Consolidated undrained capacity of shallow foundations subjectedto self-weight and horizontal in-service loading
C. VULPE� and J. J. NEWMAN†
The effect of subsea infrastructure self-weight and pipeline in-service horizontal loading on theconsolidated undrained capacity of deep-water shallow foundations was investigated by means of fullycoupled three-dimensional finite-element analyses. The results show that the undrained uniaxial andcombined capacity increase under horizontal preloading and over realistic in-field loading timeregimes. The gain in undrained capacity is quantified through simple equations incorporating a criticalstate soil mechanics framework and is defined as a function of magnitude and duration of vertical andhorizontal preload, foundation embedment ratio and soil–skirt interface roughness.
INTRODUCTIONDeep-water subsea infrastructure is designed to resist pipe-line expansion/contraction exerted during start-up and shut-down operations, in other words, in-service loading. Theduration of these operations may last months at a time. Uponapplication of foundation self-weight or in-service loading,excess pore water pressure is generated around the soil inthe vicinity of the subsea foundation. Over time, the soilconsolidates and its undrained shear strength increases,leading to an increase in bearing capacity.
The self-weight of deep-water infrastructures is low, com-monlymobilising less than 50%of the available unconsolidatedundrained capacity. The deep sea architecture is generallyconstructedwell in advance of commencement of hydrocarbonreserves extraction operations, leaving sufficient time for theexcess pore water pressure generated under the low self-weightof the structure to dissipate. The effect of self-weight (vertical)preloading and consolidation on the undrained capacity ofshallow foundations has been previously investigated (Bransby,2002; Zdravkovic et al., 2003; Chatterjee et al., 2014;Gourvenec et al., 2014; Feng & Gourvenec, 2015; Fu et al.,2015; Vulpe et al., 2016a, 2016b) but the effect of in-servicehorizontal loading on the undrained response of shallowfoundations has not been previously considered. The pipelineexpansion/contraction loading is cyclic and the soil consoli-dates following each cyclic loading event until a critical state isreached. Nonetheless, the first in-service loading scenario isexpected to generate the largest improvement in undrainedshear strength. The effect of the initial in-service horizontalload on the undrained shear strength of soil is the object of thecurrent study.
The present study proposes a method for predicting theconsolidated undrained capacity of skirted circular foun-dations as a function of relative magnitude and duration of
both foundation self-weight and in-service preload, foun-dation embedment ratio and soil–skirt interface roughness.
FINITE-ELEMENT MODELA program of over 2000 three-dimensional small-
strain finite-element analyses was performed using Abaquscommercial finite-element computer software (DassaultSystèmes, 2012). The meshes of skirted circular foundationswith embedment depth, d, to foundation diameter, D, ratiosof d/D=0, 0·10, 0·25 were modelled. Figure 1 illustrates atypical finite-element mesh used in the analyses. The freesurface of the mesh, unoccupied by the foundation, wasprescribed as a drainage boundary; the other mesh bound-aries and the foundation were modelled as impermeable.The ‘wished-in-place’ skirted foundations were represented
as rigid bodies with a single reference point (RP) located atskirt tip level along the centreline of the foundation. The skirtinternal wall–soil interface was prescribed as fully bonded(accounting for undrained response to uplift); the skirt outerwall–soil interface was prescribed as either fully bonded(rough in shear and no separation allowed) or fully smooth(frictionless).Themodified CamClay (MCC) critical statemodel (Roscoe
& Burland, 1968) was used to represent the coupled elasto-plastic pore fluid–stress behaviour of a typical kaolin clayinvestigated in the current study. The kaolin clay MCCparameters are listed in Table 1 (Stewart, 1992). A surchargeequivalent to 1 m of soil overburden was imposed on the soilmass at the free surface in order to avoid zero shear strength atthe mudline. The soil is considered to be one-dimensionallyconsolidated (K0) and the in situ effective stresses varyaccording to the prescribed soil unit weight (Table 1). Therelationship between the undrained shear strength of the soil,su, which linearly increases with depth, and the in situ effectivevertical stress, σ′v, is given by Potts &Zdravkovic (1999). Detailsof the adopted MCC model used in the current study arepresented by Gourvenec et al. (2014) and Vulpe et al. (2016a).
Limitations of the MCC modelThe MCC critical state model approach models a linear
elastic soil response inside the Von Mises circular yield
� School of Civil, Environmental andMining Engineering, formerlyCentre for Offshore Foundation Systems, University of WesternAustralia, Perth, WA, Australia.† School of Civil, Environmental and Mining Engineering,University of Western Australia, Perth, WA, Australia.
