Applied Ocean Research 41 (2013) 9–18

Contents lists available at SciVerse ScienceDirect

Applied Ocean Research

journa l homepage: www.e lsev ier .com/ locate /apor

CPT based prediction of foundation penetration in siliceous sand

T. Puckera,*, B. Bienenb, S. Henkea

aHamburg University of Technology, Institute for Geotechnical Engineering and Construction Management, Harburger Schloßstraße 20, D-21079 Hamburg, GermanybCentre for Offshore Foundation Systems, University of Western Australia, 35 Stirling Highway, Crawley, Perth, WA 6009, Australia

a r t i c l e i n f o

Article history:

Received 25 July 2012

Received in revised form 5 December 2012

Accepted 28 January 2013

Keywords:

Offshore engineering

Numerical modelling

Bearing capacity

Spudcan

a b s t r a c t

The load–penetration response of a foundation is one of the fundamental aspects of geotechnical engineering.

In sand, the bearing capacity approach requires the operative friction angle to be known, which introduces

significant uncertainty to the prediction. The predictive method developed in this paper eliminates the need

to determine the friction angle. The central concept is the direct correlation of in situ piezocone penetrometer

measurements to the load–penetration response of foundations.

The correlation factor is shown to depend primarily on the sand relative density. The footing shape has a

minor influence on the correlation factor. This study aims at large diameter foundations used in the offshore

industry, where the variation in correlation coefficient is minor. However, context is provided to previous

research on smaller diameter foundations, which shows the dependence on the footing diameter (through

the well-known stress level effect).

The proposed method is shown to perform well against load–penetration data from centrifuge experiments on

footings of different diameters and elevation shapes. The performance against field data in particular provides

significant confidence in the CPT based prediction method of foundation penetration in sand developed here.c© 2013 Elsevier Ltd. All rights reserved.

Fig. 1. Jack-up platform with spudcan footings (modified after [1]), cone tip resistance

profile and spudcan load–penetration curve (schematic).

1. Introduction

Mobile jack-up platforms (Fig. 1) are extensively used in the off-

shore energy sector, in the oil and gas industry as well as for con-

struction of offshore wind installations. The platforms footings are

penetrated into the soil until the foundation resistance equals the

platform self-weight plus any preload in the form of water ballast.

This is a significant distinction from onshore practice, where foot-

ings are placed on the (excavated) soil surface. The most important

difference, however, arises from the requirement of accurate, not con-

servative, prediction of the load–penetration curve as this critically

influences further aspects of foundation behaviour during operation,

such as stiffness, sliding resistance, storm-induced additional pene-

tration and scour. Prediction of the spudcan penetration resistance

therefore is a key step in ensuring the stability and functionality of

offshore jack-up rigs on site. Application of a factor of safety in order

to absorb uncertainties in the prediction is not helpful.

The predicted load–penetration curve is usually constructed

through application of the classical bearing capacity theory at a suc-

cession of discrete depths. This current practice requires the friction

angle to be known, with which the bearing capacity factors are eval-

uated. The influences of relative density, stress level and compress-

ibility on the operative friction angle (which is recommended to be

obtained from triaxial testing) are recognised but treated differently

* Corresponding author. Tel.: +49 428783820.

E-mail address: pucker@tuhh.de (T. Pucker).

0141-1187/$ - see front matter c© 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.apor.2013.01.005

by the relevant guidelines [2–4].

The preceding relies on one single, constant operative friction an-

gle to be applicable, which is inferred from laboratory measurements.

The obtained value reflects the test boundary conditions, which may

differ from the in situ relative density and anisotropy due to the

involved uncertainties. Additionally the mobilised friction angle de-

pends on the mean stress at failure, which is also an unknown. Al-

ternatively, charts summarising empirical relations of the friction an-

gle (via the relative density) with in situ cone penetration tests are

10 T. Pucker et al. / Applied Ocean Research 41 (2013) 9–18

p

m

f

i

i

c

e

a

s

h

d

u

p

s

m

t

d

d

d

s

o

l

t

r

l

(

m

a

o

e

a

c

j

o

2

i

T

m

i

2

v

a

fi

t

a

a

b

f

t

a

o

m

rovided in Lunne et al. [5]. Unfortunately, the bearing capacity for-

ulation is rather sensitive, with a small uncertainty in the operative

riction angle translating to a large uncertainty in the predicted bear-

ng capacity.

Furthermore, despite significant effort in producing bearing capac-

ty factors Nγ (include [6–17]) for various footing geometries (strip,

ircular, flat, conical), depth, load inclination and eccentricity, the rel-

vant factors remain uncertain. This is less a reflection of solution

ccuracy (e.g. [18] but of the influence of non-associativity on the

and behaviour. The effective dilatancy during a spudcan installation,

owever, is not only difficult to estimate, it will also not be constant

uring the penetration process.

Offshore site investigation for jack-up installation to date does not

sually include (advanced) onshore laboratory testing. In situ cone

enetration tests (CPTs), however, are often included in the offshore

ite investigation workscope. This creates a strong incentive towards

ore direct use of in situ test data, particularly from cone penetrome-

er tests. Both the ISO [3] and InSafeJIP [4] guidelines recommend such

irect correlations as an alternative to current practice. However, no

etails are provided.

This contribution therefore introduces a method to directly pre-

ict the load–penetration behaviour of a large diameter footing in

and based on CPT data, without the requirement to determine the

perative friction angle. The idea is illustrated schematically in Fig. 1.

The method developed here is based on an extensive database of

oad–penetration curves. These were obtained, in part, through cen-

rifuge experimentation and complemented by a numerical paramet-

ic study using a technique appropriate for large-deformation prob-

ems. The parametric study spans relevant foundation diameters D

10–20 m) and enclosed cone angles (120–180◦) and considers loose,

edium dense and dense silica sand.

