Conference 2,

685-691.

Houlsby, G. T. & Martin, C. T. (2003). Undrained bearing capacity factors for conical



5-22













London, 1, 180-189.





Polar Engineering Conference, ISOPE00, Seattle, 2, 485-493.

Zheng, J., Hossain, M. S. & Wang, D. (2014a). CPT based direct design approach for

spudcan penetration in non-uniform clay with an interbedded stiff layer. Proc. 14th

International Conference of the International Association for Computer Methods

and Advances in Geomechanics, Kyoto, 895-900.

Zheng, J., Hossain, M. S. & Wang, D. (2014b). Numerical modeling of spudcan deep

penetration in three-layer clays. International Journal of Geomechanics, ASCE,

10.1061/(ASCE)GM.1943-5622.0000439, 04014089.

Zheng, J., Hossain, M. S. & Wang, D. (2015). New design approach for spudcan




5-23

TABLES

Table 5.1 Summary of parameters for performed numerical analyses

Group

1st layer

non-uniform clay

2nd layer

uniform clay

3rd layer

non-uniform

clay St Note

su1s:

kPa

k1:

kPa/m t1/D

su1b:

kPa

su2:

kPa t2/D

su3s:

kPa

k3:

kPa/m

I

10 0 0.31 10 40 0.3 10 0

2.8 Centrifuge

test 10 0 0.25 10 40 0.5 10 0

2 0.6 0.38 4.7 23 0.58 8.84 0.6

II 1 1.05 0.28 5 40.5 0.15 29 2.55 3.3 Case

history

III 1~5 1~3 0.25

~0.5 4~23

40~

75

0.25~

0.75 30 0~3 3.3

Parametric

studies


5-24

FIGURES

qnet

ddp

qpeak h

P-T

d

Hcav

z

Sp

ud

ca

n

Ca

vity

K-la

ttic

e le

g

D

1

1

1st l

aye

r

3rd

la

ye

r

2nd la

ye

r

t 1

t 2

su1

su2

su3

su1b

su3s

su0

k3

k1

su1s

su

Fig

ure

5.1

Sch

em

ati

c d

iagra

m o

f sp

ud

can

fou

nd

ati

on

em

bed

ded

in

non

-un

iform

cla

y w

ith

an

in

terb

edd

ed s

tiff

cla

y

layer

sh

ow

ing i

dea

lise

d o

pen

cavit

y a

nd

corr

esp

on

din

g p

enet

rati

on

res

ista

nce

pro

file


5-25

5.2(a) Test T1 (su1 = su3 = 10 kPa, su2 = 40 kPa, t1/D = 0.31, t2/D = 0.3, rem = 1/St =

0.36; Group I, Table 5.1; Hossain et al., 2011a)

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250

No

rmalised

pen

etr

ati

on

dep

th,

d/D


CPT-basedapproach

LDFE

Centrifuge test

Bottom-up approach

Mechanism-based approach


5-26

5.2(b) Test T2 (su1 = su3 = 10 kPa, su2 = 40 kPa, t1/D = 0.25, t2/D = 0.5, rem = 1/St =

0.36; Group I, Table 5.1; Hossain et al., 2011a)

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250

No

rmalised

pen

etr

ati

on

dep

th,

d/D


CPT-based approach

LDFE

Centrifuge test

Bottom-up approach



5-27

5.2(c) Test T6 (su1 = su3 = 2 + 0.6z kPa, su2 = 23 kPa, t1/D = 0.38, t2/D = 0.58, rem =

1/St = 0.36; Group I, Table 5.1; Hossain et al., 2011b)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 50 100 150 200 250

No

rmalised

pen

etr

ati

on

dep

th,

d/D


Mechanism-based

approachLDFE

Centrifuge testBottom-up

approach

CPT-based approach


5-28

5.2(d) Case history (su1 = 1 + 1.05z kPa, su2 = 40.5 kPa, su3 = 29 + 2.55(z – t1 – t2) kPa,

t1/D = 0.28, t2/D = 0.15, rem = 1/St = 0.3; Group II, Table 5.1; InSafeJIP, 2011)

Figure 5.2 Validation of LDFE model against centrifuge test and field data

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 150 300 450 600 750 900

No

rma

lis

ed

pe

ne

tra

tio

n d

ep

th,

d/D


Mechanism-basedapproach

LDFE

Bottom-up approach

Bow

Port

Starboard

CPT-based approach


5-29

5.3(a) Squeezing (d/D = 0.08)

5.3(b) Soil backflow and deformation of the 1st-2nd layer interface (d/D = 0.23)

1st layer

2nd layer

3rd layer

1st layer

2nd layer

3rd layer


5-30

5.3(c) Trapped softer layer and deformation of soils towards the lower layer (d/D =

0.57)

5.3(d) Layered soil plug consisting of soils from 1st and 2nd layers (d/D = 0.7)

Figure 5.3 Soil failure mechanisms during spudcan penetration in non-uniform

clay with an interbedded stiff clay layer (su1 = 2 + 2z kPa, su2 = 40 kPa, su3 = 30 + (z

– t1 – t2) kPa, t1/D = 0.25, t2/D = 0.5, rem = 1/St = 0.3; Group III, Table 5.1)

1st layer

2nd layer

3rd layer

1st layer

2nd layer

3rd layer


5-31

5.4(a) t1/D = 0.25, t2/D = 0.25

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25N

orm

alised

pen

etr

ati

on

dep

th,

d/D

Normalised bearing pressure, qnet/su3s

Non-uniform

Uniform

Non-uniform

su2/su3s = 1.33 and 2.5


5-32

5.4(b) t1/D = 0.25, t2/D = 0.5

Figure 5.4 Effect of 2nd layer undrained shear strength (su2) on bearing response

(su3s/D = 0.31, k1D/su1s = 12, k3D/su3s = 0.4; Group III, Table 5.1)

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25

No

rmalised

pen

etr

ati

on

dep

th,

d/D


Non-uniform

Uniform

Non-uniform

su2/su3s = 1.33 and 2.5


5-33

5.5(a) qnet/su3s vs d/D

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30N

orm

ali

se

d p

en

etr

ati

on

de

pth

, d

/D


t2/D = 0.25, 0.5 and 0.75

Non-uniform

Uniform

Non-uniform


5-34

5.5(b) qnet/su0 vs (d – t1 – t2)/D

Figure 5.5 Effect of 2nd layer thickness ratio (t2/D) on bearing response (su3s/D =

0.31, t1/D = 0.25, k1D/su1s = 12, k3D/su3s = 0.4; Group III, Table 5.1)

0

0.4

0.8

1.2

1.6

2

0 4 8 12 16 20

No

rma

lis

ed

pe

ne

tra

tio

n d

ep

th,

(d

t 1

t 2)/

D

Normalised bearing pressure, qnet/su0

t2/D = 0.25, 0.5 and 0.75


5-35

5.6(a) qnet/su3s vs d/D

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30N

orm

alised

pen

etr

ati

on

dep

th,

d/D


k3D/su3s = 0,0.4, 0.8 and 1.2

Non-uniform

Uniform

Non-uniform


5-36

5.6(b) qnet/su0 vs (d – t1 – t2)/D

Figure 5.6 Effect of bottom layer non-homogeneity (k3D/su3s) on bearing response

(su3s/D = 0.31, t1/D = 0.5, t2/D = 0.75, k1D/su1b = 7.2; Group III, Table 5.1)

0

0.4

0.8

1.2

1.6

2

0 4 8 12 16 20 24

No

rma

lis

ed

pe

ne

tra

tio

n d

ep

th,

(d

t 1

t 2)/

D


k3D/su3s = 0,0.4, 0.8 and 1.2


5-37

Figure 5.7 Design chart for limiting cavity depth (Hcav) for spudcan penetration in

non-uniform clay with an interbedded stiff clay layer

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 2 4 6 8 10 12 14 16 18N

orm

ali

se

d l

imit

ing

ca

vit

y d

ep

th,

Hcav/D

1 12

u1b u3s 31 2

u2 u3s

s s k Dt t1 1

D s D D s

0.51 12

cav u1b u3s 31 2

u2 u3s

H s s k Dt t0.25 1 1

D D s D D s


5-38

Figure 5.8 Simplified predictive penetration resistance profile for spudcan

penetration in non-uniform clay with an interbedded stiff clay layer (su1 = 5 + 3z

kPa, su2 = 75 kPa, su3 = 30 + (z – t1 – t2) kPa, t1/D = 0.25, t2/D = 0.75, rem = 1/St = 0.3;

Group III, Table 5.1)

0

0.5

1

1.5

2

2.5

0 200 400 600 800

No

rmalised

pen

etr

ati

on

dep

th,

d/D


LDFE

23

4

Bottom-upapproach

5

Point 1

Stage (1)

(4)

Mechanism-basedapproach

(2)

(3)

(5)

(6)

Simplified profile


5-39

Figure 5.9 Conceptual model for spudcan penetration in the 2nd and 3rd layers of

non-uniform clay with an interbedded stiff layer

t1

t2 Hplug,2

Hplug,3

d

Dummy spudcan

qu

sud0

su2p

su

z

su3p

su0

Ncrsud0 or Ncdsud0

Hplug


5-40

Figure 5.10 Variation of soil plug thickness beneath the advancing spudcan in non-

uniform clay with an interbedded stiff layer (su1 = 2 + 2z kPa, su2 = 75 kPa, su3 = 30

+ (z – t1 – t2) kPa, t1/D = 0.25, t2/D = 0.5, rem = 1/St = 0.3; Group III, Table 5.1)

0

0.2

0.4

0.6

0.8

1

1.2

0 0.25 0.5 0.75 1 1.25 1.5

No

rma

lis

ed

plu

g t

hic

kn

es

s,

Hp

lug/t

2

Normalised penetration depth from the 1st-

2nd layer interface, (d t1)/D

1d t( 0.56 )

plug plug,2D

2 2

H HMax 2.05e 1, 0.1,

t t


5-41

Figure 5.11 Comparison of predicted and measured or computed qv at Point 2 for

spudcan penetration in non-uniform clay with an interbedded stiff layer

0

100

200

300

400

500

600

0 100 200 300 400 500 600

Measu

red

or

co

mp

ute

d q

vat

Po

int

2:

kP

a

Predicted qv at Point 2: kPa

Numerical analysis

Centrifuge test

10% variation

Equality


5-42

Figure 5.12 Design chart for peak resistance depth (Point 3) in the stiff layer for


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8 1

(t1

+ t

2

dp)/

D

Numerical analysis

Centrifuge test

2t

Du3s

u2 u1b

s

s s

2t

D1 2 p u3s

u2 u1s

t t d sln 0.1

D s s


5-43

Figure 5.13 Relationship between predicted and measured or computed dr/D for


0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3

Measu

red

or

co

mp

ute

d d

r/D

Predicted dr/D

Numerical analysis

Centrifuge test

Equality

0.1 variation


5-44

Figure 5.14 Simplified penetration resistance profiles for spudcan and cone in non-

uniform clay with an interbedded stiff clay layer (su1 = 1 + 1z kPa, su2 = 75 kPa, su3

= 30 + (z – t1 – t2)z kPa, t1/D = 0.5, t2/D = 0.75, rem = 1/St = 0.3; Group III, Table

5.1)

0

0.5

1

1.5

2

2.5

0 200 400 600 800 1000 1200

No

rmalised

pen

etr

ati

on

dep

th,

d/D

Net bearing pressure, qnet,sp or qnet,c: kPa

LDFE

23

Point 1

Simplified profilefor spudcan

Simplified profilefor cone

qnet,c1b

qnet,c3s

qnet,c2

Stage (1)

(2)

(3)

(4)

(5)

1

D

4


5-45

Figure 5.15 Design chart for penetration resistance ratio Rsp-c at d = t1 for spudcan

penetration in non-uniform clay with an interbedded stiff layer

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Pen

etr

ati

on

resis

tan

ce r

ati

o,

Rsp

-c

Ir = 670

Ir = 1500

Ir = 3000

Ir = 5000

Equation 5.16:Nkt = 12.7, 15.0, 17.0 and 18.5

2t1D

net,c1b net,c3s

net,c2

q q

q


5-46

Figure 5.16 Design chart for penetration resistance ratio Rsp-c at d = dp for spudcan

penetration in non-uniform clay with an interbedded stiff layer

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.4 0.8 1.2 1.6 2 2.4

Pe

ne

tra

tio

n r

es

ista

nc

e r

ati

o,

Rsp

-c

Ir = 670

Ir = 1500

Ir = 3000

Ir = 5000

Equation 5.18:Nkt = 12.7, 15.0, 17.0 and 18.5

0.50.5

net,c3s 32 1

net,c2 net,c3s

q Dt t1 1 1

q D D q


5-47

Figure 5.17 Comparison between predictions and centrifuge test data (D = 12 m,

su1 = 8.5 kPa, su2 = 25 kPa, su3 = 10 kPa, t1/D = 0.25, t2/D = 0.5, rem = 1/St = 0.36)

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250

No

rmalised

pen

etr

ati

on

dep

th,

d/D


Bottom-up approach

Centrifuge test


CPT-based approach

Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay

6-1

CHAPTER 6. SPUDCAN IN UNIFORM STIFF-SOFT-

STIFF CLAY

INTRODUCTION

Two configurations of three-layer clay profiles commonly encountered in the offshore

field, and identified as critical for potential punch-through, include (i) non-uniform clay

with an interbedded stiff clay layer and (ii) uniform stiff-soft-stiff clay. New design

approaches for assessing spudcan penetration resistance in the former soil stratification

have been presented in Chapter 5. This chapter aims to develop new design approaches

for spudcan penetration in uniform stiff-soft-stiff clay deposits.

For assessing spudcan penetration resistance in uniform stiff-soft-stiff clay, the bottom-

up approach recommended by the current design guidelines (ISO, 2012) calculates the

bearing capacities from the bottom layer to the top layer, using (a) Skempton’s (1951)

or Houlsby & Martin’s (2003) approach for single layer clay (calculation for the 3rd

layer); (b) Meyerhof & Chaplin’s (1953) squeezing approach for 2nd-3rd layer system

(calculation for the 2nd layer); and (c) Brown & Meyerhof’s (1969) punching shear

approach for the 1st-2nd layer system (calculation for the 1st layer). The undrained shear

strength of the underlying layer in the calculation for the 1st-2nd layer system is back-

calculated from the bearing capacity at the surface of the 2nd layer estimated using the

squeezing approach for the 2nd-3rd layer system.

The general deficiencies of applying the bottom-up approach for assessing spudcan

penetration resistance in three-layer clay deposits have already been discussed in

Chapter 5. However, for the stiff-soft-stiff clay deposit investigated in this chapter, the

key relevant deficiencies of the bottom-up approach include: (i) for the punching shear

approach in the 1st layer, the influence of the bottom stiff layer is usually not taken into

account unless the thickness of the 2nd layer is smaller than the calculated limiting

squeezing depth (hsq, see Figure 6.1). However, it has been confirmed that the bearing

capacity in the 1st layer is significantly affected due to the presence of the 3rd layer even

for a 2nd layer thickness of half spudcan diameter [see Figure 7 of Zheng et al. (2014)];


6-2

and (ii) for the squeezing approach in the 2nd layer, a clean spudcan without any trapped

soil plug is assumed, which is unable to estimate the earlier squeezing triggered by the

stiff soil plug brought down from the 1st layer [i.e. the actual limiting squeezing depth is

much higher than the one calculated according to ISO (2012)].

To develop design approaches based on the evolving true soil failure mechanisms, large

deformation finite element (LDFE) analyses were performed simulating continuous

spudcan penetration in three-layer uniform stiff-soft-stiff clay deposits, with strain

softening and rate dependency of the undrained shear strength taken into account. This

chapter presents the results from the parametric LDFE analyses, based on which new

mechanism-based and CPT-based design approaches are proposed, following a similar

framework of Chapter 5. The accuracy of the proposed design approaches is evaluated

through validation exercises against a centrifuge test and a reported case history. The

outcomes presented in this chapter have been documented in Zheng et al. (2015).

