influence of reaction piles on the behaviour of a test pile in static load testing

Influence of reaction piles on the behaviour of atest pile in static load testing

Pastsakorn Kitiyodom, Tatsunori Matsumoto, and Nao Kanefusa

Abstract: This paper employs a simplified analytical method to investigate the influence of reaction piles on the load–displacement behaviour of a test pile in static load testing. A parametric study is conducted to examine the effects offactors such as pile spacing ratio, pile slenderness ratio, and pile soil stiffness ratio. Several soil profiles are consideredin the study. The parametric study also includes the cases of static load testing in the lateral direction. The correctionfactors for the initial pile head stiffness obtained from static pile load tests with the use of reaction piles are given incharts. Furthermore, analyses of centrifuge modelling of axially loaded piles are carried out using the simplified analyt-ical method. Good agreements between the test results and the analysis results are demonstrated, and the applicabilityof the correction factors is verified.

Key words: reaction piles, interaction, initial pile head stiffness, static vertical load testing, static lateral load testing,simplified analytical method.

Résumé : Cet article utilise une méthode analytique simplifiée pour étudier l’influence des pieux de réaction sur lecomportement charge–déplacement du pieu d’essai dans un essai de chargement statique. On a réalisé une étude para-métrique pour examiner les effets des facteurs tels que le rapport d’espacement des pieux, le rapport de minceur, et lerapport des rigidités du sol et du pieu. On a considéré plusieurs profils de sol dans cette étude. L’étude paramétriqueinclut également les cas d’essais de chargement de pieux dans la direction latérale. Les facteurs de correction pour larigidité initiale de la tête du pieu obtenus à partir des essais de chargement statique en utilisant des pieux de réactionsont donnés dans les chartes. De plus, on a réalisé des analyses de modélisation par centrifuge de pieux chargés en di-rection axiale au moyen de la méthode analytique simplifiée. De bonnes concordances sont obtenues entre les résultatsdes essais et ceux de l’analyse, et on a vérifié l’applicabilité des facteurs de correction.

Mots clés : pieux de réaction, interaction, rigidité initiale de la tête du pieu, essai de chargement statique vertical, essaide chargement statique latéral, méthode analytique simplifiée.

[Traduit par la Rédaction] Kitiyodom et al. 420

1. Introduction

Recently, much effort has been made to review the foun-dation design codes. The design methods of foundationstructures have been changed from allowable stress design tolimit state design or performance-based design. In the frame-work of these new design criteria, estimation of the load–displacement relationship of a pile foundation is a vitalissue. The simplest way to obtain the load–displacement re-lationship of a pile is to conduct an in situ pile load testing.Many forms of pile load testing are conducted in practicewith the aim to obtain a load–displacement relationship for apile, from which the pile capacity and pile head stiffness canbe estimated. Static load testing is the most fundamentalform of testing. In the static load test, because heavy loadshave to be applied to the test pile, a reaction system is

needed to transfer the applied load to the surrounding soil.Therefore the test may take a variety of forms depending onthe means by which the reaction for the loading applied onthe test pile is supplied. As an example for the vertical loadtest of a pile, a test setup in which the reaction is suppliedby kentledge, reaction piles, or (vertical or inclined) groundanchors is employed in practice.

In Japan, most static load tests are conducted using reac-tion piles as the reaction system. The static load test hasbeen regarded as the most reliable test method, since it isgenerally believed that a “true” load–displacement relationof the pile can be directly obtained from the test. JapaneseGeotechnical Society (JGS) standard 1811-2002 (JapaneseGeotechnical Society 2002) states that, as a general rule, thedistance between the centre of the test pile and the reactionpile shall be more than three times the maximum diameter ofthe test pile, and also more than 1.5 m. Note that the mini-mum pile spacing had been prescribed as 2.5 m in the oldversion of the JGS standards. The minimum pile spacingwas reduced to 1.5 m, however, considering the increase inthe use of micropiles in Japan. The authors question thiscommon belief, however, as the interaction between the re-action piles and the test pile may influence the measuredpile settlement during the test, even for the case where thedistance between the centre of the test pile and the reaction

Can. Geotech. J. 41: 408–420 (2004) doi: 10.1139/T03-098 © 2004 NRC Canada

408

Received 16 April 2003. Accepted 3 November 2003.Published on the NRC Research Press Web site athttp://cgj.nrc.ca on 16 June 2004.