The innovation of direct correlation between cone tip resistance

nd footing behaviour recognises the similarity of the penetrating

bject (in essence two footings of different sizes). However, consid-

ration is given here also to the intrinsic differences. The validity

nd accuracy of the proposed methodology are evaluated through

omparison with measured results from centrifuge model tests and

ack-up field installations. These comparisons confirm the potential

f the new robust, simple and practical prediction method.

. Numerical model of foundation penetration

This paper relies on a number of experimental data sets obtained

n the geotechnical centrifuge at stress levels similar to the prototype.

hese data are complemented by an extensive series of large defor-

ation numerical analyses. The approach and numerical model used

n these analyses are described in this section.

.1. Lagrangian and Eulerian description

There are two alternatives to describe the movement of a small

olumetric element as a function of time: the Lagrangian approach

nd the Eulerian approach.

Lagrangian approach: The movement of the continuum is speci-

ed as a function of the material coordinates and time. This is the

raditional approach used in conventional small strain finite element

nalyses. The nodes of the Lagrangian mesh move with the material

s it deforms. The interface between two parts is accurately tracked

ecause the part surfaces are exactly defined by its nodes. Large de-

ormations may lead to severe mesh distortions and pose limitations

o this approach.

Eulerian approach: The movement of the continuum is specified

s a function of the spatial coordinate and time. This approach is

ften used in fluid mechanics. A Eulerian reference mesh, which re-

ains stationary enables the motion of the material to be traced.

Materials can move freely through a Eulerian mesh, which remains

undeformed.

2.2. Coupled Eulerian–Lagrangian (CEL) method

The coupled Eulerian–Lagrangian (CEL) method aims at capturing

the advantages both of the Lagrangian and the Eulerian method. This

approach is available in Abaqus [19] and was used for the numerical

parametric study of foundation penetration reported here. Its appro-

priateness for similar large-deformation geotechnical problems has

been shown by Qiu et al. [20] and Tho et al. [21]. In the analyses the

movement of the Eulerian material through the mesh is tracked by

computing its Eulerian volume fraction (EVF). Each Eulerian element

is designated a percentage, which represents the portion of that ele-

ment filled with a material. If an Eulerian element is completely filled

with a material, its EVF is 1; if there is no material in the element, its

EVF is 0.

2.2.1. Time integration scheme

The CEL method is implemented in Abaqus/Explicit [19]. The cen-

tral difference rule is employed for the solution of the non-linear

system of differential equations. In the explicit integration scheme

the unknown solution for the next time step can be found directly

from the solution of the previous time step, such that no iteration

is required. Another advantage is the robustness regarding difficult

contact conditions.Explicit calculations are not unconditionally stable. Numerical sta-

bility is guaranteed by introduction of the critical time step size tcrit

which depends on the characteristic element length Le and the dila-tory wave speed cd. The critical time step size is calculated in everytime step via

�tcrit = L e

cd. (1)

Therefore, both the mesh size and the material stiffness influence the

critical time step size.

In the current study the critical time step size is further reduced to

guarantee stability throughout all analyses and to take into account

different wave speeds due to the stress dependent soil stiffness.

2.2.2. Penalty contact formulation

Contact between Eulerian and Lagrangian structures is enforced

using a general contact formulation that is based on a penalty method.

The algorithm does not enforce contact between the Lagrangian ele-

ments and the Eulerian elements. The Lagrangian elements can move

through the Eulerian mesh without resistance until they encounter

an Eulerian element filled with material (EVF �= 0). The penalty con-

tact method is less strict compared to the kinematic contact method

used in the Lagrangian approach. It approximates hard pressure-

overclosure behaviour. This method allows small penetration of the

Eulerian material into the Lagrangian domain.

2.3. Numerical model of the foundation

This study is aimed primarily at jack-up spudcans. Therefore, flat

and conical circular footings with diameters D of 10, 12, 14, 16, 18

and 20 m (Fig. 2) were investigated to encompass spudcan footings

currently used in the field. The angle β enclosed by the conical geom-

etry was varied between 120◦, 150◦ and 180◦, the latter giving a flat

footing profile. Though representing a large deformation problem, the

penetration of such large footings into silica sand will not result in

complete burial at realistic stress levels. The actual discretization of

the jack-up leg is therefore irrelevant and the trusswork structure is

idealized here as a single tubular section.

The footing and the leg were modelled as a discrete rigid body,

a Lagrangian part, with its reference point located at the centre of

T. Pucker et al. / Applied Ocean Research 41 (2013) 9–18 11

Fig. 2. Footing geometry and notation.

Table 1

Characteristics of UWA silica sand.

Parameter Value

d50 0.19 mm

Index of uniformity U 1.9

ϕcv 30◦

Minimum dry density 14.9 kN/m2

Maximum dry density 18.0 kN/m2

Fig. 3. Example mesh for the numerical simulations of foundation penetration in uni-

form sand.

the lowest footing cross-section of maximum diameter as indicated

in Fig. 2. The roughness was taken as 0.5, which is appropriate for

spudcans in the field [4].

The footings are penetrated into the soil at a constant penetration

velocity (applied at the footing reference point), which was selected

based on considerations of computational efficiency whilst ensuring

the response to remain quasi-static (via the energy balance). Though

the selected footing penetration rates (≤1 m/s, depending on the

sand relative density and footing diameter) are higher than those

in the field, the numerical results are not affected due to velocity-

independency of the chosen constitutive model.

