SEISMIC BEARING CAPACITY OF PILES IN LIQUEFIABLE SOILS

525

i) Lecturer, University of Dundee, Division of Civil Engineering, Scotland, UK (j.a.knappett＠dundee.ac.uk) (formerly University of Cam-bridge, UK).

ii) Reader, University of Cambridge, Department of Engineering, UK.The manuscript for this paper was received for review on March 26, 2007; approved on June 8, 2009.Written discussions on this paper should be submitted before March 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.

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SOILS AND FOUNDATIONS Vol. 49, No. 4, 525–535, Aug. 2009Japanese Geotechnical Society

SEISMIC BEARING CAPACITY OF PILES IN LIQUEFIABLE SOILS

J. A. KNAPPETTi) and S. P. G. MADABHUSHIii)

ABSTRACT

An investigation into the base capacity of piles in passing through loose, liqueâble sand and founded in underlyingdense sand is presented based on the results of a series of dynamic centrifuge tests on instrumented model pile groups.Excess pore pressures equal in magnitude to the initial eŠective vertical stress were observed to be generated in thebearing layer of dense sand at both shallow (15 m) and deep (26 m) depths. This induced a dramatic reduction in basecapacity and consequently, large settlements of the piles by as much as ¿5D0. A spherical cavity expansion solutionfor base capacity was validated against measured values showing good agreement, provided that excess pore pressureand dynamic shear stiŠness in the bearing layer are known. A simple closed-form relationship, applicable to end-bear-ing piles, between the degree of liquefaction and the initial pile static safety factor was then developed against plungingfailure at the pile base which can be used in design.

Key words: bearing capacity, centrifuge model test, liquefaction, piles, seismic design, settlement (IGC: D7/E4/E8)

INTRODUCTION

Displacement of piled foundations during liquefactionhas been a major cause of structural collapse duringearthquake shaking in recent years (Tokimatsu et al.,1996; Tokimatsu and Asaka, 1998; Tokimatsu et al.,1998; Lin et al., 2005). While it is commonly acceptedthat lateral displacements can be severely damaging, littleattention has been paid to vertical settlement which cansimilarly lead to structural damage (Zhang and Ng,2005), despite the fact that this governs the design of pilesunder conventional static conditions. The onset of sig-niˆcant and damaging pile settlement with liquefactionduring earthquake shaking has already been established(De Alba, 1983; Knappett, 2006) and empirical relation-ships between the severity of liquefaction and pile groupsettlement have been developed (Knappett and Madab-hushi, 2008a). However, in order to develop more deter-ministic methods of predicting the onset of damaging pilesettlement, further investigation is needed to measure theloads carried by piles—both at the pile base and along theshaft—when the soil around them liqueês. This paperaims to address this issue by presenting recently collecteddynamic centrifuge test results and using these to developsimple methods of predicting the changes in pile basebearing capacity.

Comparison of these model testing studies with recentêld testing work (Rollins and Strand, 2006) has demon-strated the importance of the behaviour of the more com-petent underlying bearing layers into which the piles are

installed. In this latter work, controlled blasting was usedto generate liquefaction in a ¿10 m thick sand layerwhich the piles passed through, but not in the bearing lay-er. This condition is somewhat artiˆcial as in real earth-quakes, it is upward-propagating shear waves from deeplayers (bedrock) that generate excess pore pressures.These waves pass through the `competent' bearing layersand may therefore lead to substantial increases in excesspore pressure there. Co-seismic settlements were found tobe small in the êld tests, while in the model tests present-ed by De Alba (1983) in which the underlying soil suŠers asubstantial increase in excess pore pressure, settlementsapproaching twice the pile diameter were measured. It isalready well established that dense sands may develop sig-niˆcant excess pore pressures during undrained cyclicloading (Mitchell and Dubin, 1986) up to Du/s?v0§1.However on shearing, strong dilation occurs such that thesand has a limited strain potential, unlike liqueêd loosesands. This condition is called cyclic mobility (Castro,1975; Castro and Poulos, 1977). Further to this, Steed-man and Sharp (2001) conducted a centrifuge modellingstudy on the excess pore pressures developed in medium-dense saturated sands at high initial eŠective stress. Theresults suggested that for s?v0À200 kPa, the maximumvalue of the liquefaction ratio which could be achievedreduced by approximately 15z for each increase of s?v0 by200 kPa. This may have important implications for the li-queêd bearing capacity of deep/long pile founded indense sand. It is therefore important to additionally con-ˆrm whether competent bearing layers suŠer substantial

526

Fig. 1. Schematic layout of test, JK-12, dimensions in m at prototype scale (mm model scale)

526 KNAPPETT AND MADABHUSHI

increases in excess pore pressure which may cause a dra-matic drop in bearing capacity and increased settlementwhen disturbed by upwards-propagating shear waves.