Manuscript received 18 October 2015; revised manuscript accepted25 May 2016. Published online ahead of print 26 July 2016.Discussion on this paper closes on 1 May 2017, for further detailssee p. ii.
Vulpe, C. & Newman, J. J. (2016). Géotechnique 66, No. 12, 1028–1034 [http://dx.doi.org/10.1680/jgeot.15.T.036]
surface, defined in Abaqus by setting the flow stress ratioK=1. Changes in pore pressure result only from changes inmean effective stress. Thus, the constitutive model may notexactly replicate the actual stress path during consolidation inover-consolidated deposits at stress levels less than thepre-consolidation pressure.The undrained shear strength of clay is dependent on the
direction of the major principal stress with respect to the axisof consolidation (Duncan & Seed, 1966). That is, underisotropic and anisotropic consolidation, the soil reachesdifferent ultimate limit states. For clay, the anisotropy ofthe undrained shear strength is the result of stress-inducedanisotropy (Ohta & Nishihara, 1985). This anisotropy occurswhen the initial stress state acting during K0-consolidation ischanged by increasing shear stress up to failure underundrained conditions, along with principal stress rotation.The undrained shear strength under vertical, horizontal
or moment loading is represented by the combination ofsoil failed in triaxial compression, triaxial extension andplane strain conditions. The effect of induced anisotropy onthe undrained shear strength of soil failed in triaxialcompression and plane strain conditions is relatively negli-gible (Mayne, 1985; Toyota et al., 2014). A more pronounced
effect is observed for triaxial extension tests on clay (Mayne,1985); the difference in the undrained shear strength of soilfollowing isotropic and anisotropic consolidation is found tobe dependent on the governing shearing mechanism. Theeffect of stress-induced anisotropy on the undrained shearstrength of the clay cannot be handled by the MCC model.The effect is more pronounced for overconsolidated soils.Nonetheless, Zdravkovic et al. (2003) predicted that theundrained shear strength of overconsolidated soils followingconsolidation is likely to be conservative following finite-element analyses withMCC. TheMCCmethod is best suitedto modelling the response of normally consolidated andlightly overconsolidated soils. The current study consideredonly normally consolidated clay.
METHODOLOGYInitially, analyses were carried out to determine the
unconsolidated undrained vertical (Vuu) and horizontal(Huu) capacities for each foundation condition. Then,analyses were performed to determine the uniaxial andcombined capacity for each foundation as a function ofrelative magnitude and duration of both vertical andhorizontal preload. A vertical preload (Vp) was imposed, inundrained conditions, as a fraction of the Vuu relative to thefoundation system, taking values of Vp/Vuu = [0·1, 0·7] atintervals of 0·2 followed by full primary consolidation.Consolidation was prescribed by allowing the excess porewater pressure generated by the applied preload to dissipatethrough the imposed drainage boundary. The foundation wasthen subjected to horizontal preloading (Hp), applied at theRP, as a fraction of the relative Huu. The horizontal preloadtakes values of Hp/Huu = [0·3, 0·9] at intervals of 0·2. Periodsof consolidation corresponding to partial (20 and 50% of thefull primary consolidation) and full primary consolidationwere considered. Last, the soil was brought to failure inundrained conditions by imposing displacement-controlledprobe tests at the RP level. A list of notations for un-consolidated undrained and consolidated undrained capa-cities is summarised in Table 2.
Critical state soil mechanics frameworkGourvenec et al. (2014) proposed a simple theoretical
framework based on critical state soil mechanics (CSSM) to
D
10 D
10 D
Fig. 1. Example of finite-element mesh – cross-sectional view (d/D=0·25)
Table 1. Soil properties used in finite-element analyses
Parameter input for finite-element analyses Magnitude
Index and engineering parametersSaturated bulk unit weight: kN/m3 17·18Permeability: m/s 1·3� 10�10
Elastic parameters (as a porous elastic material)Recompression index (κ) 0·044Poisson’s ratio (ν′) 0·25Tensile limit 0
Clay plasticity parametersVirgin compression index (λ) 0·205Stress ratio at critical state (Mcs) 0·89Wet yield surface size* 1Flow stress ratio† 1Intercept (e1, at p′=1 kPa on critical state line) 2·14
*The wet yield surface size is a parameter defining the size of theyield surface on the ‘wet’ side of critical state, β. (β=1 means that theyield surface is a symmetric ellipse.)†The flow stress ratio represents the ratio of flow stress in triaxialtension to the flow stress in triaxial compression.