P. Kitiyodom, T. Matsumoto,1 and N. Kanefusa.Department of Civil Engineering, Kanazawa University,2-40-20 Kodatsuno, Kanazawa, Ishikawa 920-8667, Japan.

1Corresponding author (e-mail:[email protected]).

piles is greater than three times the test pile diameter, as alsopointed out by Latotzke et al. (1997), Poulos and Davis(1980), and Poulos (1998). In addition, in Japan at the mo-ment, there are no general rules concerning the distances be-tween the test pile and the reaction pile in lateral static pileload test standard JSF T32-83 (Japanese Society of Soil Me-chanics and Foundation Engineering 1983).

Poulos and Davis (1980) and Poulos (1998) presentedworkable charts of the correction factors for the initial pilehead stiffness obtained from static pile load tests with theuse of two reaction piles. In Japan, however, vertical pileload tests are usually conducted with four reaction piles. Inthis work, the influence of the load transfer by four reactionpiles on the load–settlement behaviour of the test pile is in-vestigated using a computer program PRAB (piled raft anal-ysis with batter piles). A parametric study of the influence ofreaction piles on the test pile is carried out to investigate theeffects of factors such as the pile spacing ratio, pile slender-ness ratio, pile soil stiffness ratio, and soil profile. The influ-ence of reaction piles in lateral pile load tests is alsoinvestigated. The correction factors for the initial pile headstiffness obtained from static pile load tests with the use ofreaction piles are given in charts for both vertical and lateralload tests. To verify the values of these correction factors,back-analyses of the centrifuge modelling of axially loadedpiles conducted by Latotzke et al. (1997) are carried out.

2. Analysis procedure

The problem is dealt with using a simplified deformationanalytical program PRAB that has been developed by Kiti-yodom and Matsumoto (2002, 2003). This program is capa-ble of estimating the deformation and load distribution ofpiled raft foundations subjected to vertical, lateral, and mo-ment loads, using a hybrid model in which the flexible raftis modelled as thin plates and the piles as elastic beams andthe soil is treated as springs (Fig. 1). Both the vertical andlateral resistance of the piles and the raft base are incorpo-rated into the model. Pile–soil–pile, pile–soil–raft, and raft–soil–raft interactions are taken into account based onMindlin’s solutions (Mindlin 1936) for both vertical and lat-eral forces. In addition, an averaging technique suggested byPoulos (1979) is incorporated into the analysis to approxi-mate the interaction between the structure members of apiled raft foundation embedded in nonhomogeneous soils.The accuracy of this approximation technique had beenexamined in Kitiyodom and Matsumoto (2003) throughcomparisons with several published solutions and three-dimensional finite element analysis. Note that the solutionsfrom the approximation technique are comparable with theclosed-form solutions of the interaction given by Mylonakisand Gazetas (1998). When using PRAB to analyze the prob-lem of a group of piles without a cap, the soil resistance(soil spring value) at the raft base is set to zero and the stiff-ness of the raft is set very small, nearly to zero.

The vertical soil springs, KzPb, at the pile base nodes and

the vertical soil springs, KzP, at the pile shaft nodes are esti-

mated using eqs. [1] and [2], respectively, following Lee(1991):

[1] KG r

h rzPb b o

s o

=− − −

41

11 2ν [ exp( */ )]

[2] KG Lr r

zP = 2π ∆

ln( / )m o

[3] r

G L

G LGG

Li i

i

n

mm

m

bs2.5

p

= −

=∑

1 1χ ν( )

χ = − −1 1exp( / )h L

where G is the soil shear modulus, Gb is the soil shearmodulus at the pile base, Gi is the shear modulus of soillayer i, Gm is the maximum soil shear modulus, h is the fi-nite soil depth, h* is the distance between the pile base andthe rigid bed stratum, L is the pile embedment length, ∆L isthe pile segment length, Li is the length of pile embedded insoil layer i, np is the total number of soil layers along thepile embedment length, rm is the influential radius, ro is thepile radius, νs is the Poisson’s ratio of the soil, and χ is thesoil depth influence factor.

