centrifuge modeling of pile-soil-pile interaction...

Scientia Iranica A (2014) 21(4), 1330{1339

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringwww.scientiairanica.com

Research Note

Centrifuge modeling of pile-soil-pile interactionconsidering relative density and toe condition

A. Saeedi Azizkandi�, M.H. Baziar, M. Modarresi, H. Salehzadeh and H. Rasouli

School of Civil Engineering, Iran University of Science and Technology, Tehran, Iran.

Received 2 June 2013; received in revised form 11 October 2013; accepted 18 June 2014

KEYWORDSPile-soil-pileinteraction;Relative density ratio;Toe and shaftinteractions;Centrifuge modeling.

Abstract. In a group of installed piles, the stresses applied from one pile to soil may haveoverlaps with another pile which leads to the changes in bearing capacity and settlementof each individual pile. In order to predict the performance of those piles, interactioncoe�cients, based on elasticity theory proposed by Mindlin, are widely applied. In thispaper, the e�ect of soil relative density and also toe condition on the interaction betweentwo similar piles in sandy soil is presented using centrifuge modeling. To achieve thisobjective, 22 tests have been conducted to investigate the e�ect of soil relative densityand another 11 tests were performed to study the contribution of pile toe and shaft in theinteractions. The results showed that the value of soil relative density has an importantrole in the coe�cient of interaction which has not been considered in previously reportedcorrelations. For this reason a modi�cation has been proposed for the Randolph andWroth equation to consider soil relative density. Accuracy prediction of the new modelwas compared with the Randolph and Wroth equation with the aid of di�erent statisticalparameters. This comparison indicated the superiority of the proposed model over previousmethods.c 2014 Sharif University of Technology. All rights reserved.

1. Introduction

In recent decades, advances in analytical and exper-imental methods have provided a better understand-ing of the deformation of piles group under loading.Advances in numerical techniques, in particular theintegral equations and the numerical boundary elementmethods [1], have made the analysis of piles group morefeasible. The introduction of interaction coe�cients,resulted from analytical studies, was one of the mostadvantageous concepts. These coe�cients, representedby �ij , have been de�ned as the displacement at the

*. Corresponding author. Tel.: +98 912 3903504E-mail addresses: [email protected] (A. SaeediAzizkandi); [email protected] (M.H. Baziar);[email protected] (M. Modarresi);[email protected] (H. Salehzadeh);[email protected] (H. Rasouli)

top of the pile i due to the load applied to the adjacentpile, j, divided by the displacement of the pile j underits own load:

�ij =

Displacement of i pile due toapplying unit load at j pile

Displacement of j pile due toapplying unit load

: (1)

Using the elastic interaction coe�cients has provideda practical method for estimating the settlement ofa piles group as well as distribution of the loadsamong individual piles. However, the value of predictedsettlement can sometimes be greater than the observedsettlement value, and there is an overall consistency be-tween the theoretical settlements and those measuredin the laboratory and �eld. The studies conducted sofar on this topic and the reported equations are mostly

A. Saeedi Azizkandi et al./Scientia Iranica, Transactions A: Civil Engineering 21 (2014) 1330{1339 1331

based on the theory of elasticity. This means that soilsand piles are assumed to remain in elastic conditionwith no sliding along the pile-soil interface, which maynot occur in real case.

Factors in uencing interaction coe�cients are in-cluded pile (L=d ratio), pile roughness, installationmethod, relative density, S=d and etc. However, in thisstudy the e�ects of relative density of sandy soil and thepile toe on the interaction coe�cients are investigated.

For this purpose, 22 centrifuge tests have beenconducted to investigate the e�ect of soil relativedensity and another 11 tests have been performed tostudy the contribution of pile toe and shaft on theinteraction coe�cient. Then, a new model for theprediction of pile-soil-pile interaction is proposed.

