深部煤炭开采中软岩巷道围岩支护问题，尤其是软岩交岔巷道围岩稳定性长期深受关注。由交岔点变形破坏内在原因分析得出，其顶板与三角区岩柱支撑体系是交岔点失稳破坏的薄弱点。基于“等效跨度”概念并结合突变理论建立交岔点顶板−岩柱系统简化受力的尖点突变模型，获得交岔点尖点突变方程及系统失稳破坏的充要判定条件。分析了工程地质因素（埋深H、岩柱弹性模量E）、巷道交岔点结构参数（交岔角度q、巷道高度h）及支护参数a对交岔点稳定性影响。得出q、E、a与控制参数v的非线性关系存在曲率变化拐点。当q＜35º，E＜16 GPa时，控制参数v对各个因素的敏感度顺序为q＞E＞ a＞h＞H，即当围岩较软弱时交岔点稳定性受岩柱强度影响较为强烈，交岔点设计角度不宜小于35º。当q≥35º，E≥16 GPa时，敏感度顺序为h＞H＞q＞a＞E，即当岩柱强度较高时交岔点稳定性受结构参数影响较大。结合丁集矿深井软岩工程实例，采用理论分析指导交岔点设计参数优化。矿压监测数据表明，优化支护设计有效地控制了西三轨回联巷交岔点围岩变形，验证了理论推导方法的正确性。The problem ofsurrounding rock support of soft rock roadway in deep coal mining

especiallythe stability of surrounding rock of soft rock intersection roadway

has beenconcerned for a long time. From the analysis of the internal causes of thedeformation and failure of the intersection

it is concluded that the roof andthe rock pillar support system in the triangle area are the weak points of theinstability and failure of the intersection. Based on the concept of‘equivalent span’ and catastrophe theory

a cusp catastrophe model of the roofrock-column system at the intersection is established and the cusp catastropheequation at the intersection and the necessary and sufficient judgmentconditions for the instability and failure of the system are obtained. Theeffects of engineering geological factors (buried depth H and elastic modulus of rock column E)

structural parameters of roadway intersection (intersection angle q and roadway height h) and supportdesign parameters a on the stabilityof intersection are analyzed. It is concluded that the non-linear relationship between q

E

a and the control parameter v has a curvature change inflection point. When q <35º and E<16GPa

the sensitivity order ofcontrol parameters to various factors is: q >E>a>h>H

that is

when the rock column isweak

the stability of the intersection is strongly affected by the strength ofthe rock column

and the design angle of the intersection should not be lessthan 35º. When q≥35º and E≥16 GPa

the order of sensitivity is: h>H>q >a>E

that is

when the strength of surrounding rock is high

the stability ofintersection is significantly affected by structural parameters. Combined withthe example of deep well soft rock engineering in Dingji mine

theoreticalanalysis is used to guide the optimization of design parameters ofintersection. The ground pressure monitoring data show that the optimizedsupport design effectively controls the surrounding rock deformation at theintersection of the west third track back link roadway

and verifies thecorrectness of the theoretical derivation.