Foundations for Dynamic Loads - Shamsher Prakash Foundation

due to earthquake loading was presented by Richard et al, (1993). The settlement andtilt of the foundation must also be considered. Gazetas and Anastasopoulos (2008)have studied the interaction effects of two adjacent buildings, founded on shallowfootings.For analysis and design of piles and pile groups under seismic loads a simpleapproach to account for nonlinear soil-pile interaction using strain dependent soilmodulus to define soil-pile stiffness and radiation damping can be used and isdiscussed in the paper. Some studies are available comparing the predicted andobserved response of piles also. In some of these studies the soil pile stiffness anddamping were arbitrarily modified to match the observed and predicted response ofthe soil pile system. A study was conducted under the supervision of the authors inwhich the data reported in literature was reanalyzed and reduction factors have beenproposed for the stiffness and radiation damping obtained by using the commonlyapproach of Novak and El-Sharnouby (1983). Using the proposed reduction factorsthe reported test data of Gle (1981) was reanalyzed. The predicted values of naturalfrequency and amplitude of vibration at various frequencies showed an excellentgeotechnical comparison with the observed data. The case of shallow foundations isdiscussed first followed by several aspects of pile behavior under dynamic loads.SHALLOW FOUNDATIONSThe problem of static bearing capacity of shallow foundations has been extensivelystudied in the past (Terzaghi (1943), Meyerhoff (1951), Vesic (1973) and manyothers. Basavanna et al. (1974) obtained analytical solutions for the bearing capacityunder transient loading conditions. The design of foundations subjected to seismicloading has generally been performed by using psedo-static approach (Prakash;1981). The foundations are considered as eccentrically loaded and the ultimatebearing capacity is accordingly estimated. Prakash and Saran (1971) proposed amethod to determine the settlement and tilt of a foundation subjected to vertical loadand moment. The response of a footing to dynamic loads is affected by the (1) natureand magnitude of dynamic loads, (2) number of pulses and (3) the strain rate responseof soil. To account for the effect of dynamic nature of the load, the bearing capacityfactors are determined by using dynamic angle of internal friction which is taken as2-degrees less than its static value (Das, 1992). Building codes such as InternationalBuilding Code (2006) generally permit an increase of 33 % in allowable bearingcapacity when earthquake loads in addition to static loads are used in design of thefoundation. This recommendation is based on the assumption that the allowablebearing pressure has adequate factor of safety for the static loads and a lower factorof safety may be accepted for earthquake loads. This recommendation may bereasonable for dense granular soils, stiff to very stiff clays or hard bedrocks but is notapplicable for friable rock, loose soils susceptible to liquefaction or pore waterpressure increase, sensitive clays or clays likely to undergo plastic flow (Day, 2006).Richards et al (1993) observed seismic settlements of foundations on partiallysaturated dense or compacted soils. These settlements were not associated withliquefaction or densification and could be easily explained in terms of seismic bearing2

capacity reduction. They have proposed a simplified approach to estimate thedynamic bearing capacity q ue and seismic settlement S Eq of a strip footingFigure 1. Failure surface in soil for seismic bearing capacity (After Richards etal, 1993; See also Prakash and Puri, 2008)Figure 1 shows the assumed failure surfaces. The seismic bearing capacity(q uE ) is given by Eq. 1:q uE = cN cE + qN qE + ½ γ BN γE (1)where, γ = Unit weight of soilD f = Depth of the foundation and q= γD fN cE , N qE , and N γE = Seismic bearing capacity factors which are functions of φ andtanψ = k h / (1-k v )k h and k v are the horizontal and vertical coefficients of acceleration due toearthquake.For static case, k h = k v , = 0 and Eq. (1) becomesq u = cN c + qN q + ½ γBN γ (2)in which N c , N q and N γ are the static bearing capacity factors. Figure 2 shows plots ofN γE /N γ , N qE /N q and N cE /N c with tan ψ and φ.tanψ = k h / (1-k v ) tan ψ = k h / (1-k v ), tanψ = k h / (1-k v ),Figure 2. Variation of N qE /N q , N γE /N γ and N cE /N c with φ and tan ψ (AfterRichard et al 1993; See also Prakash and Puri, 2008)SEISMIC SETTLEMENT OF FOUNDATIONBearing capacity-related seismic settlement takes place when the ratio k h /(1 - k v )reaches a critical value (k h /1 – k v )*. If k v = 0, then (k h /1 - k v )* becomes equal to k h * .Figure 3 shows the variation of k h * (for k v = c = 0; granular soil) with the static factor3

