均质非饱和边坡降雨入渗解析解及在黄土边坡的应用

Analytical solution of rainfall infiltration in homogeneous unsaturated slope and its application in loess slope

降雨诱发的黄土边坡失稳非常普遍。建立黄土边坡渗流场计算模型,基于非饱和土渗流控制方程。采用VG函数和Gardner函数分别描述土-水特征曲线和渗透系数曲线,利用行波约化和级数展开法推导降雨入渗解析解。利用数值反演法将模型试验数据对土-水参数拟合,证明了该解析解的有效性。对比分析试验值与解析解在不同工况下体积含水率分布规律,分析结果表明:边坡试验模型中的浅层测点体积含水率试验值与解析解较为接近,试验值在浸润锋下移的过程中所达到的体积含水率峰值相比解析解较小;边坡试验模型中的深层测点体积含水率试验值与解析解在前期存在一定误差,深层测点体积含水率解析解在初期增长速度相较于试验值较快,主要原因是较深土层浸润锋的滞后性。

Rainfall-induced instability of loess slopes is very common. Based on the governing equation for unsaturated seepage, a computational model of the seepage field of loess slope is established. The VG function and Gardner function are used to describe the soil-water characteristic curve and permeability function, respectively. The analytical solution of rainfall infiltration is derived by using traveling wave approximation and series expansion method. The validity of the analytical solution is demonstrated by fitting the model test data to the soil-water parameters using the numerical inversion method. By comparing and analyzing the distribution law of volumetric water content between the experimental value and the analytical solution under different working conditions, it is found that the test values of volumetric water content at shallow measurement points in the slope test model are closer to the analytical solution, and the peak volumetric water content reached during the downward movement of the wetting front is smaller compared to the analytical solution;the test value of volumetric water content of deep measurement points in the slope test model has some error with the analytical solution in the early stage, and the analytical solution of volumetric water content of deep measurement points grows faster in the early stage compared with the test value, which is mainly attributed to the hysteresis of wetting front in deeper soil layers.