The horizontal soil springs, KxPb and Ky

Pb, at the pile basenodes are estimated using eq. [4]:

[4] K KG r

x yPb Pb s b o

s

= = −−

32 17 8

( )νν

There are many ways to estimate the horizontal soilsprings, Kx

P and KyP, at the pile shaft nodes. In this paper, the

horizontal shaft soil spring values at each pile node are esti-mated based on Mindlin’s solutions, which are similar to thesolution of the integral method used by Poulos and Davis(1980). The equation becomes

[5] K K E Lx yP P

s= = ζ ∆

in which

[6] ζ = ρpD E/ s

where D is the pile diameter, Es is the Young’s modulus ofthe soil, p is the lateral distributed force acting along a pile

© 2004 NRC Canada

Kitiyodom et al. 409

Fig. 1. Plate–beam–spring modelling of a piled raft foundation.

element, ζ is the stiffness influence factor, and ρ is the cor-responding lateral displacement at each pile node calculatedusing the integral equation method. The accuracy of themethod for estimation of Kx

P and KyP was examined by

Kitiyodom and Matsumoto (2002).In the analytical method used in this paper, the considered

soil profile may be homogeneous semi-infinite, arbitrarilylayered, and (or) underlain by a rigid base stratum. Althoughthe method can easily be extended to include a nonlinear re-sponse as described in Section 5, the emphasis of earlierparametric analyses in Section 3 and Section 4 is placedon the load–displacement relationships of pile foundationswhere the subsoil still behaves linear elastically.

In static pile load tests, reaction piles are needed to trans-fer the load applied to the test pile to the surrounding soil.Since the soil is a continuous material, the load transfer ofreaction piles through the soil causes an opposite movementof the test pile because of interaction. As a result, if the dis-placement of the test pile is measured from a remote point ofreference, the measured displacement will be less than thetrue displacement. In this work, two types of analysis arecarried out to investigate the influence of reaction piles. Inthe first type of analysis, only the test pile is loaded by anapplied force, P, without the influence of reaction piles (seeFigs. 2a and 2c for the case of vertical and lateral pile loadtests, respectively). The test pile in the first type of analysisis referred to hereafter as a “non-influenced test pile”. Thesecond type of analysis is an idealized in situ test procedurein which a test pile is loaded by an applied force, P, whilereaction piles were loaded in the opposite direction by reac-tion forces as shown in Figs. 2b and 2d for the case of verti-cal and lateral pile load tests, respectively. The test pile inthe second type of analysis is referred to hereafter as an “in-fluenced test pile”. Note that the diameter of the reactionpiles might influence the solution of the problem. In this pa-per, however, considering the circumstance in Japan wherethe reaction piles are often used as the foundation after thetest, only the case of the reaction piles that have the samediameter as the test pile is considered.

The influence of reaction piles is presented in terms ofcorrection factor Fc for the case of a vertical pile load testand Fc

L for the case of a lateral pile load test, which are de-fined by the ratio of the initial pile head stiffness of the testpile with the use of reaction piles, KG or KG

L, to the initialpile head stiffness of the non-influenced single pile, Ki orKi

L (see Fig. 3). These correction factors can be applied tothe measured pile head stiffness, KG or KG

L, from the test toobtain a truer estimate of the actual pile head stiffness, Ki orKi

L , of the influenced test pile using eqs. [7] and [8]:

[7] K K Fi G c= /

[8] K K FiL

GL

cL= /

where Fc is the correction factor for a vertical pile load test,Fc

L is the correction factor for a lateral pile load test, KG isthe initial pile head stiffness for an influenced test pile for avertical pile load test, KG

