Dynamic response of generalized Gibson saturated soil under an embedded harmonic torsional load

This paper treats the ground soil as a saturated half space. It investigates the dynamic response of a generalized Gibson soil (whose shear modulus increases linearly with depth) subjected to an embeddd harmonic torsional load. It uses Biot's theory of saturated soil and combines the characteristics of torsional vibration. It establishes the dynamic differential equations of generalized Gibson saturated soil. Using the technique of Hankel transform, it solves the differential equations. The tangential displacement and shear stresses in Hankel transform domain with several undetermined coefficients are formulated. Using the boundary conditions including the free surface at the top of the half-space, the tangential displacements near the loading area are continuous, the shear stresses near the loading area are discontinuous and the radiation boundary condition, the undetermined coefficients are solved. Then, the tangential displacement and the shear stress of the nonhomogeneous saturated soil are expressed explicitly in Hankel inverse transform. Selected numerical examples are presented. The numerical results reveal that in the same horizontal plane, both real and imaginary parts of the tangential displacement and shear stress show very significant fluctuations. In the vertical plane, the real parts of the tangential displacement and shear stress increase with depth in the zone above the loading surface, and decrease with depth in the zone below the loading surface. Besides, the influence range of the torsional dynamic load is about two times of the action radius to the loading surface.