NUMERICAL ANALYSIS

This chapter has considered a circular spudcan of diameter D, penetrating into a three-

layer clay deposit as illustrated schematically in Figure 6.1, where the 2nd (soft) layer

with uniform undrained shear strength su2 and thickness t2 is sandwiched by the 1st (stiff)

layer of uniform undrained shear strength su1 and thickness t1; and the 3rd (stiff) layer of

uniform undrained shear strength su3.

The numerical model was first validated against centrifuge test data (Group I, Table 6.1).

Parametric study (Group II, Table 6.1) was then carried out encompassing an extensive

range of soil parameters and layer geometries of practical interest. The parameters used

in the numerical analyses are listed in Table 6.1. For convenience, the effective unit

weight of the three layers were considered to be equal (= 8 kN/m3). Further details of

the numerical analysis, such as the set-up for the numerical model, constitutive model,

and relevant elastic and plastic parameters, can be found in Chapter 2.

6.2.1 Validation of Numerical Model

Numerical analysis was first performed simulating a centrifuge model test for a spudcan

[D = 12 m, Test FS1 in Hossain (2014)] penetrating through a uniform stiff-soft-stiff


6-3

clay (su1 = 21 kPa, su2 = 8.5 kPa, su3 = 35.5 kPa, t1/D = 0.42, t2/D = 0.5, rem = 1/St =

0.36; Group I, Table 6.1). The undrained shear strengths considered in the numerical

simulation followed the average values given by Hossain (2014) who suggested a small

range of undrained shear strength for each layer. The measured and computed

penetration resistance profiles are plotted in Figure 6.2. Overall, good agreement can be

seen in terms of the form of the penetration resistance profile, depth of triggering

punch-through in the 2nd layer (associated with the initiation of soil backflow; see

Figure 6.3b), and the response in the 3rd layer. The limiting squeezing depth in the 2nd

layer is underestimated by about 0.05D by the computed profile.

6.2.2 Soil Flow Mechanisms

Soil flow mechanisms during spudcan penetration in stiff-soft-stiff clay deposit are

investigated through the instantaneous (resultant) velocity vectors plotted in Figures

6.3a~d, which are obtained from the numerical simulation of the centrifuge test (Group

I, Table 6.1). Four key features can be observed including: (i) punching shear

mechanism with the soil deformation directed predominantly vertically downward in the

1st (stiff) layer and laterally outward in the 2nd (soft) layer being restricted by the 3rd

(stiff) layer (Figure 6.3a); (ii) soil backflow around the soil plug and onto the spudcan

top (Figure 6.3b); (iii) soft soils between the stiff soil plug base and the stiff 3rd layer

squeezing out (Figure 6.3c); and (iv) the spudcan in the 3rd layer with thin layers of

trapped soils from the upper layers wrapping the bottom profile of the spudcan and

localised soil flow mechanism (Figure 6.3d).

6.2.3 Parametric Study

A parametric study was carried out varying undrained shear strengths su1 and su3, and

thickness ratios t1/D and t2/D, in an effort to investigate the punch-through and

squeezing behaviours during spudcan penetration in the 1st (stiff) layer and 2nd (soft)

layer, respectively. The selected ranges of parameters are assembled in Table 6.1. The

corresponding results are presented in this chapter in terms of the normalised net

penetration resistance qnet/su3, as a function of the normalised penetration depth d/D,

with qnet calculated using Equation 4.1. Based on the numerical results, the effects of the

varied parameters on the bearing response are discussed in the following subsections.


6-4

Effect of 1st and 3rd layer strengths (su1 and su3) or strength ratios su2/su1

and su3/su2

To investigate the effects of the undrained shear strengths of the stiff layers (and hence

strength ratios su2/su1 and su3/su2), the results of various strengths su1 = 50, 80 and 120

kPa, and su3 = 75 and 120 kPa with su2 = 40 kPa and (t1 + t2)/D = 1.0 are plotted in

Figures 6.4a to 6.4c for thickness ratios t1/D = 0.25, 0.5 and 0.75, respectively.

It can be seen that the depth and magnitude of the peak resistance in the 1st (stiff) layer

decreases and increases, respectively, as the strength ratio su2/su1 decreases with the

other parameters kept constant. For the 3rd layer strength of su3 = 75 kPa (su3/su2 = 1.88),

the squeezing in the 2nd (soft) layer is less obvious, especially for a thin 2nd layer

combined with a strong 1st layer. For instance, for t2/D = 0.25, the depth of onset of

increasing bearing pressure becomes deeper with decreasing su2/su1. The reverse trend is

shown by the penetration resistance profiles for t2/D = 0.75.

For higher su3 of 120 kPa (or higher strength ratio of su3/su2 = 3), the squeezing is

profound and the depth of triggering squeezing decreases or the limiting squeezing

depth increases with increasing su1 (or decreasing su2/su1). This is because a thicker soil

plug from the 1st layer stiff clay can be brought down by the spudcan for a lower

strength ratio su2/su1, which enhances the limiting squeezing depth.

For the cases in which a clear squeezing behaviour is observed in the 2nd layer (e.g. t2/D

= 0.75, Figure 6.4a), increasing su3 or su3/su2 marginally enhances the limiting squeezing

depth. However, for the cases with t2/D = 0.25 and 0.5 (Figures 6.4b and 6.4c), the

bearing response for the 3rd layer strength of su3 = 75 kPa (su3/su2 = 1.88, su3/su1 =

1.5~0.63) is more similar to a single layer penetration response, leading to a gradually

increase in resistance in the 2nd (soft) layer after punch-through. Therefore, no obvious

squeezing is observed and it is difficult to determine the limiting squeezing depth.

The normalised bearing pressure profile from the 2nd-3rd layer interface onwards is

slightly lower for higher su3/su2. This is probably caused by the fact that a stronger 3rd

layer allows less soil from the upper layers to be carried down by the spudcan. For

example, the somewhat ‘equivalent’ (i.e. accounting for the frictional resistance around

the periphery of the soil plug descended with the advancing spudcan) deep bearing


6-5

capacity factor for su3 = 75 kPa (su3/su2 = 1.88) ranges from 9.8 to 11.0, which reduces to

around 9.5~10.1 for su3 = 120 kPa (su3/su2 = 3).

Effect of thickness ratios (t1/D and t2/D)

The effect of thickness ratios t1/D and t2/D on the bearing response is evident in Figure

6.4, for example comparing responses for a given strength ratios su2/su1 and su3/su2 in

Figures 6.4a and 6.4b. Figure 6.5 focuses specifically on this issue by directly

comparing the bearing pressure profiles of t1/D = 0.25, 0.5 and 0.75 [with (t1 + t2)/D =

1.0] for two different strength ratios (su1 = 80 and 120 kPa or su2/su1 = 0.5 and 0.33) with

su2 = 40 kPa and su3 = 75 kPa.

The overall bearing pressure and the magnitude and depth of the peak resistance in the

1st layer increases as t1/D increases while t2/D decreases. For instance, for su2/su1 = 0.5

(Figure 6.5b), the normalised peak resistance qpeak/su3 increases from 5.5 to 7.7 and

corresponding depth dp/D from 0.12 to 0.38 as t1/D increases from 0.25 to 0.75.

For the considered 3rd layer strength of su3 = 75 kPa (su3/su2 = 1.88), no obvious

squeezing behaviour is observed. The bearing pressure starts to increase in the 2nd (soft)

layer at a depth that increases with increasing t1/D. Finally, the penetration resistance

profiles merge together regardless of the thickness ratios, giving a range of deep bearing

capacity factors between 10.1 and 10.8.


6.3.1 Limiting Cavity Depth

All the results are presented in Figure 6.6a with the normalised limiting (stable) cavity

depth, Hcav/D, plotted against [su1/(D)](t1/D)(1 + k1D/su2s)0.5 (see Equation 4.9). The

values for stiff-over-soft clay deposits from Chapter 4 are also included in the figure for

comparison. For the investigated parameters, the values of Hcav/D for spudcan

penetration in uniform stiff-soft-stiff clay deposits are significantly lower than those for

spudcan penetration in stiff-over-soft clay deposits, with the difference decreasing with

increasing t2/D. The shallower limiting cavity depth may be caused by the effect of the

stiff 3rd layer through squeezing and forcing the soil to flow back earlier onto the top of

the spudcan. As such, a new design formula for Hcav/D is proposed for spudcan


6-6

penetration in uniform stiff-soft-stiff clays, based on the stable cavity depths obtained

from the LDFE parametric study (Group II, Table 6.1), which is expressed as

0.281

cav u1 u3 1 2

u1

H s s t t0.58 1

D D s D D

(6.1)

The values of Hcav/D obtained from the centrifuge test used for validation and the

numerical analyses (Group II, Table 6.1) are compared with Equation 6.1 in Figure

6.6b. It can be seen that the cavity depths in most cases range between 0.3~0.5D, except

those for a thick and strong 1st (stiff) layer (i.e. su1 = 120 kPa and t1 0.5D).

6.3.2 Simplified Penetration Resistance Profile

A typical penetration resistance profile from the LDFE analysis of spudcan penetration

in uniform stiff-soft-stiff clay deposit (su1 = 120 kPa, su2 = 40 kPa, su3 = 75 kPa, t1/D =

0.25, t2/D = 0.75, rem = 1/St = 0.3; Group II, Table 6.1) is plotted in Figure 6.7.

According to the form of the penetration resistance profile, the major concerns for

spudcan penetration in this type of soil profile include: (i) the potential for punch-

through or rapid leg run in the 1st layer; (ii) the depth of triggering squeezing (onset of

increase of penetration resistance) in the 2nd layer; and (iii) the depth of leg plunge hP-T

if punch-through/rapid leg run occurs. To address these concerns, the penetration

resistance profile of spudcan is divided into four stages by marking Points 1~3 on the

profile as shown in Figure 6.7. The stages comprise: (1) gradual increase in penetration

resistance in the 1st layer down to the depth of peak resistance; (2) post-peak reduction

or a plateau in penetration resistance prior to increasing again in the 2nd layer; (3)

squeezing in the 2nd layer; and (4) single layer penetration response in the 3rd layer. For

the simplified profile in the 1st and 2nd layers, which is critical to address the concerns

noted previously, it is sufficient to predict the penetration resistances at the seabed and

at Points 1~3, and connect them by straight lines, as illustrated in Figure 6.7.

The penetration resistance profiles predicted by the bottom-up approach (ISO, 2012)

with and without considering a soil plug of constant thickness of t1 are also presented in

Figure 6.7. It can be seen that both predictions are conservative in the 1st and 2nd layers.

The comparison confirms the necessity to take into account the influence of the bottom


6-7

stiff layer, along with the effect of the soil plug, for predicting spudcan penetration

resistance in stiff-soft-stiff clay deposit.

To consider the soil plug trapped beneath the spudcan base, a unique form of formula is

adopted in the proposed mechanism-based design approach for the bearing capacities in

the 1st and 2nd layers, where a punching shear mechanism is assumed, and expressed as

plug,1 u1 plug,2 u2 plug,3 u1 u3

v cr ud0 0

4 H s H s H Min s ,sq N s p

D

(6.2)

where is the adjustment factor considering strain softening and rate effects and

calculated using Equation 5.4, Hplug,i is the soil plug thickness in the ith layer, p0 is the

effective overburden pressure of soils above spudcan base level, and Ncr and sud0 are,

respectively, the shallow bearing capacity factor and the local undrained shear strength

at the depth of the soil plug base. For spudcan penetration in uniform clay, the bearing

capacity factor at the depth of soil plug base can be calculated according to (Hossain &

Randolph, 2009)

plugd d dcr

d Hd d dN 6.05 1 for Min ,1.825

0.22D 3.65D D D

(6.3)

where dd is the depth of the soil plug base.

For simplicity, only the 1st layer soil carried down by the spudcan is considered in the

calculation. Therefore, the plug thicknesses in different layers during the penetration

can be expressed as Hplug,1 = Max(t1 d, 0), Hplug,2 = Min(d + Hplug – t1, t2), and Hplug,3 =

Max(d + Hplug t1 t2, 0). The total soil plug thickness is found to decrease gradually

with penetration depth, with a lower limit of 0.1t1 as a small amount of soil is observed

at the base of the deeply penetrated spudcan. Based on the results from numerical

analyses, the normalised term Hplug/t1 for all cases can be expressed as

1

df

plug plug,1D

1 1

H HMax 2e 1,0.1,

t t

(6.4)

The value of f1 is selected for each numerical analysis so that the soil plug thicknesses

picked at various depths before squeezing are best fitted by Equation 6.4. All the values

of f1 from the parametric study are plotted in Figure 6.8 and are best fitted by


6-8

0.151 1

u2 u3 1 21

u1 u1

s s t tf 0.5

s s D D

(6.5)

The value of f1 obtained from the half spudcan test corresponding to Test FS1 (Hossain,

2014) is also included in Figure 6.8, with excellent agreement obtained.

In the following subsections, design formulas are developed to predict the depths and

bearing capacities at the seabed, at Points 1~3, and in the bottom layer. Finally, a design

procedure is given.


For the simplified profile in the 1st layer, the penetration resistances at the seabed

surface (d = 0) and at punch-through (d = dp) are required. The penetration resistance at

the seabed surface can be assessed using Equation 6.2, with d = 0, Hplug = Hplug,1 = t1 and

sud0 = su2. To ensure a conservative prediction, an upper limit of 6(1 + 0.2d/D)su1

(Skempton, 1951) is suggested on the predicted bearing capacities in the 1st layer.

The penetration resistance at punch-through (Point 1) is also predicted using Equation

6.2, with the soil plug thickness estimated using Equation 6.4. The corresponding depth

dp can be calculated using

1.70.5 10.5 1

p u2 u3 u11 2 1

u1 u1

d s s st t t0.1 0.05

D s s D D D D

(6.6)

The estimations from Equation 6.6 and the peak resistance depths obtained from the

LDFE analyses and centrifuge test are compared in Figure 6.9. An upper bound of t1/D

is set. As such, Figure 6.9 or Equation 6.6 can be used to evaluate the potential for

punch-through for spudcan penetration in stiff-soft-stiff clay. For a combination of

parameters leading to dp/D t1/D, punch-through would not occur during spudcan

penetration in the 1st layer stiff clay.

With the peak resistance depth, Equations 6.4 and 6.2 can be used to estimate the

corresponding soil plug thickness and bearing capacity, respectively. However, as

discussed in Section 6.3.2 on ‘Simplified Penetration Resistance Profile’, the

penetration resistance in the 1st layer stiff clay may be underestimated by Equation 6.2


6-9

even if a soil plug of constant thickness of t1 is considered in the calculation (see Figure

6.7). This is because the influence of the stiff 3rd layer, which forces the 2nd layer soft

soils to flow laterally outward (see Figure 6.3a), is not considered in the prediction for

the bearing capacity profile in the 1st layer.

To incorporate the effect of the stiff 3rd layer in the prediction, an equivalent 2nd layer

undrained shear strength su2e is proposed. The results from the numerical analyses and

centrifuge test were used to calibrate the value of su2e so that the peak penetration

resistance qpeak is best predicted by Equation 6.2 with su2 = su2e. All the normalised

values, su2e/su2, are plotted in Figure 6.10, which can be expressed as

1 0.5 0.25 0.5

u2e u2 u3 1 2

u2 u1 u2

s s s t t0.8 0.085 1

s s s D D

(6.7)

For the soil parameters and layer thicknesses explored in this study (Group II, Table

6.1), the 3rd layer stiff clay always has a favourable effect on the peak resistance in the

1st layer, i.e. su2e/su2 1. For spudcan penetration in uniform stiff-soft-stiff clay, a value

of ≤ 1 predicted by Equation 6.7 indicates that the 3rd (stiff) layer will not affect the

penetration resistance in the 1st (stiff) layer. However, if the 1st (stiff) layer overlies two

successively softer layers (i.e. su3 < su2 < su1), it is likely that su2e/su2 < 1, but further

research should be carried out to validate Equation 6.7.

