位移函数法求解饱和层状地基中的抽水问题

Analysis of pumping in saturated multi-layered soil by using displacement function method

运用Biot固结理论,对饱和层状地基中的抽水问题进行了求解。从轴对称问题的Biot固结方程出发,通过引入位移函数以及将各个量进行Laplace和Hankel变换,得到了位移、应力、孔压和流量在z=0和任意深度处的传递矩阵关系。将这个传递矩阵关系应用于多层地基的每一层,并结合多层地基的连续条件、边界条件以及抽水作用面的连续条件,求得了饱和层状地基的抽水问题在Laplace-Hankel变换域内的解答。通过相应的逆变换,得到了该问题的真实解答,并分析了泊松比、抽水形式和时间对饱和层状地基地表位移的影响。

The problem of pumping in saturated multi-layered soil is solved by using the theory of Biot＇s consolidation. Starting from the governing equations of axisymmetric Biot＇s consolidation, introducing the displacement functions and taking the Laplace and Hankel transform to each variable, the transfer matrix relationship among displacement, stress, excess pore water pressure and flux at z = 0 and any arbitrary depth is obtained. The problem of pumping in saturated multi-layered soil in the transformed domain can be obtained by applying the relationship to each layer of multi-layered soil, and by considering the continuity conditions and boundary conditions of multi-layered soil and pumping horizon plane. The actual solutions can be acquired by inverting the Laplace-Hankel transform. The influence of Poisson＇s ratio, pumping method and time on the surface displacement of multi-layered soil is analyzed.