DYNAMIC CENTRIFUGE MODELLING

Two diŠerent soil proˆles were used in the series of cen-trifuge tests presented herein, which were conducted at80-g. The ˆrst, with test ID JK-12, consisted of a 10.4 mdeep layer of loose (Dr§35z) Fraction E silica sand,overlying a much denser layer of the same sand (Dr§85z). The thickness of this layer and all other values inthis paper are given at prototype scale. This soil proˆlewas prepared in a deep equivalent shear beam (ESB) con-tainer to reduce re‰ections of shear waves at the soilboundaries. Further details concerning the design andperformance of this container can be found in Brennan(2003) and Brennan et al. (2006). The soil layers were in-strumented with accelerometers and pore pressure trans-ducers to determine the free-êld soil response as shownin Fig. 1 and the model saturated with a solution ofMethylcellulose and water of viscosity 80 cS such that thepermeability of the soil is correctly scaled (Schoêld,1981; Madabhushi, 1994). Further information regardingthe use of Methylcellulose as a model pore ‰uid may befound in Stewart et al. (1998).

Two axially-loaded 2×2 pile groups with a pile-to-pilespacing of s＝5.6D0 were installed into these layers, ini-tially under 1-g conditions and subsequently under in-creasing self-weight during swing-up of the centrifuge.The piles were nominally models of 0.5 m diameter (D0)

steel tubular piles with closed ends, having a bendingstiŠness EI＝164 MNm2 (determined from four-pointbending tests) and an axial compressive stiŠness of EA/Lp＝0.96 MNm－1. One of the pile groups was installedsuch that the pile cap was clear of the surface of the sandto observe the behaviour of the piles alone, while theother was installed such that the pile cap was in contactwith the sand which is a more common condition forpiled foundations in the êld. Three of the model pileswere instrumented, having a sub-miniature total earthpressure cell installed into the tip with a sensing areaequal to the pile base area, and a miniature tension-com-pression load cell installed at the pile head. By measuringpile base load (Qb) and total pile load (P ) in this way, itwas also possible to determine the total shaft load (Qs) bysubtraction. Two of these instrumented piles were in-stalled in identical locations in the two pile groups (pileA—see Fig. 1), while the third was installed into thegroup with the pile cap contacting the sand to measureany frame eŠect and transfer of load between the pileswhich might occur during shaking (pile B—see Fig. 1).Bearing pressures beneath the centreline of the pile capswere also measured in both cases using surface-mountearth pressure cells and settlements of the pile groupswere measured using wire potentiometers mounted to anoverhead gantry.

The second soil proˆle (which was actually tested ˆrst)was denoted JK-06 and represented a much deeperdeposit of loose sand 21.6 m deep, again overlying a morecompetent bearing layer. This is shown schematically inFig. 2. The model preparation and densities of the sand

527

Fig. 2. Schematic layout of test, JK-06, dimensions in m at prototype scale (mm model scale)

Table 1. Static properties of tested pile groups

Test ID Earthquake ID Group ID P (MN) Qb0, ult1 (MN) K 2 Qs0, ult

2 (MN) SSF* Pile cap-soil contact?

JK-12

12.1 S1 0.45 2.44 0.66 0.317 6.13 (3.42) No

12.2 S2 0.65 2.58 0.74 0.351 4.51 (2.52) No

12.1 S3 0.45 2.44 0.66 0.317 6.13 (3.42) Yes

12.2 S4 1.25 2.44 0.74 0.351 2.24 (1.26) Yes

JK-066.1 S5 1.88 3.39 0.66 0.952 2.32 (1.41) No

6.1 S6 3.45 3.39 0.66 0.952 1.26 (0.77) No

1 Calculated following the method of Berezantzev et al. (1961) as modiêd by Cheng (2004)2 Values of K and Qs0, ult calculated as described in the text* Revised values in parentheses are based on back-calculated estimates of static base capacity

527BEARING CAPACITY OF PILES

layers were identical to those used in test JK-12. Similar 2×2 pile groups were installed as shown in Fig. 2, thoughthe piles were longer such that the embedded length in thedense sand layer remained the same as that tested inJK-12, with this length being ¿10D0. The piles in this testwere not instrumented and each group was installed withthe pile cap clear of the surface of the loose sand layer.

A summary of the static conˆgurations of the testedpile groups is given in Table 1. Static base capacity(Qb0, ult) was initially calculated using the analysis ofBerezantzev et al. (1961) as modiêd by Cheng (2004).Shaft capacity was estimated based on back-calculatedvalues of the coe‹cient of lateral earth pressure whichwere obtained using measured pile shaft loads duringswing-up of the centrifuge for pile groups S1 and S2

(which have no eŠect of the pile cap). These values of Kwere found to be between 0.66–0.74. Assuming that K0＝1－sin q＝0.45 gives K§1.5K0 such that the piles arebroadly representative of driven piles in the êld (Kul-hawy, 1984). This information was then used to computeshaft capacity for the pile groups in this study using

Qs0,ult＝(pD0Lp)・m・K šs?v0 (1)

where šs?v0 is the average vertical eŠective stress over thelength of the pile (Lp) and m is the coe‹cient of friction atthe sand-pile interface, assumed to be 0.3 for smoothpiles following the recommendations of Uesugi andKishida (1986). Further details regarding the computa-tion of static pile capacities can be found in Knappett(2006).

