考虑中间主应力的深埋圆形巷道弹塑性位移解

平面应变条件下的深埋圆形巷道一般忽略中间主应力的影响，但塑性区围岩的变形与实际情况会产生较大差异．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，在此基础上推导了理想弹塑性材料在塑性阶段的中间主应力表达式；根据所得的中间主应力表达式结合关联流动法则．不引入任何假设，得出塑性区体积扩容的关系式；进一步推导了考虑中间主应力影响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，考虑中间主应力的解答为深埋圆形巷道的计算与设计提供更为科学的理论基础．

Elastoplastic analytical solutions for displacements of deep-buried circular tunnels considering intermediate principal stress

The influence of intermediate principal stress was usually ignored for the problem of a deep-buried circular tunnel under a plane strain condition.But the deformations of surrounding rocks in a plastic area had a greater error.To consider the influence of intermediate principal stress to deep-buried circular tunnels,a plane strain hypothesis and a associated flow rule were given and Mohr-Coulomb strength criterion was precisely matched to Drucker-Prager strength criterion.The analytical expression of intermediate principal stress in a plastic state for the perfect elastoplastic material was derived from Drucker-Prager strength criterion.Combining the analytical expression and associated flow rule,any other hypothesis do not need introduced and the expression on volume dilatancy in a plastic area could be obtained.What is more,the analytical expressions of the displacement and stress in a plastic area for a deep-buried circular tunnel consider intermediate principal stress.In the expressions,the radial stress,the circumferential stress and the radius of a plastic area had the same form as the solutions of Kastner.But the form of intermediate principal stress could not be given in the solutions of Kastner and the new analytical expression of the displacement was entirely different from other literatures.Compared with the theoretic solutions of the displacement in other literatures,it was shown that the new solutions of the displacement were more reasonable.Thusly,the solutions considering intermediate principal stress could provide a reasonable theoretic basis for the calculation and design of a deep-buried circular tunnel.