Vertical-rocking-horizontal vibrations of a rigid disk resting on multi-layered soils with groundwater level

Abstract

The vertical, rocking and horizontal vibrations of a rigid disk on multi-layered soils are studied by using a coupled approach of stiffness matrix method and “integral equation method”. Considering groundwater level, the layered soils consist of a number of dry layers and saturated layers, and a bedrock at the bottom. To allow the assembly of a global equation of this layered system, the stiffness matrices of the top and bottom saturated layers are modified to match those of adjacent dry layer and bedrock using drainage conditions. Together with the mixed boundary-value conditions at the disk plane, three disk-soil interaction problem, i.e., vertical, rocking and horizontal vibration cases, can be expressed as corresponding dual integral equations for solving. The correctness of the proposed method is verified by existing solutions with good convergence. Parametric studies illustrate the effects of groundwater level, permeability of saturated soil and the hydraulic condition at dry-saturated soil interface on dynamic compliance coefficients of rigid risk and pore pressure in saturated soil layer.