L is the initial pile head stiffness foran influenced test pile for a lateral pile load test, Ki is theinitial pile head stiffness for a non-influenced test pile for a

vertical pile load test, and KiL is the initial pile head stiffness

for a non-influenced test pile for a lateral pile load test.For example, in the case of a vertical pile load test, the

larger value of Fc means that more serious errors arise in themeasured settlement of the test pile. The case of Fc = 1means that the measured settlement equals the true settle-ment of the test pile without the influence of the reactionpiles.

3. Parametric solutions for vertical pile loadtesting

Analyses were conducted for single piles and groups ofpiles embedded in semi-infinite soils, finite-depth soils, andmultilayered soils. The ranges of the dimensionless parame-

© 2004 NRC Canada

410 Can. Geotech. J. Vol. 41, 2004

Fig. 2. Cases of analysis. (a, b) Vertical load test of non-influenced (a) and influenced (b) piles. (c, d) Lateral load test ofnon-influenced (c) and influenced (d) piles.

Fig. 3. Illustration of typical load–displacement relations of non-influenced and influenced test piles and definitions of Ki and KG.

ters were set as 2–10 for the pile spacing ratio s/D, 5–50 forthe pile slenderness ratio L /D, 102–104 for the pile soil stiff-ness ratio Ep/Es, and 1–5 for the soil layer depth ratio h /L inthe case of pile foundations embedded in finite-depth soils,where Ep is the Young’s modulus of the pile and s is the pilespacing. The Poisson’s ratio of the soil was set at 0.3throughout.

3.1. Semi-infinite soilFigure 4 shows the correction factor Fc = KG/Ki for the

case of floating piles embedded in semi-infinite soils. It canbe seen that even for the case of a pile spacing ratio of 3 asrecommended in the JGS standards, the correction factormay be greater than 2. This means that the measured settle-ments in these cases may be less than half of the true settle-ments. This can lead to great overestimation of the initialstiffness of the test piles. Figure 4 also shows that the calcu-lated value of Fc decreases and the distribution of the valuesbecomes narrower as the pile spacing ratio increases, or as

© 2004 NRC Canada


Fig. 4. Correction factor, Fc, for floating piles embedded in semi-infinite soils.

Fig. 5. Comparison between correction factor, Fc, for floatingpiles embedded in semi-infinite soils with four reaction piles andthose with two reaction piles.

the pile soil stiffness ratio decreases. For small values of thepile soil stiffness ratio, the value of Fc increases as the pileslenderness ratio decreases. The opposite trend, namely withFc increasing as the pile slenderness ratio increases, can befound for large values of the pile soil stiffness ratio whereE p /Es = 5000.

The correction factor Fc = KG/Ki for the case of floatingpiles embedded in a semi-infinite soil with the use of fourreaction piles is compared in Fig. 5 with the values given byPoulos and Davis (1980) for the case of floating piles em-bedded in the semi-infinite soil with the use of two reactionpiles. The trend in the value of Fc is the same for both cases.However, the use of four reaction piles rather than two maylead to greater errors in the measured pile head stiffness. Asmentioned earlier, vertical pile load tests in Japan are usuallyconducted with four reaction piles. Therefore, hereafter onlythe influence of the load transfer by four reaction piles onthe load–settlement behaviour of the test pile will be investi-gated.

3.2. Finite-depth soilIn the previous section, the calculated values of Fc were

presented for floating piles embedded in semi-infinite homo-geneous soils. In practice, soil profiles may be underlain bya stiff or rigid base soil stratum. In this section, the calcu-lated values of Fc for floating piles and end-bearing pilesembedded in finite homogeneous soil layers are presented.

