The unsteadiness of rock slopes is often triggered by water-softening. Based on catastrophe theory and the general constitutive equations of the strain-softening section in the weak interlayer, the present study investigated the catastrophic failure mechanism of rock slopes. Using theoretical analysis, the cusp catastrophe model for the failure of a rock slope with a strain-softening section in the soft rock strata was established, and the balance equation, bifurcation set, and formulas of displacement jumping and energy jumping were deduced. The changes of displacement jumping and energy jumping following the variation of the systematic rigidity ratio are discussed with regard to the occurrence of water-softening. Regardless of which type of constitutive equation is adopted, the control variables and sudden jump values of the rock slope’s displacement and energy can be determined by the systematic rigidity ratio when the systematic rigidity ratio is constant. Whether a rock slope is stable or not depends only on the mechanical and geometrical parameters of the system itself, and is unrelated to the constitutive equation of the strain-softening section. The sudden jump values of the displacement and energy are both inversely proportional to the systematic rigidity ratio. By comparing the formula of the systematic rigidity ratio deduced under different constitutive equations with the results obtained by other studies, the results of the present study were verified through the consideration of actual engineering projects. Based on catastrophe theory, the present paper discusses the principle of correctly selecting a constitutive equation to assess the rock slope stability in practical engineering.

岩石边坡的不稳定通常是由水软化引起的。基于突变理论和弱夹层应变软化段的一般本构方程，研究了岩质边坡的破坏机理。通过理论分析，建立了软岩地层中具有应变软化段的边坡破坏的尖点突变模型，推导了平衡方程，分叉集，位移跳跃和能量跳跃的公式。针对水软化的发生，讨论了随着系统刚度比的变化而引起的位移跳跃和能量跳跃的变化。无论采用哪种类型的本构方程，当系统刚度比恒定时，可以通过系统刚度比来确定边坡位移和能量的控制变量和突跳值。岩石边坡是否稳定，仅取决于系统本身的力学和几何参数，而与应变软化段的本构方程无关。位移和能量的突然跳跃值都与系统刚度比成反比。通过将在不同本构方程下得出的系统刚度比的公式与其他研究得出的结果进行比较，通过考虑实际工程项目来验证本研究的结果。根据巨灾理论，