Similar methods representing raft as a thin plate,soil and piles as springs were also proposed by otherresearchers, Russo [2], and Klar et al. [3]. In all themethods, the interaction factor of pile to pile wasone of the most important factors. Kitiyodom andMatsumoto [4], Liang et al. [5] and Kitiyodom et al. [6]analyzed the piled raft foundation system using thisfactor. Their proposed methods could analyze thelarge piled raft system in a reasonable time using apersonal computer. In those methods, the pile behavioris assumed linear or nonlinear springs and the pile topile interaction factors have been calculated based onelastic theory [7].

2. Methods to determine the pile-soil-pileinteraction

The methods which are developed based on the theoryof elasticity, owing to the handy available charts andtables which can be easily used, are currently one of themost popular methods for estimating the settlement ofa piles group. In these methods, piles are applyingvertical loads to the soil and, following the Mindlinequations, soil is assumed to be homogeneous, linear,elastic, isotropic half-space with the Young's modulus(Es) and the Poissson's ratio (�s).

Poulos and Davis [8], for the �rst time, introducedthe concept of interaction between two piles usingMindlin equations. In order to calculate the interactionbetween two piles in this method, a group of two pilesis considered and each pile is divided into n elements.Assuming that the soil and the pile remain in elasticcondition with no sliding in the interface of soil andpile, the resulted displacement in each element of pileis equal to that of the adjacent soil. The obtainedresults from a group of two piles were introduced as theinteraction coe�cients. They presented some chartsto determine the coe�cients based on the ratio of thedistance of piles from each other to the diameter of pile(s=d).

O'Neil et al. [9] suggested that when the interac-

tion between piles is considered, it is better to use thesmall strain Young's modulus for soil, i.e. the modulusbetween the piles, instead of the modulus for the soilsurrounding the piles which represents much largerstrains. The old method for analysis of interactioncoe�cients for a group of piles [8] uses a uniform soilmodulus for calculating the settlement of a single pileand interaction coe�cients.

Poulos [10] considered the e�ect of di�erencebetween the soil modulus around pile and the modulusof soil mass in calculation of the interaction coe�cientsand settlement of a pile group.

A comparison between the results and the realdata indicated that the new analysis was able toestimate the settlements more realistically comparedto the old analysis which only considered the modulusof the soil surrounding the pile [10]. Assuming linearelastic behavior for the soil causes to overestimate theinteraction coe�cients of the piles.

Assuming that the displacement of the pile shaftcompletely follows the surrounding soil, Randolph andWroth [11] proposed separate equations for determin-ing the interaction of the toe and shaft, using theshape of deformations of the soil around the singlepile due to shaft and toe of the pile. They proposedthe interaction coe�cient of the pile shaft and theinteraction coe�cient of the pile toe, respectively, by:

� =Ln( rms )Ln( rmr0 )

; (2)

�b =�db�:S

�; (3)

rm = 2:5L(1� 0:5�); (4)

where S is the distance between the piles, r0 is theradius of the pile, db is the diameter of the toe ofthe pile, and rm is the e�ective radius of the pilewhich is calculated by Eq. (4). Base on the aboveequation, Wong and Poulos [12] have proposed otherequations for pile-to-pile interaction factors betweentwo dissimilar piles.

Jardine et al. [13] showed the importance of thenonlinear assumption for the settlement of a piles groupand load distribution using the �nite element analysis.

Using �nite element modeling of a hollow pile inhomogeneous linear elastic semi-in�nite isotropic soil,Polo and Clemente [14] proposed charts for determiningthe interaction coe�cients based on the Poisson's ratioof soil, length, diameter and distance of piles from eachother. One of the important characteristics of thismethod is its ability for considering the e�ects of thepile shaft and toe separately in the analyses.

Mandolini and Viggiani [15] considered the non-linear performance of a single pile in determining the

1332 A. Saeedi Azizkandi et al./Scientia Iranica, Transactions A: Civil Engineering 21 (2014) 1330{1339

interaction coe�cients. They used boundary elementmethod for calibrating the soil model against theload-settlement behavior of a single pile and thendetermined the interaction coe�cients between twopiles with di�erent distances. They also suggested thatafter a certain distance, the interactions became verysmall and almost disappeared. They proposed a simpleequation for determining the interaction in one of theforms:

� = A� sd

�B; (5)

� =nC +Dln(

sd

)o: (6)

Mandolini and Viggiani [15] reported the values of A,B, C and D based on four �eld studies as A = 0:57 v0:98, B = �0:60 v �1:20, C = 1:0 and D = �0:26.

