基于降阶法的土体一维非线性固结简化解析解

Simplified analytical solution of one-dimensional nonlinear consolidation of soil based on reduced order method

传统的土体固结计算均采用二阶偏微分方程,但针对非线性固结这类复杂问题,采用二阶偏微分方程求解,在大多数情况下都难以得到解析解。为此,通过降阶处理,并引入一个综合反映土体非线性特征的等效系数,给出了一个考虑土体非线性特征的简化固结解析解。该解析解可以用初等函数表示,可以更方便地计算土体各阶段的固结度和超孔隙水压力。该解析解与差分数值解在固结前期误差在4.5%以内,在固结后期最大误差在10%左右。应用该解析解,很容易考虑其他固结影响因素,为分析固结问题提供了一个新思路。

The second-order partial differential equation is used in the traditional calculation of soil consolidation.However,it is difficult to obtain analytical solutions in most cases for nonlinear consolidation problems. To solve this problem,a simplified analytical solution considering the nonlinear characteristics of soil is presented by reducing the order and introducing an equivalent coefficient that reflects the nonlinear characteristics of the soil.The analytical solution can be expressed by elementary function,which can more conveniently calculate the degree of consolidation and the excess pore water pressure at each stage of soil. The error between the analytical solution and the differential numerical solution is less than 4.5% in the early consolidation stage,and the maximum deviation is about 10% in the late consolidation stage. Based on the analytical solution,it is easier to take other factors affecting consolidation into account,which provides a new way to deal with the consolidation problem.