非饱和土半空间Lamb问题及能量传输特性

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

地球表面绝大多数土层处于非饱和状态,故采用传统饱和两相介质理论进行动力学分析时,结果往往与实际情况不符.针对这一问题,本文以非饱和半空间作为研究对象,基于连续介质力学和多孔介质理论,考虑非饱和多孔介质中各相的质量守恒方程、动量守恒方程、本构方程以及有效应力原理等基本方程,建立了以骨架位移、孔隙水压力和孔隙气压力为基本未知量的动力学控制方程.针对非饱和半空间表面在竖向集中简谐荷载作用下的动力学响应及能量传输问题,建立了频域内经典Lamb问题的轴对称计算模型,采用Helmholtz分解法,通过引入势函数Φ和Ψ表示骨架的位移分量,结合本构方程获得了不同边界条件下半空间表面位移场和能量场等物理量的解析解答,并通过数值算例对荷载参数(激振频率)、材料参数(饱和度、渗透系数)等影响因素进行了分析与讨论.结果表明:(1)饱和度的升高或者激振频率下降,都会提高非饱和半空间的表面位移幅值;(2)当渗透系数下降至一临界值时,地表位移幅值会趋于一极限值,并且透水(气)边界与不透水(气)边界条件下渗透系数的影响表现出明显的差异性.

Because unsaturated soil is widely distributed on the earth’s surface,when the traditional saturated twophase 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 functionΦandΨto 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.