Appendix spudcan fixity under combined cyclic loading

The analysis consists of three components, namely undrained effective stress Eulerian analysis of spudcan installation, mesh-to-mesh variable mapping and coupled-flow Lagrangian analysis

Post-installation pore-pressure changes around spudcan and long-term

spudcan behaviour in soft clay

Jiang Tao Yia,⇑, Ben Zhaoa, Yu Ping Lia, Yu Yanga, Fook Hou Leea, Siang Huat Goha, Xi Ying Zhangb,

a

Department of Civil & Environmental Engineering, National University of Singapore, Block E1A, #07-03, No 1 Engineering Drive 2, Singapore 117576, Singapore

b American Bureau of Shipping, ABS Plaza, 16855 Northchase Drive, Houston, TX 77060, USA

a r t i c l e i n f o

Article history:

Received 7 August 2013

Received in revised form 1 November 2013

Accepted 28 November 2013

Available online 22 December 2013

Keywords:

Eulerian analysis

Coupled-flow Lagrangian analysis

Spudcan footing

Generation and dissipation of excess

pore-pressure

Long-term bearing resistance

Rotational fixity

a b s t r a c t

This paper presents a dual-stage Eulerian–Lagrangian analysis for modelling the entire process of spudcan installation in soft clay, followed by consolidation and working load operation The analysis consists of three components, namely undrained effective stress Eulerian analysis of spudcan installation, mesh-to-mesh variable mapping and coupled-flow Lagrangian analysis for the post-installation spudcan working behaviour The results show good agreement with centrifuge model data but also highlight the importance

of replicating the hysteretic behaviour of the soil The findings also show that while a wished-in-place approach was able to model the long-term bearing response of the spudcan, rotational stiffness was over-estimated This is due to the fact that, while the wished-in-place analysis was able to model the hard-ening of the soil ahead of the spudcan, it was unable to model the softhard-ening of back-flowed soil behind spud-can The latter influences the spudcan fixity significantly, but not bearing response Although the analyses were conducted using ABAQUS, they can, in principle, be conducted using other codes

Ó 2013 Elsevier Ltd All rights reserved

1 Introduction

Spudcans are widely used as footings for offshore jack-up rigs

Spudcan installation in soft clay is essentially an undrained deep

penetration event involving soil flow and excess pore pressure

gen-eration[1] As the subsequent operational period of jack-up rig can

be as long as 5 years[2], dissipation of the excess pore pressure

will alter the state of the soil, and thus the working behaviour of

the spudcan, which includes bearing capacity and rotational fixity

Hence, the long-term spudcan behaviour is likely to be

signifi-cantly affected by post-installation changes in pore pressure

The working behaviour of spudcan foundations is often

ana-lyzed by wishing the spudcan into place with the surrounding soil

having an assumed stress state and strength distribution[3–6]

This is due to the fact that spudcan installation is a deep

penetra-tion problem which can only be addressed by large-deformapenetra-tion

approaches such as Eulerian or Arbitrary Lagrangian–Eulerian

(ALE) analysis[7,8] As most large-deformation spudcan analyses

to date[7–12]are based on total stress approaches, effective stress

and excess pore pressure cannot be computed and post-installa-tion, pore pressure dissipation cannot be analyzed

More recently, an undrained, effective stress Eulerian approach for analyzing spudcan installation in clay was proposed by Yi et al

[1], who postulated that if a coupled-flow Lagrangian analysis can

be dovetailed with such an effective stress Eulerian analysis, it may

be well suited to solving the post-installation, working behaviour

of spudcan foundations This paper realizes the above postulation

by presenting a method of conducting such a dual-stage Euleri-an–Lagrangian analysis The analysis consists of three components, namely undrained effective stress Eulerian analysis of spudcan installation, mesh-to-mesh variable mapping and coupled-flow Lagrangian analysis for the post-installation spudcan working behaviour As the undrained effective stress Eulerian analysis has been reported previously [1], this paper focuses on the mesh-to-mesh mapping and coupled-flow Lagrangian analysis Two examples are presented to illustrate the effect of consolidation

on the bearing capacity and rotational fixity of a spudcan The ana-lytical results are benchmarked against centrifuge model data and compared with results of wished-in-place analyses