The calculated values of Fc for floating piles embedded infinite homogeneous soil layers are shown in Fig. 6. The pileslenderness ratio, L /D, for all cases was set constant at 25.Also shown in Fig. 6 is the value of Fc for floating piles em-bedded in semi-infinite soils (h /L = infinity). It can be seenthat for all cases, the values of Fc for a floating pile embed-ded in a semi-infinite soil are greater than those of a floatingpile embedded in a finite homogeneous soil layer. It can bealso seen that the trend in the value of Fc for both cases isthe same. That is, the calculated value of Fc decreases andthe distribution of the values becomes narrower as the pilespacing ratio increases, or as the pile soil stiffness ratio de-

© 2004 NRC Canada


Fig. 6. Correction factor, Fc, for floating piles embedded in finite-depth soils with difference in the soil layer depth ratio, h /L (pileslenderness ratio L /D = 25).

creases. Figure 6 also shows that the calculated value of Fcfor floating piles embedded in finite soil layers decreases asthe soil layer depth ratio, h /L, decreases.

Figure 7 shows the values of the correction factor for thecase where the soil layer depth ratio h /L = 1, which is thecase of end-bearing piles resting on a rigid base stratum.Compared with the value of Fc for the correspondingfloating piles embedded in semi-infinite soils or finite homo-geneous soil layers, the values of Fc for the case of end-bearing piles resting on a rigid base stratum are smaller. Thevalue of Fc for the case of end-bearing piles decreases as thepile spacing ratio increases, which is the same trend as thatin the case of floating piles embedded in semi-infinite soilsor finite homogeneous soil layers. In the case of end-bearingpiles, however, the value of Fc increases as the pile soil stiff-

ness ratio decreases, which is the opposite trend to that ofthe calculated results for the case of floating piles. More-over, the value of Fc increases as the pile slenderness ratioincreases.

3.3. Multilayered soilFigure 8 shows the calculated values of Fc for the case of

floating piles embedded in multilayered soils. The two soilprofiles considered are also indicated in Fig. 8. Comparedwith the corresponding cases of floating piles embedded infinite homogeneous soil layers which are shown in Fig. 6,the values of Fc for the case of floating piles embedded inmultilayered soils are smaller, but the general characteristicsof variation of Fc with the pile spacing ratio and the pile soilstiffness ratio remain the same.

© 2004 NRC Canada


Fig. 7. Correction factor, Fc, for end-bearing piles on rigid base stratum.

Fig. 8. Correction factor, Fc, for floating piles embedded in multilayered soils (pile slenderness ratio L /D = 25).

4. Parametric solutions for lateral pile loadtesting

The influence of reaction piles was presented in Section 3and discussed for the case of vertical pile load tests. Inhighly seismic areas such as Japan, however, it is necessaryin some cases to conduct a lateral pile load test to obtain thepile capacity and pile head stiffness in the lateral direction.In this section, the influence of the load transfer of reactionpiles on the load–displacement behaviour of the test pile inthe lateral direction is analyzed and presented in terms of thecorrection factor Fc

L . Parametric analyses were conductedfor single piles and groups of piles embedded in semi-infinite soils and finite-depth soils. In these analyses, tworeaction piles with a constant centre-to-centre distance of 3Dwere employed, and the distance s* (see Fig. 2d) was varied.The ranges of the dimensionless parameters were set as 2–10for the pile spacing ratio s*/D, 5–50 for the pile slenderness

ratio L /D, 102–104 for the pile soil stiffness ratio Ep /Es, 1–5for the soil layer depth ratio h/L in the case of pile founda-tions embedded in finite-depth soils, and 0–0.2 for the ratio ofthe height of the loaded point (Lhp) to the pile embedmentlength (L). The Poisson’s ratio of the soil was again set at 0.3.