of safety (FS) applied to the ultimate bearing capacity [Eq, (2)], for φ = 10°, 20°, 30°,and 40° and D f /B of 0, 0.25, 0.5 and 1.0.Figure 3. Critical accelerationand Puri, 2008)*kh(After Richards et al, 1993; See also PrakashThe settlement (S Eq ) of a strip foundation due to an earthquake can be estimated as2 − 4V kS ( m ) 0.174h*Eqtan α AEAg A= (3)where V = peak velocity for the design earthquake (m/sec),A = accelerationcoefficient for the design earthquake, g = acceleration due to gravity (9.81 m/sec 2 ).tan α AE depends on φ and k h *, (Richards et al, (1993). In Figure 4, variation of tanα AE with k h * for φ of 15° - 40° is shown.Suppose a typical strip foundation is supported on a sandy soil with B = 2 m, and D f= 0.5 m, and γ = 18 KN/m 3 , φ = 34°, and c = 0. The value of k h = 0.3 and k v = 0 andthe velocity V induced by the design earthquake is 0.4 m/sec. The static ultimatebearing capacity for this footing for vertical load will be 1,000 KN/m 2 (Eq. 2). Thereduced ultimate bearing capacity for vertical load is calculated as 290 KN/m 2 (Eq 1).If the footing is designed using a FS = 3 on the static ultimate bearing capacity (i.e.,for an allowable soil pressure of 333 kN/m 2 ), the additional settlement due toearthquake will be 20.5 mm (Eq 3, Richards et al, 1993). This settlement reduces to7.0 mm if FS of 4 is used. Besides ensuring that the footing soil system does notexperience a bearing capacity failure or undergo excessive settlement, thefoundations should be tied together using interconnecting beams.Seismic bearing capacity factors for a strip footing resting on cohesionless soil weredetermined by Dormieux and Pecker (1995) using the upper bound theorem of yield.4

Figure 4. Variation of tan α AE with k h * and φ (After Richards et al 1993; Seealso Prakash and Puri, 2008)Using the classical Prandtl like mechanism, it was established that the reduction inbearing capacity was mainly caused by load inclination (Dormieux andPecker;1995).Choudhury and Subba Rao (2005) determined seismic bearing capacityfactors for shallow strip footing using the limit equilibrium approach and pseudostaticmethod of analysis. The reduction in bearing capacity under the combinedeffect of vertical and horizontal forces was explained by using smaller failure surfacecompared to case when only static vertical loads are applied.It is thus seen that presently (2009), the pseudo-static approach is being used todetermine bearing capacity and settlement and tilt of the foundations subjected toseismic loads in non-liquefying soils. Dynamic nature of the load and other factorswhich affect the dynamic response are not being accounted for. Also, no guidelinesare available design of footings in liquefying soil.PILES FOUNDATIONSPiles may often be the preferred choice of foundations in seismic areas. The seismicloading induces large displacements or strains in the soil. The shear modulus of thesoil degrades and damping (material) increases with increasing strain. The stiffness ofpiles should be determined for these strain effects. The elastic solutions fordetermining response of piles subjected to dynamic loads have been presented byseveral investigators in the past in several modes of vibrations, (Novak, 1974; Novakand El-Sharnouby, 1983; Novak and Howell, 1977; Poulos, 1971; Prakash andPuri,1988; and Prakash and Sharma, 1991). Displacement dependent spring anddamping factors for piles for vertical, horizontal and rotational vibrations have beenpresented by Munaf and Prakash (2002), Munaf et al. (2003) and Prakash and Puri(2008). The stiffness of the pile group is estimated from that of the single piles by5

