基于Richards传导方程的降雨型浅层滑坡稳定性分析

基于描述流体在多孔介质中毛细传导行为的Richards方程，Iverson（2000）推导了斜坡中任意深度处的孔隙水压力对降雨入渗的响应方程，本文在此基础上进一步推导了降雨型浅层滑坡稳定性计算表达式。该表达式考虑了坡体非饱和区饱和度和坡体重度在降雨入渗过程中的变化。算例结果表明：降雨入渗过程中浅层滑坡稳定性系数逐渐降低，且在降雨停止后的较短时间内达到最小值，之后逐渐增大，但增大速率比降低速率要低。这种变化趋势在不同初始地下水位竖向埋深情况下是一致的，但稳定性系数随初始地下水位竖向埋深增大而减小。降雨历时和降雨入渗率对浅层滑坡的稳定性均有显著影响，表现为降雨历时和降雨入渗率越长（大），稳定性系数降低幅度越大，但后者的影响受到滑坡体竖向渗透系数的控制。

ANALYSIS OF THE STABILITY OF SHALLOW LANDSLIDE TRIGGERED BY RAINFALL BASED ON RICHARDS'S COUDUCTION EQUATION

Based on the Richards's equation which describes the behaviour of capillary conduction of liquids in porous mediums, Iverson derived the equation which expresses the response of the pore-water pressure at any depth in the slope to rainfall infiltration in 2000. The formula which calculates the factor of safety of the shallow landslide trigged by rainfall infiltration was derived on the basis above in this paper. The formula takes account of the variation of the gravity and the degree of saturation in the unsaturated area in the slope under the rainfall infiltration. The results of the case study show that: the factor of safety of the shallow landslide gradually decreases with the rainfall infiltration and reaches the minimum value in a short time after the cease of rainfall infiltration. After that the factor of safety gradually increases with the rate which was lower than the one of decreasing. The variation trends above at the different initial vertical groundwater depths are similar; however, the factor of safety decreases with the increase of initial vertical groundwater depth. The duration of rainfall infiltration and rainfall infiltration rate both have the marked impact on the factor of safety of shallow landslide. The impact show that the larger of the rainfall infiltration rate or longer of the duration of rainfall infiltration, the larger decreasing amount of factor of safety is. However, the impact caused by the rainfall infiltration rate was controlled by the vertical permeability coefficient of the landslide.