Estimating the Elastic Settlementof Piled Foundations on Rock

Hisham T. Eid, M.ASCE1; and Abdalfatah A. Shehada2

Abstract: This research introduces a simple method for preliminary evaluation of the elastic settlement of piled foundations resting on rock.Despite a significant number of publications in this area, the present effort is distinguished by adopting a unique representation of rock non-homogeneity. It also considers pile–subgrade stiffness ratios that have not been covered in the literature for piled foundations on non-homogeneous media. The settlement behavior was investigated using an extensive three-dimensional finite-element (FE) analysis of differentpiled foundationmodels. Elastic settlement of single piles was also studied for comparisonwith the pile-group behavior. Charts were developedto estimate the elastic settlement of piled foundations and to help in choosing the optimum pile spacing and length that limit foundationsettlement to tolerable levels. Settlement values yielded from the FE analysis were compared with those calculated from equations commonlyused in estimating elastic settlement of foundations. DOI: 10.1061/(ASCE)GM.1943-5622.0000376. © 2014 American Society of CivilEngineers.

Author keywords: Elastic analysis; Pile foundations; Pile groups; Pile settlement; Raft foundations; Rock masses; Stiffness.

Introduction

Piles have been frequently used as reducers of foundation settlement.This is more common for heavily loaded shallow foundations restingon rock, where bearing capacity or shear failure does not govern thedesign. The efficiency of piles as settlement reducers is generallyinfluenced by the compressibility of the foundation-bearing mediumand the stress-settlement behavior of piles. Several studies have beenconducted on such subgrade-structure interaction, especially for piledrafts inwhich the superstructure loads are shared between raft and piles(e.g.,Mandolini andViggiani 1997; Poulos2001;El-Mossallamyet al.2003; de Sanctis and Russo 2008). Load sharing can be more pro-nounced in piled foundations resting on extended rock. Rock massusually exhibits a considerable stiffness near the pile head and anincreasing stiffness along the pile length.

Pile settlement at working loads has been commonly estimatedon the basis of elastic theory, as it has been shown by field tests thatload-settlement relationships are closely linear up to half of the peakcapacity. This linearity is more pronounced for piles entirely em-bedded in rock (Williams and Pells 1981; Eid 2011). In addition,small strains are expected when loading such piles, because thedesign loads are usually governed by their structural capacity ratherthan the significantly higher friction forces developed along the pileshaft. Through a literature review and a back-analysis of reportedcase histories, Leung et al. (2010) showed that adoption of the small-strain subgrade modulus leads to a good estimation of pile-groupsettlement.

Several studies have been conducted to predict the elastic be-havior of piled rafts on homogeneous media. This has been donethrough using the strip-on-springs or plate-on-springs approaches(e.g., Clancy and Randolph 1993; Poulos 1994), boundary elementmethods (e.g., Butterfield and Banerjee 1971; Kuwabara 1989),and finite difference and finite-element (FE) analyses (e.g., Zhuanget al. 1991; Lee 1993; Poulos et al. 1997). In contrast, the availableinvestigations on elastic settlement of piled rafts on nonhomogeneousmedia are few and based on using one value for each of the Young’smodulus of soil near the pile head and the rate of increase in elasticmodulus with depth (e.g., Katzenbach et al. 1998).

The main purpose of this study is to introduce a simple andreliable technique to predict the elastic settlement of piled foun-dations on rock and choose the optimum pile spacing and lengththat limit such settlement to tolerable values. Because a linearelastic behavior is adopted for rock, the study results can be validfor piled foundations resting on other subgrade types with similarexpected behavior. The goals of this study were achieved throughdeveloping relationships that correlate pile geometrical config-urations and pile–rock relative stiffness to the maximum settle-ment of piled foundations on rock (Spf ). Such settlement isexpressed as a ratio to that of the on-grade (i.e., unpiled) foun-dations (Sg). Settlement behavior of piled foundations representedby the developed relationships was checked against that of singlepile estimated using the same research technique and materialproperties. Effects of having cavities in the bearing rock on es-timating settlement of piled foundations were not addressedherein.

