SV波在饱和土体自由表面的反射

Reflection of SV Wave at the Free Surface of Saturated Soils

基于饱和两相介质弹性波动方程分析SV波在饱和土体自由表面的反射问题,引入波动方程的势函数解答,求解出二维问题中SV波入射情况下饱和土体自由场的位移、速度、加速度和应力响应。在饱和土体自由场响应解析解基础上,建立SV波入射下饱和土体自由场静、动力有限元模型。建模中考虑了如下几方面因素:(1)在不同分析步,对土体单元赋予不同材料本构。通过*model change命令进行单元生死设定,从而实现在初始应力场平衡的静力状态下采用DuncanChang本构模型,而地震波动输入时采用Davidenkov动力本构模型;(2)采用多孔介质黏弹性人工边界条件,在人工边界上分别施加固相和液相介质的弹簧和阻尼来模拟饱和土体中能量的传播;(3)将地震波转化为作用在人工边界上的等效地震荷载,施加到人工边界节点上;(4)土体单元采用4结点平面应变孔压单元(CPE4P)。有限元计算与解析解比较结果表明:SV波在垂直入射和掠入射时,竖向位移响应为零;在45°左右入射时,水平位移响应最大;60°左右入射时,竖向位移响应最大。这些结论与解析解吻合较好,本文模型为建立土-结构动力相互作用模型打下良好的基础。

Based on the elastic wave equation for a fluid-saturated porous medium,in this study,we analyzed the reflection of an SV wave at the free surface of saturated soils.Then,under incident SV waves,we calculated the displacement,velocity,acceleration,and stress responses in the free field of saturated soils.Based on the analytical solutions to these responses,we established a static-dynamic coupling finite element method model to consider the following factors:(1)We used a Duncan-Chang constitutive model during the initial stress field balance step and the Davidenkov constitutive model during the earthquake input step.(2)We used a viscous-spring artificial boundary for saturated porous media and applied some springs and damps on the artificial boundary to simulate energy propagation in saturated soils.(3)We generated the wave input by the equivalent load of the earthquake on the node of the artificial boundary.(4)We considered soil elements as 4-node plane strain pore pressure elements(CPE4 P).We then compared the numerical results with our analytical solutions and drew the following conclusions:(1)No vertical displacement response appears under vertical and grazing incidences of SV waves.(2)Peak horizontal displacement response occurs when the incident angle of an SV wave is about 45°.(3)The peak vertical displacement response is reached when the incident angle of an SV wave is about 60°.The above conclusions show good agreement with the analytical results.As such,the proposed numerical model provides a good basis for building soil-structure dynamic interaction models.