2 Solution mapping from Eulerian to Lagrangian analyses

As the undrained effective stress analysis for spudcan installa-tion has been reported by Yi et al.[1], only a brief outline will be presented herein Essentially, the effective stress computation is

0266-352X/$ - see front matter Ó 2013 Elsevier Ltd All rights reserved.

⇑ Corresponding author Address: Centre for Protective Technology, National

University of Singapore, No 12 Kent Ridge Road, Singapore 119223, Singapore.

Tel.: +65 65164566; fax: +65 67761002.

E-mail addresses: ceeyj@nus.edu.sg (J.T Yi), ceezhaoben@nus.edu.sg (B Zhao),

ceelyp@nus.edu.sg (Y.P Li), yang.yu@nus.edu.sg (Y Yang), ceeleefh@nus.edu.sg

(F.H Lee), ceegsh@nus.edu.sg (S.H Goh), xyzhang@eagle.org (X.Y Zhang), jwu@

eagle.org (J.-F Wu).

Computers and Geotechnics

j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / c o m p g e o

achieved by appropriately adding the bulk modulus of water to an

effective stress constitutive model within the user subroutine

VUMAT of ABAQUS/Explicit where the Eulerian calculation can be

conducted This allows the near-incompressibility of the soil as a

whole to be reflected in the total stress–strain matrix, and the

effective stress and pore pressure to be separately computed

with-in VUMAT In the present study, this effective stress computation

technique is used in the first, or Eulerian, stage of the analysis

The second stage of the analysis involves coupled-flow

Lagrang-ian computation As the effective stress EulerLagrang-ian analysis has to be

solved in ABAQUS/Explicit[1]while the coupled-flow Lagrangian

analysis has to be conducted in ABAQUS/Standard[13], the results

of the effective stress Eulerian analysis have to be ported over as

input to the Lagrangian analysis to perform the dual-stage

Euleri-an–Lagrangian analysis There are also some other differences

be-tween the first and second stages In the Eulerian computation,

pore pressure is treated as an integration point variable [1]; in

the Lagrangian computation, it is regarded as a nodal

degree-of-freedom[13] In addition, the Eulerian analysis requires a very fine

mesh around the spudcan to maintain computational stability and

reduce high-frequency noise For the coupled-flow Lagrangian

analysis, such a fine mesh is often unnecessary, and may, in fact,

destabilize the computation due to excessive element distortion

in regions that undergo large deformation This can occur, for in-stance, in the backflow region behind the spudcan, where the soil may undergo large deformation during consolidation All these dif-ferences mean that a robust solution mapping process is needed to transfer the solution variables, viz stresses, pore pressure and void ratio, from the Eulerian analysis to the Lagrangian analysis Since ABAQUS’ built-in mapping algorithm for advection of element vari-ables in ALE and Eulerian analyses do not support Eulerian-to-Lagrangian mapping, a solution mapping algorithm has to be developed outside ABAQUS’ environment

2.1 Interpolation methods Four interpolation methods were examined for solution map-ping, namely the nearest-neighbour interpolation (N–n) method, inverse-distance weighted (IDW) method, Delaunay triangulation with linear interpolation (DTL) and natural neighbour interpola-tion (NNI) In the nearest-neighbour interpolainterpola-tion method, the va-lue of the nearest point in the Eulerian mesh, hereafter termed

‘‘reference field’’, is assigned to prescribed point of the Lagrangian mesh, hereafter termed ‘‘destination field’’ Since the nearest neighbour interpolation only considers the nearest neighbour point, it tends to yield discontinuous, piecewise-constant interpo-lated data

