LAMB’S PROBLEM AND CHARACTERISTIC OF ENERGY TRANSMISSION IN UNSATURATED HALF-SPACE

Abstract

Because unsaturated soil is widely distributed on the earth’s surface, when the traditional saturated two-phase medium theory is used for dynamic analysis, the results are often inconsistent with the actual situation. Aiming at this problem, this paper takes unsaturated elastic half-space as the research object, firstly based on continuum mechanics and porous media theory, and then considers the basic equations of mass conservation equation, momentum conservation equation, constitutive equation and effective stress principle of each phase in unsaturated porous media, and finally, we established a dynamic control equation in which skeleton displacement, pore water pressure and pore gas pressure are basically unknown quantities. Aiming at the dynamic response and energy transmission of the unsaturated half-space surface under the action of vertical concentrated harmonic loads, an axisymmetric calculation model of the classical Lamb problem in the frequency domain is established. The Helmholtz decomposition method is used and the displacement component of the skeleton uses the potential function Φ and Ψ to represent, and combined with the constitutive equation, the analytical solutions of physical quantities such as the displacement field and energy field of the half-space surface under different boundary conditions are obtained. Finally, influencing factors such as load parameters (excitation frequency) and material parameters (saturation, permeability coefficient) are analyzed and discussed through numerical examples. The results show that: (1) An increase in saturation or a decrease in excitation frequency will increase the surface displacement amplitude of the unsaturated half-space; (2) When the permeability coefficient drops to a critical value, the surface displacement amplitude will tend to a limit value, and the influence of permeability coefficient under permeable (gas) boundary and impermeable (gas) boundary conditions shows obvious difference.