As shown previously, the behavior of piled foundations has beenaddressed in a significant number of publications over the past years.However, this study differs from the previous work by incorporatingfive aspects related to piles in rock: (1) using several values of rockmodulus near the pile head and various increasing rates of rock stiffnesswith depth; (2) considering typical pile-rock stiffness ratios that havenot been covered in the literature for piled foundations on non-homogeneousmedia; (3) developing settlement charts, the use ofwhichdoes not incorporate the commonly used interrelated parameters suchas the pile length (L) and the rock modulus near the pile base; (4)checking the foundation settlement results yielded from the FE analysis

1Professor of Civil Engineering, Qatar Univ., Doha 2713, Qatar (cor-responding author). E-mail: heid@qu.edu.qa

2Graduate Research Assistant, Qatar Univ., Doha 2713, Qatar. E-mail:as1206207@qu.edu.qa

Note. This manuscript was submitted on June 9, 2013; approved onNovember 12, 2013; published online on November 14, 2013. Discussionperiod open until October 2, 2014; separate discussions must be sub-mitted for individual papers. This paper is part of the InternationalJournal of Geomechanics, © ASCE, ISSN 1532-3641/04014059(10)/$25.00.

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against those estimated using the conventionalmethods (i.e., settlementequations based on the theory of elasticity); and (5) introducinga technique for choosing the optimum pile spacing (A) and lengthneeded to limit settlement of foundations to a certain value consideringthe effects of rock nonhomogeneity, pile–rock relative stiffness, andfoundation dimensions.

Methodology

Advanced numerical modeling has been a successful tool to solveseveral rock engineering problems (Barla and Beer 2012). As a re-sult, an extensive three-dimensional analysis was conducted onnumerical models of piled foundations to achieve the goals of thisresearch. A 7-m-wide square foundation resting on piles entirelyembedded in rock was used in the analysis. This foundation size waschosen to allow the use of three commonly used pile spacing values(i.e., 2D, 4D, and 6D), considering a pile diameter (D) of 0.5 m,without changing the foundation size (Fig. 1). Similar foundationsizes have been used by several researchers (e.g., Poulos 2001) tostudy the behavior of piled foundations. Piles were arranged in thefrequently used square pattern over the foundation area. The effect offoundation size on the study results is minimized through comparingthe settlement ratios (i.e., the values of Spf =Sg) rather than the ab-solute settlement values. Piles with slenderness ratios (L=D) of 2, 4,7, 10, 15, 20, and 30 were considered in the analysis. Greater ratios,i.e., those usually used to study the behavior of superlong piles (e.g.,Yao et al. 2012), were not included because they are used for piledfoundations on soft ground.

The elastic modulus of rock mass is taken to increase linearlyalong the pile length with a nonzero value at the pile head (E0).Poisson’s ratio for the subgrade material (ns) and piles (np) is takenas 0.25 (Fig. 2). The value of Poisson’s ratio usually ranges from 0.1to 0.3 and from 0.15 to 0.3 for rock and concrete, respectively.Variation in Poisson’s ratio of rock and concrete within these rangeshas very little effect on elastic settlement of piles (Pells and Turner1979).

To avoid using interrelated parameters, the pile–rock relativestiffness is expressed as the ratio of pile Young’smodulusEp and thetop-level subgrade Young’s modulus E0, i.e., Ep=E0. Values of 10,20, 50, 100, 200, 500, 1,000, and 2,000 were assigned to the Ep=E0

ratio. The lower four values of this ratio are typical for reinforcedconcrete piles bored in sedimentary rock masses. However, no dataare available in the literature for the elastic settlement of piledfoundations on nonhomogeneous media with Ep=E0 less than 100.The other four values of Ep=E0 were used to simulate the conditionsof piles in overconsolidated soil that exhibits a nonzero modulus atthe surface (Guo 2000). This helps in comparing the study resultswith those available in the literature.