Milonakis and Gazetas [16] suggested that thedisplacement of pile shaft does not follow the surround-ing soil completely and thus they proposed equationsconsidering the sti�ness of piles and interaction of pilewith adjacent soil. On the other hand, the e�ect ofsoil mass reinforced by the piles was not consideredin their equations and interaction coe�cients. Theyconsidered this e�ect in their model by introducingdi�raction factors. Considering the above factorsgenerally decreased the interaction coe�cients.

A number of centrifuge tests have been conductedin the present study to investigate the e�ect of relativedensity on pile-soil-pile interaction and thus to verifythe accuracy of Randolph and Wroth equations.

Russo [2] proposed an equation for calculationof interaction factor that piles located at several ofspacing (usually between 3d - 60d) by implementingnumerical boundary element analysis, given by:

� =1

1 +A(S=d)B+ C log (S=d+ 10) ; (7)

where A = 0:2795, B = 0:8991 and C = �0:0474.

3. Experimental methodology

3.1. Acceleration and scaling in centrifugetests

An specimen, having a 1=N scale of the real dimensionsin the centrifuge apparatus, under the acceleration, Ntimes the gravitational acceleration, is able to simulatethe stress levels of the real condition in a minimizedmodel. Therefore, the results of such model can be usedfor interpretation of the pile performance in prototype.The observations made in the model can be correlatedto the prototype behavior by the similarity equationsnoted in Table 1. All the models have been tested under100 g acceleration and hence the scaling coe�cient wasN = 100.

Table 1. Similarity relationships.

Property Prototype Model

Acceleration 1 NArea N 1Length N2 1Volume N3 1Velocity (projectile) 1 1Velocity (undrained conditions) 1 NMass N3 1Force N2 1Energy N3 1Stress 1 1Strain 1 1Mass density 1 1Energy density 1 1Time (dynamic) N 1Time (di�usion) N2 1Time (creep) 1 1Frequency 1 N

Figure 1. Grain-size distribution of the test sands.

3.2. Model preparationThe broken Firouzkouh sand known as 161-Firouzkouhsand with a uniform grading has been used in theexperiments (Figure 1). This is clean sand with 1% �negrains with the gradation curve similar to the Toyourastandard sand.

In Table 2, the physical and mechanical propertiesof the mentioned sands have been compared withToyoura standard sands, and in Figure 2, microscopicphotos show the angular broken structure of theFirouzkouh sand.

In order to model the hollow piles, an aluminumpipe with 90 mm total length and 80 mm embedmentlength has been used. The external and internaldiameters were 10 and 9 mm, respectively. Theprototype model of the pile is a steel pile with 1 m


Table 2. Characteristics of Firouzkouh sand.

Sand Gs emax emin D50(mm) F.C % � Cu Cc K161-Firouzkouh

sand2.658 0.97 0.55 0.27 0.2 32 2.58 0.97 0.0 125

Toyoura 2.65 0.977 0.597 0.17 0 - - - -

Figure 2. Electro-microscopic photo taken from the Firouzkouh sand.

diameter and 3.2 cm thickness with 8 m length. Inorder to model a close-ended pile, the ends of pipes,penetrated to the soil, were designed to be closed.

The e�ect of the grain size on the pile diameterhas been studied by Bolton et al. [17].

They concluded that if the ratio of pile diameterto the average particle size is greater than 20, thescale e�ect would be very small. Bolton et al. [17]also suggested the ratio of pile diameter to the averageparticle size to be greater than 20. In the present study,this ratio was 37.04 and thus the e�ect of particle sizewas neglected.

In order to measure the displacement of piles andsoil, three Linearly Variable Di�erential Transformer(LVDT) sensors have been employed. Figure 3 showsthe boundary conditions location of the piles andLVDT sensors in the centrifuge box.

