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An analytical method is developed for the interaction between two dissimilar piles subjected to vertical loadings in a finite soil layer with a rigid base. A fictitious soil column is assumed for the corresponding shaft and the moduli of the soil–pile rod are expressed as a Heaviside step function of the modulus. The vertical soil displacements and the shaft resistances are calculated as the combined contributions by the two dissimilar piles in terms of the respective local coordinate systems. The displacements and stresses in two different local coordinates are transferred from one to the other using Graf's addition theorem. The boundary value problem for the soil layer is solved using the method of separation of variables with a series of undetermined constants. The unknown constants can be determined by considering the compatibility along the interfaces of the two soil–pile rods and the surrounding soil. A parametric study is performed to investigate the effects of the properties of the soil–pile system on the interaction between the two piles. Numerical results show that, for the dissimilar piles in the stiff soil, the effects of the difference of the pile lengths on the interaction factor are negligible. Also, the interaction factor of the dissimilar piles in the soft soil depends heavily on the difference in lengths. [ABSTRACT FROM AUTHOR]

SUMMARY Within the framework of soil-pile interaction, a novel displacement scheme for the transverse kinematic response of single piles to vertically propagating S waves is proposed on the basis of the modified Vlasov foundation model. The displacement model contains a displacement function along the pile axis and an attenuation function along the radial direction. The governing equations and boundary conditions of the two undetermined functions are obtained in a coupled form by using Hamilton's principle. An iterative algorithm is adopted to decouple and solve the two unknown functions. In light of the governing equation of the pile kinematics, a mechanical model is proposed to evaluate the present method on a physical basis considering material damping. The coefficient of the equivalent Winkler spring is derived explicitly as function of the displacement decay parameter γ and soil Poisson's ratio. A parametric study is performed to investigate the effects of the soil-pile system properties on the kinematic response of single piles. The results show that the dimensionless pile length controls the transverse kinematics of piles. In terms of the theory of beams on elastic foundation, the classification limits of the dimensionless pile length may be π ∕ 4 and π, respectively. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Dynamic response of single piles to seismic waves is fundamentally different from the free-field motion because of the interaction between the pile and the surrounding soil. Considering soil-pile interaction, this paper presents a new displacement model for the steady-state kinematic response of single piles to vertically incident P-waves on the basis of a continuum model. The governing equations and boundary conditions of the two undetermined functions in the model are obtained to be coupled by using Hamilton's principle. Then, the two unknown functions are decoupled and solved by an iterative algorithm numerically. A parametric study is performed to investigate the effects of the properties of the soil-pile system on the kinematic response of single piles. It is shown that the effects of the pile-soil modulus ratio, the slenderness ratio of the pile, and the frequency of the incident excitations are very significant. By contrast, the influence of soil damping on the kinematics of the system is slight and can be neglected. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]