using group interaction factors. The contribution of the pile cap, if any, is alsoincluded. The response of the single pile or pile groups may then be determined usingprinciples of structural dynamics. The design of pile foundations subjected toearthquakes requires a reliable method of calculating the effects of earthquakeshaking and post-liquefaction displacements on pile foundations. Keys to good designinclude reliable estimates of environmental loads, realistic assessments of pile headfixity, and a mathematical model which can adequately account for all significantfactors that affect the response of the pile-soil-structure system to ground shakingand/or lateral spreading in a given situation.The equivalent spring stiffness and damping of the soil-pile system are a function ofYoung’s modulus of pile material (E p ), shear modulus of soil (G s ), and geometry ofthe piles in the group. Shear modulus and hence spring and damping factors are strainor displacement dependent. There are six independent spring factors for a piles-capsystem; ie; k x , k y , k z , in translation in x, y and z directions, respectively and k φ , k θ , k ψrotational-springs about x, y and z directions respectively. There are two rotationalcross-coupled springs; i.e.; k xφ and k yθ which include 2-components of displacement;i.e., translation and rotation about the appropriate axis. Also there are correspondingeight damping factors; i.e., c x , c y, c z , c φ , c θ , c ψ , and. c xφ and c yθ . To developdisplacement dependent relationships for the spring and damping factors, appropriaterelationships between strain and displacement are needed. Also, modulusdegradation with strain needs be built into these relationships. Stiffness and dampingin all the modes; i.e., vertical, horizontal, rocking and torsion and cross coupling inboth the x and y direction have been evaluated (Munaf and Prakash, 2002). The signconvention is explained in Fig. 5.Figure 5: Sign ConventionFor the case of earthquake loads, the response of piles under horizontal loads areimportant and are discussed here.Sliding and Rocking Stiffness and Damping FactorsBecause, the pile is assumed to be cylindrical with a radius r o, its stiffness anddamping factors in any horizontal direction are the same. However, in the pile group,the number of piles in the x and y directions may be different. Therefore the stiffnessand damping factors of a pile group are dependent on the number of piles and theirspacing in each direction, (Figure 6).6

Sliding (k x, c x )⎡ EpIp ⎤Kx= ⎢ f3 ⎥ x1(4a)⎣ r0⎦⎡ EpIp ⎤Cx= ⎢ f2 ⎥ x2(4b)⎣ r0Vs⎦Rocking (k φ , c φ ) and (k θ , c θ )⎡ EpIp ⎤Kϕ= Kθ= ⎢ f2 ⎥ φ1(5a)⎣ ro⎦⎡ EpIp ⎤Cφ= Cθ= ⎢ f2 ⎥ φ 2(5b)⎣ roVs⎦Cross-coupling (k xφ , c xφ ) and (k yθ , c yθ )⎡ EpIp ⎤Kxϕ= Kyθ= ⎢ f2 ⎥ xθ1(6a)⎣ r0⎦⎡ EpIp ⎤Cxφ= Cyθ= ⎢ ⎥ fxφ 2(6b)⎣ roVs ⎦Where;I p = moment of inertia of single pile about x or y axisr o = pile radiusE p = modulus of elasticity of pile materialV s = shear wave velocity of soil along the floating pilef x1, f x2, f xφ1, f xφ 2 , f xφ1, f xφ2 are Novak’s coefficient obtained from Table 1 forhomogeneous and parabolic soil profiles, with appropriate interpolation for ν between0.25 and 0.4.Group interaction factorFor group effect in lateral directions (Poulos, 1971), obtained a solution for α L foreach pile in the horizontal x-direction, considering departure angle β (degrees). α L ’sare a function of L, r o and flexibility K R as defined in figure 7 and departure angle β.This procedure will also apply for horizontal y- direction. The group interactionfactor (∑α L ) is the summation of α L for all the piles. Note that the groupinteractionfactor in x-direction and y-direction may be different depending on numberand spacing of piles in each direction.Group Stiffness and DampingFigure 6 shows schematically the plan and cross sections of an arbitrary pile group.This figure will be used to explain the procedure for obtaining the stiffness anddamping for a group of pile for all modes of vibration.7