In the inverse-distance weighted (IDW) method, the interpo-lated value is calcuinterpo-lated by distance-weighted averaging the values

of the reference field in the neighbourhood of the interpolated location The interpolated value f(X) is given by

f ðXÞ ¼Xk i¼1

where k is the number of original data points in the neighbourhood,

uithe reference field value of the ith original data point andxia weighting function A common basis for assigning the weighting function is the inverse power of distance d between the interpolated location and original data point This leads to

xi¼ dP=Xk

i¼1

where p is inverse-distance index A typical range of p is 2–4 and a value of 3.5 is adopted in this study; this is also the recommended value in Hu and Randolph[14]

In Delaunay triangulation with linear interpolation (DTL), the reference field is first decomposed into a collection of Delaunay triangles or ‘‘tiles’’ As shown inFig 1, for the two dimensional (2D) space (i.e plane), Delaunay triangles are constructed in such

a way that the circle circumscribing any triangle does not contain

Fig 1 Voronoi diagram and Delaunay triangulation.

any other data point The original data points of reference field

correspond to the vertices of Delaunay triangles The tile enclosing

the interpolated location is then identified, the value of the

desti-nation field at this location interpolated from the values of the

three vertices of the tile using the shape functions of a three-noded

triangular element For three-dimensional (3D) interpolations, the

triangles are replaced by tetrahedrons

The natural neighbour interpolation (NNI)[15]is related to the Voronoi cell of a node, which is an enclosed area around the node where all points are closer to this node than any other node,Fig 2a shows AsFig 1illustrates, the Voronoi cell is the geometric dual of Delaunay triangles The natural neighbours of a node are those nodes whose Voronoi cells have common boundaries with it In

6m 1.7 0.5 1.5

Spudcan dimensions

40°

0.9 LRP

(a)

(b)

A

B

Fig 3 3D Eulerian FEM model (a) undeformed and (b) deformed.

in the reference field When an node X from the destination field is

introduced, the Voronoi cells are re-defined by the new boundaries

‘ab’ to ‘fa’’, between X and P1–P6, as shown inFig 2b The natural

neighbour coordinates of X with respect to its ith neighbours

/i(X) are defined as the ratios of their respective overlapping areas

to the total area of the Voronoi cell of X, e.g the natural neighbour

coordinate of X with respect to P1 is given by

/1ðXÞ ¼ AreaðagbÞ

The interpolated value f(X) at X is then determined using

f ðXÞ ¼Xk

where k is the number of natural neighbours Ledoux and Gold[16]

noted that the natural neighbour interpolation can produce a smoother and more continuous interpolating surface, compared to the other methods, particularly for irregularly distributed data The natural neighbour interpolation scheme is similar, in principle,

to the second-order advection method implemented in the Eulerian analysis of ABAQUS, which is also based on area/volume-weighted averaging[13]

2.2 Evaluation of different mapping algorithms

To evaluate the performance of these mapping techniques, an undrained effective-stress Eulerian analysis was first conducted using the 3D finite element model of a spudcan with a diameter

of 6 m, continuously penetrated to a depth of 16.5 m in normally consolidated soft clay,Fig 3 The clay was modelled using the modified Cam-Clay model, with properties shown inTable 1 The stress, pore pressure and void ratio results were used as the refer-ence fields for spatial interpolation

The interpolation algorithms were coded using MATLAB outside

of ABAQUS environment The spudcan installation problem is 2D axisymmetric but as Eulerian analysis can only be conducted for 3D models[1], the reference field so generated is also 3D On the other hand, Lagrangian consolidation analysis can be conducted using either 2D axisymmetric or 3D mesh For this reason, the per-formance of the interpolation techniques was assessed for both 3D-to-2D-axisymmetric mapping and 3D-to-3D mapping For the former, the interpolation was only done within a radial plane of original 3D reference field For the latter, interpolation was carried out throughout the whole model

