非饱和土路基毛细作用的数值与解析方法研究

Study of analytic and numerical methods for capillary action of unsaturated soil subgrade

通过建立非饱和土毛细作用的孔隙分布的分形模型,推导获得了非饱和土毛细水的最大上升高度,同时基于Richards水分运动微分方程,引入边界及初始条件,基于Laplace变换,得到了毛细作用下非饱和土路基湿度变化的解析解;同时引入算例,将所提出的解析方法计算结果与未简化参数的数值计算结果进行了对比分析;最后考虑不同因素的影响进行了非饱和土路基毛细作用下的湿度变化分析。分析结果表明:解析求解获得的路基湿度变化趋势和未进行参数简化的数值法求解结果基本一致,证明解析解法是合理可信的;路基填筑的初始含水率越大,填土的初始吸力越小,毛细水上升的高度及湿度变化量也相应越小;透水性能较好的路基填土毛细水上升速度较快,但上升高度较小,毛细水可以在较短时间内上升到最大高度;路基的填土类型不同,路基在毛细作用下的湿度变化状态也不同,需要针对不同的填土路基进行相应的防排水措施。

Fractal model for the pore distribution of capillary action of unsaturated soil is built; the maximum rising height of capillary water in unsaturated soil is obtained. Meanwhile, based on Richards equation of water movement, boundary and initial conditions are introduced;based on Laplace transformation, analytical solution of the moisture changes in unsaturated soil subgrade under the action of capillary is obtained. Meanwhile, a calculating example is introduced;the proposed analytical solution and the numerical calculation results without parameters simplification are compared. Finally, the moisture changes under the action of capillary considering different factors in unsaturated soil subgrade are analyzed. The results show that:The results got respectively by analytical method and numerical method without simplifying parameter are consistent. It is proved that the analytic solution is reasonable and feasible. The greater the initial moisture content of subgrade filling is, the smaller the initial suction of the filling is, the smaller the rise height of capillary water and the change amount of moisture are. The rising speed of capillary water with the better subgrade filling permeability is faster. But the rise height is smaller, capillary water can rise to the largest height in a short time. Different types of subgrade filling have different moisture change states of subgrade under the action of capillary. Corresponding waterproof and drainage measures are needed according to different types of subgrade filling.