Figure 6: Plan and Cross Section of Pile GroupFigure 7: Graphical solution of α L (Poulus, 1971)Sliding and Rocking and Cross Coupled Group Stiffness and Damping FactorsTranslation along X-axiskcgxgx==∑∑∑∑kαcαxLxxLx8(7a)(7b)

Table 1. Stiffness and Damping Parameters of Horizontal Response for Pile withL/R o >25 for Homogeneous Soil Profile and L/R o >30 for Parabolic Soil Profile( Novak and El-Sharnouby, 1983)gTranslation along Y Axis (k y , c g y )∑kgyky=αcgy=∑∑∑cαLAyLy(8a)(8b)Rocking About Y- Axis (k φg, c φ g )gφ2[ k + k x + k z − z k ]1 2φ z r x cαLx1 2cφ+ czxr+ cxz2cαLxk = 2(9a)∑gφcxφ[ − z c ]c = 2(9b)∑Rocking About X- Axis (k θg, c θ g )gθcxφ2[ k + k y + k z − z k ]1 2θ z r y cαLyk = 2(10a)∑cyθ9

gθ2[ c + c y + c z − z c ]1 2θ z r x cαLyc = 2(10b)∑cyθgCross-Coupling: Translation along X Axis and Rotation about Y Axis. (k xφ , c g xφ )g 1kxφ= ∑ ( kxφ− kxzc)(11a)αcLx1∑ ( c xφ− c x z )gxφ= cαLx(11b)gCross-Coupling: Translation along Y-Axis and Rotation about X Axis. (k yθ , c g yθ )g 1kyθ= ∑ ( kyθ− kyzc)(12a)αcLy1∑ ( cyθ− cyz )gyθ=cαLy(12b)COMPARISION OF COMPUTED AND PREDICTED PILE RESPONSEThe present methods for design of pile foundations subjected to dynamic loads aregenerally based on the models developed by Novak (1974) and Novak andEl_Sharnouby (1984) and also presented by Prakash and Puri (1988) and Prakash andSharma (1990). Several researchers have attempted to make a comparison of theobserved and predicted pile response. Small scale pile tests, centrifuge and full scalepile tests have been used for this purpose (Gle, 1981; Novak and ElSharnouby, 1984;Woods, 1984; and Poulos, 2007). Woods (1984) reported results of 55 horizontalvibration tests on 11 end bearing piles 15 - 48 m long. The outer diameter of piles was35.56 cm and the wall thickness varied from 0.47 cm to 0.94 cm. Typical amplitude –frequency plot for one of the piles in soft clay is shown in Fig. 8. It may be seen fromthis plot that the observed natural frequency decreases with an increase in the value of‘ө’ (increase in ‘ө’ means an increase in dynamic force at the same frequency ofvibrations) indicating non-linear behavior. Woods (1984) also compared theobserved and computed response of the piles. The stiffness and damping values wereobtained using computer program PILAY which uses continuum modelaccommodating soil layers and assumes homogeneous soil in the layer with elasticbehavior. A typical comparison of the pile response so computed with the observedresponse is shown in Fig. 9. It may be observed from Fig.9 that the calculated andcomputed responses do not match.Efforts were made to obtain a match between observed and predicted response byusing reduced values of stiffness obtained from PILAY, which did not help much. Abetter match could, however, be obtained when a considerably softened or weakenedzone was assumed surrounding the piles (program PILAY 2) simulating disturbanceto soil during pile installation. A loss of contact of the soil with the pile for a shortlength close to the ground surface also improved the predicted response.10