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Table 2. Summary of simulated earthquakes

Test ID Earthquake ID Peak bedrock acceleration (g)

JK-06 6.1 0.25

JK-1212.1 0.31

12.2 0.30

Fig. 3. Excess pore pressures measured in Earthquake 12.1

Fig. 4. Excess pore pressures measured in Earthquake 6.1


Axial loading was applied to the piles by a combinationof the mass of the pile cap, and a series of brass andaluminium plates which were bolted to the upper surfaceof the pile cap. It should be noted that the superstructuralweight which is modelled by these plates was unable tomove. In reality, the centre-of-mass of the supportedstructure would move horizontally relative to the pilecap, which would impart an additional dynamic over-turning moment to the pile cap which is not modelled inthese tests. This will serve to increase the cyclic axial loadswhich are transferred to the piles during the earthquakessuch that the settlements presented herein are likely to bea lower-bound to the true behaviour. Further researchwould be necessary to quantify this eŠect for diŠerenttypes of superstructure.

Static safety factors (SSFs) were then calculated as thetotal pile capacity (＝Qb0,ult＋Qs0,ult) divided by the ap-plied pile head load. The total supported dead load fromthe pile cap and additional plates was assumed to be sup-ported equally across the four piles in the group for thepurposes of calculating a nominal SSF for the piles. Byinterpolating the post-liquefaction bearing capacities ob-served during the simulated earthquakes to the staticcase, back-calculated static base capacities were com-pared to the initial predicted values which were found tobe too high by a factor of approximately two. Revisedstatic safety factors (SSFs) using the back-calculatedvalues are shown in parentheses in Table 1.

Each soil model was subjected to sinusoidal strongshaking for 48 s at a fundamental frequency of 0.63 Hz(both parameters at prototype scale). This was simulatedusing the stored angular momentum (SAM) earthquakeactuator, the performance and construction of which aredetailed by Madabhushi et al. (1998). A single earthquakewas applied during test JK-06, while in JK-12, additionalload was added to the pile groups following the initialevent, with the model then being re‰own and subjected toa second earthquake of similar magnitude. Peak groundacceleration measured at the base of the container(equivalent bedrock layer) was used to quantify the mag-nitude of shaking, the values of which are given in Table2.

OBSERVED LIQUEFACTION BEHAVIOUR

The excess pore pressures developed in the free-êld inboth the shallow (JK-12) and deep (JK-06) soil proˆlestested are shown in Figs. 3 and 4 respectively. It will beseen from these two ˆgures that full liquefaction, deˆnedhere as Du/s?v0＝1, is achieved at all measured depths in

both of the earthquakes shown. Similar time histories ofexcess pore pressure were observed in earthquake 12.2which is not shown graphically.

In the work reported by Steedman and Sharp (2001) ex-cess pore pressures achieved at an initial vertical eŠectivestress of ¿250 kPa (¿25 m deep) were only 60–80z ofthe full liquefaction values achieved in the denser sandused in the tests presented herein. This is detailed in Table3. The results presented in Fig. 4 have shown that full liq-uefaction (Du/s?v0＝1) is possible even in deep, densesand strata. These high excess pore pressures will lead tolower eŠective stresses and hence, bearing capacity insuch layers would be expected to be reduced. This has im-portant implications for the settlement behaviour of end-bearing piled foundations as even deep piles founded indense sand may suŠer a signiˆcant loss of end-bearingcapacity and excessive settlement.

Liquefaction-induced SettlementThe settlements of the pile groups in which there was

no contact between the pile cap and the soil are sum-marised in Table 3 and qualitatively compared to the full-

529

Table 3. In‰uence of excess pore pressure generation on liquefaction-induced settlement (no eŠect of pile cap bearing)

Group/pile IDAt pile tip level Range of Du/s?v0 after

Steedman and Sharp (2001)

Settlement (mm)

Depth (m) Du/s?v0 Co-seismic Post-shaking

S1 15.2 1.00 0.7–1.0 1137 317

S2 15.2 0.96 0.7–1.0 635 14

S5 26.4 1.00 0.6–0.8 1480 88

S6 26.4 1.00 0.6–0.8 2342 144

Rollins and Strand (2006) 21.3 º0.2 — 7


scale test results of Rollins and Strand (2006) which like-wise exclude the contribution of the pile cap to the loadcarrying capacity of the foundation. It is immediately ob-vious from Table 3 that the excess pore pressure devel-oped in the bearing layer at pile tip level has a controllingeŠect on settlement. If full liquefaction occurs (groupsS1–S6) co-seismic liquefaction-induced settlements wereobserved to be greater than one pile diameter in all casesand as large as ¿5D0, while for Du/s?v0º0.2 in sand oflower density (Dr§50z) from the full-scale tests, hardlyany pile settlement occurred at all. It is also clear fromTable 3 that if high excess pore pressures are generated atpile tip level, the resulting co-seismic settlement is verymuch larger than any settlement which occurs post-ear-thquake. Post-earthquake settlement occurs as the sandreconsolidates during the dissipation of excess pore pres-sures. This reconsolidation generates additional down-wards shear stress along the pile shaft, which is common-ly termed downdrag. For piles founded in non-liquefyingbearing layers, downdrag-induced settlements may forman appreciable component of the total (albeit small) set-tlements that occur (Rollins and Strand, 2006). For thecases tested herein however, post-earthquake settlementis small compared to the co-seismic settlement and assuch, only the behaviour and capacity of the piles duringthe earthquake will be considered in the remainder of thispaper.

