The cantilever and tension crack-type collapses

which often occurred in steep rock slopes with nearly horizontal layered stratum

are very common in nature. This kind of perilous rock mass is not only much in quantity but also high in frequency of occurrence in mountainous areas of southwest and northwest China and Three Gorges area in China. The research shows some exogenic geological processes such as differential weathering

river erosion

seawater abrasion and carbonate dissolution can cause rock cavities and cantilevers on the surface of rock slopes. On the basis of field investigation

two kinds of failure modes for cantilever and tension crack-type collapse have been established. The two different failure modes are thick hard rock inter-bedded by thin weak layer and thin hard rock inter-bedded by weak layer respectively. According to the calculation theory of maximum bending stress for cantilever beam

the formulas of limit depth for rock cavity has been derived; and moreover

the time of failure of a collapse has been predicted using the rate of weather denudation for limestone. Analysis results show that the limit depth of rock cavity is positively correlated with the thickness of cantilever and negatively correlated with the depth of tension crack on the top of slope. According to the method of ratio of maximum tensile stress to tensile strength

a formula of safety factor has been deduced. Furthermore

the evaluation criteria for cantilever and tension crack-type collapses are given. Finally

the new method is verified by a typical case study; and the results show that some features such as concise formula and reliable calculation are obvious in the actual project application.