有限区域水位下降引发的软土层三维轴对称固结解析解

Analytical solution for axially symmetric consolidation of soft soil layer induced by drawdown of water table in a finite region

基于Biot轴对称三维固结理论，建立有限区域内水位均匀下降引发的软土层固结模型。利用Gibson—McNamee位移函数方法，对耦合固结方程进行解耦，结合Laplace变换和Hankel变换，对模型进行求解，得出计算软土层变形和内部孔隙水压力的解析表达式。通过与PLAXIS软件的有限元计算结果对比，验证了本文解答的正确性。基于水位均匀下降时的解答，推导水位不均匀下降时的土体固结计算方法。根据解析解分析水位下降范围和土体泊松比对土层固结性状的影响。分析结果表明：随着水位下降范围的增大和土体泊松比的减小，土层的沉降速率越来越快，竖向沉降、径向位移逐渐增大，土层内部初期的超静孔压上升幅度越来越大；竖向沉降影响范围为降水范围的2～3倍，径向位移最大位置为降水范围的1-2倍，受土体泊松比影响很小；与无限大范围水位下降情况相比，有限范围内水位下降引发的土层固结有显著的竖向沉降差异和径向位移，因此在实际工程中考虑降水范围是十分必要的。

Based on Biot＇s axially symmetric consolidation theory, a consolidation model of soft soil induced by the uniform drawdown of water table in a finite region was established. Using the displacement function method proposed by Gibson and McNamee, the coupled consolidation equations were decoupled. Then the problem in the paper was solved using Laplace transformation and Hankel transformation. Explicit solutions were obtained for the calculation of the deformation and the excess pore water pressure in the soil layer. The solutions were verified through the comparison with the finite element calculation results in PLAXlS. Based on the solutions in uniform water table drawdown situation, a general calculation method was proposed for non-uniform water table drawdown situation. Based on the analytical solutions, the effects of the extent of the water table drawdown and Poisson＇s ratio of soil on the consolidation properties of the soil layer were analyzed. The results show that as the Poisson＇s ratio becomes smaller and the extent of the water table drawdown becomes larger, the settlement rate becomes faster, the vertical subsidence and radial displacement on the surface of the soil layer becomes larger, and the rise of the excess pore pressure at early stage becomes larger. The effect region of the vertical subsidence and radial displacement are 2-3 times and 1-2 times the extent of the water table drawdown, respectively. Because the differential subsidence and radial displacement are very obvious under finite water table drawdown condition, it is necessary to consider the extent of water table drawdown in the practice.