MEASURED PILE LOADS IN LIQUEFIED SOIL

The load components measured in the instrumentedpiles in groups S3 and S1 (pile A for both) are shown inFig. 5. It is immediately obvious from Fig. 5 that forgroup S3, the load carried at the base of the piles (QbE)reduces with time corresponding to increasing excess porepressure at pile tip level (see Fig. 3). As the piles are set-tling during this reduction in base load, as evidenced bythe increasing overall pile group settlement (rE,avg), thedrop in the carried load can only be explained by a dropin bearing capacity. It is also clear from Fig. 5, howeverthat the base load for group S1 increased during shaking.This may be attributed to the reductions in excess porepressure beneath the pile tip which occur with shearing ofthe soil in this region due to the much higher rate of set-tlement in this group, itself a result of the lack of anyresistance to settlement from the pile cap in this case.

Figure 6 summarises the shaft and base loads in the in-strumented piles at the time instants shown in the ˆgure.With the exception of pile A in group S1, all of the pilesin Fig. 6 show a reduction in base load due to shakingand the consequent liquefaction which occurs. Regardingshaft loads, it is obvious from Fig. 5 that shaft capacitydoes not reduce to zero with liquefaction of the soil as haspreviously been assumed in various analytical studies(e.g., Boulanger et al., 2003; Haldar et al., 2007).

Superimposed on these average behaviours is a sub-stantial cyclic load component as the pile group rocks un-der the action of the inertial load which causes the piles tomove cyclically up and down. The cyclic vertical move-ment of the instrumented piles shown in Fig. 5 as rE,cyc

was estimated by assuming that the piles and cap rock asa rigid body about a point beneath the centreline of thefoundation at pile tip level. Horizontal cyclic displace-ments (Dcyc), which were computed by carefully integrat-ing measured pile cap accelerations, are then related tothe estimated cyclic vertical movement according to

rE,cyc＝s2

tan Ø Dcyc

Lp＋hCM» (2)

where s is the pile spacing (＝5.6D0 for all tests presentedherein), and hCM is the distance from the pile-cap-soil in-terface to the centreline of the accelerometers used tomeasure the pile cap lateral movement. In the absence ofany eŠect of the pile cap (i.e., group S1) it is clear fromFig. 5 that the cyclic lateral displacements of the piles areincreased. This correlates with larger cyclic shaft loadvariations compared with those observed in group S3.

The ˆnal point of note concerning Fig. 5 is that whenthe pile cap is in contact with the surface of the liqueêdsand for group S3 (and S4, which is not shown) there is asubstantial increase of pile cap bearing pressure Dqcap

with increasing settlement. The overall group settlementis also smaller for group S3 than for group S1 in whichthere is no contribution from the cap. The pile cap there-fore appears to play an important role in resisting settle-ment by generating additional bearing pressure in the li-queêd sand on which it sits; however, this eŠect will notbe discussed further in this paper which concentrates onpile capacity. A more detailed discussion of the eŠect ofthe pile cap in resisting settlement may be found in Knap-pett and Madabhushi (2008a).

In addition to showing changes in pile load distribution

530

Fig. 5. EŠect of pile cap on load transfer during liquefaction (pile A,Earthquake 12.1)


between shaft and base due to liquefaction, Fig. 6 alsodemonstrates that following liquefaction, the pile doesnot return to its initial distribution of base and shaftload. This has potential implications for the assessmentof piled foundations following earthquakes (i.e., for thepurposes of making future design changes to the support-ed superstructure) and for determining behaviour in sub-sequent earthquakes (including aftershocks). The distri-

bution of shaft and base load may be determined by con-sidering the proportion of the total pile load carried bythe base (a)

a＝Qb0

P. (3)

High values of a indicate that the piles carry most of theload in end-bearing, while low values of a suggest condi-tions closer to friction piles. Values of a have been com-puted for all six instrumented piles, both for pre-ear-thquake conditions and following dissipation of excesspore pressures, using the load components shown in Fig.6. These values are compared in Fig. 7. It is immediatelyobvious from Fig. 7 that all of the instrumented pilesmay be considered as end-bearing, carrying more thanhalf of the total pile load at the pile base. In all cases, theload distribution can be seen to change. Based on the datapresented here, it appears that the change in load distri-bution depends on whether the pile cap contributes to theoverall bearing capacity. For cases in which there is noeŠect of the pile cap, load is eŠectively transferred fromthe shaft to the base as a result of the earthquake. Forcases in which the pile cap does contribute to the bearingcapacity, load is transferred from the base to the shaft ofthe piles.

