层状边坡倾倒变形多级折断面分布深度计算模型

针对反倾层状岩质斜坡倾倒变形折断面空间展布缺乏定量判断的问题，以地质原型和变形机制分析为基础，考虑岩层自重、上覆岩层盖重、侧向压力、岩层间的摩擦力等作用，提出了岩板倾倒折断的独立悬臂梁模型和独立简支梁模型。采用板梁的最大拉应力破坏准则，推导出了倾倒变形各阶段岩层的临界折断深度公式。利用地质原型对推导的公式进行了验证，并通过离心试验获取了倾倒变形各阶段的坡形参数，对边坡各阶段折断深度进行了定量评价。研究表明：理论模型可计算倾倒变形层间剪切错动、弱倾倒破坏、强倾倒破坏等各阶段岩层的折断长度；岩层折断长度与岩层分布高程、拉应力、岩梁自身重度呈负相关，与岩层内摩擦角、岩层厚度、抗拉强度呈正相关；根据倾倒变形各阶段力学参数，计算倾倒体各级折断面分布位置，结果与地质原型和离心试验结果吻合。该研究成果对倾倒变形边坡稳定性评价具有一定的理论和实际意义。

Calculation model of multistage fracture surface distribution depth of layered slope toppling deformation

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.