piles under cyclic axial loading, study of the friction fatigue.pdf

Piles under cyclic axial loading: study of thefriction fatigue and its importance in pile behavior

Sofia Costa D’Aguiar, Arezou Modaressi, Jaime Alberto dos Santos, andFernando Lopez-Caballero

Abstract: The main point of this paper is to identify the key features and load transfer mechanisms controlling friction fa-tigue of piles under cyclic loading. Numerical modeling makes use of an advanced elastoplastic state dependent constitutivemodel, the ECP model, also known as Hujeux’s model. Therefore, the cyclic loading simulations allowed the identificationof three levels of friction degradation, depending on the amplitude of the previous maximum load cycle. Furthermore, theanalysis also offers useful insights regarding the modification of the pile static resistance once it has been cyclically loaded.All analyses are carried out considering nondisplacement piles in Toyoura sand.

Key words: friction fatigue, cyclic, nonlinear, Toyoura sand.

Résumé : L’objectif principal de cet article est d’identifier les caractéristiques clés et les mécanismes de transfert de chargequi contrôlent la fatigue de friction de pieux soumis à des charges cycliques. Le modèle numérique utilise un modèle élasto-plastique constitutif avancé dépendant de l’état du matériel, le modèle ECP, aussi connu sous le nom de modèle de Hujeux.Les simulations des chargements cycliques ont ainsi permis d’identifier trois niveaux de dégradation causée par la friction,dépendant de l’amplitude du cycle de chargement maximal précédent. De plus, l’analyse fourni des informations utiles surles modifications de la résistance statique du pieu une fois qu’il a été chargé de façon cyclique. Toutes les analyses ont étéréalisées en considérant des pieux sans déplacement placés dans du sable Toyoura.

Mots‐clés : fatigue de friction, cyclique, non linéaire, sable Toyoura.

[Traduit par la Rédaction]

Introduction

Pile shaft capacity in sand has been observed to decreasesignificantly during pile driving (Vesic 1970). This character-istic behavior is referred to as friction fatigue (Heerema1980) or the h/r effect (Bond and Jardine 1991), in which his the distance from the pile tip, and r is the pile radius. Thiseffect was observed in model-scale as well as in full-scalepile tests (Lehane et al. 1993; White and Lehane 2004; Le-hane and White 2005). Nevertheless, there is little under-standing of the underlying mechanisms of shaft frictiondegradation. Hence, friction fatigue quantification methodsare mostly based on experience and performance trendsrather than on comprehension of fundamental soil mechanics.In more recent works, according to Randolph (2003), the

physical basis of friction degradation is the gradual densifica-tion of the soil adjacent to the pile shaft under the cyclicshearing action of installation. The reduction of radial stressduring pile installation is likely dependent on volumechanges and stress level. Randolph (2003) underlines the

problem of friction fatigue by stating that “modern designmethods must take account of friction degradation, but fur-ther work is needed in order to explore how the rate of deg-radation is affected by the pile diameter, method ofinstallation (particularly blow counts during driving), andsoil modulus.”Recent works (White and Lehane 2004; Lehane and White

2005; Gavin and O’Kelly 2007) link friction fatigue degrada-tion to the number of “shearing cycles” per diameter of ad-vance of the pile penetration. Thus, for continuous jackingpiles the rate of degradation should be at its minimum. Incontrast, for driven piles this rate should be a maximum forhigh blow counts owing to the increased number of cyclesthat the soil experiences during pile penetration.Much knowledge has been gained concerning soil–pile in-

terface interaction through the interpretation of physicalmodel load tests in terms of instrumented piles and alsothrough constant normal stiffness shear tests. White and Le-hane (2004) investigated friction fatigue in model piles incentrifuge tests. The authors observed that friction fatigue

Received 18 November 2009. Accepted 7 March 2011. Published at www.nrcresearchpress.com/cgj on 30 September 2011.

S. Costa D’Aguiar.* Universidade Técnica de Lisboa, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal;Laboratoire MSS-Mat CNRS UMR 8579, École Centrale Paris, Grande Voie des Vignes, 92290 Châtenay-Malabry, France.A. Modaressi and F. Lopez-Caballero. Laboratoire MSS-Mat CNRS UMR 8579, École Centrale Paris, Grande Voie des Vignes, 92290Châtenay-Malabry, France.J. Alberto dos Santos. Universidade Técnica de Lisboa, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal.

Corresponding author: S. Costa D’Aguiar (e-mail: [email protected]).*Present address: SNCF — Innovation and Research Department, 45, rue de Londres, 75379 Paris, France.

1537

Can. Geotech. J. 48: 1537–1550 (2011) doi:10.1139/T11-032 Published by NRC Research Press

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

does not occur in the absence of loading cycles, and that hav-ing a large number of cycles leads to a large reduction inshaft friction in a given soil horizon. These findings wereconfirmed by results of cyclic constant normal stiffness(CNS) interface testing (Fahkharian and Evgin 1997; Ou-marou and Evgin 2005). It was then clear that the primaryphysical mechanism controlling friction fatigue is the cyclichistory, imparted during the pile installation, of soil elementsnear the soil–pile interface.Nonetheless, the study of the pile’s response under cyclic

loading is not only important in terms of pile drivability, butalso in terms of the modification of the soil’s initial stateafter cycling and whether this modification has repercussionson the pile’s subsequent resistance. This leads us to the im-portant role of pile installation technique on the pile’s per-formance (Meyerhof 1976; Foray et al. 1989; Fioravante etal. 1994; Chow 1997; De Nicola and Randolph 1997). There-fore, a parallel could be established between installation ef-fects and the behavior of cyclically loaded piles. Animportant insight could be gained through the identificationof the mechanisms controlling the friction fatigue.Thus the main purposes of this work are:

• First, to understand the underlying mechanisms in the pro-cess of friction fatigue of cyclically loaded piles throughthe fundamentals of soil behavior, by analyzing both thepile’s global response in terms of resistance mobilizationand the complete stress path history of a soil elementaround the pile shaft.

• Second, to link the cyclic stress history of soil that hassuffered friction fatigue to its capability (or lack thereof)to recover from a degraded state.

Therefore, in this paper, the behavior of piles under cyclic ax-ial loading is studied using a three-dimensional finite-elementnumerical model. The soil’s behavior is modeled using astate-dependent elastoplastic cyclic constitutive law (Aubryet al. 1982; Hujeux 1985). Through numerical simulationsthe amplitude and number of preloading cycles are studied,and their effects on the pile’s subsequent static resistanceare also quantified. Friction fatigue is, therefore, analyzedin terms of the pile’s load–settlement curves and the soil’sstress paths.The present analysis underlines the importance of the soil’s

initial state in terms of initial relative density and initial con-fining stress, combined with the amplitude of the first pre-load cycle, as the major factors influencing different loadtransfer mechanisms that lead to different levels of frictiondegradation.