The rate of increase in the modulus of rock mass along the pilelength is expressed as a function of E0. This rate is represented bythe factor n that was assigned values of 0.0, 0.1, and 0.2 (Fig. 2).For example, a rock with n5 0:2 indicates an increase of 0:2E0 permeter depth, whereas a homogenous rock has n5 0:0. The adoptedvalues of n reflect the commonly measured rates of increase insedimentary rock quality designation (RQD) and consequently massmodulus with depth. The direct relationship between the RQD ofa rock and its mass modulus has been proven by several researchers(e.g., Deere et al. 1967; Coon and Merritt 1970; Bieniawski 1978;Zhang and Einstein 2004; Trivedi 2013).

To compare the behavior of pile group with that of single pile,a complementary three-dimensional numerical analysis was carriedout on single pile in rock. Settlement values yielded from the nu-merical analysis on single pile were expressed in terms of the set-tlement influence factor (Ip) using the following equation:

Fig. 1. Piled square foundations considered in the study

Fig. 2. Configuration and parameters used to describe pile and sub-grade in the numerical analyses

Fig. 3. Isometric sectional view for the FE mesh used in the single-pileanalysis

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S ¼ QDE0

IP (1)

where S 5 settlement of pile head under a vertical load Q; and D5 pile diameter. A similar equation has been used by severalresearchers to estimate the elastic settlement of isolated shear socketsat the surface of a semiinfinite elastic rock. The equation considers

that the effects of end bearing and drilled shafts compression on thesettlement of the pile head are negligible.

Numerical Simulation and Verification

The numerical analyses were conducted using SAP2000 14 FE soft-ware program.An eight-node solid elementwas used to represent pilesand subgrade material. No special elements were needed at the pile/subgrade interface, because reaching the ultimate bearing capacity(i.e., the ultimate state) and consequently any relative movement atsuch interface is outside the scope of this research. The foundations

Fig. 4. FE mesh used in the pile-foundation analysis: (a) isometricsectional view; (b) cross-section view; (c) deformed cross-section view(q5 300 kPa; deformation magnification 4,0003)

Fig. 5. Comparison between results of this study for single pile andthose reported in the literature based on: (a) FE analysis of pile inhomogeneousmedia; (b) numerical analyses of pile in nonhomogeneousmedia; (c) field loading tests for piles in nonhomogeneous media

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Fig. 6. Foundation settlement ratios determined using different studies; Spf 5 settlement of piled foundation; Sg 5 settlement of on-grade foundation

Fig. 7. Elastic settlement influence factors for single piles

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were modeled with shell elements and considered rigid throughoutthe investigation. Foundation rigidity or thickness has minor effectson both of the maximum settlement and the pile-load share (Poulos2001). A uniform stress (q) was applied to foundationswith differentpile configurations and subgrade conditions to determine the cor-responding settlements and pile-load shares. Similar loading con-ditions and foundation rigidity were used by several researchers instudying settlement behavior of piled foundations (e.g., Poulos andDavis 1980; Katzenbach et al. 1998).

The FE mesh used in the settlement analyses of single piles isshown in Fig. 3. Owing to the symmetry of the considered con-figuration, two-dimensional axisymmetric analysis could have beenused. However, a three-dimensional full domain mesh was used tobe consistent with the technique used for estimating settlement ofpiled foundations in this study. As shown in Fig. 3, the mesh di-ameter used for the single-pile study was set to 25D. This mesh sizecompares well with that adopted by Donald et al. (1980) to reach anacceptable accuracy for a similar study. The three-dimensional FEmesh used in the numerical analysis of piled foundations is shown inFig. 4. It can be seen that the distance of the mesh boundary from thefoundation edges was set to 2:5B. Having such a distance minimizesthe boundary effect because the observed influence zone extends atmost 1:5B from the foundation edges. The extension decreases incase of having small pile spacing [Fig. 4(c)]. For both of the meshesused, finite elements representing the subgrade were concentrated inthe zones of high stress gradient. To ensure that each mesh issufficiently fine, several analyses were conducted using pro-gressively more elements until the results stabilized. Such a re-finement study resulted in using themeshespresented inFigs. 3 and4.For all of the considered piled foundation models, the differencebetween the maximum and minimum settlements was insignificant.

