强降雨作用下浅层滑坡尖点突变模型研究

采用非线性科学突变理论和数理统计方法分析了浅层滑坡坡体位移与降雨量、边坡稳定系数和坡体饱水面积比的关系，并结合工程实例建立了在强降雨作用下浅层滑坡的尖点突变模型，利用该模型分析了浅层滑坡突发失稳的破坏机理。研究结果表明，浅层滑坡坡体位移与降雨量的关系服从幂函数分布；边坡稳定系数与坡体饱水面积比的关系服从线性分布，边坡稳定系数随坡体饱水面积比的增大而减小；浅层滑坡一般是由强降雨触发的，强降雨是影响浅层滑坡稳定系数大小的最主要外部因素。建立的尖点突变模型揭示了浅层滑坡有时发生在强降雨过后的滞后原因。

Cusp-catastrophic model of shallow landslide under intensive rainfall

The relationship between slope-mass slide displacement and rainfall and the relationship between the safety factor of slope and the saturation-area ratio of slope-mass were analyzed by means of mathematic statistics.A cusp-catastrophic model of shallow landslide was established by means of nonlinear science catastrophe theory connected by engineering concrete example to reveal the sudden instability and failure mechanism of shallow landslide due to intensive rainfall.The relationship between slope-mass slide displacement and rainfall follows the power function distribution.The relationship between the safety factor of slope and saturation-area ratio of slope-mass follows linear distribution,in which the safety factor of slope reduces with increase of the saturation-area ratio of slope mass.Intensive rainfall leads to sudden instability of shallow landslide,and it is the most decisive factor triggering shallow landslide and the external main reason influencing the safety factor of shallow landslide.The reason why shallow landslide comes down sometimes after intensive rainfall is revealed through the established cusp-catastrophic model of shallow landslide.