Numerical model

Numerical simulation of pile behavior: backgroundAs mentioned previously, one of the goals of this work is

to determine the pile’s load–settlement resistance relationshipunder axial loads.The total load applied at the pile head is transferred to the

surrounding soil through the mobilization of shear stress andnormal stress at the pile base. Thus, the pile resistance isgenerally inferred from the equilibrium forces mobilized atthe pile shaft and base, here denoted Qs and Qb, respectively.Therefore, pile shaft and base resistance can be defined by

½1� Qs ¼Z LZ 2p

tsr dq dz

and

½2� Qb ¼Z 2pZ R

svr dr dq

where L is the pile length, R the pile radius, ts the shearstress mobilized at a given point on the pile shaft, and sv thevertical mobilized stress at the pile base.Pile behavior can then be numerically inferred through the

pile’s global response in terms of Qs and Qb or its local re-sponse in terms of the local mobilized shear stress or the ver-tical stress for the case of the shaft or the base, respectively.In this work, special attention is given to the pile shaft resist-ance, Qs, which is mainly controlled by the response of a thinlayer of soil immediately adjacent to the pile shaft (Fiora-vante 2002; Randolph 2003). Therefore, hereinafter the shearstress path is represented by the stress evolution of the soil ata given depth, obtained using the numerical results of a fi-nite-element integration of the thin elements representing thepile–soil interface.

ModelIn the present work, the GEFDyn finite element software

(Aubry et al. 1986; Aubry and Modaressi 1996) was used tocreate a three-dimensional finite-element model that was usedto analyze the behavior of a pile subjected to axial cyclic andmonotonic loads. The studied model is based on a centrifuge-model pile tested by Fioravante (2002) and Colombi (2005)(used for previous model validations in D’Aguiar et al.(2008)). This prototype-scale pile was 8.4 m long, 0.3 m indiameter, and was embedded in a 20 m depth homogeneousmedium-density Toyoura sand layer. The pile and soil weremodeled using 8-node, solid, three-dimensional elements (de-tails of the mesh can be found in Costa D’Aguiar (2008)).The Toyoura sand was modeled with the three-dimensional

elastoplastic state dependent (ECP) multimechanism soil con-stitutive model (Aubry et al. 1982; Hujeux 1985). The princi-pal characteristics of this elastoplastic model are thefollowing:

• The model is written in terms of Terzaghi effective stressin the case of saturated soils, and uses incremental plas-ticity.

• The yielding criterion is of Coulomb type.• The model takes into account the influence of compressive

effective pressure, dilatancy–contractancy, and the con-cept of critical state.

• Hardening evolution is dependent on plastic strains (bothdeviatoric and volumetric).

• Concerning cyclic behavior, kinematic hardening is a func-tion of the state parameters of the previous loading.

• The model is only defined for infinitesimal transformations.

Details of the model formulations are given in Sica et al.(2008) and in Appendix A. A summary of the model’s equa-tions and parameters is presented in Table 1.Recently, Lopez-Caballero et al. (2007) presented a strat-

egy for model parameters’ identification that permits the clas-sification of the parameters based on their utilities andestimation methods. Thus, some parameters can be directly

1538 Can. Geotech. J. Vol. 48, 2011

Published by NRC Research Press

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

determined from in situ or laboratory tests and others fromcalibration, as presented in Table 1. Parameters can also begrouped according to their role in soil behavior: first, param-eters that determine the elasticity; second, parameters that de-termine the soil’s state during loading (yield function); third,parameters governing hardening; and finally, parameters de-fining the threshold domains.Model parameters were calibrated using laboratory,

drained, triaxial test results presented by Fukushima and Tat-suoka (1984) (details in Costa D’Aguiar (2008)). The sanddensity is Dr = 40%, for which the initial earth pressure co-efficient, k0, is assumed to be 0.5 and g = 14.5 kN/m3, whereg is the soil’s bulk density. The identified soil parameters forthe ECP soil model are presented in Table 2.The soil–pile interface is considered to be totally rough

and is modeled using thin solid elements. The pile was mod-eled as a linear elastic material (Poisson’s ratio, n = 0.36;Young’s modulus, E = 8.1 GPa). It is important to note thatthe modeled pile is a nondisplacement pile, so installation ef-fects are considered to be negligible. Loading is applied tothe pile through the application of prescribed displacementsand forces.

MethodologyTwo sets of simulations were carried out

1. Cyclic loading of nondisplacement piles.2. Monotonic loading after cycling.

For the first set of simulations, cycling was applied at thepile head for different load levels, Q = 200, 400, 900, 1100,and 1300 kN and for different numbers of load cycles, N =5, 10, and 15. The maximum pile head load was kept con-stant during each cyclic loading sequence. Results of the sim-ulations were presented in terms of the effect of cyclicloading on the shaft and base resistance mobilizations indi-vidually, and of their different contributions to the final totalresistance with respect to the applied cyclic load. These re-sults help to identify different degradation rates of the pileshaft resistance with cycling. In addition, to justify these dif-ferent rates of degradation, special attention is given to theshaft–soil stress path for different points around the pile.For the second set of simulations, to evaluate the influence

of the past cyclic stress history on the capability of the soil torecover from a degraded state, monotonic reloading was ap-plied after the previous cycling (first set of simulations). For

Table 1. Constitutive relationships of multimechanism ECP models.