CONSOLIDATED UNDRAINED CAPACITY OF SHALLOW FOUNDATIONS 1029
quantify the increase in consolidated undrained uniaxialvertical capacity of surface foundations following verticalpreloading and consolidation (equation (1)). The frameworkwas successfully applied to predict gains in consolidatedundrained vertical, horizontal and moment uniaxial capacityof skirted circular foundations (Vulpe et al., 2016a, 2016b)
HVcu
Huu;MV
cu
Muu¼ 1þ fσfsuRα
Vp
Vuu
� �β
NcV ð1Þ
where the scaling factor fσfsu, which is independent offoundation size, MCC soil properties and applied soiloverburden stress (Vulpe et al., 2016a), is summarised inTable 3. Scaling factor fσfsu accounts for the non-uniformdistribution of the stress in the affected zone of soil and scalesthe gain in strength of the ‘operative’ soil element to thatmobilised during subsequent failure. Coefficients α and βaccount for the non-linear effect of the embedment on thegain in capacity. Coefficients α and β are defined for bothrough and smooth skirted circular foundations as a functionof embedment ratio for each uniaxial capacity throughpolynomial functions.
α ¼1þ α1dD
� �þ α2
dD
� �
β ¼β1dD
� �þ β2
dD
� � ð2Þ
Values of coefficients α and β are given in Table 4. R is thenormally consolidated strength ratio of the soil andNcV is thevertical bearing capacity factor for the given foundationgeometry and normally consolidated soil conditions.
RESULTSExcess pore water pressure is generated in the soil around
the foundation upon application of self-weight preloadingand then allowed to fully dissipate through the drainageboundary. Excess pore water pressure is again generatedduring in-service preloading and dissipation is prescribedthrough the same drainage boundary. The pore pressuredissipation time history, where Δu is the excess pore pressureand Δui is the initial excess pore pressure during Hp/Huupreloading, measured at the centre of the foundation baseplate at mudline level, is exemplified in Fig. 2 for both roughand smooth skirted foundations with d/D=0·1. The time isexpressed through the non-dimensional time factor T as
T ¼ cv0tD2 ð3Þ
where cv0 is the initial coefficient of consolidation at skirt tiplevel and t is the actual time passed following application ofhorizontal preload. All excess pore water pressure–timehistories display the characteristic Mandel–Cryer effect(Mandel, 1950; Cryer, 1963).
Effect of foundation embedment and soil–skirt interfaceroughness on the gain in capacityThe effect of both foundation embedment ratio and soil–
skirt interface roughness on the relative gain in uniaxialcapacity following horizontal preloading is summarised inFig. 3 for a particular case of Hp/Huu = 0·3. The relative gainin uniaxial horizontal capacity decreases with increasingembedment ratio for both rough and smooth foundations,with the smooth skirted foundations consistently showinglower relative gains compared to the rough foundation
Table 2. Definition of notation
Direction of loading Vertical Horizontal Rotational
Load Vp (preload) Hp (preload) M
Uniaxial (unconsolidated) undrained capacity Vuu Huu Muu
Consolidated undrained pure uniaxial capacity following vertical preloading VVcu HV
cu MVcu
Consolidated undrained pure uniaxial capacity following vertical and horizontal preloading VV;Hcu HV;H
cu MV;Hcu
Table 3. Stress and strength factor fσfsu for critical state interpret-ation, equation (1)
Loading direction fσfsu
V 0·43H 0·88M 0·57
2·5
2·0
∆u/∆
u i
1·5
1·0
0·5
00·0001 0·001 0·01
Time factor, T = cv0t/D2
0·1 1 10
Rough interfaceSmooth interface
d/D = 0·1
Hp/Huu = 0·3, 0·5, 0·7, 0·9Vp /Vuu = 0·1 (T99)
Fig. 2. Normalised excess pore time histories for rough and smoothskirted circular foundations with d/D=0·1 during discrete levels ofin-service (Hp/Huu) preloading
Table 4. Coefficients α and β for critical state interpretation,equation (2)
counterpart. This trend is consistent with that observed forskirted circular foundations preloaded under self-weightconditions only (Vulpe et al., 2016b).
