半透水边界砂井地基的真空预压固结解

针对砂井地基顶部存在垫层和底部存在下卧层的现状，采用半透水边界来反映它们对砂井地基固结的影响。假定地基变形符合等应变条件，考虑水平向渗透系数沿半径发生变化，建立了上下边界为半透水边界时真空预压砂井地基的固结理论，通过分离变量法获得固结度和沉降的级数解析解答，分析了底部透水系数、顶部透水系数、井阻、渗透系数沿半径分布特性对砂井地基固结度和沉降的影响规律。研究表明，当底部半透水时，最终负孔压和有效应力呈现出沿地基深度衰减的变化规律。当其它条件相同时，底部透水系数越大的地基固结度越大,但最终沉降和径向固结时间因子相同时的固结沉降却越小。当底部边界不透水时，最终沉降不会随着顶部透水系数改变而改变。但当底部边界半透水或完全透水时，最终沉降随着顶部透水系数增大而增大。顶部透水系数越大的地基固结度越大，径向固结时间因子相同时的固结沉降也越大。均匀井阻的大小不会影响负压最终竖向分布特性，也不会改变最终沉降，但会明显降低砂井地基固结度，延长固结完成时间。渗透系数径向分布模式会对砂井地基的固结度产生影响。工况一计算的固结度最大，工况二计算的固结度最小，工况三计算的固结度介于工况一和工况二之间。半透水边界对真空预压砂井地基固结过程的影响规律与堆载预压砂井地基相比存在明显不同。

Consolidation Solution for Sand-drained Ground with Impeded Boundaries Under Vacuum Preloading

In view of the facts that there were a cushion on the top and a substratum below the bottom of sand-drained ground, impeded boundaries were used to describe their effect on consolidation process of sand-drained ground. After assuming that ground deformation satisfies the condition of equal vertical strain and taking into account the radial variation of horizontal permeability coefficient, consolidation theory was formulated for sand-drained ground with top and bottom impeded boundaries under vacuum preloading. The series analytical solutions of consolidation degree and settlement were achieved by the separated variable method. The effect of the pervious coefficient of top boundary, the pervious coefficient of bottom boundary, well resistance and the radial distribution feature of permeability coefficient on the consolidation degree and settlement of sand-drained ground were analyzed. The researches show that final negative pore pressure and effective stress are exhibited to decrease with the depth of ground. When the other conditions are same, the ground with big bottom pervious coefficient has big consolidation degree, but has small final settlement and the consolidation settlement at same radial consolidation time factor. When the bottom boundary of ground is impervious, the final settlement of ground cannot change with the top pervious coefficient. But when the bottom boundary of ground is impeded or completely permeable, the final settlement increases with top pervious coefficient. The ground with big top pervious coefficient has big consolidation degree, and has big consolidation settlement at the same radial consolidation time factor too. Resistance of sand drain neither affect the final vertical distribution features of negative pressure, nor change the magnitude of the final settlement. But the resistance of sand drain can obviously reduce the consolidation degree of sand-drained ground and extend the finish time of consolidation. The radial distribution mode of permeability coefficient can affects the consolidation degree of sand-drained ground. The consolidation degree of mode I is the biggest, the consolidation degree of mode II is the smallest, and the consolidation degree of mode III fall between mode I and mode II. The effect laws of impeded boundary on the consolidation process of sand-drained ground under vacuum preloading are obviously different from those under surcharged preloading.