条形荷载下梯度非均匀非饱和土的动力响应分析

DYNAMIC RESPONSES OF GRADED NON-HOMOGENEOUS UNSATURATED SOILS UNDER A STRIP LOAD

基于多孔介质混合物理论,建立了梯度非均匀非饱和土地基模型,研究了条形荷载作用下梯度非均匀非饱和土地基的动力响应问题.通过傅里叶积分变换和Helmholtz矢量分解原理,获得频域内非饱和土地基动力响应问题的通解,结合回传射线矩阵法和边界条件,求解获得了非均匀非饱和土层中位移、应力以及孔隙压力的计算列式.假设沿深度方向梯度非均匀非饱和土的物理力学性质按幂函数连续变化,通过数值傅里叶逆变换得到了非均匀非饱和土地基中的应力、位移以及孔隙压力等物理量的数值解,分析讨论了土体非均匀性对非饱和土介质动力响应的影响规律.结果表明:土体非均匀性显著改变了非饱和土中竖向位移、正应力和孔隙压力在其深度方向上的振动模态,其中孔隙气压在其深度方向的振动频率随着梯度因子的增加而不断增大,波峰值不断靠近地表处附近;竖向位移随着梯度因子的增大不断减小;正应力和孔隙水压随着梯度因子的增大先增大后减小,并且土体非均匀程度越高,正应力与孔隙水压的幅值越大.

Based on the three-phase porous media mixed theory,a graded non-homogeneous unsaturated foundation model is established and the dynamic response of graded non-homogeneous unsaturated soils subjected to a strip load is addressed.The general solutions of dynamic response for unsaturated foundation in frequency domain are derived by using the Fourier transform and Helmholtz vector decomposition.Then the calculation formula of displacement,stress,and pore pressure of graded non-homogeneous unsaturated soil is derived by combining with the reverberation-ray matrix method(RRMM),boundary conditions and general solutions of dynamic response for unsaturated foundation in frequency domain.Assuming that the continuous variation of physical and mechanical properties of unsaturated soils along the thickness-coordinate by exponential law distribution,the numerical solutions of displacement,stress,and pore pressure then obtained by using numerical inverse Fourier transformation,and the influence of soil heterogeneity on the dynamic response of unsaturated soil is discussed.The results show that the non-homogeneous of unsaturated soil has a considerable effect on the dynamic response of unsaturated soil,which significantly changes the vibration modes of vertical displacement,normal stress and pore pressure in the depth direction.The vibration frequency of pore air pressure in the depth direction increases with the increase of gradient factor,and the peak wave is constantly near the surface.The vertical displacement decreases with the increase of gradient factor,but the normal stress and pore water pressure first increase and then decrease with the increase of gradient factor,and the higher nonhomogeneity of soil is,the greater amplitude of normal stress and pore water pressure is.