The interactions are determined using the lowingequation:

� =A�BC �D; (8)

where A is the displacement of the non-loaded pile, Bis the displacement of the non-loaded pile under theweight of LVDT sensor, C is the displacement of theloaded pile, and D is the displacement of the loadedpile under the weight of LVDT sensor.

Figure 3. Boundary conditions and test model set-up forloading tests on the pile.

The size of test box is selected such that theboundary e�ect is minimized. However in all tests,the boundary condition was similar and thereforecomparison of the centrifuge tests results is acceptable.Loading condition was also, similar for all tests. Thepile was loaded by a weight mass resting on the topof pile. The loading level was in the range of 60% ofultimate bearing capacity of the pile.

4. Test results and observations

4.1. Test programIn order to study the e�ect of relative density, foursets of experiments with various relative density ratioshave been performed. In order to investigate the e�ect


Figure 5. Settlement interaction between two piles with di�erent relative density for open-ended pile.

in near distance (S=d = 3), interaction coe�cient isapproximately equal for all of the relative densitiesbecause during the piles installation, the soil betweenthem is compressed so much that the relative densityof soil does not a�ect the interaction coe�cient.

Figure 5 shows the interaction coe�cients of open-ended piles with regard to the relative density of soilfor the tested s=d values. As can be observed for S

d < 3and S

d > 16 the variations of the interaction coe�cientcompared to the changes in relative density ratio is verysmall (almost zero). However for 3 < S

d < 16 the valueof variations are about 0.2 which is a large numberand shows that the relative density is an importantfactor in determining the interaction coe�cient of pile-soil-pile. Also, it can be concluded that for relativedensity more than about 55%, no signi�cant e�ect ofrelative density on the interaction coe�cient existedand all the curves tend to become horizontal in thisrange.

Figure 6 and Table 5 show the interaction co-e�cients calculated for close-ended piles versus theratio of the piles distance to the piles diameter (s=d)compared to the open-ended piles for 56% and 23%relative density. It can be concluded that the e�ect ofpile toe in interactions is negligible compared to thee�ect of shaft. Also, most of the interaction occurs dueto the pile shaft. With regard to the obtained results,it can be concluded that the average contribution ofthe pile toe in interactions is about 15% and 19.5% ofthe total interaction value for 56% and 23% relativedensity, respectively.

6. Comparing the results with previousmethod

6.1. Randolph and Wroth approachFigure 7 compares the interaction coe�cient of the pileshaft proposed by Randolph and Wroth [11] for sandy

Figure 6. In uence of toe condition on the settlementinteraction.

soil with Poisson's ratio of 0.25 and the ones obtained inthis study. The coe�cients proposed by Randolph andWroth are in good agreement with the experimentalresults for relative density ratios greater than 50%.However, in low relative density ratios the coe�cientsproposed by Randolph and Wroth overestimate the realvalues and are very conservative.

In the equations proposed by Randolph and


Table 5. The obtained interaction coe�cient of the close-ended piles in the current study.

Soil-pile-soil interaction factor

Spacing/diameterPile model (for Dr=56%) Pile model (for Dr=23%)

Open-ended Close-ended Open-ended Close-ended

3 0.500 0.570 0.485 0.497

5 0.320 0.428 0.114 0.182

7 0.290 0.324 0.083 0.097

9 0.206 0.210 0.046 0.063

12 0.141 0.165 0.015 0.018

16 0.048 0.062 | |

Figure 7. Comparing the centrifuge results withRandolph and Worth equation for open-ended pile.

Wroth [11], it has been assumed that no sliding occursbetween the pile and adjacent soil and the displace-ments of soil and pile shaft are equal. But as mentionedby Milonakis and Gazetas [16], the displacement of pileshaft does not completely follow the displacement ofsurrounding soil and it depends on the sti�ness of pileand the interaction of pile with surrounding soil.

Figure 8 compares the obtained coe�cients fromthe close-ended piles with equations proposed by Ran-dolph and Wroth [11]. As can be observed, theexperimental results of interaction for 56% relativedensity and close-ended pile are in good agreement withthe results reported by Randolph and Wroth [11].