Parameters measured

Description Constitutive equation Equation Directly IndirectlyElasticity Kmax ¼ Kref

p0p0ref

� �ne 1 Kref, Gref —

Gmax ¼ Grefp0p0 ref

� �ne 2 pref, ne —

Yielding function qk � sinf0ppp

0kFkrk � 0 3 f0

pp —Volumetric hardening Fk ¼ 1� b ln

p0k

pc

� �4 b, b initial state: pco —

pc ¼ pco expðb3pvÞ 5 —Deviatoric hardening rk ¼ relk þ 3

p

k

aþ3p

k

6 — relk

a = a1 + (a2 – a1) ak (rk) 7 — a1, a2Plastic potential _3

pvk ¼ _l

p

kJv 8 — —

Jv ¼ ajakðrkÞ sinj � qkpk

� �9 j aj,

Behavior domainsif rk< rhys ak(rk) = 0 10 — —if rhys< rk< rmob

akðrkÞ ¼ rk�rhys

k

rmobk

�rhys

k

� �m 11 — relas, rhys

if rmob< rk< 1 ak(rk) = 1 12 — rmob, mIsotropic mechanism:Yielding function fiso = |p′| – dpcriso 13 — —Hardening riso ¼ relasiso þ 3

p

v iso

cðpc=prefÞþ3p

v iso

14 — relasiso

3pv ¼X3

k¼1ð3pvkÞ þ ð3pvÞiso 15 — —

Note: Kmax, bulk modulus; Kref, bulk modulus measured at the mean reference pressure; p′, mean compressive stress; p0ref , effective mean reference pres-sure; ne, degree of the nonlinearity; Gmax, shear modulus; Gref, shear modulus measured at the mean reference pressure; qk, deviatoric stress; f0

pp, frictionangle at perfect plasticity; p0k , mean effective stress; Fk, volumetric hardening variable; rk, threshold domains; b governs the influence of the density or over-consolidation of the material and also the shape of the yielding function; pc, critical mean pressure; pco, critical mean effective stress that corresponds to theinitial state, defined by the initial void ratio; b, plastic compressibility modulus that introduces the influence of the densification of the material in the finalresistance; 3pv, hardening variable; relk , elastic deviatoric domain; 3pk , plastic deviatoric strain; a controls the hardening evolution; ak, hardening variable, spe-cific to each mechanism yield function and defined through the behavior domains; _lp

k , plastic multiplier; Jv, flow rule controlling the volumetric plasticdeformation; aj, hardening evolution parameter; j, characteristic angle defining the limit between dilatancy and contractancy; pk, mean pressure; rhysk , hys-teretic deviatoric domain; rmob

k , mobilized deviatoric domain; fiso, yield surface of the isotropic mechanism; d, distance of the isotropic consolidation line tothe critical state line; riso, threshold domains for the isotropic mechanism; relasiso , elastic isotropic domain; 3pv iso, isotropic volumetric plastic strain; c controlsthe isotropic hardening; pref, total mean reference pressure; 3pvk , volumetric plastic strain; k, deviatoric mechanisms.

Costa D’Aguiar et al. 1539


Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

these reloading calculations, the soil’s initial state and stressfield was that obtained at the end of the cycling (first set ofsimulations). Therefore, the soil memory (i.e., changes due tothe different soils’ loading histories) is taken into accountthrough the hardening variables of the soil model obtainedin the previous calculation (Table 1). Hence, results are com-pared in terms of the pile’s mobilized resistance and shaftstress paths. For all simulations, medium-dense Toyourasand was used, except when the effect of initial density wasstudied and friction fatigue results for the medium-densitysand are compared with a very high-density sand (Dr =93%).

Cyclic loading of nondisplacement piles

Load–settlement analysisIn Fig. 1, comparative load–settlement results are pre-

sented for the application of five cycles of different ampli-tudes, in terms of shaft (Figs. 1a and 1c) and baseresistances (Figs. 1b and 1d). Load settlement curves are pre-sented as a function of the pile’s relative head settlement, s/d,in which s is the total pile head settlement and d is the pilediameter.It is evident in Fig. 1 that there are different evolutions of

shaft and base resistances with cycling, regarding the ampli-tude of the constant cyclic load. In terms of peak shaft resist-ance at each cycle, for the higher load levels (900, 1100, and1300 kN; Fig. 1a) there is a clear reduction in the peak fric-tion with an increase of the number of cycles. For the lower

Table 2. ECP soil model parametersused for the numerical modelling ofToyoura sand (TS40) behavior with arelative density of Dr = 40%.

Parameter ValueElasticityKref (MPa) 296Gref (MPa) 222ne 0.4p0ref (MPa) 1.0

Critical state and plasticityf0

pp(°) 30b 43b 0.22pc0 (kPa) 1400

Flow rule and hardeningj (°) 30aj 1.0a1 0.0001a2 0.15c1 0.06c2 0.03m 1.0

Threshold domainsrelas 0.005rhys 0.003rmob 0.8relasiso

0.0001

Note: c1 and c2 are isotropic hardeningparameters.

Fig. 1. Comparative load–settlement results for the cyclic calcula-tions at different load levels (Q = 200, 400, 900, 1100, and1300 kN): (a) shaft resistance; (b) base resistance; magnification of(c) shaft resistance and (d) base resistance.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

load levels (200 and 400 kN; Fig. 1c) this shaft reductionwith cycling is very reduced or nonexistent.Thus, for some of the applied loads, “friction fatigue” is

observed in the shaft friction. Moreover, no degradation isobserved in the base resistance mobilization. The base load–settlement curve is affected by cycling in terms of permanentdisplacements and peak base resistance at each cycle, so thatthe loss of shaft resistance owing to friction fatigue is com-pensated for by base resistance, and the total pile head loadremains constant (Figs. 1b and 1d). Figure 2a presents theshaft resistance degradation ratio curves, which represent theratio of the maximum shaft resistance mobilized at each loadcycle, Qspeak, to the maximum monotonic shaft resistance,Qsf. Two types of degradation can be identified: nonlineardegradation for higher load levels (from 900 to 1300 kN)and linear degradation for the lower loads (400 kN). ForQ = 200 kN, the degradation can be identified as linear, butthe rate is very small compared with the other amplitudes.This degradation ratio is clearly dependent on the cyclic am-plitude, but in Fig. 2a nonlinear degradation of the shaft re-sistance occurs when, in the first cycle, the mobilized shaftresistance is equal to the maximum monotonic shaft resist-ance: Qspeak/Qsf = 1.Therefore, friction degradation can be linked to the cyclic

load amplitude regarding the load that leads to soil failure.Nonetheless, for a deeper understanding, even justification,

of this dependence of the friction fatigue on the load level,the soil stress path near the pile shaft has to be analyzed.

Friction fatigue stress analysisExperimental investigations carried out by White and Le-

hane (2004) and DeJong et al. (2006) on piles and using in-terface CNS tests have shown that the primary mechanismcontrolling friction fatigue is the cyclic history of the soil el-ement at the pile–soil interface. According to the latter au-thors, this cyclic history is recorded as a net contraction of athin layer that is confined by the far field soil. When sheared,the thin layer near the pile shaft undergoes volume changesthat control the changes in radial stress on which the shearstress mobilizations at each depth depend. Therefore, if thefriction fatigue is to be analyzed through the importance ofthe cyclic stress path, attention should be paid to the type ofvolume changes that occur during cycling. If we go back tosoil mechanics principals, before reaching perfect plasticity,and depending on the initial state and on the applied loadlevel, soil behavior can either be contractive–dilative orpurely contractive. Thus, by observing the type of frictiondegradation observed in the previous paragraph and the typeof volume changes near the pile shaft during cycling, threedifferent load transfer mechanisms can be identified.These three identified cyclic load transfer mechanisms are

studied hereinafter in terms of soil stress paths adjacent to thepile shaft at different depths.

