关键词: 非饱和土, 动力响应, 波动方程, 积分变换, 传递矩阵

Abstract:

Considering compression of solid grain and pore fluids, viscous-coupling interactions and inertial force of fluids, the dynamic governing equations for unsaturated soils are established by adopting an exact constitutive formula of saturation. These equations are highly versatile and completely compatible with Biot’s wave equations for the special case of fully saturated soils. The governing equations in cylindrical coordinates are firstly transformed into a group of state differential equations by introducing the state vector. Then the transfer matrix for layered media is derived by means of a Hankel transform. Using the transfer matrix followed by boundary and continuity conditions, solutions of steady state dynamic response for multilayer unsaturated soils are obtained. Numerical examples show that the displacement of the ground surface is mainly affected by stratum within critical depth. The relative position of soft and hard strata has a significant influence on displacement. The displacement of the ground surface increases with saturation degree since dynamic shear modulus will decrease distinctly for most soils, which is the key factor to determine displacement amplitude.

Key words: unsaturated soils, dynamic response, wave equations, integral transform, transfer matrix