6.3.4 Bearing Capacity in 2nd Layer

As shown in Figure 6.7, the penetration resistance profile in the 2nd layer can be divided

into two parts, including post-peak penetration resistance before squeezing [Stage (2)],

and penetration resistance dominated by squeezing [Stage (3)]. The former part of the

profile can be obtained by connecting Points 1 and 2, while the latter part can be

represented by the straight line connecting Points 2 and 3. The depth of Point 1 can be

predicted using Equation 6.6, and Point 3 rests at the 2nd-3rd layer interface. Therefore,

an iterative approach is suggested here to predict the depth of Point 2.

The base of the stiff soil plug actually acts like a footing base and forces the 2nd layer

soft clay to squeeze out (see Figures 6.3b and 6.3c). Therefore, it is assumed that the

squeezing response is triggered once the distance from the base of the stiff soil plug to

the 2nd-3rd layer interface is within the conventional limiting squeezing depth for


6-10

spudcan penetration in clays [a range of hsq = 0.17~0.2D observed in the centrifuge tests

by Hossain et al. (2011) and Hossain (2014)]. As such, the value of hsq = Hplug + 0.18D

is adopted, assuming a consistent limiting squeezing depth of 0.18D between clays.

Consequently, the depth of Point 2, dsq, can be calculated as

sq 1 2 sq 1 2 plug 1d t t h t t H 0.18D t (6.8)

As Hplug is also a function of penetration depth (Equation 6.4), an iterative approach is

required to calculate the value of dsq.

It is assumed that the punching shear mechanism still dominates the bearing response

when spudcan rests at Point 2 (i.e. just before triggering the squeezing response). As

such, once dsq is obtained, the corresponding bearing capacity can be estimated using

Equation 6.2, with su2 = su2e. Although Equation 6.7 is calibrated to best fit the peak

resistance in the 1st layer, the value of su2e used for the calculation of the bearing

capacity at Point 2 can also be estimated using the same equation. This is justified

considering that the influence of the 3rd (stiff) layer on the bearing capacity at Point 2,

which is closer to the 3rd layer, is more significant than that at Point 1. Hence, Equation

6.7 gives a conservative prediction for the value of su2e at Point 2.

6.3.5 Bearing Capacity in 3rd Layer

During spudcan penetration towards the 2nd-3rd layer interface, the soils between the

spudcan base and the stiff 3rd layer are mostly squeezed out, leaving the bottom profile

of the spudcan geometry wrapped by a plug consisting of thin layers of soils from the 1st

and 2nd layers (see Figure 6.3d). Therefore, it is difficult to quantify the frictional

resistance around the plug periphery. As such, instead of using Equation 6.2 to estimate

the bearing pressure at the 2nd-3rd layer interface (i.e. Point 3), a design formula is

proposed for the ratio, , between the computed or measured bearing capacity at Point 3

and that estimated using Equation 6.2 but without considering any soil plug:

0.5 1.50.25 0.5

u3 u31 2

u1

s st t0.7 0.3 1

s D D D

(6.9)

The relationship between Equation 6.9 and computed and measured data is plotted in

Figure 6.11. The gross penetration resistance at Point 3 then can be calculated as


6-11

v u3 0

d dq 6.05 1 s p

0.22D 3.65D

for d = t1 + t2 (6.10)

A fully localised failure mechanism is assumed for spudcan penetrating in the 3rd layer.

As such, the bearing pressure profile is predicted according to

1 u1 u3

v cd u3

0.4t Min s ,sq N s

D

(6.11)

where the deep bearing capacity factor Ncd considering a lower bound of soil plug

thickness is calculated as

1cd

d 0.1tN Min 10 1 0.065 ,11.3

D

(6.12)

The small amount of soil trapped underneath the spudcan can be neglected for

simplicity (i.e. t1 = 0 in Equations 6.11 and 6.12).


The proposed design approach for estimating spudcan penetration resistance in uniform

stiff-soft-stiff clay profile can be taken as a ‘top-down’ approach. The bearing capacities

are predicted at the seabed (d = 0), at punch-through (d = dp, Point 1), at the start of

squeezing (d = dsq, Point 2), and at the 2nd-3rd layer interface (d = t1 + t2, Point 3),

followed by the prediction of the bearing capacity profile in the bottom layer. A

summarised design procedure is outlined below:

1. Determine representative values of the soil properties, layer thicknesses and

spudcan geometries su1, su2, su3, , St, t1, t2, D and Vsp;

2. Calculate the constants used in the design formulas, including , f1, and su2e

using Equations 5.4, 6.5 and 6.7, respectively;

3. Estimate the gross penetration resistance, qv, at the seabed using Equation 6.2

with d = 0, Hplug,1 = t1, Hplug,2 = Hplug,3 = 0, and sud0 = su2;

4. Evaluate the depth of Point 1 (peak resistance), dp, using Equation 6.6, and then

estimate the gross penetration resistance using Equation 6.2 in combination with

Equations 6.3 and 6.4, with su2 = su2e;


6-12

5. Obtain the depth of Point 2, dsq, from the iterative calculation between Equations

6.4 and 6.8, and then predict the corresponding gross penetration resistance

using Equation 6.2 in combination with Equations 6.3 and 6.4, with su2 = su2e;

6. Estimate the gross penetration resistance at the 2nd-3rd layer interface using

Equations 6.9 and 6.10;

7. Plot the penetration resistance profile in the 3rd layer using a combination of

Equations 6.11 and 6.12;

8. Estimate the limiting cavity depth, Hcav, using Equation 6.1 and update the gross

penetration resistances to total penetration resistances using Equation 5.2.

If a complete penetration resistance profile is required, straight lines can be used to

connect the bearing capacities at different depths.


A CPT-based design approach is developed in this section for spudcan penetration in

uniform stiff-soft-stiff clay. To be consistent with practice, the correlations are

established between the net penetration resistances of spudcan (qnet,sp) and cone (qnet,c)

through a penetration resistance ratio Rsp-c = qnet,sp/qnet,c. The net penetration resistances

are calculated from the corresponding total penetration resistances qu,sp and qu,c

according to Equation 4.8. Again, a constant cone factor Nkt is used throughout the soil

profile, and is calculated according to Equation 3.7.

6.4.1 Simplified Penetration Resistance Profiles

The simplified penetration resistance profile of spudcan used for the direct correlations

is the same as that for the mechanism-based approach, as shown in Figure 6.7. The

corresponding profile of net cone tip resistance is also included, which is simplified by

neglecting the transitional zones during cone penetration near the layer interface. The

justification for this practice has been presented in Chapters 2, 4 and 5.

According to routine CPT tests, a simplified cone penetration resistance profile can be

derived, which shows useful design parameters such as net cone tip resistance in each

layer, qnet,c1, qnet,c2 and qnet,c3, and layer thicknesses, t1 and t2. With these parameters and

the Nkt factor calculated from Equation 3.7, the design formula Equation 6.1 for


6-13

estimating the limiting cavity depth can be transformed as a function of cone resistance

in each layer and cone factor according to

0.281

net,c1 net,c3cav 1 2

kt net,c1

q qH t t0.58 1

D N D q D D

(6.13)

In the following subsections, design formulas and design procedure of the CPT-based

design approach are introduced. Some design formulas are transformed from the

mechanism-based design approach, but expressed as a function of cone resistances and

cone factor. The others are proposed for the penetration resistance ratio Rsp-c at critical

depths of the simplified spudcan penetration resistance profile.


For the simplified spudcan penetration resistance profile of the 1st layer, penetration

resistance ratios are required at the seabed and at Point 1. As such, Equation 6.2 is

transformed to provide a conservative prediction for spudcan resting at the seabed, as

net,sp net,c21sp c cr

net,c1 kt net,c1 kt

q q4t 6.05R N

q N D q N

for d = 0 (6.14)

where Ncr should be calculated using Equation 6.3 with dd = t1.

For the peak resistance, the normalised depth dp/D can be transformed from Equation

6.6 and expressed as a function of cone resistances and cone factor as

1.70.5 10.5 1

p net,c2 net,c3 net,c11 2 1

net,c1 net,c1 kt

d q q qt t t0.1 0.05

D q q D D N D D

(6.15)

To obtain the penetration resistance ratio at Point 1, all the values of qnet,sp at Point 1

from the numerical analyses divided by the corresponding value of qnet,c1 are plotted in

Figure 6.12. It is found that the value of Rsp-c at Point 1 can be estimated by

net,sp 2.8x

sp c

net,c1 kt

0.5 0.25

net,c2 1 2

net,c1

q 12.7R 0.67 0.6e

q N

q t twhere x =

q D D

for d = dp (6.16)


6-14

The first bracketed term in Equation 6.16 is the design expression proposed for a cone

factor of Nkt = 12.7 (i.e. rigidity index Ir = 67). Since the bearing capacity factor of cone

increases with increasing rigidity index, while that of spudcan is hardly affected, it is of

interest to investigate the effect of Ir on the value of Rsp-c. As such, the values of Rsp-c

from numerical analyses and Equation 6.16 are plotted in Figure 6.12 for different

rigidity indices. It can be seen that the penetration resistance ratio decreases as Ir (or Nkt)

increases. For a typical range of Ir = 67~500, Rsp-c ranges between 0.2 and 0.65

For spudcan penetration in single layer clay under undrained conditions, InSafeJIP

(2011) suggests a range of Rsp-c between 0.48 and 0.67. Interestingly, for the cone

factors explored in this study, the upper bound of Rsp-c predicted by Equation 6.16 for

each value of Nkt varies within a similar range between 0.46 and 0.67. This is consistent

with the fact that the penetration resistance of spudcan in a stiff clay layer overlying soft

clay is limited by that of a spudcan penetrating in the same stiff clay layer with

(nominally) infinite depth.

6.4.3 Bearing Capacity in 2nd Layer

For the new mechanism-based design approach, the depth of Point 2, dsq, is determined

through an iterative calculation between Equations 6.4 and 6.8. The same procedure is

adopted for the CPT-based design approach, but Equation 6.5 for the coefficient f1 is

transformed and expressed as a function of net cone resistances and layer thicknesses as

0.151 1

net,c2 net,c3 1 21

net,c1 net,c1

q q t tf 0.5

q q D D

(6.17)

Once the depth of Point 2 is determined, the corresponding penetration resistance ratio

Rsp-c = qnet,sp/qnet,c2 is estimated using

net,sp 1.15

sp c

net,c2 kt

1.5 0.5 0.5

net,c2 1 2

net,c1

q 12.7R 0.67 0.05x

q N

q t twhere x =

q D D

for d = dsq (6.18)

The comparison between the estimation from Equation 6.18 and numerical data is

presented in Figure 6.13. For the typical range of soil parameters and layer geometries


6-15

considered in the current research, the resulted values of Rsp-c at Point 2 lie in the range

of 0.47~1.34.

Similarly, as the cone factor Nkt decreases from 18.5 to 12.7, Equation 6.18 estimates a

lower bound of Rsp-c at Point 2 ranging between 0.46 and 0.67, which is close to the

range given by InSafeJIP (2011) for single layer clay. This is consistent with the fact

that the penetration resistance of a spudcan in clay due to squeezing is always higher

than a spudcan in single layer clay of the same strength but without the squeezing effect.

6.4.4 Bearing Capacity in 3rd Layer

The net spudcan penetration resistance at the 2nd-3rd layer interface (Point 3) is found to

be a fraction of the net cone resistance qnet,c3 in the 3rd layer. The fraction varies as a

function of net cone resistance ratios and thickness ratios, which is calculated as

net,sp

sp c

net,c3 kt

0.5 1 0.25 0.5

net,c2 net,c3 1 2

net,c1 net,c2

q 12.7R 0.45 0.12x

q N

q q t twhere x =

q q D D

for d = t1 + t2 (6.19)

The accuracy of Equation 6.19 is demonstrated in Figure 6.14. It is seen that the value

of Rsp-c at the 2nd-3rd layer interface ranges between 0.35 and 0.68 for the considered soil

parameters and rigidity indices.

For spudcan penetration resistance in the 3rd layer, a single layer penetration response is

assumed with a fully localised soil flow mechanism. Additionally, the small amount of

soil trapped at the spudcan base can be neglected for simplicity. As such, the penetration

resistance ratio for spudcan in the 3rd layer can be expressed as Rsp-c = Ncd/Nkt, where

Ncd is the deep bearing capacity factor reported by Hossain & Randolph (2009) and is

calculated using Equation 5.15b.


Similar to the design procedure for the mechanism-based design approach, the CPT-

based design approach also predicts the penetration resistance profile from the top to the

bottom, beginning with the prediction of the co-ordinates of the key points in the first


6-16

two layers, followed by evaluating the bearing capacities in the bottom layer. Detailed

steps for using the proposed approach are listed as follows:

1. Simplify the continuous net cone tip resistance profile and pick design

parameters, such as qnet,c1, qnet,c2, qnet,c3, , St, t1, t2, D and Vsp;

2. Calculate constants and f1 using Equations 5.4 and 6.17, respectively;

3. Estimate the penetration resistance ratio at the seabed using Equation 6.14 in

combination with Equation 6.3;

4. Evaluate the depth of Point 1 (peak penetration resistance), dp, using Equation

6.15, and then estimate the corresponding resistance ratio, Rsp-c, using Equation

6.16 or Figure 6.12;

5. Obtain the depth of Point 2, dsq, from iterative calculation between Equations 6.4

and 6.8, and then predict the corresponding penetration resistance ratio, Rsp-c,

using Equation 6.18 or Figure 6.13;

6. Estimate the penetration resistance ratio at the 2nd-3rd layer interface using

Equation 6.19 or Figure 6.14;

7. Evaluate the penetration resistance ratios at different depths in the 3rd layer

according to Rsp-c = Ncd/Nkt;

8. Plot the spudcan penetration resistance profile using Equations 4.8 and 4.10,


APPLICATION

6.5.1 Centrifuge Test

The proposed design approaches are used to predict the centrifuge test used for

validation. The undrained shear strengths and layer geometries are listed in Group I,

Table 6.1. For the CPT-based design approach, the net cone penetration resistances are

back-calculated from the undrained shear strengths. As justified by Watson et al. (2000),

a cone factor of Nkt = 10.5 can be adopted for the centrifuge test. Therefore, the

measured undrained shear strength profile (su1 = 21 kPa, su2 = 8.5 kPa, su3 = 35.5 kPa)

implies that the net cone penetration resistances are qnet,c1 = 220.5 kPa, qnet,c2 = 89.25

kPa and qnet,c3 = 372.75 kPa.


6-17

The predictions from the proposed design approaches and the ISO bottom-up approach

are included in Figure 6.2. Overall, the penetration resistance profile obtained from the

centrifuge test is reasonably estimated by the proposed design approaches but

underestimated by the bottom-up approach.

For spudcan penetration in the 1st layer stiff clay, all design approaches indicate a

monotonic increase of bearing capacity – there is no potential for punch-through, which

is verified by the centrifuge test data. The proposed design approaches give a

conservative prediction at the seabed as anticipated and predict the maximum bearing

capacity at the 1st-2nd layer interface accurately. By contrast, the bearing capacity profile

from the ISO bottom-up approach is overall 20~25% lower than the centrifuge test data.

A minor punch-through incident in the 2nd (soft) layer occurred in the centrifuge test,

starting at a depth of d/D = ~0.47 with a punch-through distance of hP-T = ~0.2D. This

incident is also indicated by the mechanism-based approach and the bottom-up

approach although in the form of a plateau of penetration resistance (i.e. rapid leg run).