Fig. 8. Response curves; a decrease Fig 9. Typical response curvesin resonant frequency with increasing predicted by PILAY superimposedamplitudes. (Woods, 1984) on measured pile response.(Woods, 1984)Novak and El-Sharnouby (1984) performed tests on 102 model pile groups usingsteel pipe piles. A typical comparison of the theoretical and experimental horizontalresponse is shown in Fig.10. Plot ‘a’ shows the theoretical group response withoutinteraction effects. Response shown in plot ‘b’ was obtained by applying staticinteraction factors to stiffness only. Plot ‘c’ was obtained with arbitrary interactionfactor of 2.85 applied to stiffness only. Plot‘d’ was obtained by using an arbitraryinteraction factor of 2.85 on stiffness and 1.8 on damping respectively. Plot ‘e’ showsthe experimental data. The plot which shows an excellent match with experimentaldata was obtained by arbitrarily increasing the damping factor by 45%.Fig. 10. Experiment horizontal response curves and theoretical curves calculatedwith static interaction factors. (Novak and El-Sharnouby, 1984)The comparison of theoretical response obtained by using dynamic interactionfactors of Kaynia and Kausel (1982) is shown in plot ‘a’ in Fig.11. Plot ‘b’ in Fig. 11shows the calculated data based on dynamic analysis of Wass and Hartmann(1981).11

Fig. 11. Experimental horizontal response curve and theoretical curves.(a) Calculated with Kaynia and Kausel dynamic interaction factors(b) Calculated with Wass and Hartmann impedances(c ) Experimental (Novak and El-Sharnouby, 1984).The experimental data of Novak and EL-Sharnouby (1984) is shown by plot ‘c’.Novak and El-Sharnouby, (1984) also compared the observed response for verticaland torsional vibrations with the predicted response.Jadi (1999) and Prakash and Jadi (2001) reanalyzed the reported pile test data ofGle (1981) for the lateral dynamic tests on single piles and proposed reduction factorsfor the stiffness and radiation damping obtained by using the approach of Novak andEl-Sharnouby (1983). The suggested equations for the reduction factors are:λ G = -353500 γ 2 – 0.00775 γ + 0.3244 (16)λ c = 217600 γ 2 – 1905.56 γ + 0.6 (17)where, λ G and λ c are the reduction factors for shear modulus and damping and γ isshear strain at computed peak amplitude without correction factors. Typicalcomparison of the computed pile response using the modified values of stiffness anddamping values and the observed response is shown in figures 12-20.Fig 12 shows prediction and performance of Gle’s pile in Fig 9. Fig 13, 14 and 15are for the cases where prediction and performance matched well. However in Fig16-18, the prediction and performance does not match well. Fig 19 and 20 showsprediction and performance from other sites.COMMENTS ON PREDICTIONSNovak and El Sharnouby (1984) have attempted to match the observed and thepredicted response by adjusting, arbitrarily, the group stiffness and damping values.No guidelines were developed to modify these values.Woods (1984) used PILAY program with modified stiffness to match prediction andperformance.Jadi (1999) developed rational correction factors to both stiffness and damping tomatch the computed and predicted responses. She was successful in her efforts. Her12

Fig.12 Measured and predicted Fig. 13 Measured and predicted lateralresponse of pile of Fig. 11Dynamic Response of pile GP 13-7 (ө=2.5˚)(Prakash and Jadi 1991) (Prakash and Jadi, 2001)Fig. 14 Measured Vs arbitrarily reduced Fig. 15 Measured vs. predicted lateralDynamic Response of pile K 16-7 (ө=5˚) Dynamic Response with proposed(Prakash and Jadi, 2001)reduction factors for pile K 16-7, (ө=5˚)(Prakash and Jadi, 2001)Fig.16 Measured and predicted lateral Fig.17 Measured and predicted lateralDynamic Response of piles K16-7 Dynamic Response of pile GP 13- 7(ө=5˚)(Prakash and Jadi 2001) (ө=2.5˚) (Prakash and Jadi, 2001)13