For validation, results of the numerical simulations presented inthis study were compared with elastic settlement data reported in theliterature for single piles and piled foundations. Fig. 5 shows suchcomparison for single piles embedded in homogeneous and non-homogeneousmedia. It canbe seen that the results yielded from the two-dimensional numerical simulation of this study are in good agreementwith settlement data determined using different numerical analysistechniques and field loading tests. Settlements of piled foundations assimulated in this study are also comparable with those reported in theliterature for similar foundation and subgrade conditions (Fig. 6). Suchagreements support the reliability of the numerical analyses used in thisresearch to predict the elastic settlement of piled foundations.

Analysis and Results

The settlement influence factors determined for single piles areshown in Fig. 7 as a function of n, Ep=E0, and L=D. It can be seenthat, for the same n value, the calculated settlement is more sensitiveto the adopted value of Ep=E0 for piles embedded in subgradematerials with high stiffness, i.e., with low Ep=E0 values, such asrock. As a result, great care should be taken in measuring stiffness atthe top of these materials for estimation of the single pile settlement.

The data presented in Fig. 7 also show that Ip has a generaltendency to decrease with increasing values of n, L=D, and Ep=E0.However, the rate of such decrease diminishes for piles with highL=D and Ep=E0 ratios. Increasing pile slenderness ratios to valuesgreater than a critical one does not affect the pile head settlementbecause a small portion of load reaches the pile lower end. Fig. 8clearly shows that this behavior for Ep=E0 range is typical forconcrete piles bored in sedimentary rock masses. The results ofseveral field tests and numerical simulations (e.g., Horvath et al.

Fig. 8. Axial load distribution along depth of single pile in rock

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1980; Carrubba 1997) have shown that the contribution of toe re-sistance is significant only at relatively large displacements, i.e., atthe ultimate limit state. Consequently, under the working loads,forces transferred from the pile shaft to the surrounding rock throughskin friction are the main contributor to the settlement of pile head.Similar conclusions can be drawn from the data presented byMattesand Poulos (1969), Pells and Turner (1979), andDonald et al. (1980)for piles entirely embedded in rock of constant mass modulus.Analysis of the data developed from this study and those presented inthe literature (e.g., Fleming et al. 1992; Eid and Bani-Hani 2012)shows that the critical slenderness ratio increases with decreasing nand ns and increasing Ep=E0 values.

Especially for small pile spacing, pile slenderness ratios neededto render foundation settlements that are insensitive to pile depth aremuch higher than the critical ratios determined from the single pilestudy. Such a conclusion can be drawn through comparing the dataincluded in Fig. 7 for single piles with those presented in Fig. 9 forpiled foundations (i.e., pile groups). This can be interpreted in termsof pile interactions that are more significant in groups of small pilespacing. Fig. 9 also shows that the efficiency of using piles in re-ducing foundation settlements is directly proportional to the valuesof L=D and n. Except for low slenderness ratios, using piles becomesmore efficient in cases of having high values of Ep=E0.

Fig. 9. Settlement ratios for piled foundations yielded from the three-dimensional FE analysis as a function of pile and subgrade parameters; Spf5 settlement of piled foundation; Sg 5 settlement of on-grade foundation

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Fig. 9 can be used in predicting the settlement ratio Spf =Sg andconsequently the piled foundation settlement because the value of Sgcan be estimated with a reasonable accuracy using the commonlyused elastic-settlement equations. It should be noted that the sim-plicity of using the charts of Figs. 7 and 9 to predict the elasticsettlement of single piles and piled foundations results fromavoidingthe use of the interrelated parameters that are incorporated in all ofthe similar charts presented in the literature for estimating settlementof piles in nonhomogeneous media.

Typical values of Spf =Sg ratios are presented in Fig. 10 asa function of the pile-load share. It can be seen, as expected, thatincreasing the pile-load share reduces settlement of piled founda-tions, as more load would be transferred through piles to lesscompressible layers. In addition to having small pile spacing, highvalues of Ep=E0, L=D, and n contribute to enhancing the pile-loadshare and consequently reducing the settlement of foundations.Using deeper piles becomes less efficient in such reduction in case ofhaving low values of Ep=E0 and n (Fig. 9 and 10). Low values ofEp=E0 are typical for piled foundations on rock.