The penetration resistance profile from the CPT-based design approach shows a clear

indication of the minor punch-through failure. The punch-through distances estimated

by the mechanism-based design approach, CPT-based design approach and bottom-up

approach are hP-T = 0.17D, 0.19D and 0.28D, respectively.

The depth of triggering squeezing, dsq, where the bearing pressure starts rising sharply is

about 0.6D in the centrifuge test, with a limiting squeezing depth of hsq = ~0.32D. The

value of dsq = ~0.76D is overestimated (or hsq = ~0.16D is underestimated) by the ISO

bottom-up approach. By contrast, an improved prediction is given by the proposed

iterative approach with dsq = 0.58D or hsq = 0.34D.

For the penetration resistances at Point 3 and onwards, the predicted profiles by the new

design approaches and the ISO bottom-up approach are lower than the centrifuge test

data, with an error of 5~8%.

6.5.2 Case History

Figure 6.15 shows the measured load-penetration curves for a case history in Gulf of

Thailand from the database of InSafeJIP (2011). The jack-up rig was supported by

spudcans of D = 11.5 m, which rested at depths of d/D = 0.5~0.61 under full preload of


6-18

41 MN (= ~394.8 kPa). The undrained shear strength profile can be idealised as su1 = 50

kPa (lower bound) and 65 kPa (upper bound), su2 = 35 kPa, su3 = 80 kPa, t1/D = 0.78

and t2/D = 0.43, with St = 3.33. Based on these parameters, the penetration resistance

profiles estimated using the new mechanism-based design approach and ISO bottom-up

approach are included in Figure 6.15 for comparison.

Using su1 = 50 kPa, the bottom-up approach provides a lower bound estimate of the

penetration resistance profile, which agrees well with the measured profiles for d/D =

0.14~0.42. However, the estimated bearing pressure at the depths of final embedment is

~20% lower than the measured response, predicting a punch-through failure and a final

embedment depth of d/D = 1.1. By contrast, the mechanism-based approach provides a

reasonable prediction for the load-penetration response, indicating a peak resistance at

dp = 0.59D, which is close to the final embedment depths of Port and Starboard legs.

The corresponding estimated peak resistance is 3.6% lower than the actual full preload.

For su1 = 65 kPa, the mechanism-based design approach provides an upper bound

estimate of the penetration resistance profile. The bottom-up approach predicts the peak

resistance at the seabed surface, which is slightly lower than the intended preload.

Nevertheless, underestimated bearing pressure at final embedment depths is still

provided by the bottom-up approach, while the measured penetration resistance profiles

are bounded by those given by the new mechanism-based design approach.

CONCLUDING REMARKS

This chapter has reported a series of LDFE analyses simulating spudcan penetration in

uniform stiff-soft-stiff clay deposit. Based on the results, new mechanism-based and

CPT-based design approaches have been developed. Both approaches estimate the

penetration resistance from the top to the bottom layers of the soil profile. Using the

new design approaches, the bearing capacities can be evaluated at the seabed, at the

depth of maximum bearing capacity in the 1st layer, at the depth of triggering squeezing

and at the 2nd-3rd layer interface successively, followed by the prediction of the

penetration resistance profile in the bottom layer.

It has been found that for spudcan penetration in three-layer stiff-soft-stiff clay, the

penetration resistance in the 1st layer stiff clay is underestimated and the depth of


6-19

triggering squeezing in the 2nd (soft) layer is overestimated by the design methods

recommended by the ISO standard 19905-1. This is because the soil plug pushed down

from the 1st (stiff) layer into the underlying layer and the effect of the 3rd (stiff) layer are

neglected by the ISO bottom-up approach in the calculation of bearing capacities in the

1st and 2nd layers. These effects are considered in the new mechanism-based design

approach, with design formulas given for the variation of the soil plug thickness and the

equivalent undrained shear strength of the 2nd layer. For the depth of triggering

squeezing in the 2nd layer, an iterative approach was proposed to incorporate the effect

of the soil plug trapped by the spudcan, which leads to earlier squeezing of the 2nd layer

soft clay.

The proposed approaches were used to predict the reported data from a centrifuge test

and a case history. The comparison between the measured penetration resistance

profiles and those estimated using the ISO bottom-up approach and the proposed design

approaches demonstrated the advantages of using the new ones. Additionally, the

summarised ranges of penetration resistance ratios at critical depths, which correspond

to a typical range of soil parameters and cone factors of practical interest, can be used to

provide a first order estimation for spudcan penetration resistance in stiff-soft-stiff clay.


6-20

REFERENCE












Houlsby, G. T. & Martin, C. T. (2003). Undrained bearing capacity factors for conical











London, 1, 180-189.



Polar Engineering Conference, ISOPE00, Seattle, 2, 485-493.

Zheng, J., Hossain, M. S. & Wang, D. (2014). Numerical modeling of spudcan deep

penetration in three-layer clays. International Journal of Geomechanics, ASCE,

10.1061/(ASCE)GM.1943-5622.0000439, 04014089.

Zheng, J., Hossain, M. S. & Wang, D. (2015). Estimating spudcan penetration


Engineering, ASCE, Submitted June 2015.


6-21

TABLES


Group

1st layer

stiff clay

2nd layer

soft clay

3rd layer

stiff clay St Note

su1: kPa t1/D su2: kPa t2/D su3: kPa

I 21 0.42 8.5 0.5 35.5 2.8 Centrifuge

test

II 50~80 0.25~0.75 40 0.25~0.75 75~120 3.3 Parametric

study


6-22

FIGURES

hsq

qnet

ddp

qpeak

hP

-Td

sq

d

Hca

v

z

Sp

ud

ca

n

Ca

vity

K-l

att

ice

le

g

D

Stiff

la

ye

r

Soft

la

ye

r

Stiff

la

ye

r

t 1

t 2

su

su1

su2

su3

Fig

ure

6.1

Sch

em

ati

c d

iagra

m o

f sp

ud

can

fou

nd

ati

on

em

bed

ded

in

un

iform

sti

ff-s

oft

-sti

ff c

lay

sh

ow

ing i

dea

lise

d o

pen

cavit

y a

nd

corr

esp

on

din

g p

enet

rati

on

res

ista

nce

pro

file


6-23

Figure 6.2 Comparison of penetration resistance profiles from centrifuge test,

numerical analysis and design approaches (su1 = 21 kPa, su2 = 8.5 kPa, su3 = 35.5

kPa, t1/D = 0.42, t2/D = 0.5, rem = 1/St = 0.36; Group I, Table 6.1)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 50 100 150 200 250 300 350 400N

orm

alised

pen

etr

ati

on

dep

th,

d/D


Bottom-up approach

Centrifuge test


CPT-based approach

LDFE


6-24

6.3(a) d/D = 0.12

6.3(b) d/D = 0.45

1st layer

2nd layer

3rd layer

1st layer

2nd layer

3rd layer


6-25

6.3(c) d/D = 0.69

6.3(d) d/D = 1.16

Figure 6.3 Key features of soil failure mechanisms during spudcan penetration in

stiff-soft-stiff clay (su1 = 21 kPa, su2 = 8.5 kPa, su3 = 35.5 kPa, t1/D = 0.42, t2/D = 0.5,

rem = 1/St = 0.36; Group I, Table 6.1)

1st layer

2nd layer

3rd layer

1st layer

2nd layer

3rd layer

3rd layer

2nd layer

1st layer

Layered soil plug


6-26

6.4(a) t1/D = 0.25, t2/D = 0.75

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12

No

rmalised

pen

etr

ati

on

dep

th,

d/D


Stiff

Soft

Stiff

su3/su2 = 3;su2/su1 = 0.8

and 0.5

su3/su2 = 1.88;su2/su1 = 0.8, 0.5

and 0.33


6-27

6.4(b) t1/D = 0.5, t2/D = 0.5

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12 14N

orm

ali

se

d p

en

etr

ati

on

de

pth

, d

/D


su3/su2 = 3;su2/su1 = 0.8

and 0.5

Stiff

Soft

Stiff

su3/su2 = 1.88;su2/su1 = 0.8, 0.5 and 0.33


6-28

6.4(c) t1/D = 0.75, t2/D = 0.25

Figure 6.4 Effect of 1st and 3rd layer strengths (su1 and su3) or strength ratios (su2/su1

and su3/su2) on bearing response

0

0.5

1

1.5

2

2.5

3

0 3 6 9 12 15

No

rma

lis

ed

pe

ne

tra

tio

n d

ep

th,

d/D


Stiff

Soft

Stiffsu3/su2 = 3;su2/su1 = 0.8

and 0.5

su3/su2 = 1.88;su2/su1 = 0.8, 0.5 and 0.33


6-29

6.5(a) su2/su1 = 0.33

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12 14 16N

orm

alise

d p

en

etr

ati

on

de

pth

, d

/D


t1/D = 0.25, 0.5 and 0.75

Stiff

Stiff

Soft


6-30

6.5(b) su2/su1 = 0.5

Figure 6.5 Effect of thickness ratios (t1/D and t2/D) on bearing response

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12 14

No

rmalised

pen

etr

ati

on

dep

th,

d/D


Stiff

Soft

Stiff

t1/D = 0.25, 0.5 and 0.75


6-31

6.6(a) Comparison of limiting cavity depths after spudcan installation in stiff-over-

soft and stiff-soft-stiff clays

0

0.2

0.4

0.6

0.8

1

1.2

0 0.3 0.6 0.9 1.2 1.5N

orm

alised

lim

itin

g c

avit

y d

ep

th,

Hcav/D

Numerical analysis: Stiff-over-soft

Centrifuge test: Stiff-over-soft

Numerical analysis: Stiff-soft-stiff

0.5

u1 1 1

u2s

s t k D1

D D s


6-32

6.6(b) Design chart

Figure 6.6 Limiting cavity depth after spudcan installation in uniform stiff-soft-

stiff clay

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1 1.5 2 2.5

No

rmali

sed

lim

itin

g c

avit

y d

ep

th,

Hcav/D

Numerical analysis

Centrifuge test

1

u1 u3 1 2

u1

s s t t1

D s D D

0.281

cav u1 u3 1 2

u1

H s s t t0.58 1

D D s D D


6-33

Figure 6.7 Simplified penetration resistance profiles for spudcan and cone in

uniform stiff-soft-stiff clay (su1 = 120 kPa, su2 = 40 kPa, su3 = 75 kPa, t1/D = 0.25, t2/D

= 0.75, rem = 1/St = 0.3; Group II, Table 6.1)

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0 300 600 900 1200 1500 1800N

orm

ali

se

d p

en

etr

ati

on

de

pth

, d

/D

Total bearing pressure of spudcan, qu,sp orNet bearing pressure of cone, qnet,c: kPa

LDFE

2

3

Bottom-upapproach

Point 1

Simplified profilefor spudcan

Bottom-upapproach with soil plug

Simplified profilefor cone

(2)

(3)

Stage (4)

(1)


6-34

Figure 6.8 Design chart for coefficient f1 for spudcan penetration in uniform stiff-

soft-stiff clay

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 2 4 6 8 10 12

Co

eff

icie

nt,

f1

Numerical analysis

Centrifuge test

1 1

u2 u3 1 2

u1 u1

s s t t

s s D D

0.151 1

u2 u3 1 21

u1 u1

s s t tf 0.5

s s D D


6-35

Figure 6.9 Design chart for peak resistance depth (Point 1) in the 1st layer for

spudcan penetration in uniform stiff-soft-stiff clay

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 3 6 9 12 15

No

rma

lis

ed

pe

ak

re

sis

tan

ce

de

pth

, d

p/D

Numerical analysis

Centrifuge test

dp/D = 0.25

dp/D = 0.5

dp/D = 0.75

dp/D = 0.42

0.5 10.5 1

u2 u3 u11 2

u1 u1

s s st t

s s D D D

1.70.5 10.5 1

p u2 u3 u11 2 1

u1 u1

d s s st t t0.1 0.05

D s s D D D D


6-36

Figure 6.10 Design chart for equivalent 2nd layer undrained shear strength su2e for

spudcan penetration in stiff-soft-stiff clay

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12

No

rmalised

eq

uiv

ale

nt

str

en

gth

, s

u2e/s

u2

Numerical analysis

Centrifuge test

1 0.5 0.25 0.5

u2 u3 1 2

u1 u2

s s t t

s s D D

1 0.5 0.25 0.5

u2e u2 u3 1 2

u2 u1 u2

s s s t t0.8 0.085 1

s s s D D


6-37

Figure 6.11 Design chart for the ratio at Point 3 for spudcan penetration in stiff-

soft-stiff clay

0

0.3

0.6

0.9

1.2

1.5

0 0.3 0.6 0.9 1.2 1.5

Desig

n p

ara

mete

r fo

r b

eari

ng

cap

acit

y a

t

Po

int

3,

Numerical analysis

Centrifuge test

0.5 1.50.25 0.5

u3 u31 2

u1

s st t1

s D D D

0.5 1.50.25 0.5

u3 u31 2

u1

s st t0.7 0.3 1

s D D D


6-38

Figure 6.12 Design chart for penetration resistance ratio Rsp-c of Point 1 at d = dp

for spudcan penetration in stiff-soft-stiff clay

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8 1 1.2

Pen

etr

ati

on

resis

tan

ce r

ati

o,

Rsp

-c

Equation 6.16:Nkt = 12.7, 15.0, 17.0 and 18.5

Ir = 670

Ir = 1500

Ir = 3000

Ir = 5000

0.5 0.25

net,c2 1 2

net,c1

q t t

q D D


6-39

Figure 6.13 Design chart for penetration resistance ratio Rsp-c of Point 2 at d = dsq

for spudcan penetration in stiff-soft-stiff clay

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 2 4 6 8 10

Pe

ne

tra

tio

n r

es

ista

nc

e r

ati

o,

Rsp

-c

Ir = 670

Ir = 1500

Ir = 3000

Ir = 5000

Equation 6.18:Nkt = 12.7, 15.0, 17.0 and 18.5

1.5 0.5 0.5

net,c2 1 2

net,c1

q t t

q D D


6-40

Figure 6.14 Design chart for penetration resistance ratio Rsp-c of Point 3 at d = t1 +

t2 for spudcan penetration in stiff-soft-stiff clay

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.4 0.8 1.2 1.6 2 2.4 2.8

Pe

ne

tra

tio

n r

es

ista

nc

e r

ati

o,

Rsp

-c

Equation 6.19:Nkt = 12.7, 15.0, 17.0 and 18.5

Ir = 670

Ir = 1500

Ir = 3000

Ir = 5000

0.5 1 0.25 0.5

net,c2 net,c2 1 2

net,c1 net,c3

q q t t

q q D D


6-41

Figure 6.15 Comparison of predicted and measured load-penetration responses for

a case history (su1 = 50 kPa or 65 kPa, su2 = 35 kPa, su3 = 80 kPa, t1/D = 0.78, t2/D =

0.43, rem = 1/St = 0.3).

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 150 300 450 600 750 900

No

rma

lis

ed

pe

ne

tra

tio

n d

ep

th,

d/D


Port

StarboardBottom-upapproach:su1 = 50 kPa

Mechanism-basedapproach:

su1 = 50 kPa

Bottom-upapproach:su1 = 65 kPa

Bow

Mechanism-basedapproach:

su1 = 65 kPa

Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer

7-1

CHAPTER 7. SPUDCAN IN MULTI-LAYER SOILS

WITH AN INTERBEDDED SAND LAYER

INTRODUCTION

Stratified soil deposits with the potential for punch-through failure can be categorised

into two groups: (i) stiff-over-soft clay and (ii) sand-over-clay. Spudcan penetration in

soil profiles comprising stiff-over-soft clay layering system has been investigated in

Chapters 4, 5 and 6, with new mechanism-based and CPT-based design approaches

proposed, while that in multi-layer sediments consisting of sand-over-clay layering

system is explored in this chapter.