Generally, it can be concluded that for the soilswith high relative density, the equations proposed byRandolph and Wroth [11] give a good estimate of theinteractions, but in low relative density ratios, these co-e�cients are conservative and results in overestimatingthe settlements.

6.2. Mandolini and Viggiani approachMandolini and Viggiani [15] proposed two equationsfor the calculation of interaction coe�cients based on

Figure 8. Comparing the centrifuge results withRandolph and Worth equation for close-ended pile for 56%and 23% relative density.

the �eld analysis. One of their proposed equation doesnot give a certain value and thus for the purpose ofcomparison with the centrifuge results, its reportedrange is illustrated in Figure 9.

It can be observed that the maximum and mini-mum of Eq. (1), due to selecting the values of A andB, is almost consistent with the experimental resultsand Eq. (3) overestimates the interaction coe�cients.It is worth to note that the exact values of A andB in Eq. (1) are not speci�ed based on engineeringapplication and the user needs to judge the values ofA and B. According to Figure 9, centrifuge results arebetween the upper and lower boundary of Mandoliniand Viggiani equation with moving toward maximumwith increasing soil relative density. Therefore, it canbe concluded that the selection of A and B valuesshould be based on the relative density and the resultof centrifuge modeling is perfectly matched with theresults obtained from the �eld observation.

6.3. Polo et al. approachFigure 10 shows the interaction coe�cients of the pileshaft presented by Polo et al. [14] for a pile with the


Figure 9. Comparing the centrifuge results withMandolini and Viggiani equation.

Figure 10. Comparing the centrifuge results with Jesusand Clemente equation for the open-ended pile.

length to diameter ratio of 8 in sandy soil with Poisson'sratio of 0.25 compared with the coe�cients obtainedin the centrifuge modeling. It can be observed thatthe charts presented by Polo et al. [14] overestimatethe interactions and their proposed coe�cients are veryconservative.

Figure 11 compares the coe�cients obtained fromcentrifuge modeling for close-ended piles with thecharts proposed by Polo et al. [14]. As can be observedthe results of centrifuge modeling for 56% relativedensity show a reasonably good agreement with theresults presented by Polo et al. [14] for determining theinteractions of the pile toe.

7. Modi�cation of previous equations

The results from experimental tests clearly indicate theimportant e�ect of relative density on the interactioncoe�cient. Authors added a logarithmic function ofrelative density to the Randolph and Worth equa-

Figure 11. Comparing the centrifuge results with Jesusand Clemente equation for pile toe interaction and 56%relative density.

tion and provided a better correlation between thecentrifuge results and the relative density. Thus, anequation for calculating the interaction was eventuallyobtained using the Randolph and Wroth equation andregression method, through adding only one term,given as:

� =Ln( rms )Ln( rmr0 )

+�db�:S

�+ 0:211Ln(Dr) + 0:128: (9)

In order to assess the quality and accuracy of theproposed equation compared with previous relations,we also de�ne the statistical parameters as:

R2 =

0BBB@1�nP

(i=1)(Mi � Pi)2

nP(i=1)

(Pi � �P )2� 100

1CCCA%; (10)

RMSE =

rPni=1(Mi � Pi)2

n: (11)

The determination coe�cient (R2) is a measure of therelative correlation between two sets of variables. TheRSME is the most popular error measure, as it givesmore weight to the large errors than the smaller ones.

The predicted interaction (�)p of the originalRandolph and Worth equation with the same equationmodi�ed for the e�ect of relative density are plottedagainst the measured (�)m values in Figure 12.

The proposed equation has better performancethan the original Randolph and Wroth equation, withR2 = 92% and RMSE = 0:05 compared with R2 = 63%and RMSE = 0:1.