3D-to-2D-axisymmetric mapping andFigs 5–7show the total pore pressure (u), void ratio (e) and radial effective stress ðr0

rrÞ interpo-lated using the four methods in 3D-to-2D-axisymmetric mapping The N–n interpolation produced jagged interpolated contours with evident discontinuities The IDW algorithm produces smoother contours, but fine discontinuities are still discernible, for example

at the 250 kPa and 300 kPa contours near the bottom boundary

and NNI methods (Fig 5c and d) produced interpolated fields which are significantly smoother Both are visually so close to the original that the reference and its corresponding interpolated fields cannot be readily distinguished

To further quantify their interpolation accuracy, two set of nodes, labelled A and B, were chosen in the original reference field As Fig 4a shows, set A consists of 41 nodes in the fine mesh region and set B consists of 35 nodes in the coarse mesh region The values of the reference field at these locations repre-sent the reference values For each node, an interpolated value is then computed using the values of the surrounding nodes and then compared with its reference value The absolute difference between the interpolated and reference value is then taken to

be the interpolation error at that node.Table 2shows four statis-tical measures of the interpolation errors of the two node sets, which are

Mean absolute error MAE ¼1

n

Xn i¼1

Mean relative error MRE ¼1

n

Xn i¼1

yi y0

yi



Root mean square error RSME ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1

n

Xn i¼1ðyi y0Þ2

r

ð7Þ

Table 1

Cam-clay properties of kaolin clay (with reference to Goh [26] ).

m/s

Specific of soil at critical state at a mean effective

stress of 1 kPa (C)

3.221

(a) Reference field

(b) Destination field Fig 4 Mesh configuration in 3D-to-2D solution mapping.

Coefficient of determination R2¼ 1 

Pn i¼1ðyi y0Þ2

Pn i¼1ðyi yÞ2 ð8Þ

where n is the number of data, yiand y0the reference and

interpo-lated value of the ith point, and y the mean of the reference data As

can be seen from Table 2, the MAE, MRE and RSME show much

greater differences between the four interpolation methods than

the R2-value, indicating that they are more discriminating

Gener-ally, the interpolation errors are more significant in the dense mesh

area than coarse mesh region For node set A, the NNI method

consistently returns the smallest error For node set B, the DTL

algo-rithm performs slightly better in pore pressure and radial effective

stress interpolation while the NNI algorithm gives the lowest error

for the void ratio This may be attributed to the fact that the

reference fields change more rapidly in the dense mesh zone than

in the coarse mesh zone, as illustrated inFigs 5–7 The DTL method

assumes that field values vary linearly within each Delaunay

trian-gle It is thus more suited to capturing the gradual changes in coarse

mesh zone than the rapid changes in the dense mesh zone Overall,

the NNI algorithm appears to be effective for both dense and coarse

mesh zones

A similar exercise was also conducted for the 3D-to-3D

interpo-lation, using 131 nodes from the dense mesh area (those enclosed

within box ‘‘A’’ inFig 3b) and 68 nodes from the coarse mesh zone

(those enclosed within box ‘‘B’’ inFig 3b) As shown inTable 3, the

trend remains the same, with the NNI method returning the lowest error in the fine mesh zone as well as the void ratio field in the coarse mesh zone, and the DTL method returning the lowest error for the pore pressure and radial effective stress fields in the coarse mesh zone

the dense mesh area where rapid changes in field values occur Hence, the interpolation technique should be able to minimise the interpolation errors in this area For this reason, the NNI

meth-od was chosen as the interpolation technique for the examples below

3 Example 1: long-term spudcan bearing response 3.1 Finite element model

The first example involves the installation, unloading, long-term consolidation and reloading of a spudcan footing Spudcan installation was conducted using undrained effective stress