For spudcan penetration in two-layer sand-over-clay deposits, new mechanism-based

design approaches (Lee et al., 2013a, 2013b; Hu et al., 2014a, 2014b, 2015) have

recently been proposed for estimating the peak bearing capacity in the sand layer and

deep bearing capacity in the clay layer. However, their applicability in multi-layer soils

with an interbedded sand-over-clay layering system is yet to be examined. This chapter

focuses on spudcan penetration in clay-sand-clay deposits through large deformation

finite element (LDFE) analyses, together with some centrifuge test data reported by

Hossain (2014). Additional analyses were carried out adding a stiff bottom layer (i.e. in

soft clay-sand-soft clay-stiff clay deposit) in order to quantify the corresponding effect

on the magnitude of peak penetration resistance in the 2nd layer sand and the severity of

punch-through.

DESIGN METHODS

For assessing spudcan penetration resistance in a sand-over-clay layering system, four

design methods, as summarised in Table 7.1, are compared, including (i) load spread

method, (ii) punching shear method, (iii) Lee et al. method (Lee et al., 2013a, 2013b),

and (iv) Hu et al. method (Hu et al., 2014a, 2014b, 2015). The first two methods are

recommended in the current design guidelines – ISO standard 19905-1 (ISO, 2012),

while the other two were proposed recently.


7-2

For the load spread and punching shear methods (ISO methods; ISO, 2012), design

formulas for the penetration resistance in the sand layer (Equations 1.3 and 1.4) and in

the underlying clay layer (Equation 1.1) have been introduced in Chapter 1. Therefore,

only the design formulas for the Lee et al. and Hu et al. methods are introduced below.

Based on the observed soil failure mechanisms during continuous penetration of

spudcan foundations in two-layer sand-over-clay deposits (Teh et al., 2008), Lee et al.

(2013b) extended the punching shear model assuming inclined shear planes and the

peak resistance at the surface of the sand layer (Lee et al. method). Instead of the

punching shear coefficient Ks, a distribution factor DF is introduced, which estimates the

pressure on the shear plane from the mean vertical effective stress within the sand plug.

The peak resistance qpeak is calculated as

*

*

E

speak c,int u,int 0

E

*s s s

*

2Hq N s q 1 tan

D

D 2H 2H1 1 E tan 1 tan

D D2 E 1 tan

(Lee et al. method) (7.1)

where Nc,int is the bearing capacity factor for a flat-based circular footing on clay, which

is calculated following Houlsby & Martin (2003); su,int is the undrained shear strength of

the clay layer at the sand-clay layer interface; q0 is the surcharge on the surface of the

sand layer; Hs is the thickness of the sand layer; D is the diameter of the spudcan at

largest cross-section; s is the effective unit weight of the sand; and E* is expressed as

**

F

tanE 2 1 D 1

tan

(7.2)

with

* sin costan

1 sin sin

(7.3)

The strength parameters – effective friction angle and dilation angle are

estimated following the strength-dilatancy relationships modified from Bolton (1986).

This is an empirical method developed through calibration using the centrifuge test data

on dense sand-over-clay, leading to a linear expression for DF as


7-3

sF

HD 1.333 0.889

D (Lee et al. method) for Hs/D < 0.9 (7.4)

Hu et al. (2014a) performed centrifuge tests for spudcan penetration in medium dense

sand-over-clay, and improved Lee et al. method assuming the peak resistance at a depth

of 0.12Hs below the sand surface. Equation 7.1 was modified as (Hu et al. method)

*

*

E

speak c,int u,int 0 s s

E

*s s s

*

1.76Hq N s q 0.12 H 1 tan

D

D 1.76H 1.76H1 1 E tan 1 tan

D D2 E 1 tan

(Hu et al. method) (7.5)

Covering a wider range of centrifuge test data for spudcan penetration in surface sand

layer overlying clay, Hu et al. (2014a) proposed a nonlinear expression for the

distribution factor DF as

0.576

sF

HD 0.642

D

(Hu et al. method) for 0.16 ≤ Hs/D ≤ 1.0 (7.6)

To apply Lee et al. and Hu et al. methods for an interbedded sand-over-clay layering

system, the term q0 is calculated as equal to the overburden stress of the overlying soil.

Once qpeak is calculated, qu is then estimated by taking away the submerged weight of

the soils on top of the spudcan, i.e. Max(d – Hcav, 0), with Hcav calculated using the

iterative approach (Hossain & Randolph, 2009) suggested by ISO (2012).

The penetration resistance profile in the underlying clay layer is calculated as a function

of the normalised sand layer thickness Hs/D according to (Lee et al., 2013a; Hu et al.,

2015)

su u0

Hq 14 9.5 s

D

(Lee et al. method) (7.7)

su u0 s c

Hq 11 10.5 s 0.9H

D

(Hu et al. method) (7.8)

where su0 is the undrained shear strength at the spudcan base level and c is the

effective unit weight of the underlying clay layer.


7-4

NUMERICAL ANALYSIS

This chapter has considered a circular spudcan penetrating into a clay-sand-clay deposit

with and without a 4th layer stiff clay, as illustrated schematically in Figure 7.1, where

the 2nd layer sand with effective unit weight 2 = s has a thickness of t2 = Hs and a

relative density ID. Non-uniform undrained shear strengths were considered for the 1st

and 3rd layers as su1 = su1s + k1z and su3 = su3s + k3(z – t1 – t2), respectively, with layer

thicknesses of t1 and t3 (if there was a 4th layer, otherwise infinite) and effective unit

weights of 1 and 3. The 4th (stiff) layer was uniform of undrained shear strength su4,

effective unit weight 4 and (nominally) infinite depth.

Parametric studies were performed simulating continuous penetration of spudcan from

the seabed, with the selected parameters summarised in Table 7.2. For convenience, the

effective unit weight of the clay layers was considered to be constant and was taken as

= 8 kN/m3, while that of the sand layer was selected as s = 10 and 11 kN/m3 for ID =

45 and 90%, respectively.

Only a quarter sector of the domain was involved accounting for the symmetry inherent,

as shown in Figure 7.2. A cuboid of dense mesh was created along the trajectory of the

spudcan, with a constant element size of 0.025D. Further details of the numerical

analysis, such as the set-up for the numerical model, constitutive model, and relevant

elastic and plastic parameters, can be found in Chapter 2.

NUMERICAL RESULTS AND DISCUSSION

The penetration resistance profiles from the simulations of centrifuge test and part of the

parametric study are presented and discussed in this section, with the corresponding

parameters assembled in Table 7.3. The profiles are presented in terms of total bearing

pressure qu as a function of the normalised penetration depth, d/D or (d – t1)/D.

7.4.1 Simulation of Centrifuge Tests

Numerical analyses were performed to validate the numerical model against four

centrifuge tests reported by Hossain (2014) for spudcan penetration in clay-silica sand-

clay deposit with (D = 12 m; Test FS9) or without (D = 6 m; Tests FS12, FS13 and

FS14) a 4th layer stiff clay. The corresponding soil parameters and layer geometries


7-5

adopted in the numerical simulations are listed in Group I, Table 7.3. For Test FS9, a

medium dense sand layer (ID = 44%, t2/D = Hs/D = 0.5, 2 = s = 9.8 kN/m3) was

sandwiched by two soft clay layers (su1 = su3 = 9 kPa, t1/D = 0.25, t3/D = 0.96, 1 = 7.1

kN/m3, 3 = 7.2 kN/m3), with a bottom layer stiff clay of su4 = 36 kPa and 4 = 8

kN/m3. Tests FS12, FS13 and FS14 were carried out for a dense sand layer (ID = 89%,

2 = s = 11 kN/m3) sandwiched by two non-uniform clay layers (su1 = su3 = 0.5 +

0.75z, t1/D = 0.62, 1 = 3 = 7.1 kN/m3), with t2/D = Hs/D = 0.25, 0.33 and 0.67,

respectively.

Figure 7.3a shows the measured and computed penetration resistance profiles for Test

FS9. For this interbedded medium dense sand layer, excellent agreement can be seen

between the results from the centrifuge model test and numerical analysis in terms of

key features of the penetration resistance profile: squeezing in the 1st layer, depth and

magnitude of the peak resistance in the 2nd layer and the punch-through distance. In the

3rd layer, both the measured and computed penetration resistance profiles start

increasing sharply at a depth of ~1D, with a limiting squeezing depth of hsq/D = ~0.71.

For Tests FS12, FS13 and FS14, the penetration resistance profiles from the centrifuge

model tests and numerical simulations are compared in Figure 7.3b. Overall, for this

interbedded dense sand layer, the computed profiles are lower than the measured ones in

terms of the peak resistance and post-peak rate of reduction in the sand layer, and

bearing capacity in the bottom clay layer. The most significant error is associated with

the thickest sand layer of t2/D = Hs/D = 0.75. The same observation was presented by

Hu et al. (2015) for spudcan penetration in two-layer sand-over-clay deposit. This may

be partly due to the underestimation of the strength parameters using Bolton’s (1986)

equations, compared with the database reported by Andersen & Schjetne (2013), and

partly due to the simplification in the used sand model (Figure 2.10).

7.4.2 Effect of 1st Layer Clay

To explore the effect of the 1st layer clay on the penetration resistance, the results of

various thickness ratios t1/D = 0.5, 1.0 and 1.5, with (t3/D = 1.0) and without (t3/D = )

the presence of a 4th (stiff) layer of su4 = 100 kPa (Group III, Table 7.3) are plotted in

Figure 7.4. The undrained shear strengths of the 1st and 3rd layers are su1 = 5 + 1z kPa

and su3 = 15 + 1(z – t1 – t2) kPa, respectively, sandwiching a sand layer of ID = 45% and


7-6

t2/D = Hs/D = 0.5. The penetration resistance profile from the analysis for spudcan

penetration in single layer clay with undrained shear strength = su1 (t1/D = ; Group II,

Table 7.3) is also included in the figure to identify the depth of triggering squeezing, dsq,

(or quantify the limiting squeezing depth hsq) in the 1st layer. Potential for punch-

through is indicated by all the profiles in Figure 7.4, showing higher qpeak for thicker 1st

layer (higher t1/D).

The limiting squeezing depth in the 1st layer increases slightly with increasing t1/D, with

a small range of hsq = 0.27~0.33D. However, t1/D has minimal or no effect on the

squeezing depth in the 3rd layer (in presence of the 4th layer). The depth is found,

regardless of t1/D, as hsq = ~0.67D, which is significantly higher compared to that in the

1st layer due to the effect of the soil plug trapped at the base of the advancing spudcan.

For clay-sand-clay deposits, the predicted penetration resistance profiles using the

design methods listed in Table 7.1 are also included (only for the 2nd and 3rd layer) in

Figure 7.4 for comparison. It is seen that overly conservative estimations are provided

by the load spread and punching shear methods. By contrast, taking q0 = the overburden

stress of the overlying clay layer in the Lee et al. and Hu et al. methods provides

satisfactory estimations for the peak resistance in the sand layer. The penetration

resistance profiles predicted using the Lee et al. and Hu et al. methods also agree

reasonably well with the computed profiles in terms of the deep penetration resistance

in the 3rd layer clay in absence of the 4th layer.

7.4.3 Effect of 2nd Layer Sand

Figure 7.5a compares the penetration resistance profiles for sand layer of relative

densities ID = 45 and 90% and thickness ratios t2/D = Hs/D = 0.25, 0.5 and 0.75 with the

1st layer clay of su1 = 5 + 1z kPa and t1/D = 0.5 (Group IV, Table 7.3). The undrained

shear strength of the 3rd layer su3 = 15 + 1(z – t1 – t2) kPa was kept unchanged, with

thickness ratios t3/D = 1.0 and and su4 = 100 kPa. The effects of relative density ID

and sand layer thickness Hs/D on the peak resistance in the sand layer and deep

penetration resistance in the underlying clay layer have already been investigated by a

number of researchers for two-layer sand-over-clay deposits (Teh et al., 2008, 2010;

Lee et al., 2013a, 2013b; Hu et al., 2014a, 2014b). For spudcan penetration in clay-

sand-clay deposit with and without a 4th (stiff) layer, Figure 7.5a shows similar trends


7-7

except the effect of the 4th layer on increasing the peak resistance for dense sand (with

all Hs/D) and for loose sand (with Hs/D 0.5).

The limiting squeezing depth in the 1st layer is hsq = 0.27D, regardless of ID and Hs/D.

With the presence of the 4th layer stiff clay, hsq in the 3rd layer increases with increasing

ID and Hs/D. For ID = 45% and t3/D = 1.0, hsq in the 3rd layer increases from 0.3D to

0.76D as Hs/D increases from 0.25 to 0.75; while for a consistent value of Hs/D = 0.75,

the values of hsq in the 3rd layer are 0.76D and 0.86D, respectively, for ID = 45 and 90%.

To compare the performance of the design methods in Table 7.1, the predicted

penetration resistance profiles for t2/D = Hs/D = 0.75, ID = 45 and 90% and t3/D = are

plotted in Figure 7.5b together with corresponding numerical results. For t3/D = 1.0, the

predictions from ISO methods are also included. In absence of the 4th layer, the peak

resistance along with the effect of ID, is well predicted by the Lee et al. and Hu et al.

methods, while the ISO methods provide overly conservative predictions. However, the

influence of the 4th layer on the peak resistance cannot be captured by any method.

7.4.4 Effect of 3rd Layer Clay

Thickness ratio t3/D

The penetration resistance profiles obtained from numerical analyses of Group V in

Table 7.3 are plotted in Figure 7.6 to investigate the effect of the 3rd layer thickness ratio

t3/D. The value of t3/D was varied from 0.25 to . The other parameters were kept

constant, including strength parameters [su1 = 5 + 1z kPa, ID = 45%, su3 = 15 + 1(z – t1 –

t2) kPa, su4 = 100 kPa] and thickness ratios (t1/D = t2/D = Hs/D = 0.5).

For t2/D = Hs/D = 0.5 and t3/D 0.75, the effect of the presence of the 4th (stiff) layer on

the peak resistance in the sand layer is trivial. The effect is becoming profound as the 3rd

layer is becoming thinner (e.g. t3/D ≤ 0.5), with qpeak being 6.7 and 41.1% higher for

t3/D = 0.5 and 0.25, respectively, compared with that for t3/D 0.75.

To explore the critical value of t3/D for this influence, the values of qpeak obtained from

analyses with a 4th (stiff) layer are normalised by the corresponding value from analysis

for t3/D = , leading to a factor, . The values of for different combinations of Hs/D

and ID are plotted in Figure 7.7 as a function of t3/Hs, which is best fitted by


7-8

3 s2.2t /H1 1.5e

(7.9)

According to Equation 7.9 and Figure 7.7, a considerable increase of qpeak is found for

t3/Hs < 1.5.

The penetration resistance profiles predicted for t3/D = using the design methods in

Table 7.1 are included in Figure 7.6. For the ISO methods, the predicted profiles for

t3/D = 0.25, 0.5 and 1.0 are also included for comparison. For t3/D 0.75, the estimated

peak resistances from the Lee et al. and Hu et al. methods are reasonable (about 9.5 and

4.2% higher than computed values). By contrast, the error between the computed and

estimated peak resistances increased to 24.2 (Lee et al. method) and 27.9% (Hu et al.

method) for t3/D = 0.25.

Again, ISO methods provide overly conservative estimate for full resistance profiles in

the 2nd and 3rd layers. Note, the predicted profiles from the ISO methods with and

without the 4th layer are very similar before squeezing. This is because the estimated

limiting squeezing depth hsq in the 3rd layer clay is always lower than the lowest

thickness ratio t3/D = 0.25 considered in this study, resulting in no update of the

undrained shear strength in the calculation of the 2nd-3rd sand-clay layering system.

