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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
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
III
ISO bottom-up approach provided conservative estimation for the bearing capacity and
overestimation for the depth of triggering squeezing.
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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.
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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.
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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
Numerical Analysis ......................................................................................... 4-3
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
Concluding Remarks ..................................................................................... 4-16
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
Numerical Analysis ......................................................................................... 5-2
5.2.1 Validation of Numerical Model ..................................................... 5-2
5.2.2 Soil Flow Mechanisms ................................................................... 5-4
5.2.3 Parametric Study ............................................................................ 5-4
New Mechanism-Based Design Approach ..................................................... 5-7
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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
5.4.5 Summary Design Procedure......................................................... 5-17
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
Numerical Analysis ......................................................................................... 6-2
6.2.1 Validation of Numerical Model ..................................................... 6-2
6.2.2 Soil Flow Mechanisms ................................................................... 6-3
6.2.3 Parametric Study ............................................................................ 6-3
New Mechanism-Based Design Approach ..................................................... 6-5
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
6.3.6 Summary Design Procedure......................................................... 6-11
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
6.4.5 Summary Design Procedure......................................................... 6-15
Application .................................................................................................... 6-16
6.5.1 Centrifuge Test ............................................................................. 6-16
6.5.2 Case History ................................................................................. 6-17
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
IX
Concluding Remarks ..................................................................................... 6-18
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 Analysis ......................................................................................... 7-4
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
Concluding Remarks ..................................................................................... 7-14
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
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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.
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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.
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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
Numerical Modelling of Spudcan and Cone Penetration in Multi-Layer Soils
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
Chapter 1. Introduction
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
Chapter 1. Introduction
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
Chapter 1. Introduction
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
Chapter 1. Introduction
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
Chapter 1. Introduction
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
Chapter 1. Introduction
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.
Chapter 1. Introduction
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
Chapter 1. Introduction
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).
Chapter 1. Introduction
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.
Chapter 1. Introduction
1-11
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Chapter 1. Introduction
1-15
FIGURES
Figure 1.1 Jack-up rig and spudcan foundation
SpudcanD = 10~20 m
~170 m
Water surface
Truss-work leg
Platform
Chapter 1. Introduction
1-16
Plan View
Elevation View
1.2(a) Marathon LeToumeau Design, Class 224-C (Super Gorilla)
Chapter 1. Introduction
1-17
Plan View
Elevation View
1.2(b) Marathon LeToumeau Design, Class 116-C
Chapter 1. Introduction
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°
Chapter 1. Introduction
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)
Chapter 1. Introduction
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)
Chapter 1. Introduction
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
Chapter 1. Introduction
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)
Chapter 1. Introduction
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
Chapter 1. Introduction
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.
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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.
Chapter 2. Large Deformation Finite Element Methods
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.
Chapter 2. Large Deformation Finite Element Methods
2-16
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Chapter 2. Large Deformation Finite Element Methods
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 - - - -
Chapter 2. Large Deformation Finite Element Methods
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.
Chapter 2. Large Deformation Finite Element Methods
2-22
FIGURES
Figure 2.1 Deformation and remeshing of Eulerian elements in a time increment
After Lagrangian phase
After Eulerain phase
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
2-27
2.8(a) Cone penetration
Offset bounday
Axis of symmetryCone tip
1 m
1.5
m
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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: %
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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
Chapter 2. Large Deformation Finite Element Methods
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.
Chapter 3. Cone in Single Layer Clay and Sand
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.
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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).
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and 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
Chapter 3. Cone in Single Layer Clay and Sand
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).
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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.
Chapter 3. Cone in Single Layer Clay and Sand
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.
Chapter 3. Cone in Single Layer Clay and Sand
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.
Computers and Geotechnics 56, 50-60.
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.
Chapter 3. Cone in Single Layer Clay and Sand
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
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Walker, J. & Yu, H. S. (2010). Analysis of the cone penetration test in layered clay.
Géotechnique 60, No. 12, 939-948.
Yu, H. S. (2000). Cavity expansion methods in geomechanics. Rotterdam: Balkema.
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
.
