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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
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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
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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).
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B
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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.
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