Figure 7 additionally shows the approximate distribu-tion of load between the piles and the pile cap for the in-strumented pile tests. This is deˆned in terms of aparameter b given by

b＝4PPt

. (4)

where Pt is the total superstructural load supported by thefoundation. The average pile load P in Eq. (4) was deter-mined by taking the average value of the total pile headloads measured in piles A and B in each group. Figure 7shows that there is comparatively little change in the dis-tribution of load between the piles and pile cap followingliquefaction.

LIQUEFIED PILE BASE CAPACITY (QbE,ult)

For end-bearing piles, the pile base capacity representsthe largest individual component of load contributing tothe overall bearing capacity of the foundation. As a resultof this, in order to be able to determine a suitable axialpile load to avoid bearing capacity failure, it will be mostimportant to be able to predict the reduction in bearingcapacity at the pile base. The high excess pore pressureswhich are developed in the bearing layer at pile tip levellead to a substantial reduction in shear modulus. Thisparameter may be obtained from measurements of cyclicshear stress and shear strain inferred from accelerometermeasurements as detailed by Brennan et al. (2005).Stress-strain loops obtained in this way can be used to de-termine a representative secant shear modulus for eachindividual cycle of the earthquake. Average values ofsecant shear modulus for the soil between the pile baseand the base of the container (equivalent bedrock level)

531

Fig. 6. Summary of changes in pile loads, groups with pile cap contact

Fig. 7. Change in static pile load distribution due to liquefaction

Fig. 8. Measured dynamic shear moduli


both beneath the pile groups and in the free êld in bothtests JK-12 and JK-06 are shown in Fig. 8. These were de-termined based on a ˆrst-order estimate of shear stressesand strains using the input accelerometer and the ac-celerometers at each location at pile tip level.

The free-êld values in Fig. 8 show that the sand inboth earthquakes 12.1 and 12.2 follows the same G-gs

relationship, though the strains mobilised during the sec-ond of the two earthquakes are much lower than those inthe ˆrst earthquake. This is thought to be due to densiˆ-cation of the sand during the initial earthquake whichreduces the potential for the soil to strain under subse-quent excitation. Comparison of the two ˆrst-earthquakeconditions (earthquakes 6.1 and 12.1) show a similarrange of strain mobilisation, though the magnitude of theshear modulus is higher at greater depth for test JK-06(earthquake 6.1).

The measured values of eŠective stress and shearmodulus from the centrifuge tests have been incorporatedinto a modiêd form of the spherical cavity expansionmodel for pile base capacity originally proposed by Vesic(1972) and later modiêd by Yasufuku et al. (2001). Themethod is modiêd to account for the time varyingparameters (sv? and Gsecant) and the volumetric compres-sion is taken to be zero (i.e., assuming that the expansion

532

Fig. 9. Comparison of dynamic soil properties local to the pile groupswith free-êld values

Fig. 10. Comparison of predicted liqueêd base capacities with meas-ured base loads


is undrained and the soil therefore incompressible). Asthe values of Gsecant shown in Fig. 9 are average values ap-plicable to whole cycles of shaking, average excess porepressures (and hence sv?) for each cycle are interpolatedfrom the time-varying measured values. In this way, apseudostatic prediction of bearing capacity can be ob-tained, neglecting the more complex dynamic behaviour.

The ˆt of this model to the measured pile tip loads isshown for one of the instrumented piles in both earth-quakes 12.1 (group S3, pile B) and 12.2 (group S4, pile B)in Fig. 10. In estimating post-liquefaction bearing capaci-ty, excess pore pressures measured at pile tip level in the

free-êld are used along with shear moduli determinedmid-way between the tips of the piles and the base of thecontainer (¿10D0 beneath the pile tips) using the methoddetailed above. The excess pore pressures in the free-êldwere practically identical to those beneath the measuredbeneath the pile groups as shown in Fig. 9. This is im-portant as free-êld excess pore pressures may be deter-mined from site response analyses. The match betweenthe measured loads and predicted capacities late in theearthquake (after bearing capacity failure has occurred)suggests that bearing capacity reduces as excess pore pres-sures increase until, when the capacity is less than the ini-tial pile base load (Qb0), the carried load has to reduce tomatch the lower capacity—the pile simply cannot sustainmore load than the instantaneous capacity. The goodagreement shown in Fig. 10 is particularly signiˆcant forthe determination of liqueêd bearing capacity in designsituations as free êld excess pore pressures and shearmoduli can be straightforwardly determined using readilyavailable site-response tools such as CYCLIC 1D(http://cyclic.ucsd.edu/; Yang et al., 2003), suggestingthat the data from these simple analyses for a given soilproˆle and earthquake can be used to predict post-li-quefaction base capacity.