Euleri-an Euleri-analysis with the mesh shown inFig 3a The soil domain was discretized into eight-noded Eulerian brick elements, whose con-stitutive behaviour was represented using the modified Cam-Clay (MCC) with parameters as shown in Table 1 The spudcan was modelled as a rigid Lagrangian body as its deformation is expected

to be much smaller than that of the soil Spudcan–soil interaction

Radial distance (m)

-25

-20

-15

-10

-5

Radial distance (m)

-25 -20 -15 -10 -5

Radial distance (m)

-25 -20 -15 -10 -5 0

Radial distance (m)

-25

-20

-15

-10

-5 0

Unit: kPa

Fig 5 Pore pressure (u) field before and after mapping (denoted by dash and solid line respectively).

was modelled using the Eulerian–Lagrangian contact algorithm

which is an extension of ABAQUS’ general contact formulation

[13] The Eulerian–Lagrangian contact is based on an enhanced

im-mersed boundary method which can automatically compute and

track the interface between the Eulerian soil domain and

Lagrang-ian spudcan body The intrusion of LagrangLagrang-ian body can push

material out of the Eulerian elements so that no overlap exists

be-tween the Lagrangian body and the material in the Eulerian

do-main Friction was not considered in the analysis as the contact

friction model in ABAQUS/Explicit only deals with total, not

effec-tive, stress Hossain et al.[10]found that, for the deeply penetrated

spudcan, spudcan–soil friction does not appear to affect the critical

cavity depth and bearing capacity factor significantly

The spudcan was penetrated down to a depth of 16.5 m or 1.4 D

below mudline,Fig 3b The boundary of the deformed mesh was

then extracted from one radial section of Eulerian model and used

to define the initial geometry of the axi-symmetric Lagrangian

model inFig 8 Four-noded bilinear Lagrangian elements with

dis-placement and pore-pressure degrees-of-freedom were used for

the consolidation analysis As noted by Yi et al.[17], the first-order

element appears to be numerically more stable than the

higher-or-der element in solving problems with relatively large deformation

since it is less susceptible to element gross distortion Zhou et al

[5] similarly used four-noded quadrilateral elements to model the extraction of spudcan Zhang et al.[4]and Templeton[3]also made use of first order hexahedral elements to study the bearing capacity and rotational fixity of spudcan The soil in the Lagrangian analysis was modelled using ABAQUS’ built-in modified Cam-clay (MCC) model with the same property set (Table 1) The spudcan deformation was again idealised as a rigid body

The Lagrangian consolidation analysis was conducted in three stages The first stage was a dummy stage with a very short dura-tion of 15 min, to re-establish stress equilibrium after soludura-tion mapping When solution variables were mapped from Eulerian to Lagrangian mesh via spatial interpolation, some amount of stress and pore pressure errors are inevitably introduced, thereby result-ing in some out-of-balance forces within the Lagrangian mesh Allowing these out-of-balance forces to equilibrate helps to reduce subsequent errors and enhance computational stability

The second stage modelled the consolidation process after re-moval of the spudcan preload; the latter being modelled by a 25% reduction in axial loading from the penetration load while drainage was permitted at the top soil surface In reality, the jack-up rig can

be stationed at a location for several years[2], during which it can

be subjected to highly variable loading conditions In order to study the effects of consolidation, a 5-year duration was prescribed for

Radial distance (m)

-25

-20

-15

-10

-5

0

Radial distance (m)

-25 -20 -15 -10 -5 0

(a) N-n

Radial distance (m)

-25

-20

-15

-10

-5

0

Radial distance (m)

-25 -20 -15 -10 -5 0

(b) IDW

Fig 6 Void ratio (e) field before and after mapping (denoted by dash and solid line respectively).

this stage and the only loading on the spudcan being the dead and

working live load from the jack-up in the form of a static axial load

This does not detract from the aim of this paper which is to present

a method of analyzing long-term behaviour of spudcan The

intro-duction of a ‘‘quiet’’ consolidation period of 5 years also allows the effect of consolidation to be fully manifested In the third stage, the spudcan was re-loaded to evaluate its post-consolidation load– displacement response To accommodate the large soil deformation

Radial distance (m)

-25

-20

-15

-10

-5

Radial distance (m)

-25 -20 -15 -10 -5

(a) N-n

Radial distance (m)

-25

-20

-15

-10

-5

0

Radial distance (m)

-25 -20 -15 -10 -5 0

(c) DTL

(b) IDW

(d) NNI

Unit: kPa

Fig 7 Radial effective stress ðr0

rr Þ field before and after mapping (denoted by dash and solid line respectively).