2.4. Numerical model of the soil domain

The soil in the numerical model was given the characteristics of

the silica sand (Table 1) used in centrifuge testing at the University of

Western Australia (UWA).

The relative density DR was varied in the parametric study, cov-

ering loose (20%), medium dense (45%) and dense sand (75%). As

the target application concerns offshore foundations, the effective

unit weight was considered. However, since foundation penetration

is assumed to be fully drained, the pore pressure response was not

modelled numerically.

The soil was modelled as an Eulerian domain. Abaqus requires CEL

analyses to be performed in three dimensions due to the Eulerian

element type available, which is an 8 node element with reduced

integration. Taking advantage of the axisymmetry of the problem,

the soil domain is modelled as a quarter of a cylinder. An example

mesh of the numerical model is shown in Fig. 3a. Fig. 3b illustrates

the capability of the CEL approach to model the footing penetration

into the sand.

Velocity boundary conditions are imposed on the soil domain,

preventing vertical movement at the base and lateral movement at the

sides, respectively. Only vertical movement of the footing is allowed.

2.5. Constitutive model

The hypoplastic constitutive model of von Wolffersdorff [22] with

the extension of intergranular strain by Niemunis and Herle [23] is

used in this paper. The constitutive model is able to realistically repro-

duce the nonlinear and inelastic behaviour of granular materials like

sand. Specific characteristics of sands are considered, including dila-

tancy, different stiffnesses for loading and unloading paths, barotropy

and pycnotropy. The stiffness and the peak friction angle depend on

the current stress state T (barotropy) and the current void ratio e

(pycnotropy). The latter enables changes from contractive to dilatant

behaviour to be modelled, one of the main advantages of the hy-

poplastic constitutive model, and a critical state can be obtained. The

failure surface of the model matches the failure criterion of Matsuoka

and Nakai [24]. In the hypoplastic formulation, the strain is not di-

vided into elastic and plastic components. The constitutive model is

expressed by the tensor function of Eq. (2):

◦T= M (T , e, δ) : D (2)

where◦T is the objective stress rate, D the strain rate and M a fourth

order tensor, which depends on the current Cauchy stress T, the void

ratio e and the intergranular strain δ [23].

The hypoplastic parameters for the UWA silica sand (Table 2) were

calibrated against standard laboratory tests including the angle of

repose, oedometer and triaxial tests on loose and dense samples, see

Fig. 4. The first oedometer was performed on a sample with a void

ratio e = 0.70 and the second on a sample with a void ratio e = 0.56.

The sample of the triaxial test has an initial void ratio e = 0.65 and

is consolidated to a K0 stress state with σ 1 = 120 kPa and σ 2 = 60

kPa. The shear process in the triaxial test is performed with drained

conditions.

The parameters hs and n mainly influence the compression be-

haviour. The dilatancy and contractancy are influenced by the actual

void ratio and its relative position to the critical void ratio ec0 with

the limits ed0 and ei0. The exponents α and β influence the effective

friction angle. The cyclic behaviour and the small strain stiffness are

controlled by R, mR, mT, βR and χ .

2.6. Validation of the numerical model

The numerical model was validated by comparison with two sepa-

rate example sets of centrifuge test results. Despite being small scale

experiments, the centrifuge environment of enhanced gravity (ng)

results in stress levels comparable to the prototype. Therefore, cen-

trifuge test data are well suited to validate the numerical models.

White et al. [25] investigated the penetration of flat and conical

circular footings into the same sand that is used for the numerical

12 T. Pucker et al. / Applied Ocean Research 41 (2013) 9–18

Table 2

Hypoplastic material parameters for silica sand.

Parameter Value Description

ϕc 30 Critical state friction angle (◦)

hs 1354 Granular hardness (MPa)

n 0.34 Exponent

ed0 0.49 Minimum void ratio

ec0 0.76 Critical void ratio

ei0 0.86 Maximum void ratio

α 0.18 Exponent

β 1.27 Exponent

R 1 x 10−4 Max. value of intergranular strain

mR 5.16 Stiffness ratio at a change of

direction of 180◦

mT 3.07 Stiffness ratio at a change of

direction of 90◦

βR 0.58 Exponent

χ 5.74 Exponent

Fig. 4. Comparison of the hypoplastic constitutive model against standard laboratory tests; left: loose oedometric test; centre: dense oedometric test; right: medium dense triaxial

test.

Fig. 5. Validation of numerical model.

a

v

i

i

C

t

W

d

d

d

a

nalyses here. The largest equivalent prototype footing diameter in-

estigated was 4.8 m, less than half the size of the footings considered

n this study. The centrifuge test results of the β = 150◦ cone penetrat-

ng into dry sand of 54% relative density are compared in Fig. 5 with

EL results obtained using the same footing geometry and soil condi-

ions. The footing roughness was assumed as α = 0.5, consistent with

hite et al. [25]. Further, a comparison with centrifuge data of footing

iameters relevant to this study is included in Fig. 5. The prototype

iameter of this flat footing is 12 m [26]. The relative density of the

ry UWA silica sand sample was 45%. The footing base was modelled

s rough in the CEL analysis, corresponding to the experiment.

The data are presented in terms of the nominal bearing pressure

qnom (vertical load V divided by the full footing area A) and the pene-

tration depth w normalised by the full footing diameter D. In particular

over the range of bearing capacity pressures qnom relevant in practice

(up to ∼1000 kPa), the numerical results demonstrate a close match

with the experimental data, providing confidence in the numerical

model. In practice a penetration depth w/D about 0.1 in middle dense

to dense sand and up to 0.25 w/D in loose sand, see Orvey [27], is

expected.