Because the subgradematerial properties (i.e., values ofE0 and n)are site specific and cannot be practically modified, themagnitude offoundation settlement reduction due to piling mainly depends on theA and L=D used. Fig. 9 can be used in a preliminary design techniquethat provides the optimum A and L=D values needed to limit set-tlement of foundations to a certain value. Fig. 11(a), which isdeducted from Fig. 9 for simplicity, illustrates the use of sucha technique to achieve a settlement reduction, Spf =Sg, of 0.6 in caseof having a subgrade with Ep=E0 and n of 100 and 0.1, respectively.It can be seen that the required settlement reduction can be fulfilledusing three alternatives, i.e., pairs of A and L=D values. The cost ofadopting each an alternative would govern the final choice. On theother hand, only small spacing can be used to achieve a settlementreduction of 0.6, regardless of the values of L=D, for foundations ona rockwithEp=E0 and n of 20 and 0.1, respectively [Fig. 11(b)]. Thiscan be interpreted in terms of the low pile-load share for foundations

resting on rocks of high modulus and consequently the relativelylimited effect of using deeper piles for settlement reduction (Fig. 10).

Elastic settlement of foundations has been frequently estimatedusing a basic equation suggested by Terzaghi (1943). The equationform and its associated parameters used in estimating elastic set-tlement of on-grade foundations and piled foundations are shown inFig. 12. Settlements of on-grade foundations and piled foundationsestimated using this equation, i.e., ðSgÞe and ðSpf Þe, were comparedwith the corresponding values determined from the FE analysis(i.e., Sg and Spf ). The comparison results are shown in Fig. 13. It canbe seen that, for on-grade foundations, the equation generally yieldssettlement values that are in some agreement with those determinedusing the FE analysis, especially for subgrades with high values ofE0 and n [Fig. 13(a)]. On the other hand, the equation tends tosignificantly overestimate the settlement of piled foundations, es-pecially for cases of high Ep=E0 and L=D ratios and small A values(i.e., cases of high pile-load share) as shown in Fig. 13(b). Forexample, this overestimation, i.e., the magnitude of ðSpf Þe=Spf , canreach a value of about 2.84 for piled foundations with A and L=D of2D and 20, respectively, resting on a uniformweak sedimentary rock(e.g., case of n5 0 and Ep=E0 5 100). This may lead to over-designing piled foundation resting on most of the rock types. Sucha conclusion supports the importance of using the results of thisstudy in estimating the elastic settlement of piled foundations.

Conclusions

Using a unique representation of the subgrade nonhomogeneity, FEanalyses were conducted to study the elastic settlement behavior ofpiled foundations on rock. Low values of pile–subgrade relativestiffness that are typical for piles in sedimentary rocks, yet notcovered in the literature for piles in nonhomogeneous media, wereconsidered in the analyses. The study shows that having rock as thefoundation subgrade significantly lowers the pile-load share and

Fig. 10. Settlement ratios of foundations as a function of pile-load share

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Fig. 11. Some uses for results of the present study: (a) determining alternative pairs of pile length and pile spacing that lead to a certain reduction infoundation settlement; (b) limiting the alternatives shown in plot a to only one in case of having a higher subgrade modulus

Fig. 12. Schematic drawing showing the parameters and equations conventionally used in estimating the elastic settlement of foundations

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consequently decreases the efficiency of using long piles asfoundation settlement reducers. Dimensionless charts are in-troduced based on the results of the numerical analyses to estimatethe elastic settlement of piled foundation as a function of the set-tlement of on-grade foundation, pile slenderness ratio, pile–rockrelative stiffness, and rock nonhomogeneity. The charts can be used,before detailed design of piled foundations, to choose the optimumpile spacing and length that limit settlement to the desired value.Numerical examples are given to illustrate the applications and theimportance of the presented charts in settlement analysis of piledfoundations on rock.