Strength parameters su3s and k3

To explore the effect of the 3rd layer undrained shear strength, two series of numerical

analyses were performed for (i) su3s = 7.5, 15 and 30 kPa with k3 = 1 kPa/m; and (ii) k3

= 1, 2 and 3 kPa/m, with su3s = 15 kPa. The 3rd layer thickness ratio was varied as t3/D =

1.0, 1.5 and , with the other parameters kept constant as su1 = 5 + 1z kPa, ID = 45%, su3

= 15 + 1(z – t1 – t2) kPa, su4 = 100 kPa and t1/D = t2/D = Hs/D = 0.5 (Group VI, Table

7.3). Figure 7.8 shows the computed penetration resistance profiles. The penetration

resistance increases with increasing su3s or k3, with the effect of the former being more

profound. These are related to the increase of the strength ratio between clay and sand,

and hence the increase of end bearing capacity and frictional resistance of the sand plug.

For spudcan penetration in the 3rd layer, the limiting squeezing depths are hsq =

0.67~0.74D for t3/D = 1.0 and hsq = 0.5~0.61D for t3/D = 1.5, with lower values in the

ranges resulted from higher value of su3s or k3. This is caused by the soil plug carried

down by the advancing spudcan from the 1st and 2nd layers, which somewhat diminishes


7-9

with penetration depth and at a slightly higher rate for a stronger clay layer (i.e. higher

strength parameters su3s and k3).

SUGGESTED IMPROVEMENTS

7.5.1 Peak Resistance in Sand Layer

As discussed previously, for clay-sand-clay deposits, the peak resistance in the 2nd layer

sand can be estimated by Hu et al. and Lee et al. methods with reasonable accuracy.

However, in presence of the stiff 4th layer with t3/Hs < 1.5, all design methods provide a

conservative estimation. This can be improved in two ways: (i) multiply the estimated

qpeak from Lee et al. or Hu et al. method by (Equation 7.9); or (ii) use an equivalent

shear strength sues at the sand-clay layer interface that incorporates the influence of the

4th (stiff) layer. Design formulas for sues are developed in this section.

The results from numerical analyses and a centrifuge test with t3/Hs ≤ 2.0 were used to

calibrate the values of sues for each design method, with the normalised values of sues/su3s

plotted in Figure 7.9. For ISO methods (Figure 7.9a), design formulas are derived from

curve fitting to provide a relatively conservative estimation of sues and expressed as

1

ues 3 3D

u3s s u3s

s t k D1.4 0.6I 1

s H s

for load spread method (7.10)

1

ues 3 3D

u3s s u3s

s t k D1.5 0.8I 1

s H s

for punching shear method (7.11)

The relative density ID is expressed as a decimal. For t3/Hs > 2.0, sues/su3s = 1.4 and 1.5

can be adopted for the load spread and punching shear methods, respectively.

For the Lee et al. and Hu et al. methods (Figure 7.9b), a consistent design formula can

be used and expressed as

1.410.5

ues s 3 3 3

u3s s u3s

s H t t k D0.9 0.14 1 1.0

s D H s

(7.12)

A lower bound of 1.0 is set for Equation 7.12, indicating that the 3rd layer clay is thick

enough to avoid the effect of the stiff 4th layer. Note, in these soft clay-sand-soft clay-


7-10

stiff clay deposits, Equations 7.10~7.12 are proposed to estimate the effect of the thin

soft (3rd) clay layer, interbedded between the sand layer and the bottom stiff clay layer,

on the peak resistance in the sand layer. The effect of the adjacent top layer is

considered implicitly in the design formulas of the Lee et al. or Hu et al. or ISO method.

7.5.2 Limiting Squeezing Depth

For spudcan penetration in the 3rd layer clay confronting a stiff 4th layer, hsq increases

significantly due to the soil plug trapped by the advancing spudcan. The layered soil

plug consists of clay and sand from the 1st and 2nd layers, respectively. As the sand is

much stronger than the clay, the base of the soil plug acts like a footing base and forces

the 3rd layer soft clay to squeeze out. Therefore, it is assumed that the squeezing

response is triggered once the distance from the base of the soil plug to the 3rd-4th layer

interface is within the conventional limiting squeezing depth for spudcan penetration in

clays [a range of hsq = 0.17~0.2D observed in the centrifuge tests reported by Hossain et

al. (2011) and Hossain (2014)]. As such, hsq/D = Max(Hplug/D + 0.18, 0.25) is adopted

in the 3rd layer, with a lower bound of hsq/D = 0.25 observed from the numerical

analyses and assuming a consistent limiting squeezing depth of 0.18D between clays.

The depth dsq/D is thus calculated as

sq 1 2 3 sq 1 2 3 plugd t t t h t t t Max H 0.18D ,0.25D

(7.13)

Once the thickness of the plug Hplug at d = dsq is known, the limiting squeezing depth hsq

then can be determined. As such, a design formula is proposed to estimate the evolution

of soil plug thickness as a function of spudcan penetration depth, and expressed as

2 1f d t /D

plug s 1H / H f e

(7.14)

Examples of the evolution of soil plug thickness are plotted in Figure 7.10 for su1 = 5 +

1z kPa, ID = 90%, su3 = 15 + 1(z – t1 – t2) kPa and t1/D = t2/D = Hs/D = 0.5 with t3/D =

0.25, 0.5, 1.0 and and su4 = 100 kPa. For analyses with a 4th (stiff) layer, only the soil

plug thickness before the depth of triggering squeezing was used. The soil plug

thickness Hplug/Hs at different penetration depths, obtained from each numerical

analysis, was used to calibrate the coefficients f1 and f2, with f1 expressed as


7-11

1 0.5

s s 31

H H tf 0.8 0.2 Min ,1.0 1.0

D D

(7.15)

Figure 7.10 shows that the soil plug thickness decays at a higher rate for lower t3/D.

According to all the numerical data, it is found that this effect is prominent for t3/D <

1.0 or t3/Hs ≤ 1.5. As such, f2 is expressed as

32

0.5 s u3s 32 D

3 s

H s kf 0.18 1.4 I

D D

for t3/D 1.0 or t3/Hs > 1.5 (7.16)

0.51 22

0.5 3 s u3s 32 D

s 3 s

t H s kf 1.2 I

DH D D

for t3/D < 1.0 or t3/Hs ≤ 1.5 (7.17)

The relationship between Equations 7.15~7.17 and the corresponding numerical data is

plotted in Figure 7.11. The estimated evolution of Hplug/Hs from Equation 7.14 is also

plotted in Figure 7.10 showing reasonable agreement with the numerical data before the

depth of squeezing.

As dsq and Hplug are both a function of penetration depth, an iterative approach is

required between Equations 7.13 and 7.14 to calculate the value of dsq (or hsq).

OVERALL PERFORMANCE OF DESIGN METHODS

7.6.1 Peak Resistance in Sand Layer

The normalised peak resistance depths, (dp – t1)/Hs, measured from the centrifuge tests

and computed from the numerical analyses are plotted in Figure 7.12 as a function of

the corresponding measured (qpeak,meas) or computed (qpeak,comp) peak resistance. The

values suggested by Teh et al. (2010) and Hu et al. (2014a), and Lee et al. (2013a) from

centrifuge tests on spudcan and flat-based foundations are also included in the figure.

For a spudcan penetrating with a trapped soft clay layer (from the surface layer), (dp –

t1)/Hs ranges from 0.017 to 0.233, with the average value of 0.132 lying close to 0.12

suggested by Teh et al. (2010) and Hu et al. (2014a) for a clean spudcan.

The design methods listed in Table 7.1 with and without suggested improvements are

used to estimate the peak resistance for the numerical analyses and centrifuge tests.


7-12

Figure 7.13 shows the ratios of the estimated (qpeak,est) to measured or computed peak

resistances, as a function of the corresponding measured or computed values. The Lee et

al. method is only applicable for Hs/D < 0.9 (see Equation 7.4) and hence it was not

used to predict the cases with Hs/D 0.9.

Without suggested improvements, the Lee et al. and Hu et al. methods provide

reasonable estimations for most cases (i.e. 0.85 ≤ qpeak,est/qpeak,meas or qpeak,est/qpeak,comp ≤

1.15) except those with a thin 3rd layer, while the ISO methods provide conservative

peak resistances for all cases presented. This is mainly because (i) in the ISO methods,

lower (i.e. using Ks in the punching shear method) or no contribution (in the load spread

method) from frictional resistance around the sand plug periphery is considered; and (ii)

in the punching shear method, the projected bearing area of the underlying clay layer (=

A) is smaller than that observed in centrifuge tests. The estimations are improved by

multiplying the estimated peak resistance by the factor (Equation 7.9) or using the

equivalent shear strength sues (Equations 7.10~7.12). The statistics for the performance

of different methods are also compared in Table 7.4.

7.6.2 Bearing Capacity in Clay Layer

The penetration resistances in the clay layer that underlies the sand layer are predicted at

depths of D/2 and D below the sand-clay layer interface for cases with the absence of

squeezing effect at these depths. The ratios of estimated to measured or computed

values are shown in Figure 7.14. Reasonable estimations are provided by the Lee et al.

and Hu et al. methods with the error mostly less than 15%, while overly conservative

estimations are provided by the ISO methods due to the absence of the contribution

from the soil plug.

Overall, the ratios for the Lee et al. and Hu et al. methods increase with increasing

magnitude of measured penetration resistances, with underestimation and

overestimation for low-magnitude and high-magnitude resistances, respectively. This is

probably due to the soil plug thickness, which diminishes gradually (at a low rate)

during penetration in the clay layer, but is assumed to be constant in the calculation of

Lee et al. and Hu et al. methods.


7-13

7.6.3 Limiting Squeezing Depth

According to the numerical analyses, the limiting squeezing depths for a clean spudcan

penetrating in the 1st clay layer underlain by a sand layer range between hsq/D = 0.27

and 0.33, with higher hsq/D for higher t1/D. The corresponding estimations from ISO

recommended method (Equation 1.6) are hsq/D = 0.23, 0.16 and 0.12 for t1/D = 0.5, 1

and 1.5, respectively, which are 15~64% lower than the computed values.

For the limiting squeezing depth in the 3rd layer clay with the influence of a trapped soil

plug, the estimations from the ISO method (Equation 1.6) and the proposed method

(Equations 7.13~7.17) are compared in Figure 7.15. The ISO method always

underestimates hsq with a maximum error of 0.89D. By contrast, the proposed method

predicts most cases within an error of 0.1D, except those with a thin clay layer of t3/D

≤ 0.5. For t3/D > 0.5, the proposed method provides a satisfactory estimation for the

limiting squeezing depth.

CPT-BASED DESIGN APPROACH

A CPT-based design approach is developed in this section correlating the net

penetration resistances between spudcan (qnet,sp) and cone (qnet,c) in interbedded sand-

clay layering system. The spudcan penetration resistances are from the numerical

analyses (Table 7.2). The corresponding cone bearing capacity factor for the clay layers

and cone tip resistance for the sand layer are calculated using Equation 3.7 and 3.12,

respectively. Design formulas are proposed for the penetration resistance ratio Rsp-c =

qnet,sp/qnet,c at the peak and in the underlying clay layer. Once the values of Rsp-c are

determined, Equations 4.8 and 4.10 can then be used to estimate the spudcan penetration

resistance directly from the net cone tip resistances.

For spudcan penetration in clay-sand-clay deposits, the average depth of attaining the

peak resistance can be taken as 0.132D below the sand layer surface, as discussed

previously. The value of Rsp-c at the peak is calculated as the ratio between qnet,sp at the

peak and qnet,c at the mid-height of the sand layer (i.e. at d = t1 + Hs/2). All the computed

values of Rsp-c are plotted in Figure 7.16a, with the line of best fit expressed as


7-14

net,sp 1.1

sp c

net,c

0.5 0.250.5

net,c3s1.2 s 3 3D

kt 3 kt s s

qR 0.06x

q

qH twhere x I 1 Max ,0.9

D N D N H

for d = dp (7.18)

As shown in Figure 7.16b, for spudcan penetration in the clay-sand-clay deposits with

and without a 4th layer stiff clay, Equation 7.18 provides reasonable estimates for the

peak penetration resistance in the sand layer with the error mostly less than 10%. The

effect of the adjacent top layer is incorporated implicitly in the measured cone

resistance.

As the Lee et al. method provides a reasonable estimate for the penetration resistance in

the clay layer that underlies the sand layer (see Figure 7.14), Equation 7.7 is

transformed to calculate the penetration resistance ratio in the clay layer as

net,sp ssp c kt

net,c3

q HR 14 9.5 / N

q D

(7.19)

CONCLUDING REMARKS

In this chapter, LDFE analyses simulating continuous spudcan penetration in clay-silica

sand-clay deposits with and without a 4th layer stiff clay have been carried out. The

numerical model has been validated against centrifuge test data with reasonable

agreement obtained. Parametric studies have been conducted, varying the layer

geometries and strength parameters within a practical range, mainly to investigate the

effect of each layer on the bearing responses in the sand layer and its underlying clay

layer. Four design methods have been used to predict the centrifuge tests and numerical

analyses, including two ISO (2012) methods load spread and punching shear methods,

and two recently developed methods – Lee et al. and Hu et al. methods. Interpretation of

the computed and estimated penetration resistance profiles led to the following key

conclusions.

Overall, for an interbedded sand layer overlying a clay layer of the thickness

1.5Hs, Lee et al. and Hu et al. methods were capable of estimating the peak


7-15

resistance in the sand layer by considering the overlying clay layer as equivalent

surcharge, with most overestimation and underestimation less than 15%.

For t3/Hs < 1.5, the peak resistance was considerably increased by the presence of

the 4th layer stiff clay, compared to those for t3/Hs 1.5. Design formulas were

proposed to improve the design methods in order to quantify this effect.

The depth of the peak resistance in the sand layer for a spudcan penetrating with a

trapped soft clay layer was about 0.017~0.233Hs below the surface of the sand

layer, with an average of 0.132Hs.

The limiting squeezing depth in the 1st layer non-uniform clay overlying a sand

layer for a clean spudcan without any trapped soils was about 0.27~0.33D, with

higher value for deeper clay-sand layer interface. It increased significantly in the

3rd layer clay for the spudcan with a soil plug. An iterative approach was proposed

to incorporate the effect of the evolving soil plug in estimating the limiting

squeezing depth.

In addition, a CPT-based design approach has been developed, correlating the peak

penetration resistance of spudcan in the sand layer and the deep penetration resistance in

the underlying clay layer with the net cone tip resistances.


7-16

REFERENCE

Andersen, K. H. & Schjetne, K. (2013). Database of friction angles of sand and

consolidation characteristics of sand, silt, and clay. Journal of Geotechnical and


Bolton, M. D. (1986). The strength and dilatancy of sands. Géotechnique 36, No. 1, 65-

78.

Hanna, A. M. & Meyerhof, G. G. (1980). Design charts for ultimate bearing capacity of

foundations on sand overlying soft clay. Canadian Geotechnical Journal 17, No.

2, 300-303.









Houlsby, G. T. & Martin, C. M. (2003). Undrained bearing capacity factors for conical







Journal 51, No 10, 1151-1164.






ISO (2012). ISO 19905-1: Petroleum and Natural Gas Industries – Site Specific

Assessment of Mobile Offshore Units – Part 1: Jack-ups. Geneva, Switzerland:



7-17


overlying clay soils: experimental and finite-element investigation of potential




1285-1297.


London, 1, 180-189.

Teh, K. L., Cassidy, M. J., Leung, C. F., Chow, Y. K., Randolph, M. F. & Quah, C. K.

(2008). Revealing the bearing failure mechanisms of a penetrating spudcan

through sand overlying clay. Géotechnique 58, No. 10, 793-804.