Loose sand samples are not technically feasible to be tested in

the centrifuge. Though load–penetration curves on dense sand are

available, those of White et al. [25] were not deemed reliable as some

of these were softer than the results obtained on medium dense sand.

The experiments of Bienen et al. [26] were not designed to obtain full

load–penetration curves, such that the available data are insufficient

to assess the CEL results for the higher relative density.

2.7. Overview of the numerical parameteric study

Table 3 provides a summary of the numerical CEL analyses con-

ducted within this parametric study. All parameter combinations

were considered.

3. Results of CEL analyses

Example results of the CEL parametric study are presented in Figs.

6 and 7 in terms of the bearing pressure qnom and the normalised

penetration depth w/D. The bearing pressure qnom = V/A is calculated

by fraction of the vertical load V and the area A.

T. Pucker et al. / Applied Ocean Research 41 (2013) 9–18 13

Table 3

Summary of calculations.

Parameter Value considered

D (m) 10, 12, 14, 16, 18, 20

DR 20%, 45%, 75%

β (◦) 120, 150, 180

Fig. 6. Load–penetration curves for different cone angles β , a footing diameter D = 10

m and relative density DR = 45%.

Fig. 7. Load–penetration curves for β = 150◦ , varying footing diameter and relative

sand density.

Fig. 6 compares the load–penetration response of the three foot-

ing shapes (enclosed angles of 120◦ and 150◦, respectively, and a flat

footing with constant diameter D = 10 m). Corresponding to Fig. 2,

zero penetration is achieved as the lowest cross-section of the full

footing diameter is level with the original soil surface. Therefore, the

conical footings mobilise resistance already at negative normalised

penetration. The footing shape in elevation determines the initial

mobilisation of bearing capacity, with the initial part of the curves

in Fig. 6 exhibiting a steeper gradient the lower the enclosed angle

of the footing (i.e. the sharper the cone). The shallow general shear

failure mechanism, identified through examination of the CEL instan-

taneous velocity plots, is mobilised at different penetration depths

[28]. At larger penetration depth (w/D ∼ 0.2), however, the three

curves merge as the response becomes independent of the cone an-

gle (within the range investigated here).

In order to predict a load–penetration curve it is therefore not suf-

ficient to step through a bearing capacity analysis at discrete depths,

taking into account the conical footing shape (for instance by using

the bearing capacity factors developed by Cassidy and Houlsby [9]

for conical footings). This is because the initial capacity mobilisation

differs depending on the cone angle, whilst the capacity at larger

penetration depths becomes independent of the cone angle.

Fig. 7 shows the CEL results of a 150◦ conical footing, the most

relevant for typical spudcan designs. The load–penetration curves

for a 10 m and a 20 m diameter footing in both medium dense and

dense sand are presented. The figure illustrates both the effect of sand

relative density and the increase in bearing pressure with increasing

foundation size. This results in the larger diameter footing offering

similar bearing capacity on medium dense sand as the foundation of

half the diameter on the same sand in a dense state.

4. Cone penetrometer resistance profile

The cone penetration resistance qc depends on the stress state σ ′p

and the void ratio e as indicated in Eq. (3), which has been suggested

in similar form by various researchers [29–31].

qc = C 0 · pa

(σ ′

p

pa

)C 1

· exp(C 2 ·DR ) (3)

where C0, C1 and C2 are dimensionless constants, σ ′p the mean effec-

tive initial stress and DR the relative density given as real number. DR

is defined as

DR = emax − e

emax − emin, (4)

σ ′P as

σ ′P = σ ′

v + 2 · σ ′h

3. (5)

The reference pressure pa is taken as 100 kPa. The parameter emax is

the maximum and emin the minimum void ratio of the soil.

While numerous results of miniature cone penetrometer tests in

the same silica sand are available form centrifuge testing performed

at UWA, these cannot be relied upon for the development of a direct

correlation method. This is because the 7 mm diameter CPT, when

tested at 200 g, represents a prototype diameter of 1.4 m, i.e. 39 times

the diameter of a standard CPT.

The CPT profiles used in the remainder of this paper to investigate

the correlation between cone penetration resistance and the bear-

ing capacity of large diameter (spudcan) foundations are therefore

established on the basis of numerical CEL analyses, similar to those

described in detail above. The parameters C0, C1 and C2 for the UWA

silica sand are provided in Eq. (6), whilst Fig. 8 demonstrates a fit of

the approximation in comparison with the numerical results. In Fig.

8 Dcone is the diameter of the CPT cone. Additionally, the results of

the approximation equation are validated against two centrifuge CPT

data, see Fig. 9.

qc = 128 · pa

(σ ′

p

pa

)0.65

· e(2.38·DR ) (6)

5. Development of CPT based prediction method of foundation

penetration in sand

Predicted spudcan load–penetration curves are typically con-

structed from bearing capacity calculations at a series of discrete

depths. This requires knowledge of the operative friction angle, which

can be obtained from laboratory triaxial testing or estimated from

cone tip resistance data (indirect correlation).

5.1. Current guideline recommendations: friction angle from triaxial

testing

The SNAME [2] guidelines recommend compensation for the dif-

ferences between bearing capacities predicted with friction angles

ϕ′ derived from triaxial tests, which may be in the range of 30–40◦,

and observed behaviour of spudcan penetration in the field through

14 T. Pucker et al. / Applied Ocean Research 41 (2013) 9–18

Fig. 8. Comparison of CPT-profiles from CEL simulation (solid lines) and calculated

CPT-profile (dashed lines).