Full primary consolidation following horizontal preloadingThe relative gain in uniaxial capacity following vertical
and horizontal preloading and full primary consolidation iscompared to the relative gain in uniaxial capacity followingvertical preloading only and full primary consolidation forsurface foundations (equation (1)) in Fig. 4. The effect ofrelative in-service loading on the relative gain in capacity ismanifested through an additional relative increase in bothhorizontal and moment capacity for all preload levels. As aresult of horizontal preloading and consolidation, the soildensifies laterally around the foundation skirts, close to themudline. The gain in capacity is represented by the intersec-tion between the zone of increase in soil shear strength andthe kinematic mechanism at failure. For both ultimatehorizontal and moment loading, the shearing mechanismcuts through the relatively shallow soil layer, thus intersectingthe zone of increase in shear strength.In order to evaluate the relative increase in uniaxial
horizontal and moment capacity following vertical andhorizontal preloading, the results from Fig. 4 are reinter-preted by adopting a link between gains in capacity followingsole vertical preloading and combined vertical and horizon-tal preloading, respectively. Thus, Fig. 5 illustrates theevolution of the proportion of maximum potential gain inundrained horizontal, GH, and moment, GM, capacityfollowing vertical and horizontal preloading and fullprimary consolidation as a function of the consolidatedundrained uniaxial capacity following vertical preloadingand full primary consolidation
GH ¼HV;Hcu �Huu
HVcu �Huu
¼ aHVp
Vuu
� �bH
GM ¼MV;Hcu �Muu
MVcu �Muu
¼ aMVp
Vuu
� �bMð4Þ
where HVcu and MV
cu are determined from the CSSM frame-work (equation (1)) and Huu and Muu from numericalsolutions (Vulpe, 2015). Non-dimensional fitting coefficientsaH and aM are given in Table 5 as a function of d/Dand soil–skirt interface roughness. Fitting coefficient b
takes the form
bH;rough ¼� 0�92 dDþ 0�51
� �Hp
Huuþ 0�16 d
Dþ 0�08
� �
bH;smooth ¼� 0�72 dDþ 0�51
� �Hp
Huuþ 0�04 d
Dþ 0�08
� �
bM;rough ¼� 0�91 dDþ 0�31
� �Hp
Huuþ 0�77 d
Dþ 0�25
� �
bM;smooth ¼� �15�33 dD
� �2
þ4�03 dD
� �þ 0�33
" #(
� Hp
Huuþ 16�27 d
D
� �2
�4�03 dD
� �þ 0�26
)
ð5Þand incorporates the effect of applied relative horizontalpreload, foundation embedment ratio and soil–skirt interfaceroughness. Fig. 5 and Fig. 6 illustrate good agreementbetween the finite-element analyses and equation (4) irre-spective of foundation embedment ratio and soil–skirtinterface roughness. They also show that the potential forincrease in capacity decreases with increasing relative verticalpreloading. The soil densification increases as a result ofincreasing vertical preload and consolidation, resulting inless opportunity for further reduction in void ratio in the nextconsolidation step.
2·4
2·2
2·0
1·8
1·6
1·4
1·2
1·00 0·1 0·2 0·3
Relative preload, Vp/Vuu
0·4 0·5 0·6 0·7
Con
solid
ated
und
rain
ed h
oriz
onta
l cap
acity
/U
ncon
solid
ated
und
rain
ed h
oriz
onta
l cap
acity
Rough interfaceSmooth interface
d/D = 0
d/D = 0·1
d/D = 0·25
Hp/Huu = 0·3
Fig. 3. Effect of embedment and soil–skirt interface roughness on therelative gain in uniaxial horizontal capacity after vertical andhorizontal preloading and full primary consolidation
2·4
2·2
2·0
1·8
1·6
1·4
1·2
1·00 0·1 0·2 0·3
(a)Relative preload, Vp/Vuu
0·4 0·5 0·6 0·7Con
solid
ated
und
rain
ed h
oriz
onta
l cap
acity
/U
ncon
solid
ated
und
rain
ed h
oriz
onta
l cap
acity
Equation (1)
Current study
Hp/Huu ↑ = 0, 0·3, 0·5, 0·7, 0·9
Hp/Huu ↑
Rough interfaced/D = 0
2·0
1·8
1·6
1·4
1·2
1·00 0·1 0·2 0·3
(b)Relative preload, Vp/Vuu
0·4 0·5 0·6 0·7Con
solid
ated
und
rain
ed m
omen
t cap
acity
/U
ncon
solid
ated
und
rain
ed m
omen
t cap
acity
Equation (1)
Current study
Hp/Huu ↑ = 0, 0·3, 0·5, 0·7, 0·9
Hp/Huu ↑
Rough interfaced/D = 0
