3D NON-AXISYMMETRICAL DYNAMIC RESPONSE OF UNSATURATED SOILS

The paper derives dynamic governing equations for unsaturated soils by adopting Bishop’s effective stress formula and van Genuchten’s capillary pressure function. These equations consider the compression of solid grain and pore fluids, the viscous-coupling interactions and the inertial forces of fluids. By introducing the displacement function and making use of Cauchy-Reimann conditions, the 3D wave equations in rectangular coordinates are transformed into two uncoupled governing differential equations. Then, with the help of double Fourier transform, general solutions of displacement and stress as well as pore pressure are obtained. With boundary conditions imposed, dynamic responses of unsaturated half-space under arbitrary distributed harmonic loads are solved. The influence of saturation on dynamic shear modulus is considered in numerical calculations, and an empirical formula is raised here to describe the relations between saturation and shear modulus. Numerical results show that (1) with the increase of saturation, the displacement of ground surface increases firstly, then decreases when soils are nearly saturated; (2) permeability of pore and drainage conditions of ground surface have insignificant effects on the displacement when soils are nearly saturated.