强降雨作用下岩质边坡失稳的尖点突变分析

根据岩质边坡的地质力学模型,综合考虑降雨、应变软化、水致弱化等因素,给出岩质边坡软弱夹层介质的本构关系,从系统能量的角度出发,建立尖点突变模型,经过数理推导得出岩质边坡失稳的判据。通过实例计算表明：运用刚性极限平衡法计算得边坡稳定性系数Kc为0.989,小于1,即边坡不稳定;运用尖点突变理论计算得边坡系统的控制变量a为0.078,大于0,即边坡稳定,与实际相符。说明本文给出的强降雨作用下岩质边坡稳定性的判据正确,并优于刚性极限平衡法。

Cusp Catastrophe Analysis of Rock Slope Failure under Strong Rainfall

The criterion of the rock slope failure was mathematically inferred and achieved by researching the geomechanical model of the rock slope, giving an overall consideration of the rainfall, strain softening, water weakening and other factors, finding the constitutive relationship of the rock slope＇ s soft interlayer dieletric, establishing the cusp catastrophe model from the perspective of the energy system, etc. Calculations show the side slope is instable when the slope stability factor Kc is 0. 989 and less than 1, by using the rigid limit equilibrium method, and the side slope is stable when the slope＇ s system control vari- ables a is 0.078, greater than 0, by using the cusp catastrophe theory. The result is the same with the reality. Therefore this paper＇ s the criterion to decide the rock slope＇ s stability index under the condition of heavy rainfall in is correct and better than the rigid limit equilibrium method.