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
Chapter 3. Cone in Single Layer Clay and Sand
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
Cone penetration resistance, qu,c: kPa
q0/(Dc) = 0, 42, 84, 126.1, 168.1, 210.1 and 252.1
Numerical analysis
Equation 3.8
Chapter 3. Cone in Single Layer Clay and Sand
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%
Chapter 3. Cone in Single Layer Clay and Sand
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
Cone penetration resistance, qu,c: kPa
Equation 3.8Numerical analysis
Equation 3.12
ID = 45% 60% 75% 90%
Chapter 3. Cone in Single Layer Clay and Sand
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.
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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.
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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.
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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)
Chapter 4. Spudcan in Stiff-over-Soft Clay
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)
Chapter 4. Spudcan in Stiff-over-Soft Clay
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)
4.5.4 Summary Design Procedure
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 ;
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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.
Chapter 4. Spudcan in Stiff-over-Soft Clay
4-17
REFERENCE
Brown, J. D. & Meyerhof, G. G. (1969). Experimental study of bearing capacity in
layered clays. Proc. 7th International Conference on Soil Mechanics and
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
spudcan foundations on stiff-over-soft clay. Proc. Offshore Technology
Conference, Houston, OTC 19907.
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.
Hossain, M. S. & Randolph, M. F. (2011). Discussion on ‘Deep-penetrating spudcan
foundations on layered clays: centrifuge tests’. Géotechnique 61, No. 1, 85-87.
Hossain, M. S., Zheng, J., Menzies, D., Meyer, L. & Randolph, M. F. (2014). Spudcan
penetration analysis for case histories in clay. Journal of Geotechnical and
Geoenvironmental Engineering, ASCE 140, No. 7, 04014034.
Hu, P., Stanier, S. A., Cassidy, M. J. & Wang, D. (2014a). Predicting peak resistance of
spudcan penetrating sand overlying clay. Journal of Geotechnical and
Geoenvironmental Engineering, ASCE 140, No. 2, 04013009.
Hu, P., Wang, D., Cassidy, M. J. & Stanier, S. A. (2014b). Predicting the resistance
profile of a spudcan penetrating sand overlying clay. Canadian Geotechnical
Journal 51, No 10, 1151-1164.
Hu, P., Wang, D., Stanier, S. A. & Cassidy, M. J. (2015). Assessing the punch-through
hazard of a spudcan on sand overlying clay. Géotechnique, in press.
ISO (2012). ISO 19905-1: Petroleum and natural gas industries – Site specific
assessment of mobile offshore units – Part 1: Jackups. Geneva, Switzerland:
International Organization for Standardization.
Lee, K. K., Cassidy, M. J. & Randolph, M. F. (2013a). Bearing capacity on sand
overlying clay soils: experimental and finite-element investigation of potential
punch-through failure. Géotechnique 63, No. 15, 1271-1284.
Chapter 4. Spudcan in Stiff-over-Soft Clay
4-18
Lee, K. K., Randolph, M. F. & Cassidy, M. J. (2013b). Bearing capacity on sand
overlying clay soils: a simplified conceptual model. Géotechnique 63, No. 15,
1285-1297.
Ma, H., Zhou, M., Hu, Y. & Hossain, M. S. (2015). Interpretation of layer boundaries
and shear strengths for soft-stiff-soft clays using CPT data: LDFE analyses.
Journal of Geotechnical and Geoenvironmental Engineering, ASCE, in press.
Menzies, D. & Roper, R. (2008). Comparison of jackup rig spudcan penetration
methods in clay. Proc. Offshore Technology Conference, Houston, OTC 19545.
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.
Skempton, A. W. (1951). The bearing capacity of clays. Building Research Congress,
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.
Walker, J. & Yu, H. S. (2010). Analysis of the cone penetration test in layered clay.
Géotechnique 60, No. 12, 939-948.
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
resistance profile in stiff-over-soft clays. Canadian Geotechnical Journal,
Submitted July 2015.
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.
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Bearing pressure, qu: kPa
Stiff
Soft
E2UNU-I-T 3E2UNU-II-T 5
Centrifuge test
LDFE, corrected su
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Normalised bearing pressure, qnet/sub0
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Normalised bearing pressure, qnet/sub0
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Normalised bearing pressure, qnet/sub0
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Normalised bearing pressure, qnet/sub0
Stiff
Soft
St = 5, 2.8 and 1
Seabed
Chapter 4. Spudcan in Stiff-over-Soft Clay
4-31
Figure 4.8 Design chart for normalised depth of peak resistance (dp/D) for spudcan
penetration in stiff-over-soft clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
4-32
4.9(a) Design chart for normalised peak resistance (qpeak/subs) for spudcan
penetration in stiff-over-soft clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Normalised bearing pressure, qnet/sub0
Upper bound, Ncd = 15.5
Lower bound,Ncd = 9.8
Chapter 4. Spudcan in Stiff-over-Soft Clay
4-39
Figure 4.14 Design chart for deep bearing capacity factor (Ncd) for spudcan
penetration in stiff-over-soft clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
4-41
Figure 4.16 Design chart for penetration resistance ratio Rsp-c at d = dp for spudcan
penetration in stiff-over-soft clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Chapter 4. Spudcan in Stiff-over-Soft Clay
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
Bearing pressure, qu: kPa
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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,
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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.