Teh, K. L., Leung, C. F., Chow, Y. K. & Cassidy, M. J. (2010). Centrifuge model study

of spudcan penetration in sand overlying clay. Géotechnique 60, No. 11, 825-842.


7-18

TABLES

Met

ho

d

Sa

nd

la

yer

Cla

y l

ay

er

Note

s D

esi

gn

fo

rm

ula

P

ara

mete

rs

Lo

ad

spre

ad

met

ho

d

n

s =

3 i

s ad

op

ted

Nc,

int a

nd

Nc

are

calc

ula

ted

foll

ow

ing S

kem

pto

n (

19

51

)

Fo

r no

n-u

nif

orm

cla

y,

s ub i

s

taken

as

the

aver

age

shea

r

stre

ngth

over

a d

epth

of

D/2

bel

ow

layer

inte

rfac

e o

r

spud

can b

ase

Punch

ing

shea

r

met

ho

d

T

he

form

ula

of

Ks

sug

ges

ted

by I

nS

afe

JIP

(20

11

),

wh

ich i

s d

eriv

ed f

rom

Han

na

& M

eyer

ho

f’s

(19

80

)

char

t, i

s u

sed

:

Lee

et

al.

met

ho

d

Pea

k r

esis

tance

dep

th i

s

0.0

5H

s b

elo

w t

he

sand

layer

surf

ace

Nc,

int i

s ca

lcula

ted

fo

llo

win

g

Ho

uls

by &

Mar

tin (

20

03

)

Hu e

t al

.

met

ho

d

Pea

k r

esis

tance

dep

th i

s

0.1

2H

s b

elo

w t

he

sand

layer

surf

ace

Nc,

int i

s ca

lcula

ted

fo

llo

win

g

Ho

uls

by &

Mar

tin (

20

03

)

2

vc,i

nt

ub

0

sTq

Ns

p0.2

5D

2/A

n

vc,i

nt

ub

0s

0s

2T

qN

sp

T2p

Kta

nD

*

*

pea

kc,i

nt

u,i

nt

0

E

s

s

*

E

*s

s

qN

sq

2H

1ta

nD

D

2E

1ta

n

2H

2H

11

Eta

n1

tan

DD

*

*

pea

kc,i

nt

u,i

nt

0s

s

E

s

s

*

E

*s

s

qN

sq

0.1

2H

1.7

6H

1ta

nD D

2E

1ta

n

1.7

6H

1.7

6H

11

Eta

n1

tan

DD

**

F

tan

E2

1D

1ta

n

*si

nco

sta

n1

sin

sin

Rp

RDea

kI

IQ

lnq

1

0

I 4

crit

R2.6

5I

crit

0.8

0

.6

sub

sK

tan

2.5

s/

D

s

F

s

HD

1.3

33

0.8

89

D

Hfo

r 0.9

D

0.5

76

s

F

sHD

0.6

42

D

Hfo

r 0.1

61.0

D

vc

ub

0q

Ns

p

s

uu

0

Hq

14

9.5

sD

s

uu

0

scH

q11

10.5

sD

0.9

H

Tab

le 7

.1 D

esig

n f

orm

ula

s fo

r sp

ud

can

pen

etra

tion

in

san

d-o

ver

-cla

y


7-19


1st layer soft clay 2nd layer sand 3rd layer soft clay

4th

layer

stiff

clay

su1s:

kPa

k1:

kPa/m t1/D

ID:

% t2/D (Hs/D)

su3s:

kPa

k3:

kPa/m t3/D

su4:

kPa

5 1 0.5~1.5

45

and

90

0.25~1 7.5~30 1~3 0.25~1.5

and 100


7-20

Table 7.3 Selected groups of LDFE analyses used for discussion

Group

1st layer soft clay 2nd layer

sand 3rd layer soft clay

4th

layer

stiff

clay Remarks

su1s:

kPa

k1:

kPa/m t1/D

ID:

%

t2/D

(Hs/D)

su3s:

kPa

k3:

kPa/m t3/D

su4:

kPa

I

9 0 0.25 44 0.5 9 0 0.96 36

Centrifuge

tests

0.5 0.75 0.62 89 0.25 4.4 0.75 - -

0.5 0.75 0.62 89 0.5 5.53 0.75 - -

0.5 0.75 0.62 89 0.67 6.28 0.75 - -

II 5 1 - - - - - -

Single

layer clay

of su1

III 5 1 0.5~

1.5 45 0.5 15 1

1.0 and

100

Effect of

t1/D

IV 5 1 0.5

45

and

90

0.25~

0.75 15 1

1.0 and

100

Effects of

ID and

Hs/D

V 5 1 0.5 45 0.5 15 1 0.25~1.5

and 100

Effect of

t3/D

VI 5 1 0.5 45 0.5 7.5~

30 1~3

1.0, 1.5

and 100

Effects of

su3s and k3


7-21

Table 7.4 Statistics for performance of different design methods

Ratios Formulas Design methods

Statistical indices

Min Max Mean,

RSS*

qpeak,est/qpeak,meas

and

qpeak,est/qpeak,comp

Original

Load spread method 0.340 0.853 0.638 8.583

Punching shear

method 0.333 0.847 0.613 9.691

Lee et al. method 0.627 1.282 1.020 1.054

Hu et al. method 0.620 1.218 0.998 0.854

Improved

through

Lee et al. method 0.865 1.282 1.086 0.930

Hu et al. method 0.826 1.218 1.066 0.577

Improved

through

sues

Load spread method 0.478 1.199 0.961 0.836

Punching shear

method 0.514 1.235 0.958 0.806

Lee et al. method 0.865 1.282 1.059 0.622

Hu et al. method 0.826 1.218 1.035 0.367

New CPT-based design

approach 0.833 1.097 0.989 0.182

qD/2,est/qD/2,meas

and

qD/2,est/qD/2,comp

Original

Load spread method

0.485 0.733 0.580 4.498 Punching shear

method

Lee et al. method 0.743 1.126 0.910 0.417

Hu et al. method 0.821 1.137 0.955 0.189

qD,est/qD,meas

and

qD,est/qD,comp

Original

Load spread method

0.540 0.751 0.641 2.255 Punching shear

method

Lee et al. method 0.775 1.221 0.986 0.285

Hu et al. method 0.854 1.229 1.021 0.206

* Residual sum of squares, RSS = [(ratio – 1)2]


7-22

FIGURES

hsq

ddp

din

t

dsq

z

Sp

ud

ca

n

Ca

vity

K-l

att

ice

le

g

D

1

1

2

st

H

Cla

y

Sa

nd

Cla

y

Cla

y

t 1

t 2 =

Hs

t 3

d

T

Hca

v

su1,

1

I D,

2 =

s

su3,

3

su4,

4

su1s

su

k1

k3

su3s =

su

,int

qnet

qpeak

Fig

ure

7.1

Sch

em

ati

c d

iagra

m o

f sp

ud

can

fou

nd

ati

on

em

bed

ded

in

cla

y-s

an

d-c

lay d

eposi

t w

ith

a 4

th l

ay

er s

tiff

cla

y

show

ing i

dea

lise

d o

pen

cavit

y a

nd

corr

esp

on

din

g p

enet

rati

on

res

ista

nce

pro

file


7-23

Figure 7.2 Numerical model used in parametric study for spudcan penetration in

multi-layer soils with an interbedded sand layer

Void layer

Spudcanrigid body

1st layer clay

2nd layer sand

3rd layer clay

4th layer clay


7-24

7.3(a) Test FS9 (su1 = su3 = 9 kPa, ID = 44%, su4 = 36 kPa, t1/D = 0.25, t2/D = Hs/D =

0.5, t3/D = 0.96; Group I, Table 7.3)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 50 100 150 200 250 300 350 400 450

No

rmalised

pen

etr

ati

on

dep

th,

d/D


Centrifuge test

LDFE


7-25

7.3(b) Tests FS12, FS13 and FS14 (su1 = su3 = 0.5 + 0.75z, ID = 89%, t1/D = 0.62;

Group I, Table 7.3)

Figure 7.3 Comparison of centrifuge test and numerical analysis

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3

0 50 100 150 200 250 300 350 400 450 500N

orm

alised

pen

etr

ati

on

dep

th,

d/D


Centrifuge

LDFE

t2/D = Hs/D = 0.75

0.25

0.5


7-26

Figure 7.4 Effect of 1st layer thickness ratio (t1/D) on penetration resistance (su1 = 5

+ 1z kPa, ID = 45%, su3 = 15 + 1(z – t1 – t2) kPa, su4 = 100 kPa, t2/D = Hs/D = 0.5;

Group III, Table 7.3)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500 600

No

rma

lis

ed

pe

ne

tra

tio

n d

ep

th,

(d

t 1)/

DBearing pressure, qu: kPa

For each design method,From left: t1/D =0.5, 1.0 and 1.5

Seabed

LDFE:

t3/D =

LDFE:t3/D = 1.0

LDFE:

t1/D =

Hu et al. method

Lee et al. method

Load spread method

Punching shear method


7-27

7.5(a) LDFE analyses

0

0.5

1

1.5

2

2.5

3

0 100 200 300 400 500 600

No

rma

lise

d p

en

etr

ati

on

dep

th,

d/D


t2/D = 0.25, 0.5and 0.75

t1/D =

ID = 45% & t3/D =

ID = 90% & t3/D =

ID = 45% & t3/D = 1.0

ID = 90% & t3/D = 1.0

Line


7-28

7.5(b) Comparison of estimated and computed results for t2/D = Hs/D = 0.75

Figure 7.5 Effects of relative density (ID) and thickness ratio (Hs/D) of 2nd layer

sand on penetration resistance (su1 = 5 + 1z kPa, su3 = 15 + 1(z – t1 – t2) kPa, su4 =

100 kPa, t1/D = 0.5; Group IV, Table 7.3)

0

0.5

1

1.5

2

2.5

3

0 150 300 450 600 750

No

rmalised

pen

etr

ati

on

dep

th,

d/D


LDFE:

LDFE:

t1/D =

t2/D = 0.75

ID = 45% and 90%

ID = 45% and 90%

Hu et al. method

Lee et al. method

Load spread method



7-29

Figure 7.6 Effect of 3rd layer thickness ratio (t3/D) on penetration resistance (su1 = 5

+ 1z kPa, ID = 45%, su3 = 15 + 1(z – t1 – t2) kPa, su4 = 100 kPa, t1/D = t2/D = Hs/D =

0.5; Group V, Table 7.3)

0

0.5

1

1.5

2

2.5

3

0 100 200 300 400 500 600 700

No

rmalised

pen

etr

ati

on

dep

th,

d/D


LDFE:

t3/D =

LDFE: t3/D = 1.5

1.0

0.75

0.5

0.25

Hu et al. method

Lee et al. method

Load spread method



7-30

Figure 7.7 Effect of t3/D on increasing the peak resistance in sand layer

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5

Rati

o b

etw

een

peak r

esis

tan

ces w

ith

an

d

wit

ho

ut

a 4

thla

yer

sti

ff c

lay,

Normalised 3rd layer thickness, t3/Hs

ID = 90% & t2/D = 0.25

ID = 90% & t2/D = 0.5

ID = 90% & t2/D = 0.75

ID = 45% & t2/D = 0.25

ID = 45% & t2/D = 0.5

ID = 45% & t2/D = 0.75

ID = 90% & t2/D = 0.25

ID = 90% & t2/D = 0.5

ID = 90% & t2/D = 0.75

ID = 45% & t2/D = 0.25

ID = 45% & t2/D = 0.5

ID = 45% & t2/D = 0.75

3 s2.2t /H1 1.5e


7-31

7.8(a) Effect of su3s

0

0.5

1

1.5

2

2.5

3

0 150 300 450 600 750

No

rmalised

pen

etr

ati

on

dep

th,

d/D


t3/D = 1.0

t3/D = 1.5su3s = 7.5 kPa

su3s = 15 kPa

su3s = 30 kPa

Line


7-32

7.8(b) Effect of k3

Figure 7.8 Effect of 3rd layer strength parameters (su3s and k3) on penetration

resistance (su1 = 5 + 1z kPa, ID = 45%, su4 = 100 kPa, t1/D = t2/D = Hs/D = 0.5; Group

VI, Table 7.3)

0

0.5

1

1.5

2

2.5

3

0 150 300 450 600 750

No

rmalised

pen

etr

ati

on

dep

th,

d/D


t3/D = 1.0

t3/D = 1.5k3 = 1 kPa/m

k3 = 2 kPa/m

k3 = 3 kPa/m

Line


7-33

7.9(a) ISO methods

1

1.5

2

2.5

3

3.5

4

4.5

5

0 1 2 3 4 5

No

rma

lis

ed

eq

uiv

ale

nt

un

dra

ine

d s

he

ar

str

en

gth

, s

ues/s

u3s

Load spread method


1

ues 3 3D

u3s s u3s

s t k D1.5 0.8I 1

s H s

1

3 3D

s u3s

t k DI 1

H s

1

ues 3 3D

u3s s u3s

s t k D1.4 0.6I 1

s H s


7-34

7.9(b) Lee et al. and Hu et al. methods

Figure 7.9 Design charts for equivalent undrained shear strength sues at sand-clay

layer interface

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

0 1 2 3 4 5

No

rma

lis

ed

eq

uiv

ale

nt

un

dra

ine

d s

he

ar

str

en

gth

, s

ues/s

u3s

Lee et al. method

Hu et al. method

1.410.5

ues s 3 3 3

u3s s u3s

s H t t k D0.9 0.14 1 1.0

s D H s

10.5

s 3 3 3

s u3s

H t t k D1

D H s


7-35

Figure 7.10 Evolution of soil plug thickness (su1 = 5 + 1z kPa, ID = 90%, su3 = 15 +

1(z – t1 – t2) kPa, t1/D = t2/D = Hs/D = 0.5, su4 = 100 kPa)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

No

rmalised

so

il p

lug

th

ickn

ess,

Hp

lug/H

s

Normalised penetration depth from sand

layer surface, (d t1)/D

Series5

t3/D =

Squeezing

t3/D = 1.0

t3/D = 0.5

(dsq t1)/D

t3/D = 0.25

Equation 7.14


7-36

7.11(a) Design chart for f1

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5

Co

eff

icie

nt,

f1

1 0.5

s s 31

H H tf 0.8 0.2 Min ,1.0 1.0

D D

1 0.5

s s 3H H tMin ,1.0

D D


7-37

7.11(b) Design chart for f2 for t3/D 1.0 or t3/Hs > 1.5

0

0.15

0.3

0.45

0.6

0.75

0.9

0 0.15 0.3 0.45 0.6 0.75 0.9

Co

eff

icie

nt,

f2

2

0.5 s u3s 3D

3 s

H s kI

D D

32

0.5 s u3s 32 D

3 s

H s kf 0.18 1.4 I

D D


7-38

7.11(c) Design chart for f2 for t3/D < 1.0 or t3/Hs ≤ 1.5

Figure 7.11 Design charts for coefficients f1 and f2 for spudcan penetration in clay-

sand-clay deposit

0

0.4

0.8

1.2

1.6

2

2.4

0 0.6 1.2 1.8 2.4 3 3.6

Co

eff

icie

nt,

f2

0.51 22

0.5 3 s u3s 32 D

s 3 s

t H s kf 1.2 I

DH D D

220.5 3 s u3s 3

D

s 3 s

t H s kI

DH D D


7-39

Figure 7.12 Depths of peak resistance dp from centrifuge tests and numerical

analyses

0

0.05

0.1

0.15

0.2

0.25

0 200 400 600 800 1000

(dp

t 1)/

Hs

qpeak,meas or qpeak,comp: kPa

Teh et al. (2010) and Hu et al. (2014a)

