在开采埋藏较深的矿床时，往往需要留设一定宽度的永久矿柱来保证采场的稳定性，因此科学合理地设计矿柱宽度至关重要。以贵州某磷矿为研究对象，运用Hoek-Brown强度准则与矿柱面积承载理论推导了房柱法开采时采场矿柱安全系数表达式；在分析矿柱承载机理的基础上，利用矿柱尖点突变理论建立方形矿柱失稳突变模型，得到方形矿柱失稳的充要条件，并通过数值模拟和现场试验进行验证分析。结果表明：矿山安全矿柱宽度应大于5.8 m，安全系数不小于1.5，在数值模拟验证和实际生产中，取矿柱宽度为6 m；当矿柱宽度设计为6 m时，采场矿柱最大沉降位移为14.75 mm，最大应力为3.88 MPa，均在矿柱稳定可控范围之内；数值模拟结果与现场监测结果基本吻合，且矿柱表面未发生明显破损和开裂现象。

When exploitating deep-buried ore deposits, it is necessary to leave permanent pillars with certain width to ensure the stability of the mining area. Therefore, the reasonable design of pillar width is vital to its safety. Taking a phosphate mine in Guizhou as an example, this study derives an expression for the safety factor of pillars in mines using the filling method based on the Hoek-Brown strength criterion and pillar area load-bearing theory. Specifically, we analyzed the load-bearing mechanism of the pillars and established a square pillar instability model using the cusp catastrophe theory to obtain the necessary and sufficient conditions for the instability of square pillars. Results indicate that the width of the mine safety pillar should exceed 5.8 m in width, and the safety factor should not be less than 1.5. In the numerical simulation verification and actual production, the pillar width is set at 6 m. When the width of the pillar is designed to be 6 m, the maximum settlement displacement of the stope pillar is 14.75 mm, and the maximum stress is 3.88 MPa, which are within the stable and controllable range of the pillar. The numerical simulation results are basically consistent with the field monitoring results, and there is no obvious damage and cracking on the surface of the pillar. It shows that the cusp catastrophe theory is proved to be valid in explaining the mechanical mechanism of the instability of the pillar structure in mined-out areas, and its feasibility is validated in the stability analysis and parameter design of the pillars.