考虑中间主应力的深埋圆形隧道弹塑性统一解

为了充分考虑中间主应力对深埋圆形隧道的影响，在平面应变假设下将统一强度准则精确匹配为Drucker-Prager强度准则，推导了考虑剪胀特性的理想弹塑性材料在塑性阶段的中间主应力表达式，并结合非关联流动法则推导出深埋圆形隧道塑性区的应力与位移统一解.结果表明，经典的Kastner解为所得应力与位移统一解的特殊情况.同时，根据应力与位移统一解公式并结合实际算例，分析了中间主应力和围岩剪胀角对深埋圆形隧道塑性区的影响规律.

Elastoplastic Unified Solutions to Deep-buried Circular Tunnels Considering Intermediate Principal Stress

Taking into consideration the influence of intermediate principal stress on deep-buried circular tunnels, and under plane strain hypothesis, the unified strength criterion was precisely matched to the Drucker-Prager strength criterion. The analytical expression of intermediate principal stress in plastic state for the perfect elastoplastic material with dilatancy was derived from the Drucker-Prager strength criterion. Combining the analytical expression of intermediate principal stress and non-associated flow rule, unified solutions for stress and strain of the tunnel plastic area were obtained. The result shows that the classic solutions of Kastner are special cases of the unified solutions. A practical engineering instance was given according to the unified solutions and the regularities which intermediate and dilation angle act on the surrounding rock of the deep buried circular tunnel plastic area were discussed.