4.1. Semi-infinite soilFigure 9 shows the correction factor F K Kc

LGL

iL= / for the

case of piles embedded in semi-infinite soils. It can beclearly seen that the calculated values of Fc

L in the case ofthe lateral pile load test are smaller than the calculated val-ues of Fc in the case of the vertical pile load test. Figure 9also shows that the trend is the same as in the case of thevertical pile load test, i.e., the value of Fc

L decreases as thepile spacing ratio increases, or as the pile soil stiffness ratiodecreases. In the case of the vertical pile load test, for smallvalues of the pile soil stiffness ratio, the value of Fc in-creases as the pile slenderness ratio decreases. The opposite

© 2004 NRC Canada


Fig. 9. Correction factor, FcL, for piles embedded in semi-infinite soils.

trend, where the value of Fc increases as the pile slendernessratio increases, can be found for large values of the pile soilstiffness ratio where Ep /Es = 5000. In the case of the lateralpile load test, however, this change in trend of the correctionfactor is not found.

For all of the calculated values of FcL shown in Fig. 9, it is

assumed that the lateral load was applied at the ground sur-face level. In practice, however, the lateral load is applied ata point above the ground surface level. In this study, the ef-fects of the distance between the point of applied load andthe ground surface level, Lhp, were analyzed. The calculatedvalues of Fc

L for the case of piles embedded in semi-infinitesoils with different heights of the loading point are shown inFig. 10. For all values of the pile soil stiffness ratio, the cal-culated value of Fc

L decreases as the ratio of the height ofthe loading point to the pile embedment length, Lhp /L, in-creases.

4.2. Finite-depth soilIn this section, the calculated values of Fc

L for piles em-bedded in finite homogeneous soil layers are presented. Fig-ure 11 shows the calculated values of Fc

L for piles with apile slenderness ratio of L /D = 5. The values of Fc

L in thecase of finite homogeneous soil layers are slightly smallerthan the corresponding values of Fc

L in the case of a semi-infinite homogeneous soil. The values of Fc

L for piles with apile slenderness ratio of L /D = 50 are shown in Fig. 12. Inthis case, the values of Fc

L are almost the same, regardless ofthe value of h /L. This is thought to be due to the differencein the deformation profile of the laterally loaded pile. Basedon the analysis results, in the case of L /D = 5, the pile de-formed like a short pile in which all parts of the pile leaneddue to the lateral load, and lateral displacement opposite tothe loading direction occurred at the pile toe. On the otherhand, in the case of L /D = 50, only the top parts of the pile

© 2004 NRC Canada


Fig. 10. Correction factor, FcL, for piles embedded in semi-infinite soils with different heights of the loading point (pile slenderness ra-

tio L /D = 25).

near the loading point deformed laterally, and no lateral dis-placement occurred at the pile toe. Thus, in the case of a pilewith a large value of L /D, the value of Fc

L for the pile em-bedded in a semi-infinite homogeneous soil can be used forthe pile embedded in a finite soil layer.

5. Back-analysis of centrifuge model testresults

Latotzke et al. (1997) conducted centrifuge model tests onpiles in dense sand with an aim to investigating the influenceof the load transfer of reaction piles to the soil on the load–settlement behaviour of the test pile. Figure 13 schematicallyshows two kinds of tests and the geometrical arrangement ofthe piles. In the first test, a single pile with a diameter of30 mm at model scale was modelled in the system to deter-mine the “true” load–settlement behaviour of the non-influenced test pile. The test pile was pushed down by a

hydraulic jack that was fixed on a spreader bar that trans-ferred the reaction forces to the walls of a strong cylinderbox with a diameter of 750 mm. In the second test, one testpile and four reaction piles were employed to model the insitu pile test procedure. By using two hydraulic jacks, thetest pile and the group of four reaction piles were loadedseparately at the same time. To ensure uniform distributionof the upward load on each reaction pile, the upward loadingof the reaction piles was achieved by loading a steel ropethat is steered around on several pulleys and hinge-connected on both ends with two reaction piles mounted at asmall steel bar. In this test, the least distance between thecentre of the piles was 4.5 times the pile diameter. The di-mensions of the reaction piles are equal to the dimensions ofthe test pile. Applying a centrifuge acceleration level of n =45, a prototype pile with a diameter of D = 1.35 m and anembedded length of L = 9.9 m was modelled. In both kindsof the tests, the model piles were loaded after the centrifuge

© 2004 NRC Canada


Fig. 11. Correction factor, FcL, for piles embedded in finite-depth soils with difference in the soil layer depth ratio, h /L (pile slender-

ness ratio L /D = 5).

was spun up to the target speed to produce an acceleration of45g.