Table 2

Errors for 3D-to-2D-axisymmetric interpolation (bolded rows indicated method with the lowest error measures).

Pore pressure (u)

Void ratio (e)

Radial effective stress ðr0

rr Þ

anticipated in the spudcan re-loading stage, the nonlinear geometry

option of ABAQUS/Standard was activated in the Lagrangian

analy-sis This feature involves transferring the state of the model at the

end of one step to the next step as its initial state Also, since

con-ventional infinitesimal strain measures might not be appropriate

given the large deformations and distortions, logarithmic strains

were adopted

3.2 Analysis results

con-solidation As shown inFig 9d, after about 180 days of

consolida-tion, pore pressure is fairly close to hydrostatic This is also

reflected in the plots of excess pore pressure normalised by the

in situ effective vertical stress, hereafter termed excess pore

pres-sure ratio[1], Fig 10a–d As Fig 10a shows, just after spudcan

installation, very significant excess pore pressure is present down

to a depth of about 1.5 times the radius below the spudcan tip

Much of this excess pore pressure dissipated within about

6 months after installation The actual time required for

consolida-tion will depend upon the modulus of the soil and its coefficient of

permeability However, the properties used herein are fairly

repre-sentative of medium plasticity clay Hence the duration is not

en-tirely unrealistic for such soils

effective stress (p0) and undrained shear strength (su) (i.e those be-fore and after 5 years consolidation) The undrained shear strength

suis inferred from Wroth’s[18]relationship

su¼M

2p

0 Ri

2

 K

ð9Þ

where Riis the isotropic overconsolidation ratio andK= (k j)/k Both sets of contours reflect a similar pattern, with the largest in-crease beneath the spudcan base, and a zone of weak, back-flowed soil behind the spudcan The increase in undrained shear strength is also reflected in the ‘‘strength improvement ratio’’, defined as the ratio of the long-term, post-consolidation undrained shear to the

in situ shear strength [19], shown in Fig 13a–d The long-term strength improvement ratio contour is similar in shape to the short-term excess pore pressure contour (Fig 10a) This is not sur-prising since the dissipation of excess pore pressure translates into mean effective stress, and therefore strength increase Both the un-drained shear strength (Fig 12) and strength improvement ratio plots (Fig 13) indicate the formation of a hardened soil plug be-neath the spudcan and a zone of weak soil behind the spudcan Within the hardened soil plug, soil strength increases by as much

as 80% (Fig 13d) At a depth of about R below the spudcan tip, the strength improvement ratio is approximately 1.5

stage)’’ in the graph) of the spudcan from installation through re-moval of preload, consolidation to reloading The penetration depth in the graph corresponds to the distance from the spudcan conical tip to the mudline As can be seen, the reloading response differs significantly from the initial loading response The post-consolidation spudcan foundation behaves as if it had been pre-loaded to a much higher level The Lagrangian analysis could not continue beyond Point F as excessive mesh distortion caused the computation to terminate This is not surprising since the total set-tlement from Point B to Point F is approximately 3 m, which is quite large for a Lagrangian computation At the turning Point E, the reloading settlement is approximately 1.6 m, which is more than 10% of the spudcan diameter In subsequent discussion, Point

E will be considered as the point at which failure was initiated Comparison of the bearing pressure at Point E with the pre-con-solidation penetration resistance, that is Point B, indicates a signif-icant increase in resistance of about 58% Yi et al.’s [1] results indicated that the bearing capacity factor during installation is about 12.5 Applying the same bearing capacity factor to the

Table 3

Errors for 3D-to-3D interpolation (bolded rows indicated method with the lowest error measures).