Fig. 4. Normalised gain in undrained uniaxial capacity after verticaland horizontal preloading and full primary consolidation for surfacefoundation with rough interface: (a) horizontal capacity; (b) momentcapacity
CONSOLIDATED UNDRAINED CAPACITY OF SHALLOW FOUNDATIONS 1031
Partial consolidation following horizontal preloadingFinite-element analyses incorporating partial consolida-
tion following horizontal preloading were carried out inorder to simulate realistic in-field in-service loading con-ditions. Fig. 7 illustrates the progression of the potential gainin undrained horizontal and moment capacity as a functionof consolidation time for surface circular foundations.A relationship between the consolidation time, representedby time factor T, and the proportion of maximum potentialgain following vertical and horizontal preloading and fullprimary consolidation is proposed
GH;p ¼HV:H
cu;p �HVcu
HV;Hcu �HV
cu
¼ 11þ ðVp=VuuÞ=0�7
� �mHðT=T50Þn½ �
GM;p ¼MV:H
cu;p �MVcu
MV;Hcu �MV
cu
¼ 11þ ðVp=VuuÞ=0�7
� �mMðT=T50Þn½ �
ð6Þ
from which predictions of relative gains in undrained uniaxialcapacity following partial consolidation, HV:H
cu;p and MV:Hcu;p ,
may be quantified. The non-dimensional time factor, T50,representing the time required for 50% of the full primaryconsolidation to occur under Vp/Vuu= 0·7, is given in Table 6for each embedment ratio and soil–skirt interface roughness.Fitting coefficients mH and mM are given in Table 7. Fittingcoefficient n is �1·20 irrespective of foundation type. Fig. 7and Fig. 8 indicate good agreement between the finite-elementanalysis results and the relative gains in undrained uniaxialcapacity derived from equation (6), irrespective of d/D andsoil–skirt interface roughness.
Consolidated undrained VHM capacityFailure envelopes in normalised horizontal and moment
load space (HM) for rough skirted foundations withd/D=0·25 under unconsolidated undrained (UU) (Vulpe,2015) and consolidated undrained consolidations (Vulpeet al., 2016b and current study) are compared in Fig. 9.Notations T20 and T50 represent the non-dimensional timerequired for 20 and 50% of the full primary consolidation tooccur. Full primary consolidation is denoted by T99. Thepositive effect of in-service preloading and consolidation isevident even in early consolidation stages (T20). A simplealgebraic equation accounting for the effect of vertical andhorizontal preloading on the HM failure envelope couldnot be formulated. This is as a result of the convoluted path
Table 5. Fitting coefficient aH and aM for determining the gain incapacity following full primary consolidation for rough and smoothskirted circular foundations
Fig. 5. Proportion of the potential maximum gain in uniaxialhorizontal and moment capacity following vertical and horizontalpreloading and full primary consolidation (equation (4)), GH and GM,for surface foundations (d/D=0): (a) horizontal capacity, GH;(b) moment capacity, GM
8
7
6
5
4
3
2
3·5
3·0
2·5
2·0
1·5
1·0
10 0·1 0·2 0·3 0·4 0·5 0·6 0·7
Gai
n in
cap
acity
follo
win
g V
p an
d H
ppr
eloa
ding
and
full
prim
ary
cons
olid
atio
n, G
M
Gai
n in
cap
acity
follo
win
g V
p an
d H
ppr
eloa
ding
and
full
prim
ary
cons
olid
atio
n, G
M
(a)Relative preload, Vp/Vuu
0 0·1 0·2 0·3 0·4 0·5 0·6 0·7
(b)Relative preload, Vp/Vuu
d/D = 0·25Rough interface
Equation (4)
0·3
0·5
0·7
0·9
Hp/Huu
d/D = 0·25Smooth interface
Equation (4)
0·3
0·5
0·7
0·9
Hp/Huu
Fig. 6. Proportion of the potential maximum gain in uniaxialmoment capacity following vertical and horizontal preloading andfull primary consolidation (equation (4)), GM for rough and smoothskirted foundations with d/D=0·25: (a) rough soil–skirt interface;(b) smooth soil–skirt interface
‘a point’ from the UU failure envelope travels during bothvertical preloading and consolidation followed by horizontalpreloading and consolidation towards the consolidatedundrained (CU) failure envelope.