Notation

The following symbols are used in this paper:A 5 pile spacing;B 5 foundationwidth (used in elastic-settlement equation);

B 5 equivalent pier width (used in elastic-settlementequation);

D 5 pile diameter;E 5 subgrade Young’s modulus (used in elastic-

settlement equation);E0 5 top level subgrade Young’s modulus;Ep 5 Young’s modulus of pile material;I 5 factor depends on foundation rigidity and dimensions

(used in elastic-settlement equation);Ip 5 settlement influence factor for single pile;L 5 pile length;n 5 rate of increase in subgrade modulus with depth;q 5 uniform stress imposed on foundation surface;q 5 stress applied at L=3 on the equivalent pier (used in

elastic-settlement equation);S 5 settlement of single pile under a load Q;Sg 5 settlement of on-grade foundation;

Fig. 13. Ratios between settlement values estimated using the elastic-settlement equation and the FE method for: (a) on-grade foundations; (b) piledfoundations

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ðSgÞe 5 settlement of on-grade foundation determined usingthe elastic-settlement equation;

Spf 5 settlement of piled foundation;ðSpf Þe 5 settlement of piled foundation determined using the

elastic-settlement equation;np 5 Poisson’s ratio for the pile material;ns 5 Poisson’s ratio for the subgrade material;Y 5 foundation length (used in elastic-settlement

equation); andY 5 equivalent pier length (used in elastic-settlement

equation).

References

Barla, M., and Beer, G. (2012). “Special issue on advances in modeling rockengineering problems.” Int. J. Geomech., 10.1061/(ASCE)GM.1943-5622.0000242, 617.

Bieniawski, Z. T. (1978). “Determining rock mass deformability: Experi-ence from case histories.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr.,15(5), 237–247.

Butterfield, R., and Banerjee, P. K. (1971). “The elastic analysis of com-pressible piles and pile groups.” Geotechnique, 21(1), 43–60.

Carrubba, P. (1997). “Skin friction of large-diameter piles socketed intorock.” Can. Geotech. J., 34(2), 230–240.

Clancy, P., and Randolph, M. F. (1993). “An approximate analysis pro-cedure for piled raft foundations.” Int. J. Numer. Anal. Methods Geo-mech., 17(12), 849–869.

Coon, R. F., and Merritt, A. H. (1970). “Predicting in situ modulus ofdeformation using rock quality indices.” Special Technical Publication477, ASTM, West Conshohocken, PA, 154–173.

de Sanctis, L., and Russo, G. (2008). “Analysis and performance of piledrafts designed using innovative criteria.” J. Geotech. Geoenviron. Eng.,10.1061/(ASCE)1090-0241(2008)134:8(1118), 1118–1128.

Deere, D. U., Hendron, A. J., Patton, F. D., and Cording, E. J. (1967).“Design of surface and near surface construction in rock.”Proc., 8thU.S.Symp. on Rock Mechanics, C. Fairhurst, ed., American Institute ofMining, Metallurgical and Petroleum Engineers, New York, 237–302.

Donald, I. B., Chiu, H. K., and Sloan, S.W. (1980). “Theoretical analyses ofrock socketed piles.” Proc., Int. Conf. on Structural Foundations onRock, Vol. 1, Balkema, Rotterdam, Netherlands, 303–316.

Eid, H. T. (2011). “Geotechnical considerations on the design of piled raftson rock.” Proc., 6th Int. Structural Engineering and Construction Conf.(ISEC6), Research Publishing Services, Singapore, 653–658.

Eid, H. T., and Bani-Hani, K. (2012). “Settlement of axially loaded pilesentirely embedded in rock—Analytical and experimental study.” Geo-mech. Geoeng., 7(2), 139–148.

El-Mossallamy, Y., Schmidt, H., Gundling, E., and Loschner, J. (2003).“Pile raft foundation of a railway bridge in tertiary clay.” Proc., 4th Int.Seminar on Deep Foundations on Bored and Auger Piles, Millpress,Rotterdam, Netherlands, 387–393.

Fleming, W. G. K., Weltman, A. J., Randolph, M. F., and Elson, W. K.(1992). Piling Engineering, 2nd Ed., Halstead Press, Ultimo, Australia.

