Dynamic structure - soil interaction under the action of vertical ground motion, part I: the axisymmetric problem

In the epicenter area, the acceleration for the vertical component plays an important role in the anti-seismic design. Supposing that a rod is erected on a rigid circular foundation, and the foundation is 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 typically idealized as vertically propagating, vertical steady-state motion and the ground is idealized as a linear, homogeneous, isotropic elastic half-space. For the contact between the foundation and the ground, two cases are considered: (a) the contact is perfectly smooth, namely, there is no shear stress on the contact surface; (b) the contact is assumed to be welded along the contact surface. The use of Hankel and Laplace transform methods yields respectively for the two cases dual integral equations or simultaneous dual integral equations. Both of them are solved by means of the infinite series about some orthogonal function. For the three cases of rigid ground, smooth contact, and welded contact, results are presented for the response of the structure-soil system to the incident excitation. For the cases of smooth and welded contacts, the stress distribution along the bottom surface of the foundation is investigated.