岩质边坡稳定性评价的尖点突变理论模型

A Cusp Catastrophe Theory Model for Evaluation of Rock Slope Stability

考虑岩质边坡后缘张裂隙中的孔隙水压力及地下水对软弱结构面的物理化学作用,将软弱结构面分为应变硬化区和应变软化区,建立单平面滑动破坏的岩质边坡力学模型,引入尖点突变理论,建立尖点突变模型,推导岩质边坡突变失稳的充要力学条件判据,并重新推导极限平衡法的临界稳定系数。结果表明,分叉集方程等于0为岩质边坡突变失稳充要力学条件判据;由于滑面处含水量不同,稳定系数小于1,边坡不一定会发生失稳;稳定系数大于1,边坡也不一定稳定。

Considering the pore water pressure in tensile cracks at the trailing edge of the rock slope and the physicochemical effect of groundwater,this study divided the weak structural plane into strain hardening area and strain softening area,and established a mechanical model of rock slope with single plane sliding failure.Introducing the theory of cusp catastrophe,this work established a cusp catastrophe model and derived mechanical condition criterion of catastrophe instability of rock slope,then re-derived the critical safety coefficient of limit equilibrium.Results show that when the bifurcation set equation equals to 0 is the mechanical condition criterion of catastrophe instability of the rock slope.Due to the different water content at the slip surface,when the stability coefficient is less than 1,the slope does not necessarily become unstable,when the stability coefficient is greater than 1,the slope is not necessarily stable.