Dynamic Interaction Between an Embedded Disc and a Nonhomogeneous Saturated Stratum Under Torsional Excitation

摘要

Assuming the shear modulus of nonhomogeneous soil increased linearly with depth, taking into account the characteristics of torsional vibration, the dynamic motion equations of a nonhomogeneous saturated soil were established. By using Hankel integral transform, the tangential displacement and shear stresses in Hankel transform domain were formulated. The upper surface of the nonhomogeneous saturated stratum underlain by bedrock was free, and there was no shear stress in the upper surface. The lower surface of the stratum was fully bonded to bedrock, and the displacement in the lower surface was zero. In the plane where the foundation was embedded, mixed boundary conditions were considered. Thus, the dual integral equations of a rigid disc embedded in a nonhomogeneous saturated stratum were established. By appropriate transform, the dual integral equations were converted to a Fredholm integral equation of the second kind, which could be solved by numerical method, thus the torsional dynamic response problem was solved. Comparing with the relation between a static torque and angular displacement, the dynamic compliance coefficient andthe torsional angular amplitude were given. The problem was reduced to a simplify case and compared with previous research results. Selected numerical studies indicate that both the embedment depth of the foundation and the degree of soil's nonhomogeneity have an influence on the dynamic compliance coefficient, the torsional angular amplitude and the resultant contact shear stress.