8. Conclusions

In this study, in order to study the e�ect of soil relativedensity ratio and the amount of interaction of thepile toe in determining the pile-soil-pile interaction


Figure 12. Measured versus predicted interactioncoe�cient.

coe�cient, 33 centrifuge tests have been performed.These tests have been conducted using the uniformcircular pile models under the vertical static load insandy soil. The results showed that:

1. The relative density ratio of soil has an importantrole in determining the interaction coe�cients. Thereason for decrease of pile-soil-pile interaction insmall value of relative density can be explainedas the occurrence of relative displacement betweenthe interface of soil and pile which causes, inturn, a decrease in the pile-soil interaction andconsequently decreases the pile-soil-pile interactioncoe�cient.

2. The interaction coe�cients proposed by Randolphand Wroth [11] are very consistent with the exper-imental results for relative density ratios greaterthan 50%, but in small value of relative densityratios their model overestimates the results and arevery conservative.

3. Two equations proposed by Mandolini and Vig-giani [15], which have been obtained from �eldcases, were compared with the experimental resultsand showd that the range of one of their equationsis very consistent with the experimental results butthe second equation overestimates the interactioncoe�cients.

4. The interaction due to the toe of the pile isnegligible compared to the contribution of the shaft,and the average e�ect of the pile toe in this studywas about 17% of the total interaction value.

5. The charts presented by Polo et al. [14] to calculatethe interactions, due to considering the pile shaft,overestimates the interaction. However, their pre-sented charts for estimating the interaction of thepile toe are almost consistent with the centrifugetests results.

Acknowledgement

The authors would like to thank the Geotechnical Engi-neering Research Centre (GERC) of Iran University ofScience and Technology for supporting the presentedresearch and the GERC sta� for their contributionduring the centrifuge work.

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European Conf. Soil Mech. Found. Eng., 1, pp. 315(1991).

8. Poulos, H.G. and Davis, E.H. \The settlement behav-ior of single axially loaded incompressible piles andpiers", G�eotechnique, 18, pp. 351-371 (1968).

9. O'Neill, M.W., Ghazzaly, O.I. and Ha, H.B. \Anal-ysis of three dimensional pile groups with non-linearsoil response and pile-soil-pile interaction", Proc. 9thO�shore Tech. Conf., 2, pp. 245-256 (1977).

10. Poulos, H.G. \Modi�ed calculations of pile groupsettlement interaction", J. Geotech. Eng., ASCE, 114,pp. 697-706 (1988).

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Biographies

Alireza Saeedi Azizkandi received his BS degreein Civil Engineering from Iran University of Scienceand Technology, Iran, in 2006, and an MS degree in

Geotechnical Engineering from University of Tehran,Iran, in 2009, where he is currently a PhD degree stu-dent. His research interests include dynamic analysis ofpiled foundation, liquefaction, and arti�cial intelligenceapproaches. He has published and presented numerouspapers in various journals and national and interna-tional conferences.

Mohhamad Hassan Baziar is professor of Civil En-gineering at Iran University of Science and Technology.He received his PhD degree in Geotechnical Engineer-ing from RPI, USA, in 1991. His research interestsinclude a broad area of topics in geotechnical andEarthquake Engineering. He is also reviewer for manyjournals such as Geotechnical and GeoenvironmentalEngineering (ASCE), Soil Dynamics and EarthquakeEngineering, Computers and Geotechnics.

Mehdi Modarresi received his BS degree in Civil En-gineering from Islamic Azad University, South Tehranin 2010. In 2013, he received his MS degree from IranUniversity of Science and Technology. His researchinterests include focusing on modeling of pile-soil-pile interaction, laboratory work and Element scaletesting.

Hossein Salehzadeh is Associate Professor of CivilEngineering at Iran University of Science and Tech-nology. He received his PhD degree in GeotechnicalEngineering from Manchester University, UK, in 1997.He has been the author of several books in the �eld ofGeotechnical Engineering (In Persian).

Habib Rasouli received his BS degree in Civil Engi-neering from University of Kurdistan, Sanandaj, Iran2010. In 2013, he received his MS degree from IranUniversity of Science and Technology. His researchinterests include focusing on modeling of granular layere�ects to reduce settlement of non-connected piled raft,laboratory work and element scale testing.

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