Guo, W. (2000). “Vertically loaded single piles in Gibson soil.” J. Geotech.Geoenviron. Eng., 10.1061/(ASCE)1090-0241(2000)126:2(189), 189–193.

Horvath, R. G., Kenney, T. C., and Trow, W. A. 1980. Results of tests todetermine shaft resistance of rock-socketed drilled piers.Proc., Int. Conf.on Structural Foundations on Rock, Vol. 1, Balkema, Rotterdam,Netherlands, 349–361.

Katzenbach, R., Arslan, U., Moormann, C., and Reul, O. (1998). “Piled raftfoundation-interaction between piles and raft.”Darmstadt Geotechnics:Proc., Int. Conf. on Soil-Structure Interaction in Urban Civil Engi-neering, Vol. 2, Darmstadt Univ. of Technology, Darmstadt, Germany,279–296.

Kuwabara, F. (1989). “An elastic analysis for piled raft foundations ina homogeneous soil.” Soils Found., 29(1), 82–92.

Lee, I. K. (1993). “Analysis and performance of raft and raft-pile systems.”Proc., 3rd Int. Conf. on Case Histories in Geotechnical Engineering,Vol. 2, University of Missouri, Rolla, MO, 1331–1345.

Leung,Y., Soga, K., Lehane, B., andKlar, A. (2010). “Role of linear elasticityin pile group analysis and load test interpretation.” J. Geotech. Geo-environ. Eng., 10.1061/(ASCE)GT.1943-5606.0000392, 1686–1694.

Mandolini, A., and Viggiani, C. (1997). “Settlement of piled foundations.”Geotechnique, 47(4), 791–816.

Mattes, N. S., and Poulos, H. G. (1969). “Settlement of single compressiblepile.” J. Soil Mech. and Found. Div., 95(1), 189–208.

Pells, P. J. N., and Turner, R.M. (1979). “Elastic solutions for the design andanalysis of rock-socketed piles.” Can. Geotech. J., 16(3), 481–487.

Poulos, H. G. (1994). “An approximate numerical analysis of pile-raft in-teraction.” Int. J. Numer. Anal. Methods Geomech., 18(2), 73–92.

Poulos, H. G. (2001). “Piled raft foundation: Design and applications.”Geotechnique, 51(2), 95–113.

Poulos, H. G., and Davis, E. H. (1980). Pile foundation analysis and design,Wiley, New York.

Poulos, H. G., Small, J. C., Ta, L. D., Sinha, J., and Chen, L. (1997).“Comparison of some methods for analysis of piled rafts.” Proc., 14thInt. Conf. on Soil Mechanics and Foundation Engineering, Vol. 2,Balkema, Rotterdam, Netherlands, 1119–1124.

SAP2000 14 [Computer software]. Berkeley, CA, Computers and Struc-tures, Inc.

Terzaghi, K. (1943). Theoretical soil mechanics, Wiley, New York.Trivedi, A. (2013). “Estimating in situ deformation of rock masses using

a hardening parameter and RQD.” Int. J. Geomech., 10.1061/(ASCE)GM.1943-5622.0000215, 348–364.

Williams, A. F., and Pells, P. J. N. (1981). “Side resistance rock socketsin sandstone, mudstone, and shale.” Can. Geotech. J., 18(4), 502–513.

Yao, W., Liu, Y., and Chen, J. (2012). “Characteristics of negative skinfriction for superlong piles under surcharge loading.” Int. J. Geomech.,10.1061/(ASCE)GM.1943-5622.0000167, 90–97.

Zhang, L., and Einstein, H. H. (2004). “Using RQD to estimate the de-formation modulus of rock masses.” Int. J. Rock Mech. Min. Sci.Geomech. Abstr., 41(2), 337–341.

Zhuang, G. M., Lee, I. K., and Zhao, X. H. (1991). “Interactive analysis ofbehavior of raft-pile foundations.” Proc., Geo-Coast ’91, Vol. 2, CoastalDevelopment Institute of Technology, Tokyo, 759–764.

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