The overall failure mode of a tower-shaped unstable rock mass associated with bottom compression-induced fracturing frequently occurs on the steep-high slope with a gentle dip angle in the karst regions

and its damage-catastrophe mechanism belongs to a key issue in the mountainous disaster discipline. Taking a collapse case of Zengziyan unstable rock mass #W12 in Nanchuan District of Chongqing

China

for example

a damage-catastrophe geomechanical model considering the load and the water-weakening effect was built. A damage constitutive equation and a total damage degree evolution equation were derived based on the strain equivalence principle

and the water-weakening function was developed into a cubic function in one unknown for the softening coefficient. Then

the geomechanical model was simplified into an equivalent spring model and the damage-fold catastrophe model was established by the energy balance theory. Finally

the failure criterion and eigenvalue expression of critical displacement mutation for the tower-shaped unstable rock mass were obtained. The results show that when the unstable rock mass #W12 fails

the control variant determining the stability of a fold catastrophe model is –0.003 251

which is less than zero

demonstrating that the system turns into an unstable state. The initial calculated value of the theoretical displacement mutation of 148.70 mm is smaller than the first inflection point of the measured value of 154.34 mm

and the relative error is about 3.65% which tends to be safer. The theoretical damage constitutive curve and evolution curve are consistent with the numerical results obtained in the literature

suggesting that the theoretical model has a good applicability. The research outcome can be applied to predicting the damage evolution process and the eigenvalue of critical displacement mutation for the compression-induced fracturing and failure of a tower-shaped unstable rock mass. It also provides a theoretical basis for monitoring and early-warning of the steep-high unstable rock mass collapse and disaster prevention and mitigation in limestone area.