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平面应变条件下的深埋圆形巷道问题一般忽略中间主应力的影响,但这会与塑性区围岩的实际情况产生较大差异。为了充分考虑中间主应力对深埋圆形巷道的影响,基于平面应变假设与非关联流动法则将Mohr-Coulomb准则精确匹配为Drucker-Prager准则,在此基础上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,中间主应力与剪胀角密切相关;根据所得的中间主应力表达式结合非关联流动法则,不引入任何假设,得出深埋圆巷塑性区由于剪胀角而发生体变的关系式;进一步推导了考虑中间主应力和剪胀特性的深埋圆形巷道塑性区应力位移解析式,其中径向应力、切向应力及塑性区半径的表达式与卡斯特奈(Kastner)解完全一致,但卡斯特奈(Kastner)解无法得出中间主应力,而新的位移解析式则与以往的文献完全不同;经与以往文献的位移理论解比较分析知,新的位移解答更加合理。因此考虑中间主应力和剪胀特性的解答为深埋圆形巷道的计算与设计提供一定的理论基础。
The problem of deep buried circular roadway under plane strain generally neglects the influence of intermediate principal stress, but this will have a big difference with the actual situation of surrounding rock in plastic zone. In order to fully consider the influence of intermediate principal stress on the deep circular roadway, based on the plane strain assumption and the non-associated flow rule, the Mohr-Coulomb criterion is exactly matched to the Drucker-Prager criterion. Based on this, The middle principal stress of plastic material is closely related to the dilatancy angle in the plastic phase. According to the obtained intermediate principal stress expression combined with the non-associated flow law, no assumptions are made, and the plastic zone of the deep round alley is obtained as a result of Dilatancy angle and body deformation. The analytical formula of stress-displacement of plastic zone in deep buried roadway with intermediate principal stress and dilatancy is further derived. The expression of radial stress, tangential stress and plastic zone radius Which is completely consistent with Kastner’s solution. However, the Kastner solution can not derive intermediate principal stress, and the new displacement analytical formula is totally different from the previous literature. Comparative analysis shows that the new displacement solution is more reasonable. Therefore, the solution considering intermediate principal stress and dilatancy characteristics provides a theoretical basis for the calculation and design of deep-buried circular roadways.