Torsional dynamic characteristics of rigid disc on generalized Gibson stratum

Dynamic characteristics of a rigid disc,which rests on a saturated stratum with shear modulus increasing linearly with the depth,subjected to harmonic torque,are investigated.On the basis of Biot’s theory of the saturated soil,dynamic differential equations of generalized Gibson soil are established.Considering the traits of torsional vibration,the differential equations are solved by using the technique of Hankel transform,and the shear stresses and radial displacement in Hankel transform domain are formulated.Considering the boundary conditions at the upper and lower surfaces of the stratum,a set of dual integral equations are established.By mathematical method,the dual integral equations are solved,and the dynamic compliance coefficient and angular amplitude of the foundation are expressed explicitly.Numerical examples are presented to investigate the influence of the shear modulus gradient and permeability coefficient on the results.