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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).
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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.
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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.
NEW MECHANISM-BASED DESIGN APPROACH
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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)
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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.
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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)
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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).
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
5-13
5.3.7 Summary Design Procedure
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.
NEW CPT-BASED DESIGN APPROACH
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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)
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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)
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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.
5.4.5 Summary Design Procedure
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,
with the limiting cavity depth estimated using Equation 5.13.
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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.
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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.
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
5-21
REFERENCE
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layered clays. Proc. 7th International Conference on Soil Mechanics and
Foundation Engineering, Mexico, 2, 45-51.
Hossain, M. S. & Randolph, M. F. (2009a). Effect of strain rate and strain softening on
the penetration resistance of spudcan foundations on clay. International Journal
of Geomechanics, ASCE 9, No. 3, 122-132.
Hossain, M. S. & Randolph, M. F. (2009b). New mechanism-based design approach for
spudcan foundations on single layer clay. Journal of Geotechnical and
Geoenvironmental Engineering, ASCE 135, No. 9, 1264-1274.
Hossain, M. S. & Randolph, M. F. (2009c). New mechanism-based design approach for
spudcan foundations on stiff-over-soft clay. Proc. Offshore Technology
Conference, Houston, OTC 19907.
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.
Hossain, M. S. (2014). Experimental investigation of spudcan penetration in multi-layer
clays with interbedded sand layers. Géotechnique 64, No. 4, 258-276.
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
multi-layered fine-grained soils. International Journal of Physical Modelling in
Geotechnics 11, No. 3, 100-115.
Hossain, M. S., Zheng, J., Menzies, D., Meyer, L. & Randolph, M. F. (2014). Spudcan
penetration analysis for case histories in clay. Journal of Geotechnical and
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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
footings on clay. Géotechnique 53, No. 5, 513-520.
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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ISO (2012). ISO 19905-1: Petroleum and natural gas industries – Site specific
assessment of mobile offshore units – Part 1: Jackups. Geneva, Switzerland:
International Organization for Standardization.
InSafeJIP (2011). Improved guidelines for the prediction of geotechnical performance
of spudcan foundations during installation and removal of jack-up units, Joint
Industry Funded Project. Woking, UK: RPS Energy.
Ma, H., Zhou, M., Hu, Y. & Hossain, M. S. (2015). Interpretation of layer boundaries
and shear strengths for soft-stiff-soft clays using CPT data: LDFE analyses.
Journal of Geotechnical and Geoenvironmental Engineering, ASCE, in press.
Meyerhof, G. G. & Chaplin, T. K. (1953). The compression and bearing capacity of
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Walker, J. & Yu, H. S. (2010). Analysis of the cone penetration test in layered clay.
