Pillars are often reserved asymmetrically in the mining process. The roof deflection curve under non-equal span conditions of adjacent stopes is derived by considering the roof-pillar system as a rock beam-pillar model. The pillar instability condition under asymmetric mining is determined based on instability theory and cusp catastrophe theory. Pillar burst represents the equilibrium stability of the roof-pillar system. The pillar failure may be in a violent manner or a gentle manner, depending on the post-peak stiffness ratio of the roof-pillar system. By calculating the factor of safety (FOS) and roof-pillar stiffness ratio K , the pillar stability with different stope spans can be evaluated. The theoretical results are validated by comparison with a case study and numerical simulation. When the stope spans are not equal, the pillar is affected by small-eccentric compression. Four pillar failure patterns under eccentric compression are proposed and explained. The main factors affecting pillar burst appear to include the geometric parameters and mechanical properties of the roof-pillar system. It is difficult to change the mechanical properties, but the stiffness ratio K can be increased by improving the geometric parameters, so as to minimize the burst tendency. Once K < 1 and the critical compression failure load is reached, the pillar on the larger stope span side fails first, and then, the whole pillar loses its stability. Considering the external work during the pillar unstable failure, the rockburst energy index is optimized.

中文翻译：

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基于尖点突变模型的非对称开采中柱爆失稳机制

在采矿过程中，支柱经常被不对称地保留。将顶柱系统视为岩梁柱模型，推导出相邻采场非等跨条件下的顶板挠度曲线。基于失稳理论和尖点突变理论确定了非对称开采下的支柱失稳条件。支柱爆裂代表屋顶支柱系统的平衡稳定性。立柱失效可能是剧烈的，也可能是温和的，这取决于顶柱系统的峰值后刚度比。通过计算安全系数（FOS）和顶柱刚度比 K ，可以评估不同采场跨度的柱稳定性。通过与案例研究和数值模拟的比较来验证理论结果。当采场跨度不相等时，支柱受到小偏心压缩的影响。提出并解释了偏心压缩下的四个支柱破坏模式。影响支柱爆裂的主要因素似乎包括顶柱系统的几何参数和力学性能。机械性能很难改变，但可以通过改善几何参数来提高刚度比 K，从而最大限度地减少爆裂倾向。一旦 K < 1 且达到临界压缩破坏载荷，较大采场跨度一侧的支柱首先破坏，然后整个支柱失去稳定性。考虑柱体不稳定破坏时的外功，对岩爆能量指标进行优化。影响支柱爆裂的主要因素似乎包括顶柱系统的几何参数和力学性能。机械性能很难改变，但可以通过改善几何参数来提高刚度比 K，从而最大限度地减少爆裂倾向。一旦 K < 1 且达到临界压缩破坏载荷，较大采场跨度一侧的支柱首先破坏，然后整个支柱失去稳定性。考虑柱体不稳定破坏时的外功，对岩爆能量指标进行优化。影响支柱爆裂的主要因素似乎包括顶柱系统的几何参数和力学性能。机械性能很难改变，但可以通过改善几何参数来提高刚度比 K，从而最大限度地减少爆裂倾向。一旦 K < 1 且达到临界压缩破坏载荷，较大采场跨度一侧的支柱首先破坏，然后整个支柱失去稳定性。考虑柱体不稳定破坏时的外功，对岩爆能量指标进行优化。以尽量减少爆裂倾向。一旦 K < 1 且达到临界压缩破坏载荷，较大采场跨度一侧的支柱首先破坏，然后整个支柱失去稳定性。考虑柱体不稳定破坏时的外功，对岩爆能量指标进行优化。以尽量减少爆裂倾向。一旦 K < 1 且达到临界压缩破坏载荷，较大采场跨度一侧的支柱首先破坏，然后整个支柱失去稳定性。考虑柱体不稳定破坏时的外功，对岩爆能量指标进行优化。