Back-analyses of these centrifuge test results are carriedout in this section. The design charts given in earlier sec-tions are also used to estimate the value of the correctionfactor Fc for these centrifuge data. To consider nonlinear be-haviour of the soil in the analyses, a hyperbolic relationshipbetween shear stress and shear strain is employed as sug-gested by Randolph (1977), Kraft et al. (1981), and Chow(1986). The tangent shear modulus of the soil, Gt, is givenby

[9] G GR

t inif

f

= −

1

2ττ

where Gini is the initial shear modulus of the soil, Rf is thehyperbolic curve fitting constant, τ is the shear stress, and τfis the shear stress at failure.

With the tangent shear modulus in eq. [9], the vertical soilspring values, Kz

Pb, at the pile base nodes and the verticalsoil spring values, Kz

P, at the pile shaft nodes (eqs. [1] and[2]) are estimated by means of eqs. [10] and [11]:

[10] KG r

h r

P R

PzPb bi o

s o

b f

f

=− − −

× −

41

11 2

12

ν [ exp( */ )]

[11] KG L

rr

r rr r

zP ini

m

o

m o

m o

=−−

+ −

− −

2π

ββ

ββ β

∆

ln( )

( ) ( )

in which

[12] β = τ τοr Ro f f/

© 2004 NRC Canada


Fig. 12. Correction factor, FcL, for piles embedded in finite-depth soils with difference in the soil layer depth ratio, h /L (pile slender-

ness ratio L /D = 50).

where Gbi is the initial shear modulus of the soil at the pilebase, Pb is the mobilized base load, Pf is the ultimate baseload, β is the nonlinear influence factor, and τo is the shearstress at the pile–soil interface.

The vertical soil spring values from eqs. [10] and [11]were incorporated into the computer program PRAB. Athigh soil strains, yielding of the soil at the pile–soil inter-faces occurs and slippage begins to take place. This phenom-enon is considered in the program by adopting maximumshaft resistance and maximum end-bearing resistance of thevertical soil springs at the pile nodes. In this program, pile–soil–pile interaction is still taken into account based onMindlin’s solutions. Randolph (1994) suggested that the ap-propriate shear modulus for estimating interaction effects isthe “low-strain” or initial shear modulus, Gini. When theshear strength of the soil is fully mobilized at a particularnode, full slippage takes place at the node. Further increasesin the load acting on the pile will not increase the soil reac-tion at that node. Also, further increases in the loads at theremaining nodes will not cause further increase in displace-

ment of that particular node because of the discontinuityresulting from full slippage taking place. Thus, there is nofurther interaction through soil between that particular nodeand the remaining nodes.

In this analysis, to model cohesionless sandy soil, a shearmodulus linearly increasing with depth was employed. Ashaft resistance distribution linearly increasing with depthwas also employed and expressed as a function of the shearmodulus. The Poisson’s ratio of the soil was assumed as 0.3.

Figure 14a presents a comparison between the measuredload–settlement behaviour of the non-influenced test pileobtained from the centrifuge test and that calculated usingPRAB. Figure 14a shows that the calculated load–settlementcurve matches very well with the measured curve. For thecalculated results in Fig. 14a, a linearly increasing shearmodulus profile was used with G = 0 MN/m2 at the groundsurface increasing linearly to G = 52.5 MN/m2 at the base ofpile. The shaft resistance was set as G/120, the maximumvalue of the base resistance was set at 14 MN/m2, and thehyperbolic curve fitting constant Rf for the pile shaft nodes

© 2004 NRC Canada


Fig. 13. Two kinds of centrifuge model tests. (a) Non-influenced test pile. (b) Influenced test pile. All dimensions in metres.

