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In the present study an analytical procedure is developed, based on finite element approach, to determine the bending moment and lateral deflection response of a free headed single pile with floating tip embedded in both dry and saturated cohesionless soils subjected to combined action of vertical and lateral loadings, using the modulus of subgrade reaction method. Also the numerical results using MIDAS GTS are obtained to validate the proposed analytical solution. It is observed under static conditions, when the vertical load is increased from zero to the 'ultimate' pile capacity at 0.03D deflection level (where D is the diameter of the pile), the lateral load carrying capacity of the fixed headed and free headed flexible piles is increased by 43.27% and 26%, respectively embedded in dry dense sand. Similarly for fixed headed piles embedded in dry and saturated loose sand, the bending moment is increased by 25% and 27%, respectively when vertical loads varies from zero to ultimate pile capacity for a constant lateral load of 200kN.Thus the above analysis is useful for practical design purpose to estimate the lateral load carrying capacity of a single pile by knowing the allowable deformation and vertical load acting on the pile.

Summary In the present study an analytical procedure based on finite element technique is proposed to investigate the influence of vertical load on deflection and bending moment of a laterally loaded pile embedded in liquefiable soil, subjected to permanent ground displacement. The degradation of subgrade modulus due to soil liquefaction and effect of nonlinearity are also considered. A free headed vertical concrete elastic nonyielding pile with a floating tip subjected to vertical compressive loading, lateral load, and permanent ground displacement due to earthquake motions, in liquefiable soil underlain by nonliquefiable stratum, is considered. The input seismic motions, having varying range of ground motion parameters, considered here include 1989 Loma Gilroy, 1995 Kobe, 2001 Bhuj, and 2011 Sikkim motions. It is calculated that maximum bending moment occurred at the interface of liquefiable and nonliquefiable soil layers and when thickness of liquefiable soil layer is around 60% of total pile length. Maximum bending moment of 1210 kNm and pile head deflection of 110 cm is observed because of 1995 Kobe motion, while 2001 Bhuj and 2011 Sikkim motions amplify the pile head deflection by 14.2 and 14.4 times and bending moment approximately by 4 times, when compared to nonliquefiable soil. Further, the presence of inertial load at the pile head increases bending moment and deflection by approximately 52% when subjected to 1995 Kobe motion. Thus, it is necessary to have a proper assessment of both kinematic and inertial interactions due to free field seismic motions and vertical loads for evaluating pile response in liquefiable soil.