Pore pressure (u)

Void ratio (e)

Radial effective stress ðr0

rr Þ

Fig 8 Lagrangian FEM model for 2D-axisymmetric coupled flow calculation.

post-consolidation bearing capacity obtained from Point E would

lead to an equivalent strength increase of about 58%, which is

the strength increase at the spudcan axis at a depth of 0.7R beneath

the tip (Fig 13d) Using the strength increase at a depth of R

be-neath the tip with the same bearing factor would lead to a bearing

capacity increase of about 50%, which is slightly conservative This

suggests that one may be able to estimate the post-consolidation

bearing capacity of the spudcan by using the post-consolidation

strength of the soil at a depth of R below the tip

3.3 Comparison with centrifuge results

The computed result inFig 14was compared with the

load-set-tlement curve measured in a centrifuge spudcan model in normally

consolidated kaolin under 100-g model gravity The modelling

equipment as well as preparation and test procedures have been

reported by Li et al.[20]and will not be repeated herein The

cen-trifuge test modelled the same sequence of events as those

simu-lated in the numerical analysis The trends indicated by the

centrifuge and numerical results are similar throughout the entire

sequence of events The centrifuge measurements show a slightly

lower penetration resistance during installation than the

com-puted resistance The comcom-puted and measured consolidation

set-tlements agree remarkably well On the other hand, during reloading, the centrifuge data indicate a stiffer response than the numerical results

The preceding overestimate of penetration resistance during installation occurs probably because the analysis does not consider the effect of strength degradation as soil flows around the spudcan, which was similarly noted by Hossain et al.[10] The observed dis-crepancy during reloading, on the other hand, is likely related to the occurrence of partial consolidation in the experiment at the beginning of the reloading stage In the centrifuge experiment, a closed-loop servo-control hydraulic loading system was employed

to actuate the spudcan model A load control mode was adopted during consolidation stage to maintain a working load level on the spudcan, which was subsequently switched to displacement mode at the beginning of the reloading stage Due to the change

of control mode and the enhanced soil stiffness after consolidation, some time was required for the servo-control hydraulic loading system to build up the needed hydraulic pressure to achieve the target penetration rate (i.e the undrained rate) As a consequence, some partial consolidation might have occurred before the un-drained target penetration rate was attained The resulting partial consolidation would lead to a stiffer soil response than the numer-ical prediction

Radial distance (m)

-25

-20

-15

-10

-5

Unit: kPa

Radial distance (m)

-25 -20 -15 -10 -5

Radial distance (m)

-25

-20

-15

-10

-5

0

Radial distance (m)

-25 -20 -15 -10 -5 0

Fig 9 Total pore pressure contours (a) at the beginning of consolidation, (b) after 35 days consolidation, (c) after 90 days consolidation, (d) after 180 days consolidation.

0 0.5 1 1.5 2 2.5 3

Radial distance, r/R

-1.5

-1

-0.5

0

0.5

1

Radial distance, r/R

-1.5 -1 -0.5 0 0.5 1

Radial distance, r/R

-1.5

-1

-0.5

0

0.5

1

Radial distance, r/R

-1.5 -1 -0.5 0 0.5 1

(a) (b)

(c) (d)

Fig 10 Excess pore pressure ratio contours (a) at the beginning of consolidation, (b) after 35 days consolidation, (c) after 90 days consolidation, (d) after 180 days consolidation Horizontal and vertical co-ordinates are normalised by the spudcan radius.

Radial distance (m)

-25

-20

-15

-10

-5

0

Radial distance (m)

-25 -20 -15 -10 -5 0

Unit: kPa

0