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Watson, P. G., Suemasa, N. & Randolph, M. F. (2000). Evaluating undrained shear
strength using the vane shear apparatus. Proc. 10th International Offshore and
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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
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Zheng, J., Hossain, M. S. & Wang, D. (2014b). Numerical modeling of spudcan deep
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Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Bearing pressure, qu: kPa
CPT-basedapproach
LDFE
Centrifuge test
Bottom-up approach
Mechanism-based approach
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Bearing pressure, qu: kPa
CPT-based approach
LDFE
Centrifuge test
Bottom-up approach
Mechanism-based approach
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Bearing pressure, qu: kPa
Mechanism-based
approachLDFE
Centrifuge testBottom-up
approach
CPT-based approach
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Bearing pressure, qu: kPa
Mechanism-basedapproach
LDFE
Bottom-up approach
Bow
Port
Starboard
CPT-based approach
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay 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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay 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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Normalised bearing pressure, qnet/su3s
Non-uniform
Uniform
Non-uniform
su2/su3s = 1.33 and 2.5
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Normalised bearing pressure, qnet/su3s
t2/D = 0.25, 0.5 and 0.75
Non-uniform
Uniform
Non-uniform
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Normalised bearing pressure, qnet/su3s
k3D/su3s = 0,0.4, 0.8 and 1.2
Non-uniform
Uniform
Non-uniform
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Normalised bearing pressure, qnet/su0
k3D/su3s = 0,0.4, 0.8 and 1.2
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Bearing pressure, qu: kPa
LDFE
23
4
Bottom-upapproach
5
Point 1
Stage (1)
(4)
Mechanism-basedapproach
(2)
(3)
(5)
(6)
Simplified profile
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
5-42
Figure 5.12 Design chart for peak resistance depth (Point 3) in the stiff layer 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 0.2 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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
5-43
Figure 5.13 Relationship between predicted and measured or computed dr/D for
spudcan penetration in non-uniform clay with an interbedded stiff layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Chapter 5. Spudcan in Non-Uniform Clay with an Interbedded Stiff Clay Layer
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
Bearing pressure, qu: kPa
Bottom-up approach
Centrifuge test
Mechanism-based approach
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)];
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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.
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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.
NEW MECHANISM-BASED DESIGN APPROACH
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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.
6.3.3 Bearing Capacity in 1st Layer
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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).
6.3.6 Summary Design Procedure
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;
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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.
NEW CPT-BASED DESIGN APPROACH
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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.
6.4.2 Bearing Capacity in 1st Layer
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)
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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.
6.4.5 Summary Design Procedure
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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,
with the limiting cavity depth estimated using Equation 6.13.
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.
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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.
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
6-20
REFERENCE
Brown, J. D. & Meyerhof, G. G. (1969). Experimental study of bearing capacity in
layered clays. Proc. 7th International Conference on Soil Mechanics and
Foundation Engineering, Mexico, 2, 45-51.
Hossain, M. S. & Randolph, M. F. (2009). New mechanism-based design approach for
spudcan foundations on single layer clay. Journal of Geotechnical and
Geoenvironmental Engineering, ASCE 135, No. 9, 1264-1274.
Hossain, M. S. (2014). Experimental investigation of spudcan penetration in multi-layer
clays with interbedded sand layers. Géotechnique 64, No. 4, 258-276.
Hossain, M. S., Randolph, M. F. & Saunier, Y. N. (2011). Spudcan deep penetration in
multi-layered fine-grained soils. International Journal of Physical Modelling in
Geotechnics 11, No. 3, 100-115.
Houlsby, G. T. & Martin, C. T. (2003). Undrained bearing capacity factors for conical
footings on clay. Géotechnique 53, No. 5, 513-520.
InSafeJIP (2011). Improved guidelines for the prediction of geotechnical performance
of spudcan foundations during installation and removal of jack-up units, Joint
Industry Funded Project. Woking, UK: RPS Energy.
ISO (2012). ISO 19905-1: Petroleum and natural gas industries – Site specific
assessment of mobile offshore units – Part 1: Jackups. Geneva, Switzerland:
International Organization for Standardization.
Meyerhof, G. G. & Chaplin, T. K. (1953). The compression and bearing capacity of
cohesive layers. British Journal of Applied Physics 4, 20-26.
Skempton, A. W. (1951). The bearing capacity of clays. Building Research Congress,
London, 1, 180-189.
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, 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
resistance in stiff-soft-stiff clay. Journal of Geotechnical and Geoenvironmental
Engineering, ASCE, Submitted June 2015.
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
6-21
TABLES
Table 6.1 Summary of parameters for performed numerical analyses
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Bearing pressure, qu: kPa
Bottom-up approach
Centrifuge test
Mechanism-based approach
CPT-based approach
LDFE
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Normalised bearing pressure, qnet/su3
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Normalised bearing pressure, qnet/su3
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Normalised bearing pressure, qnet/su3
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Normalised bearing pressure, qnet/su3
t1/D = 0.25, 0.5 and 0.75
Stiff
Stiff
Soft
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Normalised bearing pressure, qnet/su3
Stiff
Soft
Stiff
t1/D = 0.25, 0.5 and 0.75
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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)
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Chapter 6. Spudcan in Uniform Stiff-Soft-Stiff Clay
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
Bearing pressure, qu: kPa
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.
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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.