Fig.18 Measured and predicted lateral Fig.19 Measured and predicted lateralDynamic Response of pile LF 16 Dynamic Response of pile I-WES(ө=10˚)(Prakash and Jadi 2001) vibrator λ G = 0.31, λ c = 0.5(Prakash and Jadi, 2001)Fig.20 Measured vs. Reduced predicted lateral Dynamic Response of the 2.4”Pile tested by Novak and Grigg, 1976, λ G = 0.44, λ c = 0.34, (Prakash and Jadi,2001)approach, however is more scientific and more efforts needs to be devoted to developrelationships for correction factors for different modes of vibration.CONCLUSIONSConsiderable attention has been paid to the design of foundations for earthquakeloads, both for shallow foundations and piles. Efforts have been made to understandthe behavior of the foundations under seismic loading. However the shallowfoundations are mostly designed using the equivalent static approach.For the case of pile foundations, many efforts have been made for comparing thepredicted and observed response of single piles and pile groups under dynamicloading and arbitrary modifications to stiffness and damping were made. Jadi’s(1999) method of modifying shear modulus and damping appears reasonable.14

However this has been tested against a limited data base. More analyses are needed tomake this tool easily usable in practice.REFERENCESBasavanna, B.M., Joshi, V.H. and Prakash, S. (1974). “Dynamic bearing Capacity OfSoils under Transient Loading.” Bull. Indian Soc. Earthquake Tech., Vol.2, No. 3,pp.67-84.Choudhury, D. and Subba Rao, K.S. (2005). “Seismic Bearing capacity of Shallowstrip Foundations”, Geotechnical and Geological Engineering, Vol.23, No. 4, pp.403-418.Das, B.M.(1992). Principles of Soil Dynamics, PWS Kent.Day, R. W. (2002). Geotechnical Earthquake Engineering Handbook, McGraw HillDormieux , L. and Pecker, A. (1995). “Seismic Bearing Capacity of Foundations onChesionless Soils”, J. Geot. Engg. Dn. ASCE, Vol. 121,No 3, pp. 300-303.Gazetas, D. and Anastasopoulos, I., (2008). “Case Histories of Foundations on top ofa Rupturing Normal Fault during the Kocaeli 1999 Earthquake”, SixthInternational Conference on Case Histories in Geotechnical EarthquakeEngineering and Symposium in Honor of Professor James K. Mitchell, CD Rom,Aug. 11-19, Arlington, Virginia.Gle, D. R., (1981). “The Dynamic Lateral Response of Deep Foundations”, PhDdissertation, University of Michigan, Ann Arbor.Jadi, H. (1999). “Prediction of lateral Dynamic Response of single Piles Embedded inClay.” MS Thesis, UMR, Rolla.Kaynia, A.M., and Kausel, F., (1982). “Dynamic behavior of Pile Groups.” Proc.Second International Conference on numerical Methods in Offshore Piling,Austin, TX, pp. 509-532.Meyerhoff, G.G. (1951). “The Ultimate Bearing capacity of Foundations.”Geotechnique,Vol.2, pp. 301-332.Munaf, Y. and Prakash, S. [2002],”Displacement Dependent Spring and DampingFactors of Soil Pile Systems,” Proc. 12 th ECEE, London Paper No. 763.Munaf. Y, S. Prakash and T. Fennessey [2003] “ Geotechnical Seismic Evaluationof Two Bridges in SE Missouri” Proc PEEC, Christchurch NZ Paper No-5, CD-ROMNovak, M. (1974). Dynamic stiffness and damping of piles, Con. Geot. J. Vol. II No4, pp. 574-598.Novak, M.(1991). “Piles Under Dynamic Load.” Proceedings; second internationalConference on Recent Advances in Geotechnical Earthquake Engineering and SoilDynamics, St. Louis, March 11-15.Novak, M. and El Sharnouby, E.B. (1983). Stiffness and Damping Constants forSingle Piles, J. Geot. Engg. Dn. ASCE, Vol. 109 No 7, pp 961-974.Novak, M. and El Sharnouby, E.B. (1984). “Evaluation of Dynamic Experiments onPile Groups”, J. Geot. Engg. Dn. ASCE, Vol. 101,No 6, pp. 737-756.Novak, M and Howell, J.H (1977).”Torsional Vibration of Pile Foundation”. J.Geotech. Eng. Div., Am. Soc. Civ. Eng. 103 (GT-4), 271-285.15