Fig. 9. Comparison of CPT-profiles from centrifuge data (solid lines) and calculated

CPT-profile (dashed lines).

a

o

t

m

c

i

T

n

i

b

t

l

e

b

5

t

o

c

l

o

p

t

B

t

c

5◦ reduction of the measured laboratory peak friction angle. A table

f estimated operative friction angles is provided in case no labora-

ory data is available. For loose to medium dense sand, these recom-

ended values are as low as 15◦. The ISO guidelines [3] recommend

areful consideration in the friction angle selection, with triaxial test-

ng to be carried out at the relevant relative density and stress level.

he friction angle resulting from this testing protocol, however, does

ot account for compressibility. Similar to ISO, the guidelines result-

ng from the recent InSafe Joint Industry Project [4], recommend the

earing capacity prediction to be based on a realistic friction angle, i.e.

he friction angle obtained from triaxial testing at the relevant stress

evel and relative density. In contrast to the other guidelines, how-

ver, the InSafeJIP guidelines recommend reduction of this theoretical

earing capacity, not the friction angle, by a mobilisation factor.

.2. Currently available methods (indirect correlation)

Several empirical methods are reported in Lunne et al. [5] to de-

ermine the friction angle from CPT data. One approach is to rely

n empirical correlations to estimate the in situ relative density. In

onjunction with soil gradation characteristics and the in situ stress

evel, ϕ′ can be estimated based on an empirical correlation [32]. The

ther approach is to find ϕ′ directly. Robertson and Campanella [33]

roposed a relationship between cone tip resistance, vertical effec-

ive stress and the friction angle based on calibration chamber tests.

oth approaches introduce uncertainty in the derivation of the fric-

ion angle, which is used in the bearing capacity calculation. It is not

lear that the friction angle obtained from the empirical correlations

is appropriate for use in the prediction of a load–penetration curve of

a large diameter foundation such as spudcans that exert high stresses

on the soil. The Schmertmann [32] correlation suggests a peak fric-

tion angle ϕ′ = 37◦ for a uniform medium sand. The cone resistance

qc expected in a medium dense sand at vertical effective stress levels

corresponding to the low penetration typical of spudcans (2–4 m) ap-

proaches the limits of the Robertson and Campanella [33] chart, which

suggests friction angles of 40–44◦ for this case. Based on comparisons

of bearing capacity predictions and observed field penetrations, the

SNAME [2] guidelines on the other hand suggest a friction angle ϕ′ =25◦ to be appropriate for spudcan footings on siliceous sand. This brief

discussion indicates the level of uncertainty attached to the selection

of an appropriate friction angle to use in load–penetration predictions

for spudcans.

Further, currently available bearing capacity factors neither ac-

count for non-associativity (though even then the question remains

what angle of dilation is appropriate at which penetration depth)

nor the conical shape of the footing, as discussed in the introduction.

Loukidis and Salgado [15] investigate the bearing capacity of strip

and circular footings in sand using a non-associated flow rule and de-

velop more realistic bearing capacity factors. However, Loukidis and

Salgado [15] use a constant dilatation angle ψ which does not con-

sider the influence of compaction processes due to the penetration

process.

Unfortunately, the bearing capacity approach is rather sensitive

to the operative friction angle assumed, compounding the level of

uncertainty attached to the load–penetration prediction.

5.3. Proposal of new direct correlation method

Rather than inferring a friction angle from the cone penetration

resistance to use in the bearing capacity equation, a direct correla-

tion of the cone tip resistance qc with the penetration resistance of

a footing is developed here. Especially in the case of spudcans, both

the cone penetrometer tip and the footing represent conical objects

penetrating into the soil, albeit of significantly different size.

For ease of practical use, a correlation via a constant factor f is

proposed, as outlined in Eq. (7):

qnom = V

A= f · qc · Aeff

A(7)

where qnom is the footing bearing pressure (i.e. the vertical load V

with respect to the full projected bearing area A), qc the cone tip

resistance and Aeff the effective bearing area of the conical footing.

The penetration depths of the cone penetration resistance is equal to

the spudcan penetration depths defined by the reference point in Fig.

2.

The current effective bearing area is found through, in effect, rep-

resentation of the conical footing by a flat footing of equivalent vol-

ume at the same penetration depth (Eqs. (8) and (9)). The notation is

explained schematically in Fig. 10.

Voleff =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

1

3zeff ·

(Deff

2

)2

π if zeff ≤ htip(1

3htip + (

zeff − htip

)) ·(

Deff

2

)2

π if zeff > htip

(8)

Aeff = Volef f

zeff(9)

where Voleff is the current volume not occupied by the soil (Fig. 10)

and zeff is the current footing penetration depth, measured from the

soil surface to the lowest point on the footing.

The conversion of a conical into a flat footing with equivalent

volume accounts for the influence of the cone angle β on the load–

penetration curve. Thus, the initial dependence of the resistance

T. Pucker et al. / Applied Ocean Research 41 (2013) 9–18 15

Fig. 10. Illustration of notation used to calculate the equivalent footing.

Table 4

Correlation factors f.

DR β (◦) D (m)

10 12 14 16 18 20

120◦ 0.33 0.36 0.37 0.38 0.38 0.39

20% 150◦ 0.35 0.37 0.38 0.39 0.40 0.41

180◦ 0.36 0.38 0.39 0.40 0.41 0.42

120◦ 0.31 0.34 0.35 0.36 0.38 0.40

45% 150◦ 0.34 0.35 0.37 0.40 0.41 0.42

180◦ 0.40 0.40 0.41 0.41 0.42 0.43

120◦ 0.21 0.22 0.23 0.23 0.24 0.25

75% 150◦ 0.23 0.23 0.24 0.25 0.25 0.26

180◦ 0.24 0.25 0.25 0.26 0.26 0.27

Fig. 11. Comparison of predicted load–penetration curves (solid lines) with numerical

results (dashed lines).

mobilisation on the cone angle is captured. Further, with increas-

ing footing embedment, the influence of the footing elevation shape

diminishes [28] as the effective bearing area of the conical footing

approaches the full bearing area of the flat footing and the spudcan

resistance becomes independent of the elevation shape of the footing

(i.e. conical or flat) at larger penetration depths (Fig. 6).