533

Fig. 11. Theoretical model of bearing capacity failure in liquefyingsoil

Fig. 12. Reduction in base capacity with increased excess pore pres-sure


LIMITING SSF FOR LIQUEFIED BEARINGCAPACITY FAILURE

It can be seen from Fig. 6 that the piles investigated inthis study are end-bearing piles, carrying signiˆcantlymore load at the base compared to the shaft under static(initial) conditions. This is a common conˆguration forpiles in liquefaction-susceptible regions in which the pilesare driven through soft liqueâble layers to bear in morecompetent underlying layers. It is reasonable to assumethat the pile groups will suŠer bearing capacity failurewhen the post-liquefaction base capacity drops below theinitial pile base load, as shown schematically in Fig. 11.This will certainly be a conservative criterion as it wasdemonstrated in Fig. 5 that both the pile shaft and pilecap can additionally contribute to the bearing capacity asthe soil liqueês. Whether bearing capacity failure occursduring earthquake shaking will be dependent both on thedegree of liquefaction at the pile tip which governs thecapacity, and by the SSF of the pile (which will in‰uencethe initial base load carried). Consideration of the formof the bearing capacity solution of Vesic (1972) suggeststhat the liqueêd base capacity can be seen to vary as

qbE,ult1(sv?)3－sin q

3(1＋sin q). (5)

This assumes that the variation in the bearing capacitydue to the reduction in shear modulus (Figs. 8 and 9) issmall compared to the eŠect of eŠective stress. This haspreviously been demonstrated by Knappett and Madab-hushi (2008b). The value of sv? at any particular timeinstant during liquefaction is given by

sv?＝s?v0«1－ØDus?v0»$ (6)

As the ultimate base capacity at Du/s?v0＝0 should beequal to the static base capacity (qb0,ult), this suggests that

qbE,ult

qb0,ult＝

QbE,ult

Qb0,ult＝«1－ØDu

s?v0»$

3－sin q3(1＋sin q)

. (7)

The ˆt of this expression to the measured data obtainedfrom the centrifuge model tests is shown in Fig. 12. Bear-ing capacity failure will occur at the tip of the piles whenQbE,ult＝Qb0, i.e., when the liqueêd base capacity reducesbelow the initial base load carried under static conditions.The value of Du/s?v0 at which failure occurs can be fur-ther related to the SSF of the pile by acknowledging thatQb0 and Qb0,ult are related to the total pile load carried andtotal pile capacity respectively according to

Qb0＝a・P (8)Qb0,ult＝ault・Pult (9)

in which the values of a and ault are indicative of the pileinstallation conditions (i.e., the degree of pile capacitymobilisation during driving/jacking) and the workingloads applied to the pile under static conditions. By sub-stitution of these relationships into Eq. (7), the limitingSSF for a given amount of excess pore pressure develop-ment at the tip of the pile is then given by

SSF＝Ø aault

» 1

«1－ØDus?v0

»$3－sin q

3(1＋sin q)

. (10)

The parameter a in Eq. (10) corresponds to the propor-tion of total pile load (P ) prior to shaking (static condi-tions) which is carried at the base of the pile, while ault issimilarly the proportion of the ultimate pile capacity(Pult) which is provided by the pile base. As Du/s?v0 can bedetermined for a given earthquake and soil proˆle usingnumerical site response programmes (as mentioned previ-ously), Eq. (10) can be used to select a suitable SSF fordesign purposes to avoid bearing capacity failure duringliquefaction.

Equation (10), which represents an ultimate limitingstate of pile behaviour, is compared with the limiting SSF

534

Fig. 13. Comparison of bearing capacity model with limiting displace-ment model of Knappett and Madabhushi (2008a)

Table 4. Critical excess pore pressure ratios required causing perfor-mance criteria to be exceeded

CriterionDu/s?v0, pile tip

SSF＝2 SSF＝3

0.1D0 settlement 0.61 0.75

Bearing capacity 0.72 0.87


based on a serviceability-based criterion presented byKnappett and Madabhushi (2008a) in Fig. 13. This wasbased around determining the limiting SSF such that ver-tical settlements do not exceed 0.1D0 and is described byEq. (11).

SSF＝1＋5.5ØDus?v0

»3.5

. (11)

Equation (11) was determined based on an empirical ˆtto settlement data obtained from a larger database ofcentrifuge test data, which includes the two tests de-scribed herein. It can be seen that for a given amount ofliquefaction Du/s?v0, a slightly larger SSF is generally re-quired if the settlements are to be kept small (º0.1D0).Additionally it would suggest that at low excess porepressures, bearing capacity failure is associated with dis-placements of approximately 0.1D0 while at larger excesspore pressures, the settlement-based limiting state is moredemanding than the bearing capacity criteria. For com-mon factors of safety used in static pile design, the degreeof excess pore pressure rise at the tip corresponding tomeeting one or other of the performance criteria areshown in Table 4. Figure 13 (or alternatively, Eqs. (10)and (11)) may be used in pile design to select suitable stat-ic safety factors (and therefore suitable axial loads) forpiles founded in liqueâble cohesionless soils.