Cyclic mechanism 1: Maximum shaft resistance and criticalstate is reached during the first load cycle (Q = 1300 and1100 kN)For a deep analysis of the friction fatigue observed during

cyclic loading, the global behavior of the soil adjacent to thepile shaft at 1.89 and 6.93 m depths is presented in Figs. 3,4, and 5. Shear stress evolution is plotted against the relative

head displacement in Fig. 3, normal stress is plotted againstshear stress in Figs. 4a and 5a, and volumetric changes dur-ing each cycle are plotted against the mean confining pres-sure in Figs. 4c and 5b.Results show a clear reduction of the shear stress, observed

for different depths along the pile shaft during the differentcycles (Fig. 3). In addition, as verified for the shaft resist-ance, shear stress reaches a plateau level in the first load and

Fig. 2. Shear resistance degradation ratio : (a) medium dense sand;(b) dense sand. Qspeak, maximum shaft resistance at each cycle; Qsf,maximum static shaft resistance.

Fig. 3. Comparison of cyclic shear stress mobilization (N = 5 atQ = 1300 kN), for two points adjacent to the pile shaft at 1.89 m(solid line) and 6.39 m depths (dashed line).



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

in the subsequent cycles indicating that failure has beenreached. In Fig. 4a (with cycling) the stress path confirmsthat the reduction in shear stress is also caused by the reduc-tion of normal stress during loading. Nonetheless, at the be-ginning of each load cycle, the normal stress does not changesignificantly at the top of the pile (z = 1.89 m) and tends tolessen at deeper depths (z = 6.4 m).

In terms of volume changes, each cycle begins with a briefcontraction phase before dilation begins. During each cycle,the phase transformation (changing from contraction to dila-tion) is reached for higher contraction (D3v in Fig. 4b), andsmaller dilation is required to reach a critical state (stabiliza-tion of stress changes and volume changes for increasing de-formation). So, to reach failure at each cycle the maximumshear stress tends to be reduced. The main mechanisms offriction fatigue are analyzed and well captured by the soilmodel. Nevertheless, it is necessary to explain the increasingcontraction and dilation reduction when the number of cyclesincreases.In this analysis, the effect of cyclic loading on the volu-

metric strain with respect to the critical state is illustrated inFig. 4c, in which the small squares mark the end of a loadcycle and the cumulative volumetric strain is plotted as afunction of the mean stress, p. As the behavior is governedby the distance to the critical state, the critical state line(CSL), simulated through triaxial tests at different confiningpressures, is plotted in the same figure.

Two important aspects can be pointed out concerning theposition of the initial state at the beginning of each load cycle(colored squares in Fig. 4c) with respect to the CSL. First,the confining pressure at the beginning of each cycle hassmall variations, but tends to decrease with increasing num-ber of cycles. Second, in terms of volume change, there is areduction in the soil densification, due to the positive perma-

Fig. 4. Cyclic soil stress paths for N = 5 at Q = 1300 kN, for apoint adjacent to the pile shaft at 1.89 m depth: (a) shear and nor-mal stresses; (b) increment of volumetric strain at each cycle andmean stress; (c) volumetric strain and mean stress (CSL, criticalstate line).

Fig. 5. Cyclic soil stress paths for N = 5 at Q = 1300 kN, for apoint adjacent to the pile shaft at 6.4 m depth: (a) shear and normalstresses; (b) volumetric strain and mean confining stress.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

nent volumetric strains. Therefore, owing to these permanentvolume changes, the initial state after each cycle is closer tothe CSL. It is this modification of the initial state that ex-plains that soil behavior at each cycle is modified and thatfriction fatigue occurs with cycling.

Cyclic mechanism 2: Maximum shaft resistance is notreached after the first load cycle (Q = 400 kN)Comparing the stress path results of simulations where

Q = 400 kN with Q = 1300 kN, different trends are ob-served. The reduction in the shear stress (Fig. 6a; with cy-cling) is very small when compared with mechanism 1 (Q =1300 kN). In Fig. 6b, one can observe that the stress pathmoves progressively to the left (reduction of the confiningstress). In addition, it is possible to see that there is no signif-icant modification of the stress path after the first cycle. Thisis the first important difference between mechanisms 1 and 2.This observation is based on the fact that the volumetricstrains do not change significantly after the first load cycle(Fig. 6c); the soil contracts and dilates with very small accu-mulation of permanent volumetric strain for z = 4.4 m andwith accumulation of contraction at shallow depth, z =1.89 m. The second difference, and the most important, re-garding mechanism 1 is that the critical state is reached nei-ther for the analyzed depths, nor for the entire pile shaft.Besides, in contrast with mechanism 1, as the number ofcycles increases the initial state, at the beginning of eachcycle, is moving farther from the CSL. In terms of the crit-ical state concept, the farther an initial state is from the CSL,the denser the soil state. That is why there is a very small in-crease in the dilation with each load cycle. For this reason,during the load cycles, the normal and shear stresses presenta slight decrease during cycling and, for five cycles, neverreach a plateau level.

Cyclic mechanism 3: Maximum shaft resistance andtransformation phase are not reached after the first loadcycle (Q = 200 kN)For the applied load level (Q = 200 kN), a different con-

figuration of the cyclic stress path is obtained. As can beseen in Fig. 7c, the applied load was not sufficient to triggerthe transformation phase. Therefore, contractive behavior isobtained during the application of the five cycles for both an-alyzed depths. According to these volumetric changes, thenormal stress decreases (Fig. 7b). Nevertheless, shear stressreduces linearly (Fig. 7c) with very little accumulation of per-manent pile head settlement. Thus, the initial state after eachcycle is shifted farther from the CSL and the accumulation ofcontractive volumetric strain leads to the densification of thesoil around the pile shaft (Fig. 7c).There is therefore a “memory phenomenon” that can be

characterized by the maximum value of the cyclic stress ampli-tude. Volume changes depend on the position of the stress statewith respect to the contractant domain (in general q′/p′ < M)defined by monotonic triaxial testing. If the stress path issituated entirely within this region, the cycles will producea progressive compaction, even for initially dense materials(Biarez and Hicher 1994).Thus, for the analyzed case, even if the soil is densified

the stress path remains in the contractant domain during cy-cling. After five cycles the stress path still did not reach the

intrinsic curve, so the transformation phase did not takeplace. This supports the fact that for this load level (Q =200 kN for N = 5) there is no friction fatigue.This behavior is the typical behavior of cyclic mobility,

where there is a complete reversal of stress during cyclingand the maximum strength is not reached.It could be expected that with an increasing number of

cycles (N > 5), as the confining pressure reduces, the stresspath reaches the dilatant domain so that compaction and dila-tion will occur.

