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The interaction between a soil layer and an end bearing pile in vertical vibration induced through the frictional interface is theoretically investigated. The pile is assumed to be vertical and elastic, whereas the soil is considered as a linear visco‐elastic layer with hysteretic damping. Slip between the pile and the soil is allowed to occur along the frictional interface, in which the hysteretic frictional stress is linearized to permit modal decomposition. Approximate solutions of the pile and the soil for steady‐harmonic loads are obtained in closed form by composing the wave modes of the layer. The displacement amplitudes of the pile and the soil, the critical slip force, the stiffness of the pile head, and the modal stiffness contribution of the soil to the pile are evaluated numerically with respect to the ratio of applied force level to the slip stress level and the slenderness ratio, at various frequencies.

A non-linear seismic response analysis method for 2-D saturated soil-structure system with an absorbing boundary is presented. According to the 3-D strain space multimechanism model for the cyclic mobility of sandy soil, a constitutive expression for the plane strain condition is first given. Next, based on Biot's two-phase mixture theory, the finite element equations of motion for a saturated soil-structure system with an absorbing boundary during earthquake loadings are derived. A simulation of the shaking table test is performed by applying the proposed constitutive model. The effectiveness of the absorbing boundary is examined for the 2-D non-linear finite element models subjected to random inputs. Finally, a numerical seismic response analysis for a typical saturated soil-structure system is performed as an application of the proposed method.

SUMMARYThe cyclic mobility behaviour of sand by the three-dimensional (3-D) strain space multimechanism model based on the micromechanics of granular material is investigated. The constitutive properties are characterized by the volumetric and shear mechanisms for the initial isotropic soil. The 3-D shear mechanism is decomposed into a number of microscopic plane-strain shear mechanisms in various orientations, each of which in turn consists of a number of microscopic simple shear mechanisms. Using an appropriate summation of mechanisms, the total deformation behaviour can be obtained by evaluating contributions from each mechanism. Based on the some assumptions, the dilatancy model proposed by Iai et al. ' is extended from the two-dimensional (2-D) space to the 3-D space. Comparisons of theoretically predicted results are made with experimental measurements.