Based on the CEL parametric study, the following correlation fac-

tors f are suggested (Table 4).

Load–penetration curves obtained with this direct correlation ap-

proach (dotted lines) are compared with the numerical results (solid

lines) in Fig. 11.

Fig. 12 shows predictions with the proposed direct correlation

approach and load–penetration curves obtained from experiments in

the geotechnical centrifuge, where stress similitude to the prototype

is maintained. The 12 m diameter flat footing results [26] are the same

as in Fig. 5. The load–penetration curves of the 10 m diameter spudcan

are available for two relative sand densities (DR ≈ 84% [34], and DR ≈37% as well as 84% [34]). The spudcan base encloses an angle of 154◦,

and it has a small central tip with an enclosed angle of 74◦. Before the

correlation, the spudcan shape is converted to an equivalent conical

footing (following [2–4]) of 10 m diameter and 1.21 m cone height,

resulting in an enclosed cone angle of 153◦.

6. Case study: in situ spudcan penetration prediction

The proposed correlation method was applied without any modi-

fications to three jack-up spudcan field installations. These were part

of the InSafe Joint Industry Project, the largest database of jack-up

field data that have been collected to date [35]. The confidential na-

ture of the project does not allow details of the cases to be shared.

However, Table 5 provides a summary of the values that are relevant

to this study, without compromising confidentiality. In all three cases,

the spudcan diameter was just under 18 m, with the bearing pressure

at full preload of about 600 kPa. The spudcan has a tip at the bottom

which has to be considered calculating the equivalent embedded vol-

ume. The cone tip resistance qc at the spudcan preload penetration

depths of 1.6–1.8 m suggests that the sand at sites 1 and 3 was dense

and medium dense at site 2.

The comparisons in Figs. 11 and 12 illustrate the performance

of this simple, practical method that eliminates the determination

of a friction angle appropriate in the prediction of load–penetration

curves of large diameter flat or conical footings, against numerical and

centrifuge experimental data, respectively. Table 5 further demon-

strates that the correlation factors applicable to spudcan installations

in the field are similar to those applicable to the centrifuge and nu-

merical data (Table 4). This provides confidence in the proposed direct

correlation method with the factors listed in Table 4 for loose, medium

dense and dense siliceous sand.

7. Discussion of the proposed new direct correlation method

Ratios of bearing pressure to cone tip resistance have been pub-

lished by a number of researchers, of which Randolph et al. [36] pro-

vide a summary. These ratios, obtained for small diameter founda-

tions (mainly piles) from full scale tests, calibration chamber tests,

and numerical analysis, vary within a range of 0.1–0.2 for medium

dense and dense sands at 0.1D embedment. At 0.05D embedment,

the published ratios tend to lie within a range of 0.1–0.14. Lee and

Salgado [37] propose correlation factors of between 0.2 and 0.36 for

small diameter footings (1–3 m) at w/D = 0.2. The authors are not

16 T. Pucker et al. / Applied Ocean Research 41 (2013) 9–18

Table 5

Correlation method applied to jack-up spudcan field installations.

Case Vertical load Diameter Bearing pressure Penetration depth

Cone tip resistance

qc Corr. factor f

(MN) D (m) (kPa) (m) (MPa)a

1 144.2 17.9 573.0 1.8 7.4 0.23

2 150.0 17.8 604.7 1.6 4.0 0.45

3 147.2 17.8 591.3 1.7 8.0 0.24

a The cone top resistance qc is taken at the tip of the cone with a volume equivalent to the embedded volume of the spudcan.

Fig. 12. Comparison of predicted and measured load–penetration curves: (a) 10 m

diameter spudcan on medium dense sand, (b) 10 m diameter spudcan on dense sand,

(c) 12 m diameter flat footing on medium dense and dense sand.

Fig. 13. Influence on stress level effect on correlation factor on medium dense sand.

aware of a published approximation function that provides the cor-

relation coefficient with depth.

The correlation factors of Lee and Salgado [37] and this study are

shown in Fig. 13. Further included are factors obtained with the cor-

relation method proposed here and the small diameter footing data

of White et al. [25]. The foundation size introduces a stress level ef-

fect, which is well recognised by geotechnical engineers. The present

study confirms the findings by Lee and Salgado [37] that the corre-

lation factor (i) decreases as the relative density increases and (ii)

increases non-linearly with the footing diameter, as shown in Fig. 14.

The proposed method suggested here uses a depth independent

correlation factor, which facilitates application in practice. Examina-

tion of the load–penetration curve predictions obtained with mea-

sured data and numerical CEL results suggests that the error intro-

duced by a constant correlation factor is small in comparison with the

measurement accuracy during jack-up spudcan installation. There-

fore, a more accurate description of the correlation factor with pene-

tration depth is not being pursued so as not to increase the complexity

of the method unnecessarily for practical application.

Further, the correlation method proposed here is versatile as it re-

lates the measured cone tip resistance profile directly to the spudcan

response. This is in contrast to the method proposed in the InSafeJIP

report [35], for instance, where the CPT profile is approximated with

a constant gradient, which is then correlated to the spudcan load–

penetration curve. This adds complexity in profiles where the sand

relative density changes with depth, resulting in changes to the qc

gradient.