have quantified the effect of relative magnitude and durationof self-weight and in-service horizontal preloading, em-bedment ratio and soil–skirt interface roughness on the
Table 6. Non-dimensional time factor for 50% partial consolidation,T50, for Vp/Vuu = 0·7
d/D Rough interface Smooth interface
0 0·18 —0·1 0·22 0·180·25 0·26 0·22
1·0
0·8
0·6
0·4
0·2
00·0001 0·001 0·01 0·1 1 10
d/D = 0Rough interface
0·3
0·5
0·7
0·9
Hp/Huu
d/D = 0Rough interface
0·3
0·5
0·7
0·9
Hp/Huu
Vp/Vuu = [0·1, 0·7]T99
Vp/Vuu = [0·1, 0·7]T99
Equation (6)
Equation (6)
(a)Time factor, T = cv0t/D2
0·0001 0·001 0·01 0·1 1 10
(b)Time factor, T = cv0t/D2
Gai
n in
cap
acity
follo
win
g V
p an
d H
ppr
eloa
ding
and
par
tial c
onso
lidat
ion,
GH
,p
1·0
0·8
0·6
0·4
0·2
0
Gai
n in
cap
acity
follo
win
g V
p an
d H
ppr
eloa
ding
and
par
tial c
onso
lidat
ion,
GM
,p
Fig. 7. Proportion of the potential maximum gain in uniaxialcapacity following vertical and horizontal preloading and partialconsolidation (equation (6)) for surface foundations: (a) horizontalcapacity, GH,p; (b) moment capacity, GM,p
Table 7. Fitting coefficients mH and mM for determining the gain incapacity following partial consolidation for rough and smooth skirtedcircular foundations
Fig. 8. Proportion of the potential maximum gain in uniaxialhorizontal capacity following vertical and horizontal preloading andpartial consolidation (equation (6)), GH,p, for rough and smoothskirted foundations with d/D=0·25: (a) rough soil–skirt interface;(b) smooth soil–skirt interface
d/D = 0·25Rough interface
Hp/Huu = 0 (T99)Vulpe et al. (2016b)
Hp/Huu = 0·9T20, T50, T99
Vp/Vuu = 0·3 2·0
1·5
1·0
0·5
–1·5 –0·5 0·5Normalised horizontal space
Nor
mal
ised
mom
ent s
pace
1·50
UUVulpe (2015)
Fig. 9. Normalised HM failure envelopes of rough skirted circularfoundations with d/D=0·25 for Vp/Vuu = 0·3 under various dissipationscenarios
CONSOLIDATED UNDRAINED CAPACITY OF SHALLOW FOUNDATIONS 1033
multi-directional undrained capacity of skirted circularfoundations. The results show that the undrained uniaxialand combined capacity increase under horizontal preloadingand over realistic in-field loading time regimes.Approximating expressions incorporating a CSSM frame-work for prediction of consolidated undrained uniaxialcapacity of smooth and rough skirted circular foundationshave been proposed.
This study has highlighted the potential conservatism infoundation design by not accounting for the enhanced soilundrained shear strength following foundation self-weightand in-service loading and consolidation in determiningultimate limit states.
ACKNOWLEDGEMENTThe first author was supported through ARC grant
CE110001009 during the time in which the work describedin this paper was performed. This support is gratefullyacknowledged.
NOTATIONaH, aM, bH,rough,
bH,smooth, bM,rough,bM,smooth
non-dimensional fitting coefficients
cv0 in situ coefficient of consolidationD foundation diameterd skirt length
fσfsu scaling factorGH, GM proportional maximum gain in bearing
capacity following vertical and hori-zontal preloading and full primaryconsolidation
GH,p, GM,p proportional maximum gain in bearingcapacity following vertical and hori-zontal preloading and partialconsolidation
Hp horizontal preloadHuu unconsolidated undrained horizontal
capacityK0 in situ earth pressure coefficient of
normally consolidated depositmH, mM, n fitting coefficients
NcV, NcH, NcM, NcVsmooth,
N cHsmooth, N cM
smoothnon-dimensional bearing capacityfactors
R normally consolidated undrainedstrength ratio
su undrained shear strengthT non-dimensional time factor
cu consolidated undrained pure uniaxialcapacity following vertical and hori-zontal preloading
α, β fitting coefficientsΔu excess pore water pressureΔui initial excess pore water pressureσ′v in situ vertical effective stress
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