Fig. 6. Cyclic soil stress paths for N = 5 at QT = 400 kN, for apoint adjacent to the pile shaft at depths of 1.89 m (solid line) and4.4 m (dashed line): (a) shear and relative pile head displacement;(b) shear and normal stresses; (c) volumetric strain and mean con-fining stress.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

Effect of initial density on friction fatigueTo highlight the importance of the soil’s initial density in

the mechanism controlling friction fatigue, the same set ofcyclic simulations (same number of cycles and load ampli-tude) was carried out for a dense Toyoura sand (Dr = 93%).The stress paths obtained for the dense sand are compared

with that of the medium dense sand, for the same depth (z =4.4 m) and the same applied load (Q = 1300 kN), in Fig. 8.The following can be underlined:

• higher shear stress is mobilized with less permanent pilehead displacement for the denser sand in the first andsubsequent cycles (Fig. 8a);

• the denser sand does not reach the critical state or the max-imum static resistance in the first cycle; and

• the transformation phase is reached but not the critical state(Fig. 8c).

Thus, changes in the soil density have a direct influenceon the soil’s initial state, and therefore, the cyclic amplitude

Fig. 8. Comparison of cyclic stress path (N = 5 at Q = 1300 kN) fora medium dense sand (dashed line) and a dense sand (solid line) at adepth of 4.4 m at the pile shaft: (a) shear and relative pile head dis-placement; (b) shear and normal stresses; (c) volumetric strain andmean confining stress.

Fig. 7. Cyclic soil stress paths for N = 5 at Q = 200 kN, for a pointadjacent to the pile shaft at a depth of 4.4 m: (a) shear and relativepile head displacement; (b) shear and normal stresses; (c) volumetricstrain and mean confining stress.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

will have an impact on the soil’s stress history. The cyclicmechanisms activated for the application of a given cyclic(Q = 1300 kN) are not the same, and for the example pre-sented in this paragraph, the medium dense sand activates cy-clic mechanism 1 with a nonlinear degradation of shearstress, while the dense sand activates mechanism 2 with alinear degradation of shear stress.

Summary of the cyclic mechanismsBy studying the stress path in the soil around the pile

shaft, it is discovered that the initial load cycle can changethe soil’s state with respect to the critical state line, depend-ing on the applied load amplitude. Therefore, different stresspaths for a given number of cycles show that it is the firstcycle amplitude that determines the rate of friction degrada-tion, which is determined by whether or not the critical stateor transformation phase is reached. Thus, friction fatigue phe-nomena, for a small number of applied load cycles, can besummarized by three different levels of friction degradation:

Cyclic mechanism 1: during the initial load cycle, thecritical state is reached. In subsequent cycles:

• nonlinear degradation of shaft resistance with cyclingtakes place;

• the soil experiences compaction and dilation;• the soil state moves towards the CSL (Fig. 4c), so to

a less-dense state; and• during each cycle, the critical state is reached again,

but there is a progressive increase in compactionand decrease in dilation, resulting in a clear reduc-tion of the mobilized normal and shear stressesfrom cycle to cycle.

Cyclic mechanism 2: during the first load cycle, the cri-tical state is not reached, but passage from contractiveto dilative behavior is present (the transformationphase). In subsequent cycles:

• linear degradation of shaft resistance takes place;• the soil experiences compaction and dilation (Fig. 6c);

• the mean and normal stresses decrease (Fig. 6b); and• the initial state moves farther from the CSL with pro-

gressive accumulation of permanent dilative volu-metric strain (Fig. 3b), and shear stress decreasessmoothly.

Cyclic mechanism 3: during the first load cycle, thetransformation phase is not reached. In subsequent cy-cles:

• linear degradation of shaft resistance happens veryslowly;

• the soil experiences compaction (Fig. 7b);• the mean stress decreases, there is no friction fatigue

until the stress path touches the intrinsic line (cyclicmobility), perfect plasticity (t = sn tan f) is notachieved, and there is a total stress reversal duringcycling; and

• the initial state moves farther from the CSL becauseof soil densification by cycling (Fig. 7c).

These findings provide initial insight into the primarymechanisms that lead to friction fatigue. The cyclic rate of

degradation is primarily dependent on the load level appliedduring the first load cycle, on the initial confining stress, andon the relative density of the soil, which will determine theposition of the soil with respect to its critical state.

Monotonic loading after cyclingTo evaluate the effects of friction fatigue on the modifica-

tion of the soil initial state, and the impact of the stress his-tory on its ability to recover from a degraded state, reloadcalculations were carried out after cycling. These reload cal-culations consider, as the initial state, the soil state and stressfield generated at the end of the cycling. The soil memorydue to the different soils’ loading histories is taken into ac-count through the hardening variables of the previous calcu-lation (Table 1).

Effect of the cyclic amplitude for a given number of cyclesFigure 9 shows the load settlement curves for the static re-

load, subsequent to the application of five cycles of differentamplitudes (Q = 200, 400, and 1300 kN), compared with themonotonic simulation results obtained with no previous cy-cling. The load–settlement curves presented are apparentones (relative to the initial state before monotonic reload andafter cycling); residual loads are not taken into account anddisplacements are set to zero after cycling, as it is done incommon load testing practice (Fellenius et al. 2000). Resid-ual loads are commonly taken to be the loads that are lockedin the pile when its total head load is removed. In Fig. 1,these shaft and base residual loads are visible in the unload-ing peaks. Shaft and base residual loads are negative andpositive, respectively, and are in equilibrium (Qsres + Qbres =Q = 0). Thus, the existence of residual loads does not affectthe total load estimation of the pile but affects the proper def-inition of the load distribution between the pile shaft and thepile base (Costa D’Aguiar 2008).After the application of five cycles with different ampli-

tudes the soil initial state is modified, so now the effects ofsoil loading history on the pile resistance mobilization andof previous cycling on pile–soil performance are ready for in-vestigation.

