Soil-structure interaction in coupled rocking and sliding vibration — the plane problem

Abstract

For a strip wall erected on a rigid strip foundation and supported on the surface of the ground, the dynamic soil-structure interaction under the action of horizontal ground motion is investigated. The ground motion is idealized as vertically propagating, horizontal steady-state motion. Because the horizontal ground motion brings about sliding vibration of the foundation as well as rocking vibration, the coupled rocking and sliding vibration of the soil-structure system is considered in this paper. For the contact between the ground and the foundation, the following assumptions are made: (a) the contact is assumed to be welded, that is to say, the motion of the foundation is consistent with the ground; (b) the horizontal translation at each point on the bottom surface of the foundation is equal to a constant; (c) the distribution of the normal displacements under the foundation remains linear in the rocking vibration. For comparison, the case of uncoupled vibration is considered also. The use of Fourier transform method yields dual integral equations (for the case without coupled effect) or simultaneous dual integral equations (for the case with coupled effect). Both of them are solved by means of infinite series of orthogonal functions, and Jacobi polynomials. The numerical results show that there are significant differences between the displacement of the foundation, the relative displacements of the top of the wall with respect to its base, and the distributions of contact stresses beneath the foundation, for the cases with and without the coupling effect.