Dynamic structure - soil interaction under the action of vertical ground motion, Part II: the plane problem

For a strip wall erected on a rigid strip foundation and supported on the surface of the ground, the dynamic structure-soil interaction under the action of the vertical ground motion is investigated. The ground motion is idealized as vertically propagating, vertical steady-state motion. For the contact between the foundation and the ground, two cases are considered: (a) the contact is perfectly smooth; (b) the contact is assumed to be welded along the contact surface beneath the foundation. The use of Fourier and Laplace transform methods yields dual integral equations (for the case without friction) or simultaneous dual integral equations (for the case with welded contact). Both of them are solved by means of infinite series of orthogonal functions, the Jacobi polynomials. The displacement of the foundation, the response of the system to the incident excitation, and the distributions of contact stresses beneath the foundation are presented. The numerical results show that there are significant differences between the relative displacements of the top of the wall with respect to its base, for the cases of smooth and welded contact.