Cyclic mechanism 1Cyclic mechanism 1 (Q = 1300 kN) has about half of the

maximum shaft resistance in the monotonic case. The shearstress mobilization is smaller than that obtained in the mono-tonic calculation. This can be explained by the difference involume changes (Fig. 10a) that occured during reload, whichare controlled by the initial state of the soil just before reload.This initial state was different than the undisturbed state (noprevious cycling), and was closer to the critical state line, sothe volume changes for cyclic mechanism 1 are smaller thanthe ones obtained for the virgin monotonic reload (Fig. 10a).The base resistance is clearly reinforced by the application

of high-amplitude cycling, which mobilizes cyclic mecha-nism 1. This is caused by, on one hand, the residual loadbeing locked-in, and on the other hand, the high base stiff-ness increase due to preloading that the base had to undergoto compensate for the high friction fatigue (Fig. 1). As seenpreviously, the base resistance mobilization during cycling isdominated by the generation of friction fatigue, because the



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

pile has to settle more during cycling to compensate for fric-tion loss and to keep the pile’s head-load constant. Therefore,as the preload cyclic amplitude increases, the shaft resistance,in a subsequent reload to failure, tends to decrease. Concern-ing the base, the opposite effect is observed. Thus, for the fi-nal mobilized total resistance (Fig. 9c), the effect of thefriction fatigue is compensated by a large gain in base resist-ance mobilization. Thus, the application of previous cyclesbefore testing to failure, with higher amplitude, can be bene-ficial to increase pile resistance, despite the friction fatiguegenerated during cycling.

The importance of the soil state is translated in the modelthrough the volumetric hardening variable, Fk, which de-pends on the critical mean pressure, pc, (Table 1, indicatedas equations 4 and 5).

Cyclic mechanism 2In terms of shaft resistance (Fig. 9a), cyclic mechanism 2

(Q = 400 kN) presents a small degradation of the shaft com-pared to the monotonic one. As in mechanism 1, it is evidentthat the soil has a “memory” and that shaft resistance is notrecoverable. Concerning base resistance, a very small in-crease in the initial stiffness can be verified, but no consider-able changes in mobilized resistance are observed (Fig. 9b).

Cyclic mechanism 3In the case of cyclic mechanism 3 (Q = 200 kN), there is a

small increase in shaft resistance (Fig. 9a). Nonetheless, theeffect of the soil densification, observed in the cyclic loadtransfer mechanism 3, justifies the small increase of the max-imum shaft resistance during the static reload. This differencein the shaft soil response is due to the different loading his-tories of the soils, and thus their different initial states justbefore reloading (Fig. 10a). After cycling as the initial stateof the soil is farther from the CSL it experiences higher vol-ume changes during shearing, therefore, it mobilizes highershear stress compared to the monotonic case and other simu-lations (Fig. 10b).

Fig. 9. Effect of the pre-loading cyclic amplitude (Q = 200, 400,and 1300 kN) on the subsequent reload to failure compared with themonotonic load settlement curve: (a) shaft resistance; (b) base resis-tance; (c) total resistance.

Fig. 10. Reload stress paths, after cyclic preloading N = 5, Q =200 kN, and Q = 1300 kN, compared with the monotonic one:(a) volumetric strain and mean confining stress; (b) shear and nor-mal stresses.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

Effect of the number of cycles for a given cyclic amplitudeIn this section, the effect of the applied number of cycles

for cyclic mechanism 2 (Q = 400 kN) is studied.Load–settlement curves for monotonic loading, and reload

after cyclic loading, with different numbers of cycles, arepresented in Fig. 11. After the five cycles at Q = 400 kN,the monotonic reload reaches almost the same maximumshaft resistance as that of the monotonic load (Fig. 11a).Nonetheless, a load recovering is observed for the base resist-ance (Fig. 11b).Normal stress decreases with the application of cyclic

loading, however, subsequent monotonic loading causes dila-tion as the “steady-state” strength is being mobilized. Hence,for an applied load level in which the maximum shaft resist-ance is not reached there is almost complete stress reversal interms of the shaft shear stress.In addition, from the load–settlement curves plotted in

Fig. 11, one can observe that shaft resistance decreases whenthe preceding number of applied load cycles increases. Forbase resistance, as expected, the initial stiffness increases ow-ing to the increase of the previous preload during cycling, tocompensate for friction fatigue. The loss of shaft resistance,with an increasing number of preceding load cycles, is notcompensated by the base resistance mobilization, so total re-sistance is smaller than the monotonic total resistance mobi-lized with no preceding cycles (Fig. 11c). This is in contrastwith the effect of cycling when higher load levels are ap-plied, such as in the case of cyclic mechanism 1 (previoussection).Nevertheless, for relative head displacements that vary

from 0% to 4%–5%, cycling produces a small increase in ini-tial stiffness, due to both base and shaft resistances.In summary, increasing the number of cycles of Q =

400 kN — cyclic mechanism 2 — applied previously to themonotonic loading to failure, leads to a small reduction ofthe pile total resistance mobilization subsequent to cycling,because total reversal of mobilized shear stress is not possi-ble, and this reduction is not completely compensated for bythe gain in base resistance due to preloading during cycling.Another important aspect is the base resistance progressive

activation with the application of preloading cycles. This ac-tivation is translated through an increase in the initial stiff-ness and strength of the reload, compared to the monotonicloading (due to the high preloading and displacements mobi-lized), but final base resistance, at perfect plasticity, remainsunchanged. This feature is observed when the base resistanceof a bored pile is compared with that of driven or jackedpiles under very large displacements (Fioravante et al. 1994).In this way, a first parallel can be established between instal-lation effects and the behavior of cyclically loaded piles.

ConclusionsThe main purpose of the presented work was to understand

the mechanisms underlying the process of friction fatigue inpiles that are cyclically loaded at constant amplitude, usingthe fundaments of soil behavior, and also to link the cyclicstress history of soil that has suffered friction fatigue to itscapability to recover, or not, from a degraded state. A numer-ical model using an ECP model was then used to capture theeffect of cycling on the pile’s load–settlement response dur-

ing and after cycling and to study the complete soil historynear the pile shaft. The analysis of the numerical simulations’results allowed the following conclusions to be drawn.

1. Three cyclic mechanisms are identified and justified dueto their importance regarding:

• the type of degradation rate of the shaft friction; and• the impact of friction fatigue on the ability to recover

from a degraded state.2. Two types of degradation rates of shaft resistance were

identified: nonlinear and linear. Either can occur, de-pending on whether the critical state is reached in the

Fig. 11. Effect of the number of preloading cycles, Q = 400 kN, onthe subsequent reload to failure compared with the monotonic load–settlement curve: (a) shaft resistance; (b) base resistance; (c) totalresistance.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

first load cycle (cyclic mechanisms 1) or not (cyclic me-chanisms 2 and 3).

