层状非饱和土地基的轴对称稳态动力响应  

Axisymmetric steady state dynamic response of layered unsaturated soils

作　　者：徐明江 魏德敏[2] 何春保[3] 

机构地区：[1]广州市建筑科学研究院有限公司 [2]华南理工大学土木与交通学院 [3]华南农业大学水利与土木工程学院

出　　处：《岩土力学》2011年第4期1113-1118,1124,共7页Rock and Soil Mechanics

基　　金：国家自然科学基金资助项目(No.10272046)

摘　　要：考虑土颗粒、孔隙流体的压缩性及各相物质间的黏性、惯性耦合作用,采用理论上更加严谨的饱和度本构关系式,建立了非饱和土的动力控制方程。该组方程与饱和土的经典Biot波动方程完全兼容,因此,具有更广泛的适用性。通过引入一组状态向量,在圆柱坐标系下将非饱和土满足的波动方程转化为状态方程组,利用Hankel变换,求解状态方程组,得到了传递矩阵。结合边界条件及层间接触连续条件,求解了层状非饱和地基的稳态动力响应问题。数值算例表明:土层对地表动位移的影响主要集中在临界深度范围内;软硬土层的相对次序对地表动位移幅值有显著影响;饱和度增大会引起土的物理参数发生相应的改变,尤其是动剪切模量通常降幅较大,而动剪切模量是决定位移幅值的关键因素,最终的结果是导致地表动位移幅值明显增大。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.

关 键 词：非饱和土 动力响应 波动方程 积分变换 传递矩阵 

分 类 号：TU435[建筑科学—岩土工程]