Load–penetration curves of spudcans in the field are expected to

be smoother than the penetration profiles with the much smaller

cone. The direct correlation method as it is currently proposed does

not include an averaging mechanism. However, this could be incor-

porated without adding significant complexity. An averaging distance

of 0.3D is considered as appropriate, which is similar to the averaging

distance suggested for layered soils in the InSafeJIP [4].

Similar to the cone penetrometer, only end bearing of the spudcan

is considered in the proposed correlation method. Back-flow, such

that sand comes to rest on top of the penetrating spudcan, as well as

sidewall friction are neglected.

T. Pucker et al. / Applied Ocean Research 41 (2013) 9–18 17

Fig. 14. Influence of DR , D and β on the correlation factor f.

The differences between the cone and spudcan penetration re-

sistances are summarised in the correlation factor. This includes the

failure mechanism, which will be a deep cavity expansion style mech-

anism for the cone for any penetration depths other than within ∼10

cone diameters of the soil surface, and the shallow general shear fail-

ure mechanism for the spudcan.

Only normally consolidated sands were considered here. It is well

known that the cone penetrometer resistance is influenced not only

by the vertical, but also the horizontal effective soil stresses in situ [5].

While this is included in the CPT approximation provided in Eq. (6),

it is acknowledged that validation of the direct correlation method

for spudcan load–penetration curves on over-consolidated sand is

outside the scope of this paper.

Further research to extend the direct correlation approach to un-

cemented carbonate sand is currently ongoing.

The proposed method assumes fully drained behaviour both in

the cone penetration test and in the penetration of the much larger

footing. Procedures for footing penetrations in less permeable soils

where there is the possibility of partial drainage are discussed in Lee

and Randolph [38] and Houlsby and Cassidy [39].

8. Conclusions

Bearing capacity is one of the geotechnical problems that has re-

ceived considerable research attention. This approach is sensitive to

the operative friction angle assumed which, especially in the case of

offshore soils, may be subject to significant uncertainty. The predictive

method suggested here directly links site investigation data obtained

in situ from piezocone penetrometer tests to load–penetration curves

of large diameter footings, thus eliminating the need to determine a

friction angle.

The method is demonstrated to perform well against load–

penetration data from centrifuge experiments. Importantly, it is

shown to perform well against field data. This provides significant

confidence in the use of the method in practice. The correlation fac-

tors obtained in this study broadly align with previous research on

much smaller diameter foundations. Based on the extensive paramet-

ric study conducted herein, differentiation of the correlation factor

with regards to the sand relative density, the footing diameter and

elevation shape is offered.

In addition to offering a practical approach that eliminates the re-

quirement of determining the operative friction angle, the proposed

new direct correlation method can be used to obtain the harden-

ing law in macro-elements for site-specific assessment of jack-up

spudcan capacity under combined loading in the operational phase

of deployment.

Acknowledgments

The present work forms part of the research in the research

training group “Seaports for Container-Ships of Future Generations”

and the project “Finite element based multicriterial numerical op-

timization of geotechnical structures in the service limit state”

(GR-1024-9-1) funded by the German Research Foundation (DFG).

The funding is greatly appreciated. The second author is the recipi-

ent of an Australian Research Council (ARC) Postdoctoral Fellowship

(DP110101603). The work described here forms part of the activities

of the Centre for Offshore Foundation Systems (COFS), the ARC Cen-

tre of Excellence in Geotechnical Science and Engineering, and the

Lloyds Register Educational Trust (The LRET), an independent charity

working to achieve advances in transportation, science, engineering

and technology education, training and research worldwide for the

benefit of all. This support is gratefully acknowledged.

References

[1] Reardon M. Review of the geotechnical aspects of jack-up unit operations.

Ground Engineering. 1986;19(7):21–6.[2] SNAME. Site specific assessment of mobile jack-up units. SNAME (Society of

Naval Architects and Marine Engineers). 1st ed., Technical and Research Bulletin5-5A, New Jersey; 2008.

[3] ISO. Petroleum and natural gas industries site-specific assessment of mobileoffshore units. Part 1. Jack-ups. International Organization for Standardization,

ISO/FDIS 19905-1; 2011.

[4] Osborne JJ, Teh KL, Houlsby GT, Cassidy MJ, Bienen B, Leung CF. InSafeJIP. Im-proved guidelines for the prediction of geotechnical performance of of spudcan

foundations during installation and removal of jack-up units. Available fromhttp://insafe.woking.rpsplc.co.uk/download.asp.

[5] Lunne T, Robertson P, Powell J. Cone penetration testing in geotechnical practice.London: Spon Press; 1997.

[6] Drescher A, Detournay E. Limit load in translational failure mechanisms for

associative and non-associative materials. Geotechnique. 1996;43(3):443–56.[7] Manoharan N, Dasgupta S. Bearing capacity of surface footings by finite ele-

ments. Computers and Structures. 1995;54(4):563–86.

18 T. Pucker et al. / Applied Ocean Research 41 (2013) 9–18

[25] White D, Teh K, Leung C, Chow Y. A comparison of the bearing capacity of flat

and conical circular foundations on sand. Geotechnique. 2008;58(10):781–92.[26] Bienen B, Gaudin C, Cassidy M. Centrifuge tests of shallow footing behaviour on

sand under combined vertical-torsional loading. International Journal of Physi-cal Modelling in Geotechnics. 2007;7(2):1–21.

[27] Orvey R. Predicting spudcan penetration in loose sand from measured site soil

parameters. In: Proceedings of 7th international conference on offshore siteinvestigation and geotechnics 2012, London, UK. 2012, pp. 589–96.