3. In the case of nonlinear degradation rates for the shaft re-sistance (cyclic mechanisms 1), it was verified that thecritical state was approached with the dilation of a thinlayer around the pile shaft. Therefore, at the beginning ofeach new cycle the soil’s state moves towards the CSLand, therefore, to a less dense state. This stress historyhas implications on the capability of soil to recover froma degraded state and thus, in monotonic reloading piles,maximum shaft resistance is highly reduced in compari-son with a similar pile, in the same soil, that has notbeen previously cyclically loaded.

4. In the case of linear degradation rates for the shaft resis-tance, depending on the amplitude of the cyclic loading,the transformation phase (changing from contractive todilative behavior) can be reached.

5. If the transformation phase is reached in the first cycle, butthe critical state is not (cyclic mechanism 2), in the sub-sequent cycles the soil experiences compaction and dila-tion and the mean and normal stresses decrease. Thus,the soil’s initial state after each cycle moves fartherfrom the CSL with progressive accumulation of perma-nent dilative volumetric strain and the shear stress de-creases smoothly. For this cyclic mechanism, aftercycling, soil around the pile shaft can partially recover.A small decrease in the maximum shaft resistance mobi-lized in reloading is obtained compared to the “virgin”(no previous application of cycling) shaft resistance.

6. If the transformation phase is not reached in the first cycle(cyclic mechanism 3), in the subsequent cycles the soilexperiences progressive compaction, the mean stress de-creases, thus the soil is densified by cycling, and the in-itial state after each cycle moves farther from the CSL.As a result of this densification after cycling, in staticreload, the soil around the pile shaft can recover totallyand even present a higher shaft resistance comparedwith the “virgin” shaft resistance.

7. From the obtained results, it is possible to point out someanalogies with installation effects. The base is first loadedto failure during installation and then reloaded. Thus,base “activation” can be easily obtained using the cyclicloading of the pile and, when reloaded, the base willhave a stiffer load–settlement response. The cyclic load-ing of the shaft leads to friction fatigue. That is whyjacked and driven piles present different shaft capacities,because different levels of friction fatigue are attained re-garding the number and the amplitude of the cycles, im-posed during installation.

ReferencesAubry, D., and Modaressi, A. 1996. GEFDyn. Version X.X

[computer program]. Manuel scientifique, École Centrale Paris,LMSS-Mat, Paris.

Aubry, D., Hujeux, J.C., Lassoudire, F., and Meimon, Y. 1982. Adouble memory model with multiple mechanisms for cyclic soilbehaviour. In Proceedings of the First International Symposium onNumerical Models in Geomechanics, Zurich, Switzerland, 13–17September 1982. Balkema, Rotterdam, the Netherlands. pp. 3–13.

Aubry, D., Chouvet, D., Modaressi, A., and Modaressi, H. 1986.GEFDyn: Logiciel d’analyse de comportement mecanique des sols

par elements finis avec prise en compte du couplage sol–eau–air.Version GEFDYN 5 [computer program]. Manuel scientifique,École Centrale Paris, LMSS-Mat, Paris.

Biarez, J., and Hicher, P.I. 1994. Elementary mechanics of soilbehaviour: Saturated remoulded soils. A.A. Balkema, Rotterdam,the Netherlands.

Bond, A.J., and Jardine, R.J. 1991. Effects of installing displacementpiles in a high OCR clay. Géotechnique, 41(3): 341–363. doi:10.1680/geot.1991.41.3.341.

Chow, F.C. 1997. Investigations into displacement pile behaviour foroffsore foundations. Ph.D. thesis, Imperial College, London.

Colombi, A. 2005. Physical modelling of an isolated pile in coarsegrained soils. Ph.D. thesis, University of Ferrara, Ferrara, Italy.

Costa D’Aguiar, S. 2008. Numerical modelling of soil-pile axial loadtransfer mechanisms in granular soils. Ph.D. thesis, École CentraleParis, Paris,, and Universidade Técncica de Lisboa, InstitutoSuperior Técnico, Lisbon, Portugal.

D’Aguiar, S.C., Modaressi-Farahmand-Razavi, A., Lopez-Caballero,F., and Santos, J. 2008. Soil-structure interface modeling:Application to pile axial loading. In Proceedings of the 12thInternational Conference of the International Association forComputer Methods and Advances in Geomechanics (IACMAG),Goa, India, 1–6 October 2008. pp. 957–965.

DeJong, J.T., White, D.J., and Randolph, M.F. 2006. Microscaleobservation and modelling of soil-structure interface behaviourusing particle image velocimetry. Soils and Foundations, 46(1):15–28. doi:10.3208/sandf.46.15.

Fakharian, K., and Evgin, E. 1997. Cyclic simple-shear behavior of sand-steel interfaces under constant normal stiffness condition. Journal ofGeotechnical and Geoenvironmental Engineering, 123(12): 1096–1105. doi:10.1061/(ASCE)1090-0241(1997)123:12(1096).

Fellenius, B.H., Brusey, W.G., and Pepe, F. 2000. Soil set-up,variable concrete modulus, and residual load for taperedinstrumented piles in sand. In Proceedings of the SpecialtyConference on Performance Confirmation of Constructed Geo-technical Facilities, Amherst, Mass., 9 April 2000. AmericanSociety of Civil Engineers, New York. pp. 98–114. doi:10.1061/40486(300)6.

Fioravante, V. 2002. On the shaft friction modelling of non-displacement piles in sand. Soils and Foundations, 42(2): 23–33.

Fioravante, V., Jamiolkowski, M., and Pedroni, S. 1994. Modellingthe behaviour of piles in sand subjected to axial load. InProceedings of the International Conference Centrifuge ’94,Singapore, 31 August – 2 September 1994. Edited by C.F. Leung,F.H. Lee, and T.S. Tan. A.A. Balkema, Rotterdam, the Nether-lands. pp. 455–460.

Foray, P., Genevois, J.M., and Labenieh, S. 1989. Effet de la mise enplace sur la capacité portante des pieux dans les sables. InProceedings of the 12th International Conference on SoilMechanics and Foundation Engineering, Rio deJaneiro, Brazil,13–18 August 1989. Balkema, Rotterdam, the Netherlands. Vol. 2,pp. 913–914.

Fukushima, S., and Tatsuoka, F. 1984. Strength and deformationcharacteristics of saturated sand at extremely low pressures. Soilsand Foundations, 24(4): 30–48.

Gavin, K.G., and O’Kelly, B.C. 2007. Effect of friction fatigue onpile capacity in dense sand. Journal of Geotechnical andGeoenvironmental Engineering, 133(1): 63–71. doi:10.1061/(ASCE)1090-0241(2007)133:1(63).

