无限长均质斜坡降雨入渗解析解

降雨是导致边坡失稳的最主要的环境因素，研究降雨入渗对边坡稳定性的影响，关键和难点是计算降雨入渗在边坡土体中引起的渗流场。采用Fourier积分变换分别对降雨强度小于和大于土体饱和渗透系数情况下的斜坡入渗解析解进行了推导，并给出了这两种情况下斜坡入渗解析解的统一表达式。该解不仅能反映非饱和土特性及斜坡的影响，还能反映当降雨强度大于土体饱和渗透系数时，坡面边界由流量边界转化为水头边界的动态变化过程，便于更全面地对降雨情况下斜坡的入渗规律进行研究。通过与有限元软件的计算结果进行对比，证明该解是稳定可靠的，且其形式简单，计算效率高；该解可精确计算坡面积水时间及任意时间点及空间点的孔隙水压力值，并用于评估降雨入渗对非饱和土斜坡稳定性的影响。

Analytical solutions for rainfall infiltration into homogenous infinite slopes

Rainfall is the main environmental factor for the failure of slopes. To study the effect of the rainfall on the slope stability, the most important thing is to obtain the seepage field in slopes under rainfall condition. By using the Fourier integral transform, the analytical solutions for water infiltration into the slopes under rainfall, of which the intensity is less or more than saturated permeability coefficient of soils, are developed, and the unified analytical expression for water infiltration into the slopes under the two rainfall conditions is presented. The analytical solution can consider the dynamic changing process, in which the boundary condition of slopes changes from flux boundary to pressure one, as well as the properties of unsaturated soils and the effect of slopes. It is convenient to study the laws of water infiltration into slope more comprehensively. By comparing the analytical solutions with those obtained from numerical simulation, it is proved that the analytical solutions are reasonable, simple and efficient in computation. They can be used to calculate the ponding time and the pore water pressure at arbitrary point of the slope at any time, as well as to evaluate the effect of the rainfall infiltration on the stability of unsaturated soil slopes.