砂墙地基二维固结自由应变解

将含竖向排水体地基的三维固结变形问题等效为平面应变问题进行数值分析时，砂墙地基二维固结解析解答是合理确定其等效固结计算参数的重要依据。为辨析现有砂墙地基等应变固结近似解答的适用性，针对微单元土体严格的二维固结微分方程，考虑对地基固结有重要影响的井阻作用，以及涵盖完全透水和不完全透水的更一般边界面排水条件，推求得到了其自由应变解答。并与现有解答进行对比分析，同时，分析了泊松比效应以及水平和竖向排水对地基固结的影响。结果表明，现有砂墙地基的等应变固结解答虽然近似，但已有足够精确；砂墙地基以水平向固结为主，竖向固结几乎可以忽略不计；地基固结速率随着泊松比的增大而增大，在将竖向排水体等效为砂墙时，应考虑其作用影响。

Free-strain solutions for two-dimensional consolidation with a sand-wall drain

Three-dimensional problems of consolidation with vertical drains are sometimes simplified as plane-strain ones to facilitate the operation of numerical analyses. It requires establishing an equivalent relationship between the three-dimensional consolidation with a vertical drain and the two-dimensional consolidation with a sand-wall drain. Analytical solutions for two-dimensional consolidation with a sand-wall drain are, therefore, the important basis for determining the equivalent consolidation parameters. To analyze the applicability of the existing approximate solutions of equal-strain consolidation with a sand-wall drain, an analytical solution for free-strain consolidation is derived based on the rigorous governing equations for soil element volume. An important effect of drain resistance on consolidation is considered. A general drainage boundary condition is taken into consideration, including fully drained condition and impeded drainage condition. Comparisons are made between the existing solutions and the proposed solution. In addition, the effects of Poisson’s ratio, vertical and horizontal drainage on consolidation are investigated. It is shown that the existing solutions for consolidation with a sand-wall drain are approximate but sufficiently accurate. The consolidation is mainly governed by horizontal consolidation. Vertical consolidation is however negligible. Consolidation rate increases with the increase of Poisson’s ratio. This factor should be considered when a sand-wall drain is equivalent to a vertical drain.