CONCLUSIONS

A series of dynamic centrifuge model tests have been

presented in which vertical failure and settlement of piledfoundations in liqueâble soils has been investigated. Set-tlements occurring during shaking were found in all casesto be damagingly large (in excess of one pile diameter)which was correlated with an increase in excess pore pres-sure to full liquefaction conditions in what is convention-ally considered to be non-liqueâble soil. Such an in-crease in excess pore pressure was observed at depths upto ¿26 m in very dense sand, which has important impli-cations for the bearing capacity of long piles. The settle-ments were also found to be very much larger than down-drag induced settlements induced post-shaking by thereconsolidation of liqueêd sand around the piles. Addi-tionally, non-zero pile shaft loads were observed in fullyliqueêd soil in all tests, contrary to commonly accepteddesign assumptions. A spherical cavity expansion solu-tion was modiêd to pseudostatically predict base capaci-ty in liquefying soil. This was found to give excellentagreement with measured loads from the centrifuge tests.Based on these ˆndings, an analytical solution waspresented which allows for the determination of a suita-ble static safety factor in pile design to avoid bearingcapacity failure for given liquefaction conditions.

ACKNOWLEDGEMENTS

The authors would like to sincerely thank the technicalstaŠ at the Schoêld Centrifuge Centre in Cambridge fortheir invaluable assistance with the centrifuge testingwork. Financial support for the ˆrst author and theproject was provided by the Engineering and PhysicalSciences Research Council (EPSRC) and is acknowledgedwith thanks.

NOTATION

A＝Pile base areaDr＝Relative densityD0＝Pile (outside) diameterE＝Young's Modulus

G(gs )＝Shear modulusGsecant＝Secant shear modulus for a single cycle of shaking

hCM＝OŠset between bottom of pile cap and displacement measure-ment point

K(0)＝Coe‹cient of lateral earth pressure (at rest)Lp＝Pile lengthP＝Nominal load per pilePt＝Total superstructural load supported by piled foundation

Pult＝Ultimate static pile capacityQbE＝Base load (during earthquake)

QbE,ult＝Liqueêd (seismic) base capacity (＝qbE,ult･A)qbE,ult＝Liqueêd (seismic) base capacity

Qb0＝Initial base loadQb0,ult＝Static base capacity (pre-earthquake, ＝qb0,ult･A)qb0,ult＝Static base capacity (pre-earthquake)

QsE＝Shaft load (during earthquake)QsE,ult＝Liqueêd (seismic) shaft capacity

Qs0＝Initial shaft loadQs0,ult＝Static shaft capacity (pre-earthquake)SSF＝Static safety factor

a＝Proportion of total pile load carried at the pile tip (＝Qb0/P )ault＝Proportion of total pile capacity provided by the pile tip (＝

Qb0,ult/Pult )


b＝Proportion of total superstructural load supported by piles(＝4P/Pt)

gs＝Soil shear strainDcyc＝Lateral cyclic displacement of pile cap/pile headDu＝Excess pore pressure

q＝Critical state soil friction anglem＝Coe‹cient of frictionn＝Poisson's ratio

rE＝Earthquake-induced settlementrE,avg＝Average (monotonic) earthquake-induced settlementrE,cyc＝Cyclic earthquake-induced settlement

sv?＝Instantaneous vertical eŠective stresss?v0＝Initial vertical eŠective stress

REFERENCES

1) Berezantzev, V. G., Khristoforov, V. S. and Golubkov, V. N.(1961): Load bearing capacity and deformation of piled founda-tions, Proc. 5th ICSMFE, Paris, France, 11–15.

2) Boulanger, R. W., Kutter, B. L., Brandenberg, S. J., Singh, P. andChang, D. (2003): Pile foundations in liqueêd and laterallyspreading ground during earthquakes: centrifuge experiments andanalyses, Report No. UCD/CGM-03/01, University of California,Davis.

3) Brennan, A. J. (2003): Vertical drains as a countermeasure to earth-quake-induced soil liquefaction, PhD Thesis, University of Cam-bridge, UK.

4) Brennan, A. J., Madabhushi, S. P. G. and Houghton, N. E. (2006):Comparing laminar and equivalent shear beam (ESB) containersfor dynamic centrifuge modelling, Proc. 6th Int. Conf. on PhysicalModelling in Geotechnics '06, Hong Kong, 171–176.

5) Brennan, A. J., Thusyanthan, N. I. and Madabhushi, S. P. G.(2005): Evaluation of shear modulus and damping in dynamic cen-trifuge tests, Journal of Geotechnical and Geoenvironmental En-gineering, 131(12), 1488–1497.

6) Castro, G. (1975): Liquefaction and cyclic mobility of saturatedsands, Journal of the Geotechnical Engineering Division,101(GT6), 551–569.

7) Castro, G. and Poulos, S. J. (1977): Factors aŠecting liquefactionand cyclic mobility, Journal of the Geotechnical Engineering Divi-sion, 103(GT6), 501–516.

8) Cheng, Y. M. (2004): Nq factor for pile foundations by Berezan-tzev, Geotechnique, 54(2), 149–150.

