【摘要】 离散元法适用于模拟露天开采后的非均质岩质台阶边坡在重力荷载作用下的非线性变化，但缺乏明晰量化的边坡失稳判据，难以精确获取边坡安全系数。针对该问题，基于尖点突变理论结合重力增加法，建立了边坡水平方向平均位移与重力系数的尖点突变模型，将边坡临界失稳判据量化为确定的位移突变特征值。通过对不同节理间距和连通率进行组合模拟，揭示了不同组合下边坡临界位移及安全系数变化规律。分析表明：该模型能够有效确定边坡失稳临界位移及安全系数；当节理连通率为0.70时，边坡的临界失稳位移整体高于节理连通率为0.70以上的组合；随着节理间距的增大，边坡临界失稳时沿节理面形成范围更大的滑体，对应较大的临界失稳位移。该研究结果为节理岩体区域边坡位移监测及位移预警阈值提供了理论依据。更多还原

【Abstract】 The discrete element method is particularly effective for simulating the nonlinear deformation of heterogeneous rock slopes subjected to gravitational loads following open-pit mining. Traditional methodologies often suffer from ambiguous criteria for determining slope instability,thereby complicating the accurate assessment of the slope’s safety factor. To address this issue,a cusp catastrophe model was developed,establishing a relationship between the average horizontal displacement of the slope and the gravitational coefficient. This model quantifies the critical instability criterion as a definitive displacement catastrophe value.Using the discrete element program MatDEM,simulations were conducted with varying combinations of joint spacing and connectivity to examine the changes in critical displacement and safety factors under different conditions. Case analyses indicate that this model effectively determines the critical displacement and corresponding safety factor at the point of slope failure. Notably,when joint connectivity is 0.70,the critical instability displacement is generally higher compared to scenarios with greater connectivity. For joint spacings ranging from 1 to 3 meters,an increase in spacing results in a larger sliding mass along the joint surface,which consequently leads to a rise in the critical instability displacement. The gravity increase method,grounded in cusp catastrophe theory,models the evolution of slopes under realistic conditions by incrementally increasing the gravitational load. This approach is particularly well-suited for jointed rock masses that exhibit complex nonlinear deformation behaviors. Unlike the strength reduction method,it obviates the need for recalibrating material parameters before each calculation,thereby enhancing computational efficiency. The study’s findings indicate that joint spacing and connectivity have a significant impact on slope stability. With uniform joint spacing,increased connectivity results in a lower safety factor,whereas with uniform connectivity,larger joint spacing leads to a higher safety factor. These findings are consistent with practical engineering conditions,underscoring the importance of considering joint spacing and connectivity in slope stability analysis. The developed model and results provide a scientific basis for determining monitoring point placement and setting warning thresholds for slope displacement in jointed rock mass regions.更多还原