Aiming at the lack of quantitative judgment on the spatial distribution of the toppling deformation fracture surface of the anti-dip layered rock slope

this paper develops an independent cantilever beam model and an independent simply supported beam model for the rock slab toppling and breaking based on the analysis of the geological prototype and deformation mechanism. The proposed models can consider the self-weight of the rock layer

the weight of the overlying rock layer

the lateral pressure

and the friction between the rock layers. The maximum tensile stress failure criterion of the slab beam was used to deduce the critical fracture depth formula of the rock stratum in each stage of the toppling deformation. The proposed method was verified by geological prototypes. The slope shape parameters of each stage of toppling deformation were obtained by centrifugal test

and the fracture depth of each stage was quantitatively evaluated in this paper. The research shows that the theoretical model can calculate the fracture length of rock formations at various stages

such as the shear dislocation between layers of toppling deformation

weak toppling failure

and intensive toppling failure. The fracture length is positively correlated with the internal friction angle

the thickness

and the tensile strength of rock strata

and is negatively correlated with the distribution elevation of rock strata

tensile stress and the weight of rock beam. According to the mechanical parameters of each stage of the toppling deformation

the distribution positions of the fracture surfaces of the toppling rock strata at all levels are calculated

and the results are consistent with the geological prototype and centrifugal test results.