Fig. 14. Back-analysis results. (a) Non-influenced test pile. (b) Influenced test pile.

and pile base nodes was set at 0.9 and 0.8, respectively. Allof these identified values were employed again in the analy-sis of the influenced test pile. A comparison between themeasured load–settlement behaviour of the influenced testpile obtained from the centrifuge test and the calculated be-haviour is shown in Fig. 14b. The figure shows that there isrelatively good agreement between the two results. Focusingon the initial pile head stiffness (initial tangent lines),Fig. 14 shows that the calculated values match very wellwith the measured values both in the non-influenced test pileand in the influenced test pile.

In Fig. 15, the calculated and measured values of the cor-rection factor, Fc, at low load are plotted against the totalload Q. The calculated values agree reasonably with themeasured values, especially in the initial stage.

Using the design chart, for L /D = 9.9/1.35 = 7.3, h /L =23.4/9.9 = 2.4, s/D = 6.79/1.35 = 5.0, Ep /(Es)average at 2/3 pile

embedment length = 27 000/91 = 296.7, and from Figs. 4 and 6,the correction factor, Fc, can be estimated as 1.3. This valueis comparable to the measured value. Thus, the validity ofthe proposed values for the correction factor as given inworkable charts in earlier sections of this paper is thought tobe supported.

6. Conclusions

The influence of the load transfer of reaction pilesthrough the soil on the load–displacement behaviour of thetest pile in static load testing was investigated using a sim-plified analytical program, PRAB. A parametric study wasconducted to demonstrate the effects of factors such as pilespacing ratio, pile slenderness ratio, pile soil stiffness ratio,and soil profiles for both vertical and lateral pile load tests.It was found that the presence of reaction piles leads to ameasured pile head stiffness that is greater than the real(non-influenced) value for both vertical and lateral loading.Correction factors for the initial pile head stiffness obtainedfrom the static pile load tests with the use of reaction pileswere given in charts. These values for the correction factors

were verified through back-analysis of the centrifuge modeltest results.

Acknowledgement

This study was supported by Grant-in-Aid for ScientificResearch (grant 12450188) of the Japanese Ministry of Edu-cation, Culture, Sports, Science and Technology.

References

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Fig. 15. Calculated and measured values of the correction factor.

List of symbols

D pile diameterEp Young’s modulus of the pileEs Young’s modulus of the soilFc correction factor for the vertical pile load test

FcL correction factor for the lateral pile load testG soil shear modulus

Gb soil shear modulus at the pile baseGbi initial soil shear modulus at the pile baseGi soil shear modulus of the soil layer i

Gini initial soil shear modulusGm maximum soil shear modulusGt tangent shear modulus of the soilh soil layer depth

h* distance between the pile base and the rigid base stra-tum

KG initial pile head stiffness for influenced test pile forthe vertical pile load test

KGL initial pile head stiffness for influenced test pile for

the lateral pile load testKi initial pile head stiffness for non-influenced test pile

for the vertical pile load testK i

L initial pile head stiffness for non-influenced test pilefor the lateral pile load test

KzP vertical soil springs at pile shaft nodes

KzPb vertical soil springs at pile base nodes

KxP, Ky

P horizontal soil springs at pile shaft nodesKx

Pb, KyPb horizontal soil springs at pile base nodesL pile embedment length

∆L pile segment lengthLhp height of loading point

Li pile embedment length in soil layer in centrifuge acceleration level

np total number of soil layers along the pile embedmentlength

p lateral distributed force acting along a pile elementP applied load

Pb mobilized base loadPf ultimate base loadQ total load

rm influential radiusro outer pile radiusRf hyperbolic curve fitting constant

s, s* pile spacingw pileβ nonlinear influence factor

νs Poisson’s ratio of the soilρ lateral displacement at each pile nodeτ shear stress

τf shear stress at failureτo shear stress at the pile–soil interfaceχ soil depth influence factorζ stiffness influence factor

© 2004 NRC Canada


influence of reaction piles on the behaviour of a test pile in static load testing

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