Lee et al. (2013a)for spudcans

Lee et al. (2013a) forflat-based foundations

0.15

0.12

0.05


7-40

Figure 7.13 Performance of design methods on estimating peak resistance for

spudcan penetration in multi-layer soils with an interbedded sand layer

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

0 200 400 600 800 1000

qp

eak,e

st/q

peak,m

eas

or

qp

eak,e

st/q

peak,c

om

p


Hu et al. method

Lee et al. method

Load spread method


Hu et al. method

Lee et al. method

Load spread method


Hu et al. method

Lee et al. method

Improved through sues

Without improvement

Improved

through


7-41

Figure 7.14 Performance of design methods on estimating deep penetration

resistance in the 3rd layer clay for spudcan penetration in multi-layer soils with an

interbedded sand layer

0.4

0.55

0.7

0.85

1

1.15

1.3

1.45

1.6

0 100 200 300 400 500 600

qD

/2,e

st/q

D/2

,meas

or

qD

/2,e

st/q

D/2

,co

mp

or

qD

,est/q

D,m

eas

or

qD

,est/q

D,c

om

p

qD/2,meas or qD/2,comp or qD,meas or qD,comp: kPa

Hu et al. method

Lee et al. method

ISO methods

Hu et al. method

Lee et al. method

ISO methods

qD,est/qD,meas orqD,est/qD,comp

qD/2,est/qD/2,meas orqD/2,est/qD/2,comp


7-42

Figure 7.15 Performance of proposed and ISO-recommended methods on

estimating limiting squeezing depth for spudcan penetration in clay with a trapped

sand plug

-0.7

-0.5

-0.3

-0.1

0.1

0.3

0.5

0.7

0.9

0 1 2 3 4 5

(hsq/D

) meas

(hsq/D

) esto

r

(hsq/D

) co

mp

(hsq/D

) est

Normalised 3rd layer thickness, t3/Hs

or t3/D

t3/Hs

t3/D

t3/Hs

t3/D

Proposedmethod

t3/Hs

t3/D

t3/Hs

t3/D

ISOmethod


7-43

7.16(a) Design chart for penetration resistance ratio Rsp-c at peak for spudcan

penetration in multi-layer soils with an interbedded sand layer

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1

Pen

etr

ati

on

resis

tan

ce r

ati

o,

Rsp

-c

Equation 7.18

0.5 0.250.5

net,c3s1.2 s 3 3D

kt 3 kt s s

qH tI 1 Max ,0.9

D N D N H


7-44

7.16(b) Performance of design formula

Figure 7.16 Relationship between predicted and computed data of peak resistance

using CPT-based design approach for spudcan penetration in multi-layer soils

with an interbedded sand layer

0.7

0.8

0.9

1

1.1

1.2

1.3

0 200 400 600 800 1000

qp

eak,e

st/q

peak,m

eas

or

qp

eak,e

st/q

peak,c

om

p


Chapter 8. Concluding Remarks

8-1

CHAPTER 8. CONCLUDING REMARKS

INTRODUCTION

In this thesis, large deformation finite element (LDFE) analyses have been carried out to

investigate spudcan penetration resistance in stratified soil sediments of up to four

layers consisting of surface or interbedded strong layer (i.e. stiff clay or sand). Four

configurations of soil profile have been investigated, including: (i) two-layer stiff-over-

soft clay deposit; (ii) three-layer non-uniform clay with an interbedded stiff clay layer;

(iii) three-layer uniform stiff-soft-stiff clay; and (iv) clay-sand-clay deposits with and

without a 4th layer stiff clay. Numerical analyses were also performed simulating cone

penetration test (CPT) in single layer clay and sand deposits.

Based on the numerical results combined with the existing centrifuge test data, the

evolving soil flow mechanisms during spudcan penetration in stratified deposits were

presented, and new mechanism-based and CPT-based design approaches were proposed

for assessing spudcan penetration resistance in multi-layer soils. The performance of the

proposed design approaches were evaluated by comparing with the measured data from

centrifuge tests and case histories, with improved predictions obtained compared with

those from the design methods suggested in the current design guidelines ISO 19905-1

(ISO, 2012). The new design approaches for each configuration of soil profile, which

were proposed based on the numerical results of this study, are applicable to the

selected ranges of soil parameters in the corresponding chapter. For soil parameters

beyond the ranges studied in this thesis, the proposed formulas should be used with

caution.

Using the proposed design formulas is an effective and efficient way to predict spudcan

penetration resistance. However, this study also shows that if an advanced numerical

model is available and detailed numerical analysis procedures are established, LDFE

analyses for each jack-up leg on each location may provide accurate and continuous

penetration resistance profiles provided expertise, time and cost permit.

The contributions and findings from this research are summarised below.


8-2

KEY CONTRIBUTIONS AND FINDINGS

8.2.1 Implementation of Advanced Soil Models

A subroutine compatible with Abaqus/Explicit has been programmed to implement the

strain softening and rate dependent clay model, and the modified Mohr-Coulomb

(MMC) sand model in ALE (Arbitrary Lagrangian-Eulerian) and CEL (Coupled

Eulerian-Lagrangian) analyses, as detailed in Chapter 2. The subroutines were not only

used in this research, but also contributed to the studies of Hu et al. (2014, 2015) and

Kim et al. (2015). In all these studies, validation of the numerical models against

centrifuge tests demonstrated satisfactory agreement.

8.2.2 Cone Penetration in Single Layer Clay and Sand Deposits

For cone penetration in clay deposit, the effect of soil strength non-homogeneity on the

shallow and deep cone factors was negligible. The depth dkt of attaining the steady state

penetration resistance increased with increasing rigidity index. For shallow penetration

response, profiles of the normalised cone factor Nkt,s/Nkt showed a somewhat unique

trend, which increased with the normalised cone tip penetration depth dtip/dkt.

Expressions were proposed for estimating the depth dkt and shallow cone factor Nkt,s.

For deep penetration response, the deep cone factor Nkt increased with strain softening

and rate parameters , log(vfield/Dcref), rem and 95, with the rate parameter μ identified

as the most influencing factor. An expression was also proposed for estimating Nkt

factors as a function of rigidity index and strain softening and rate parameters. For a

range of soil parameters commonly encountered in offshore site investigation, the

proposed design expression for Nkt provided a range of cone factors that fell within the

range that was suggested based on a worldwide, high-quality database.

For cone penetration in sand deposit, the design formula proposed by Senders (2010)

was modified with new values for the coefficients calibrated against the numerical

results. The modified design formula was shown to provide improved predictions in

terms of both shallow and deep penetration resistances.


8-3

8.2.3 Spudcan Penetration in Layered Deposits

Two-layer stiff-over-soft clay

Parametric LDFE analyses were performed for spudcan penetration in stiff-over-soft

clay deposits. The results showed that the depth of peak resistance in the stiff layer

increased with increasing strength ratio subs/sut at the layer interface between lower and

upper layers, increasing thickness ratio t/D of the stiff layer and increasing strength non-

homogeneity factor kD/subs of the soft layer. The average deep bearing capacity factor

Ncd for spudcan penetration in the soft clay increased with decreasing subs/sut, increasing

t/D, and decreasing kD/subs. The computed and measured Ncd factors ranged between

9.8 and 15.5. The effect of sensitivity St was found to be significant when St increased

from 1 to a typical value of 2.8, leading to a decrease of the depth and magnitude of the

peak resistance and a ~25% reduction of deep bearing capacity. With further increase of

St from 2.8 to 5, the peak resistance was marginally affected while the deep penetration

resistance was reduced further by 10%.

Based on the centrifuge test data and LDFE results, new mechanism-based and CPT-

based design approaches were proposed for predicting spudcan penetration in stiff-over-

soft clay deposits. The approaches provide estimates of (i) the peak penetration

resistance and its depth in the stiff layer, (ii) the resistance at the stiff-soft layer

interface, and (iii) the penetration resistance profile in the soft layer. The design formula

suggested by ISO for punch-through was also improved to predict the peak penetration

resistance in the stiff layer. Comparison between the predictions using the ISO method,

recently developed methods and proposed approaches, and the measured data from

centrifuge tests demonstrated the improvement by the proposed approaches.

Non-uniform clay with an interbedded stiff clay layer

The soil flow mechanisms observed in the numerical analysis were consistent with those

observed from centrifuge tests reported by Hossain et al. (2011). For spudcan

penetration in the 1st soft layer, the bearing response was dominated by squeezing, with

the computed limiting squeezing depth of about ~0.18D similar to the measured one

from centrifuge tests. Moreover, in contrast to ISO recommendation, the soft soil in

between the advancing spudcan base and the stronger layer did not squeeze out


8-4

completely. Instead, some of the trapped soft material was forced into the underlying

layers.

Based on the results of LDFE analyses, new mechanism-based and CPT-based design

approaches were developed for assessing spudcan penetration resistance in non-uniform

clay with an interbedded stiff clay layer. Predictions using the proposed approaches

were found to be in good agreement with measured load-penetration profiles, with

underestimation or overestimation in terms of penetration resistance or penetration

depth at critical points being mostly less than 5 %. The peak penetration resistance at

punch-through (if any), the depth of triggering punch-through and the likelihood and

severity of punch-through were also well predicted. The ISO bottom-up approach

provided a relatively less accurate estimation of the penetration resistance profile, with

underestimation of the bearing capacity (or overestimation of penetration depth) and

inaccurate identification of the likelihood and severity of punch-through.

Uniform stiff-soft-stiff clay

Key features of soil flow mechanisms have been revealed for spudcan penetration in

stiff-soft-stiff clay deposit, which included: (i) punching shear mechanism with the soil

deformation directed predominantly vertically downward in the 1st (stiff) layer and

laterally outward in the 2nd (soft) layer being restricted by the 3rd (stiff) layer; (ii) soil

backflow around the soil plug and onto the spudcan top; (iii) soft soils between the stiff

soil plug base and the stiff 3rd layer squeezing out; and (iv) the spudcan in the 3rd layer

with thin layers of trapped soils from the upper layers wrapping the bottom profile of

the spudcan and localised soil flow mechanism.

The penetration resistance in the 1st layer stiff clay was underestimated and the depth of

triggering squeezing in the 2nd (soft) layer was overestimated by the design methods

recommended by the ISO standard 19905-1 (ISO, 2012). This is because the soil plug

pushed down from the 1st (stiff) layer into the underlying layer and the effect of the 3rd

(stiff) layer are neglected by the ISO bottom-up approach in the calculation of bearing

capacities in the 1st and 2nd layers.

A new mechanism-based design approach and an alternative CPT-based design

approach were proposed for assessing spudcan penetration resistance in uniform stiff-

soft-stiff clay deposits, with the LDFE data used to calibrate the approaches. Using the


8-5

new design approaches, the bearing capacities can be evaluated at the seabed, at the

depth of maximum bearing capacity in the 1st layer, at the depth of triggering squeezing

and at the 2nd-3rd layer interface successively, followed by the prediction of the

penetration resistance profile in the bottom layer.

The proposed approaches were used to predict the reported data from a centrifuge test

and a case history. The comparison between the measured penetration resistance

profiles and those estimated using the ISO bottom-up approach and the proposed design

approaches demonstrated the advantages of using the new ones.

Clay-sand-clay deposits with and without a 4th layer stiff clay

LDFE analyses were performed simulating spudcan penetration in clay-sand-clay

deposits with and without a 4th layer stiff clay. The results from numerical analyses and

reported centrifuge tests were used to validate four design methods including two ISO

(2012) methods load spread and punching shear methods, and two recently developed

methods – Lee et al. and Hu et al. methods, which led to the following key conclusions.

Overall, for an interbedded sand layer overlying a clay layer of the thickness

1.5Hs, Lee et al. and Hu et al. methods were capable of estimating the peak

resistance in the sand layer by considering the overlying clay layer as equivalent

surcharge, with most overestimation and underestimation less than 15%.

For t3/Hs < 1.5, the peak resistance was considerably increased by the presence of

the 4th layer stiff clay, compared to those for t3/Hs 1.5. Design formulas were

proposed to improve the design methods in order to quantify this effect.

The depth of the peak resistance in the sand layer for a spudcan penetrating with a

trapped soft clay layer was about 0.017~0.233Hs below the surface of the sand

layer, with an average of 0.132Hs.

The limiting squeezing depth in the 1st layer non-uniform clay overlying a sand

layer for a clean spudcan without any trapped soils was about 0.27~0.33D, with

higher value for deeper clay-sand layer interface. It increased significantly in the

3rd layer clay for the spudcan with a soil plug. An iterative approach was proposed

to incorporate the effect of the evolving soil plug in estimating the limiting

squeezing depth.


8-6

In addition, a CPT-based design approach has been developed, correlating the peak

penetration resistance of spudcan in the sand layer and the deep penetration resistance in

the underlying clay layer with the net cone tip resistances.

RECOMMENDATIONS FOR FUTURE RESEARCH

8.3.1 LDFE Analyses Covering Broader Range of Parameters

In this research, the ranges of parameters adopted in the LDFE analyses were selected

deliberately so that punch-through failure could be observed in the numerical

simulations. Therefore, the new design approaches proposed based on the numerical

results of this study are applicable to cases where the potential for punch-through exists.

However, the combination of soil parameters and layer geometries for multi-layer soils

is much more diverse than those that have been explored. As such, analyses could be

undertaken, covering a broader range of parameters that has not been encompassed in

this research, in order to validate and refine the proposed design formulas. Critically,

more field data are required to enhance the accuracy of the proposed design approaches.

8.3.2 Advanced Sand Models

A MMC model was adopted to simulate the shear behaviours of sand layer. The MMC

model is based on the classic Mohr-Coulomb (MC) yield criterion but extending to

incorporating the linear evolution of friction and dilation angles as a function of

accumulated equivalent plastic strain. As negative dilation angle and hence the

contraction of sand are not allowed in the MC model, the MMC model was only used to

simulate medium dense to dense silica sands.

However, it is recognised that calcareous sand and very loose to loose silica sand are

also prevalent in the offshore field. Therefore, advanced constitutive models capable of

simulating the compressibility and crushability of sands, as well as compatible for

LDFE analysis are required. Further numerical study could be conducted to investigate

the penetration response of spudcan in very loose or loose silica sand or calcareous sand.


8-7

8.3.3 Generalisation of Design Methods

The mechanism-based and CPT-based design approaches proposed in each chapter of

this thesis are limited to the application for a particular configuration of soil profile.

Therefore, a general design approach for multi-layer soil profile is required. To achieve

this objective, the continuous penetration resistance profiles of spudcan presented in this

research could be used. For instance, based on the results for spudcan penetration in

soft-stiff-soft clay and stiff-soft-stiff clay profiles, design formulas could be proposed to

quantify the effect of the 3rd layer on the bearing capacity of squeezing in the 1st soft

layer and of punch-through in the 1st stiff layer, respectively.

Numerical and experimental studies should be extended to obtain continuous

penetration resistance profiles of spudcan in the other configurations of multi-layer soil

profiles, such as a strong layer overlying two successive weak layers and a weak layer

overlying two successive strong layers. A generalised design approach then could be

developed combining the design formulas proposed for each configuration of soil

profile.

8.3.4 Consolidation and Extraction Problems

This research only investigated the behaviours of spudcan concerned with the

installation of jack-up rig in multi-layer soils. Further research is suggested to study the

behaviours of spudcan foundation in multi-layer soils during the operation and

extraction processes, especially for soil layers of different drainage conditions.


8-8

REFERENCE




Hu, P., Wang, D., Cassidy, M. J. & Stanier, S. A. (2014). Predicting the resistance


Journal 51, No 10, 1151-1164.



ISO (2012). Petroleum and natural gas industries – Site specific assessment of mobile

offshore units – Part 1: Jack-ups. International Organization for Standardization,

ISO 19905-1.

Kim, Y., Hossain, M. S., Wang, D. & Randolph, M. F. (2015). Numerical investigation

of dynamic installation of torpedo anchors in clay. Ocean Engineering 108, 820-

832.

Documents

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