瑞利波在非均匀饱和地基中的传播特性

考虑地基横观各向同性和非均匀性，建立孔隙率、密度、剪切模量及渗透系数同时随深度变化的非均匀饱和地基模型，模型中考虑参数间的耦连影响，并引入非均匀因子表征地基的不均匀程度。基于Biot多孔介质理论建立以土骨架位移和孔隙水压力为基本未知量的控制方程，采用微分算子法对控制方程进行解耦求解，推导出非均匀饱和地基中瑞利波的频散方程。将推导结果分别退化到均匀饱和地基和单一弹性地基，验证了结果的正确性。通过数值算例，对非均匀饱和地基中瑞利波的传播速度、衰减系数及位移分布进行分析。结果表明：在低频区，饱和地基的非均匀性对瑞利波传播速度、衰减和位移都有显著影响，质点运动轨迹也由此发生变化；随着频率的升高，这种影响逐渐减小，当频率趋于无穷大时，瑞利波速度收敛于弹性地基中的波速；地基非均匀性增大了瑞利波的传播阻抗性，瑞利波位移加速衰减，传播深度小于均匀饱和地基。随着非均匀性增大，质点竖向位移的衰减快于水平位移，这种差异造成质点椭圆运动轨迹的扁率减小。此外，地基中非均匀土层厚度越小，则地基非均匀程度越高，对瑞利波的传播影响越大。

Propagation characteristics of Rayleigh wave in non-homogeneous saturated foundation

In this study, a model of non-homogeneous saturated foundation is established by considering the transverse isotropy and non-homogeneity of foundation. In this model, the porosity, density, shear modulus and permeability coefficient change along the depth, and the coupling effect between parameters are also considered. Meanwhile, a parameter, non-uniform factor, is introduced to characterize the degree of non-homogeneity of foundation. The governing equation is established based on the Biot porous media theory. The differential operator method is applied to solve the control equation, and then the dispersion equation of Rayleigh wave in non-homogeneous saturated foundation is deduced. Results are verified by degrading the deduced results to homogeneous saturated foundation and single elastic foundation, respectively. Moreover, the propagation velocity, attenuation coefficient and displacement distribution of Rayleigh wave are analyzed using numerical examples. Results show that the non-homogeneity of saturated ground has significant influence on Rayleigh wave propagation velocity, attenuation, and displacement. Additionally, the particle trajectory is changed accordingly. This effect gradually decreases with an increase in the frequency. As the frequency approaches infinity, the Rayleigh wave velocity converges to the wave velocity in homogeneous elastic foundation. The non-homogeneity of foundation increases the impedance of Rayleigh wave propagation and accelerates the attenuation of Rayleigh wave displacement. In addition, the propagation depth is less than that of homogeneous saturated foundation. With the increase in non-homogeneity, the attenuation of vertical displacement of particles is more affected and the attenuation speed is faster than that of horizontal displacement. This difference leads to a small oblateness of the elliptical particle trajectory. Moreover, a smaller thickness of the non-homogeneity soil layer results in more non-homogeneous foundation, which has greater impacts on Rayleigh wave propagation.