外荷载随时间变化下软土地基一维大变形固结通解

The general analytical solutions for one-dimensional large deformation consolidation of soft soils with time-dependent loading

对于外荷载随时间变化下软土地基一维大变形固结问题,基于已有固结控制方程,对方程中控制变量进行变量代换,并采用分离变量法求得一维大变形固结通解。该通解所用求解方法简便,解答形式简单,便于运算。利用所求通解,给出几种常见加荷形式下固结解析解的表达式。通过对所得特解展开分析,并将所提解析解和有限差分解进行对比,验证所提解析解的正确性。基于所求解答,对固结性状展开分析。结果表明:在两级瞬时加荷形式下,延长第1级加荷时间会减慢固结速率,并降低超孔隙水压力最大值;在两级线性加荷形式下,加荷速率增大到一定程度后对固结速率的影响较小;在循环加荷形式下,循环加荷时间越长,固结度曲线趋于稳定后变化幅度越大;当外荷载随时间变化时,最终荷载越大,沉降固结速率越快,而孔压固结速率越慢。分析结果可为软土地基的堆载施工过程提供理论指导。

For the problem of one-dimensional large deformation consolidation of soft soils with time-dependent loading,based on the existing governing equation of consolidation,the general analytical solutions for one-dimensional large deformation consolidation are obtained by using the method of variable substitution and separation variable.The method used in solving the general analytical solutions is simple,and the solutions have a clear form,which is convenient for calculations.Referring to the general analytical solutions,the expressions for analytical solutions of consolidation under several common loading patterns are given.By analyzing the specific analytical solution presented in the paper and comparing the proposed analytical solution with finite difference solution,the correctness of the proposed analytical solutions is verified.Based on the solutions proposed,the consolidation behaviors are analyzed.The results show that under two-stage instantaneous loading pattern,the consolidation rate slows down and the maximum value of excess pore water pressure decreases with the extension of first-stage loading time.Under two-stage linear loading pattern,the effect of increasing the loading rate on the consolidation rate is small when the loading rate increases to a certain extent.Under cyclic loading pattern,with the increase of cyclic loading time,the variation range of the consolidation degree curves becomes larger after it tends to be stable.Under the time-dependent loading,the consolidation rate defined by settlement increases with the increase in the final loading,while the consolidation rate defined by pore water pressure decreases.The analysis results can provide theoretical guidance for the actual loading construction process of soft soils.