中文摘要：

对基于Biot固结理论的层状土体中抽水引起三维流固耦合问题进行了研究,根据半解析数值原理建立了该问题的有限层求解格式,其中利用形函数中三角函数系的正交性实现了加权余量方程按不同级数项的解耦。在编制计算程序验证有限层法正确性的基础上,利用有限层计算结果研究了泊松比、渗透各向异性和抽水形式对地表沉降的影响。结果表明：泊松比和渗透各向异性对地表沉降均有较大影响,在抽水井附近抽水形式的影响也不可忽略。最后通过算例对比分析说明了有限层法处理土体层状非均质的能力。

英文摘要：

Based on the Biot＇s theory,the coupled consolidation of multilayered soil due to pumping is studied.The finite layer numerical scheme for solving the above problem is presented by using the semi-analytical numerical analysis principle.Moreover,by means of the orthogonality of the trigonometric function series in shape functions,the weighted residual equations are decoupled into several independent ones associated with different series of modes.A computer program is developed for solving the finite layer equations,and the validity of the present method is performed through the comparison between the numerical results and other available solutions.The influences of Poisson＇s ratio,the anisotropy of permeability and pumping method on the deformation and the subsidence of the soil are studied based on the finite layer solutions.The finite layer numerical results show that the above three factors have great influences on the subsidence of the soil due to pumping.The influences of the pumping method connot be ignored near the pumping wells.Finally,the applicability of the present method in analyzing pumping in multilayered soil is demonstrated.