Pecker, A. (1996). Seismic Bearing Capacity of Shallow Foundations, 11 th WorldConference on earthquake engineering, Acapulco, Mexico.Poulos, H.G (1971). “Behavior of Laterally Loaded Piles.” II Piles Groups. J. SoilMech. Div., Am. Soc. Civ. Eng. 97(SM-5), 733-751.Poulos, H.G. (1975). “Lateral load Deflection Prediction for Pile Groups”, Journal,Geotechnical Engineering Div., ASCE, Vol. 101, No. GT1, pp. 19-34.Poulos, H.G.,(2007). “Ground Movements – a Hidden Source of Loading on DeepFoundations”, DFI , Journal, Vol.1, No. 1, pp. 37-53.Prakash, S., (1981). “Soil Dynamics.” McGraw Hill, New York. Reprinted SPFoundation, Rolla, MO.Prakash, S. and Jadi, H. (2001). “Prediction of Lateral Dynamic Response of SinglePiles Embedded in Fine Soils.” Proc. Fourth Intern. Conf. On Recent Advances inGeot. EQ. Eng. And Soil Dyn., San Diego, CA.Prakash, S. and Puri, V.K. (1988). “Foundation for Machines Analysis and Design.”John Wiley &Sons, New York.Prakash, S. and Puri, V.K.,(2008). “Piles Under Earthquake Loads”, GeotechnicalEarthquake Engineering and Soil Dynamics IV, CD-ROM, May 18-22,Sacramento, CAPrakash, S. and Saran, S. (1971). “Bearing capacity of Eccentrically LoadedFootings.” J. Soil Mech. And Found. Div., ASCE, VOl. 117, No. 11, pp.95-111.Prakash, S. and Sharma, H.D. (1990). “Pile Foundations in Engineering Practice”.John Wiley and Sons, NY.Prasad, S.K., Chandrahara, G.P., Nanjundaswamy, P. and Revansiddappa, K. (2004).Seismic Bearing Capacity of Ground from Shake Table Tests, IGC -2004, Vol. 1,Warangal.Richards, R., Elms, D.G. and Budhu, M. (1993). Seismic Bearing Capacity andSettlement of Foundations, Journal of Geotechnical Engineering Division, ASCE,Vol. 119, No. 4, April, pp 662-674.Terzaghi, K. (1943). “Theoretical Soil Mechanics.” John Wiley and Sons, NY.Vesic, A.S.,(1973). “Analysis of Ultimate Loads of Shallow Foundations”, J. SoilMech. And Foundation Div. , ASCE, Vol. 99, No. 1, pp.45-73.Wass , G. and Hartmann, H.G. (1981). “ Pile Foundations Subjected to HorizontalDynamic Loads”, European Simulation Meeting. “Modeling and Simulating ofLarge Scale Structural Systems.” Capri, Italy, p.17Woods, R.D. (1984). “Lateral Interaction between Soil and Pile.” ProceedingsInternational Symposium on Dynamic Soil Structure Interaction, Minneapolis,MN, pp. 47-54.16