[28] Bienen B, Henke S, Pucker T. Numerical study of the bearing behaviour of circularfootings penetration into sand. In: Proc. of 13th international conference of

international association for computer methods and advances in geomechanics(IACMAG). 2011, pp. 939–44.

[29] Hsu H-H, Huang A-B. Calibration of cone penetration test in sand. In: Proc. ofNational Science Council, vol. 23. 1999, pp. S579–S590.

[30] Jamiolkowski M, Lo Presti D, Manassero M. Evaluation of relative density and

shear strength of sands from cone penetration test (CPT) and flat dilatometer(dmt). In: JT Germain, TC Sheahan, RV Whitman (Eds.), Soil behaviour and soft

ground construction ASCE, GSP; 2003, vol. 119, pp. 201–38.[31] Grabe J, Konig F. Zur aushubbedingten Reduktion des Drucksondierwider-

standes. Bautechnik. 2004;81(7): S569–S577.[32] Schmertmann J. Guidelines for cone penetration test, performance and design.

US Federal Highway Administration, Washington, DC. Report FHWA-TS-78-209;

1978.[33] Robertson P, Campanella R. Interpretation of cone penetrometer test. Part I.

Sand. Canadian Geotechnical Journal. 1983;20(4):718–33.[34] Bienen B, Cassidy M, Gaudin C. Physical modelling of the push-over capacity of

a jack-up structure on sand in a geotechnical centrifuge. Canadian GeotechnicalJournal. 2009;46(2):190–207.

[35] Osborne J, Houlsby G, Cassidy M, Randolph M, Leung C, Teh K, et al. Insafe jip,

first year progress report. In: RPS Energy; 2009.[36] Randolph M, Jamiolkowski M, Zdravkovic L. Load carrying capacity of founda-

tions. In: Skempton memorial conference - advances in geotechnical engineer-ing 1. London, UK. 2004, pp. 207–40.

[37] Lee J, Salgado R. Estimation of bearing capacity of circular footings on sandsbased on cone penetration test. Journal of Geotechnical and Geoenvironmental

Engineering (ASCE). 2005;131(4):442–52.

[38] Lee J, Randolph M. Penetrometer-based assessment of spudcan penetration re-sistance. Journal of Geotechnical and Geoenvironmental Engineering (ASCE).

2011;137(6):587–96.[39] Houlsby G, Cassidy M. A simplified mechanically based model for predict-

ing partially drained behavior of penetrometers and shallow foundations.Geotechnique Letters. 2011. http://dx.doi.org/10.1680/geolett.11.00031.

[8] Frydman S, Burd H. Numerical studies of bearing-capacity factor Nγ . Journal of

Geotechnical and Geoenvironmental Engineering (ASCE). 1997;123(1):20–9.[9] Cassidy M, Houlsby G. Vertical bearing capacity factors for conical footings on

sand. Geotechnique. 2002;52(9):687–92.[10] Erickson H, Drescher A. Bearing capacity of circular footings. Journal of Geotech-

nical and Geoenvironmental Engineering (ASCE). 2002;128(1):38–43.

[11] Kumar J. Effect of footing–soil interface friction on bearing capacity factor Nγ .Geotechnique. 2004;54(10):677–80.

[12] Hjiaj M, Lyamin A, Sloan S. Numerical limit analysis solutions for the bear-ing capacity factor Ngamma. International Journal of Solids and Structures.

2005;42(5):1681–704.[13] Martin C. Exact bearing capacity calculations using the method of character-

istics. In: Proc. 11th international conference of the international associationfor computer methods and advances in geomechanics (IACMAG), vol. 4. Torino,

Italy. 2005, pp. 441–50.

[14] Lyamin A, Salgado R, Sloan S, Prezzi M. Two- and three-dimensional bearingcapacity of footings in sand. Geotechnique. 2007;57(8):647–62.

[15] Loukidis D, Salgado R. Bearing capacity of strip and circular footings in sandusing finite elements. Computers and Geotechnics. 2009;36:871–9.

[16] Perkins S, Madson C. Bearing capacity of shallow foundations on sand: a relativedensity approach. Journal of Geotechnical and Geoenvironmental Engineering.

2011;126(6):521–30.

[17] Loukidis D, Salgado R. Effect of relative density and stress level on the bearingcapacity of footings on sand. Geotechnique. 2011;61(2):107–19.

[18] Martin C. New software for rigorous bearing capacity cal calculations. In: Proc.British geotechnical association international conference on foundations (ICOF).

Dundee, UK. 2003, pp. 581–92.[19] Dassault Systemes. Abaqus user manual version 6.10; 2010.

[20] Qiu G, Henke S, Grabe J. Application of a coupled Eulerian-Lagrangian ap-

proach on geomechanical problems involving large deformation. Computersand Geotechnics. 2010. http://dx.doi.org/10.1016/j.compgeo.2010.09.002.

[21] Tho K, Leung C, Chow Y, Swaddiwudhipong S. Eulerian fi-nite element technique for analysis of jack-up spudcan pen-

etration. International Journal of Geomechanics (ASCE). 2011.http://dx.doi.org/10.1061/(ASCE)GM.1943-5622.0000111.

[22] von Wolffersdorff P-A. A hypoplastic relation for granular materials with a

predefined limit state surface. Mechanics of Frictional and Cohesive Materials.1996;1:251–71.

[23] Niemunis A, Herle I. Hypoplastic model for cohesionless soils with elastic strainrange. Mechanics of Frictional and Cohesive Materials. 1997;2:279–99.

[24] Matsuoka H, Nakai T. A new failure for soils in three-dimensional stresses.In: Proceedings IUTAM - symposium on deformation and failure of granular

materials. 1982, pp. 253–63.