饱和土中伴有排水问题的爆炸场动力反应Green函数计算

饱和土在动力作用下伴有排水的反应是工程中常见的现象,其计算也是一个非常复杂的数学力学问题。根据已经求得的集中力作用下两相饱和介质Green函数基本解,得到球坐标的扩张源固相位移时域Green函数的表达式。再以物理的方法推导出球坐标中心扩张源时域流相的压力Green函数;以及相对应的注入流相后,场点的时域固相位移Green函数和流相压力Green函数的表达式。再结合导出的两相饱和介质Lamb方程,进行动力排水问题的计算,解决饱和土爆炸场中伴有排水的动力反应计算问题。

Green function for calculation of dynamic response of explosion field with drainage in saturated soil

It is a common phenomenon that vibration or shock of explosion field is accompanied with drainage under dynamic load in saturated soil.Based on the already derived 3-dimensional Green function of a two-phase saturated medium in time domain,the displacement Green function of solid-phase of a two-phase saturated medium with expansion source in spherical coordinate Grr(basic solution) was deduced.The corresponding pressure Green function of solid-phase G4r was also obtained with physical method.Likewise,the displacement and pressure Green functions Gr4 and G44 of fluid-phase were provided.Linking with Lamb integral formula(the representative theorem) for two-phase saturated medium,the dynamic responses of the explosive field with drainage in saturated soil were calculated.The nondimensional displacement,pore pressure and drainage flux were illustrated by figures in the paper.