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand 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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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-
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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.
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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.
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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.
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
7-16
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multi-layered fine-grained soils. International Journal of Physical Modelling in
Geotechnics 11, No. 3, 100-115.
Houlsby, G. T. & Martin, C. M. (2003). Undrained bearing capacity factors for conical
footings on clay. Géotechnique 53, No. 5, 513-520.
Hu, P., Stanier, S. A., Cassidy, M. J. & Wang, D. (2014a). Predicting peak resistance of
spudcan penetrating sand overlying clay. Journal of Geotechnical and
Geoenvironmental Engineering, ASCE 140, No. 2, 04013009.
Hu, P., Wang, D., Cassidy, M. J. & Stanier, S. A. (2014b). Predicting the resistance
profile of a spudcan penetrating sand overlying clay. Canadian Geotechnical
Journal 51, No 10, 1151-1164.
Hu, P., Wang, D., Stanier, S. A. & Cassidy, M. J. (2015). Assessing the punch-through
hazard of a spudcan on sand overlying clay. Géotechnique, in press.
InSafeJIP (2011). Improved guidelines for the prediction of geotechnical performance
of spudcan foundations during installation and removal of jack-up units, Joint
Industry Funded Project. Woking, UK: RPS Energy.
ISO (2012). ISO 19905-1: Petroleum and Natural Gas Industries – Site Specific
Assessment of Mobile Offshore Units – Part 1: Jack-ups. Geneva, Switzerland:
International Organization for Standardization.
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
7-17
Lee, K. K., Cassidy, M. J. & Randolph, M. F. (2013a). Bearing capacity on sand
overlying clay soils: experimental and finite-element investigation of potential
punch-through failure. Géotechnique 63, No. 15, 1271-1284.
Lee, K. K., Randolph, M. F. & Cassidy, M. J. (2013b). Bearing capacity on sand
overlying clay soils: a simplified conceptual model. Géotechnique 63, No. 15,
1285-1297.
Skempton, A. W. (1951). The bearing capacity of clays. Building Research Congress,
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.
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
7-19
Table 7.2 Summary of parameters for performed numerical analyses
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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]
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Bearing pressure, qu: kPa
Centrifuge test
LDFE
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Bearing pressure, qu: kPa
Centrifuge
LDFE
t2/D = Hs/D = 0.75
0.25
0.5
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Bearing pressure, qu: kPa
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Bearing pressure, qu: kPa
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
Punching shear method
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Bearing pressure, qu: kPa
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
Punching shear method
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Bearing pressure, qu: kPa
t3/D = 1.0
t3/D = 1.5su3s = 7.5 kPa
su3s = 15 kPa
su3s = 30 kPa
Line
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Bearing pressure, qu: kPa
t3/D = 1.0
t3/D = 1.5k3 = 1 kPa/m
k3 = 2 kPa/m
k3 = 3 kPa/m
Line
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Punching shear 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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
qpeak,meas or qpeak,comp: kPa
Hu et al. method
Lee et al. method
Load spread method
Punching shear method
Hu et al. method
Lee et al. method
Load spread method
Punching shear method
Hu et al. method
Lee et al. method
Improved through sues
Without improvement
Improved
through
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
Chapter 7. Spudcan in Multi-Layer Soils with an Interbedded Sand Layer
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
qpeak,meas or qpeak,comp: kPa
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.
Chapter 8. Concluding Remarks
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.
Chapter 8. Concluding Remarks
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
Chapter 8. Concluding Remarks
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
Chapter 8. Concluding Remarks
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.
Chapter 8. Concluding Remarks
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.
Chapter 8. Concluding Remarks
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.
Chapter 8. Concluding Remarks
8-8
REFERENCE
Hossain, M. S., Randolph, M. F. & Saunier, Y. N. (2011). Spudcan deep penetration in
multi-layered fine-grained soils. International Journal of Physical Modelling in
Geotechnics 11, No. 3, 100-115.
Hu, P., Wang, D., Cassidy, M. J. & Stanier, S. A. (2014). Predicting the resistance
profile of a spudcan penetrating sand overlying clay. Canadian Geotechnical
Journal 51, No 10, 1151-1164.
Hu, P., Wang, D., Stanier, S. A. & Cassidy, M. J. (2015). Assessing the punch-through
hazard of a spudcan on sand overlying clay. Géotechnique, in press.
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.
Recommended