基于齐次化构建原理的非饱和土瞬态渗流问题解析解

Analytical solution of transient seepage problem in unsaturated soil based on principle of homogeneous construction

非饱和渗流现象在地表广泛存在,其在诸多岩土工程实践方面具有重要价值。通过使用Gardner指数型土水特征曲线及渗透系数函数,对描述非饱和渗流的Richards方程和相应定解条件进行线性化及无量纲化。而后,基于齐次化构造原理对线性无量纲化的入渗控制方程等价分解,并采用分离变量技术进行解析计算,得到了无量纲渗透系数、渗流速率、体积含水量和基质吸力水头的解析表达式。选取典型土层作为研究对象,分析土层稳定渗流时地表入渗速率突增情形下的渗流演变规律。结果表明:湿润峰向土层深处的移动速度随时间逐渐减慢。粗粒土的饱和渗透系数对非饱和渗流由稳态发展到再次稳态有显著的影响。距离地表越近,渗流速度增大到稳态需要的时间越短;距离地表越远,其受地表边界作用发生响应的时间越晚。基质吸力水头和体积含水量的垂直方向上的分布仅取决于边界条件。

Unsaturated seepage phenomenon exists widely on the earth's surface,which has important value in many geotechnical engineering practices.The Richards equation describing unsaturated seepage and the corresponding definite conditions are linearized and dimensionless by using the Gardner exponential soil-water characteristic curve and the permeability function.Then,based on the principle of homogeneous construction,the linear dimensionless seepage governing equation is equivalently decomposed,and the separation variable technique is used for analytical calculation.The analytical expressions for the dimensionless permeability coefficient,seepage rate,volumetric water content and matric suction head are obtained.Two typical soil layers are selected as the research objects to analyze the seepage evolution laws under the sudden increase of surface infiltration rate.The results show that the movement speed of wetting front to the depth of soil layer decreases gradually with time.The saturated permeability coefficient of coarse-grained soil has a significant effect on the development of unsaturated seepage from steady state to re-steady one.The closer to the surface,the shorter the time required for the seepage velocity to increase to the steady state;the farther away from the surface,the later the response time of infiltration rate to the surface boundary.The vertical distribution of matric suction head and volumetric water content depends only on the boundary conditions.