Heerema, E.P. 1980. Predicting pile driveability: heather as anillustration of the friction fatigue theory. Ground Engineering,13(Apr): 15–37.

Hujeux, J.C. 1985. Une loi de comportement pour le chargementcyclique des sols. In Génie parasismique. Edited by V. Davidovici.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

Presses de l’École nationale des ponts et chaussees (ENPC), Paris.pp. 278–302.

Lehane, B.M., and White, D.J. 2005. Lateral stress changes and shaftfriction for model displacement piles in sand. Canadian Geotech-nical Journal, 42(4): 1039–1052. doi:10.1139/t05-023.

Lehane, B.M., Jardine, R.J., Bond, A.J., and Frank, R. 1993.Mechanisms of shaft friction in sand from instrumented pile tests.Journal of the Geotechnical Engineering Division, ASCE, 119(1):19–35. doi:10.1061/(ASCE)0733-9410(1993)119:1(19).

Lopez-Caballero, F., Razavi, A.M.-F., and Modaressi, H. 2007.Nonlinear numerical method for earthquake site response analysisI — elastoplastic cyclic model and parameter identificationstrategy. Bulletin of Earthquake Engineering, 5(3): 303–323.doi:10.1007/s10518-007-9032-7.

Meyerhof, G.G. 1976. Bearing capacity and settlement of pilefoundations. Journal of the Geotechnical Engineering Division,ASCE, 102(3): 195–228.

De Nicola, A., and Randolph, M.F. 1997. The plugging behaviour ofdriven and jacked piles in sand. Géotechnique, 47(4): 841–856.doi:10.1680/geot.1997.47.4.841.

Oumarou, T.A., and Evgin, E. 2005. Cyclic behaviour of a sand–steelplate interface. Canadian Geotechnical Journal, 42(6): 1695–1704.doi:10.1139/t05-083.

Randolph, M.F. 2003. Science and empirism in pile foundationdesign. Géotechnique, 53(10): 847–875. doi:10.1680/geot.2003.53.10.847.

Sica, S., Pagano, L., andModaressi, A. 2008. Influence of past loadinghistory on the seismic response of earth dams. Computers andGeotechnics, 35(1): 61–85. doi:10.1016/j.compgeo.2007.03.004.

Vesic, A.S. 1970. Tests on instrumented piles, Ogeechee river site.Journal of the Soil Mechanics and Foundations Division, ASCE,96(SM2): 561–584.

White, D.J., and Lehane, B.M. 2004. Friction fatigue on displacementpiles in sand. Géotechnique, 54(10): 645–658. doi:10.1680/geot.2004.54.10.645.

Appendix AThe ECP multimechanism model’s elasticity is supposed to

obey an isotropic nonlinear elastic behavior, where the bulkand shear moduli (Kmax and Gmax) are functions of the meancompressive stress (p′), as follows:

½A1� Kmax ¼ Kref

p0

p0ref

� �ne

½A2� Gmax ¼ Gref

p0

p0ref

� �ne

where Kref and Gref are the bulk and shear moduli measuredat the mean reference pressure (p0ref) and ne is the degree ofthe nonlinearity.This model can take into account the soil behavior in a

large range of deformations and the representation of all irre-versible phenomena is made by four coupled elementaryplastic mechanisms: three deviatoric and one volumetric. Thecoupling of the mechanisms is made through the volumetricdeformations. Adopting the soil mechanics sign convention(compression positive), the deviatoric primary yield surfaceof the (k) plane is given by:

½A3� fkðs¼0; rk; 3pvÞ ¼ qk � p0krkF sinf0

pp k 2 ½1; 2; 3�

where

½A4� F½p0; pcð3pvÞ� ¼ 1� b lnp0

pc

½A5� pc ¼ pc0eb3

pv

½A6� rk ¼ relask þ 3pk

aþ 3pk

� �

• f0pp is the friction angle at the perfect plasticity;

• pc0 is the critical mean effective stress that corresponds tothe initial state, defined by the initial void ratio;

• b is the plastic compressibility modulus that introduces theinfluence of the densification of the material in the finalresistance;

• b governs the influence of the density or overconsolidationof the material and also the shape of the yielding func-tion; and

• a controls the hardening evolution, by controlling rk and isdefined through the following relation:

½A7� a ¼ a1 þ ða2 � a1ÞaðrkÞ• a(r) is defined through the behavior domains:

½A8� aðrÞ ¼

pseudo� elastic domain :

0 r < rhys

hysteretic domain :

r � rhys

rmob � rhys

� �m

rhys < r < rmob

mobilized domain :

1 rmob < r < 1

8>>>>>>>>>>>><>>>>>>>>>>>>:

The evolution of the plastic deviatoric deformations fol-lows an associated flow rule:

½A9� _3¼p

k

¼ _lp

k

@fk

@ s¼k

where, _lp

k is the plastic multiplier, and can be obtained writ-ing the consistency relationship.The evolution of the volumetric plastic deformation is

given by a flow rule based on a Roscoe-type dilatancy rule(Schofield and Wroth 1968).

½A10� _3pvk ¼ _l

pJ k

½A11� J k ¼ ajaðrÞ sinj� qk

pk

� �

where j is the characteristic angle defining the limit betweendilatancy (_3pv < 0) and contractancy.The isotropic mechanism is only activated under the iso-

tropic part of the loading and it produces only volumechanges. The yield function is described by



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

½A12� fiso ¼ jp0j � dpcriso

where

½A13� riso ¼ relasiso þ ð3pvÞisocðpc=p0refÞ þ ð3pvÞiso

in which ð3pvÞiso ¼R t

0ð_3pvÞiso dt.

The parameter d defines the distance of the isotropic con-solidation line to the critical state line in the plane (e–lnp′) or(3pv–lnp′). The parameter c controls the isotropic hardening.

The four mechanisms (three deviatoric and one isotropic)are coupled through the hardening variable 3pv:

½A14� 3pv ¼X3k¼1

ð3pvkÞ þ ð3pvÞiso

ReferenceSchofield, A.N., and Wroth, C.P. 1968. Critical state soil mechanics.

McGraw-Hill, New York.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y N

anya

ng T

echn

olog

ical

Uni

vers

ity (

NT

U)

on 1

2/04

/11

For

pers

onal

use

onl

y.

piles under cyclic axial loading, study of the friction fatigue.pdf

Documents

friction fatigue heerema1980

levels of friction degradation

pile diameter

pile tip

pile radius

friction fatigue

toyoura sand

pile static resistance