9) De Alba, P. A. (1983): Pile settlement in liquefying sand deposit,Journal of Geotechnical Engineering, 109(9), 1165–1179.

10) Haldar, S., Sivakumar Babu, G. L. and Bhattacharya, S. (2007):Buckling and bending of slender piles in liqueâble soils duringearthquakes: a probabilistic analysis, Design of Foundations inSeismic Areas: Principles and Some Applications.

11) Knappett, J. A. (2006): Piled foundations in liqueâble soils: ac-counting for axial loads, PhD Thesis, University of Cambridge.

12) Knappett, J. A. and Madabhushi, S. P. G. (2008a): Liquefactioninduced settlement of pile groups in liqueêd and laterally spread-ing soils, Journal of Geotechnical and Geoenvironmental Engineer-ing, 134(11), 1609–1618.

13) Knappett, J. A. and Madabhushi, S. P. G. (2008b): Designingagainst pile-tip bearing capacity failure in liqueâble soil, Proc.BGA 2nd Int. Conf. on Foundations, Dundee, UK, 2, 1237–1246.

14) Kulhawy, F. H. (1984): Limiting tip and side resistance, fact or fal-lacy, Symposium on Analysis and Design of Pile Foundations,ASCE, San Francisco, 80–98.

15) Lin, S., Tseng, Y., Chiang, C. and Hung, C. L. (2005): Damage ofpiles caused by lateral spreading-back study of three cases, SeismicPerformance and Simulation of Pile Foundations in Liqueêd andLaterally Spreading Ground, ASCE Geotechnical Special Publica-tion No. 145, 121–133.

16) Madabhushi, S. P. G. (1994): EŠect of pore ‰uid in dynamic cen-trifuge modelling, Proc. Centrifuge `94, Balkema, Rotterdam,127–132.

17) Madabhushi, S. P. G., Schoêld, A. N. and Lesley, S. (1998): Anew stored angular momentum based earthquake actuator, Proc.Centrifuge '98, Tokyo, Japan, 111–116.

18) Mitchell, R. J. and Dubin, B. I. (1986): Pore pressure generationand dissipation in dense sands under cyclic loading, Canadian Geo-technical Journal, 23(3), 393–398.

19) Rollins, K. M. and Strand, S. R. (2006): Downdrag forces due toliquefaction surrounding a pile, Proc. 8th National Conference onEarthquake Engineering, San Fransisco, CA.

20) Schoêld, A. N. (1981): Dynamic and earthquake geotechnical cen-trifuge modelling, Technical Report CUED/D-SOILS/TR104,University of Cambridge, UK.

21) Steedman, R. S. and Sharp, M. J. (2001): Liquefaction of deepsaturated sands under high eŠective conˆning stress, Proc. 4th Int.Conf. on Recent Advances in Geotechnical Earthquake Engineer-ing and Soil Dynamics, San Diego, CA, USA, Paper no. SPL1.

22) Stewart, D. P., Chen, Y. R. and Kutter, B. L. (1998): Experiencewith the use of methylcellulose as a viscous pore ‰uid in centrifugemodels, ASTM Geotechnical Testing Journal, 21(4), 365–369.

23) Tokimatsu, K. and Asaka, Y. (1998): EŠects of liquefaction-in-duced ground displacements on pile performance in the 1995 Hyo-goken-Nambu earthquake, Soils and Foundations (Special Issue),163–177.

24) Tokimatsu, K., Mizuno, H. and Kakurai, M. (1996): Buildingdamage associated with geotechnical problems, Soils and Founda-tions (Special issue), 219–234.

25) Tokimatsu, K., Oh-Oka, H., Satake, K., Shamoto, Y. and Asaka,Y. (1998): EŠects of lateral ground movement on failure patterns ofpiles in the 1995 Hyogoken-Nambu earthquake, GeotechnicalEarthquake Engineering and Soil Dynamics III, ASCE Geo-technical Special Publication No. 75, 1175–1186.

26) Uesugi, M. and Kishida, H. (1986): Frictional resistance at yield be-tween dry sand and mild steel, Soils and Foundations, 26(4),139–149.

27) Vesic, A. S. (1972): Expansion of cavities in inˆnite soil mass, Jour-nal of the Soil Mechanics and Foundations Division, 98(SM3),265–289.

28) Yang, Z., Elgamal, A. and Parra, E. (2003): Computational modelfor cyclic mobility and associated shear deformation, Journal ofGeotechnical and Geoenvironmental Engineering, 129(12),1119–1127.

29) Yasufuku, N., Ochiai, H. and Ohno, S. (2001): Pile end-bearingcapacity of sand related to soil compressibility, Soils and Founda-tions, 41(4), 59–71.

30) Zhang, L. M. and Ng, A. M. Y. (2005): Probabilistic limiting toler-able displacements for serviceability limit state design of founda-tions, Geotechnique, 55(2), 151–161.

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SEISMIC BEARING CAPACITY OF PILES IN LIQUEFIABLE SOILS