考虑中间主应力的横观各向同性深埋圆隧弹塑性解

平面应变条件下的深埋圆形交通隧道问题一般忽略中间主应力影响，但塑性区围岩的变形与实际情况会产生较大差异。岩土与地下工程中多遇到层状岩体，常将其处理为横观各向同性固体材料。充分考虑中间主应力对深埋圆形隧道的影响，基于平面应变假设得出了与横观各向同性材料相适应的Drucker-Prager准则并将其与Mohr-Coulomb准则精确匹配，在此基础上推导了考虑剪胀特性的横观各向同性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，推导出横观各向同性深埋圆形隧道围岩塑性区应力位移解析式；结合实际算例，分析了横观各向同性参数与围岩剪胀角对横观各向同性深埋圆形公路隧道围岩塑性区位移的影响规律。为深埋圆形交通隧道的计算和设计提供更为合理的理论基础。

Elastoplastic solutions to deep-buried circular tunnels in transversely isotropic rock masses considering intermediate principal stress

The influence of intermediate principal stress is usually ignored for the problem of a deep-buried circular traffic tunnel under plane strain condition. But the deformation of surrounding rocks in plastic area has greater error. A number of layered rock masses occur in geotechnical and underground engineering and they are often treated as the transversely isotropic solid materials. To consider the influence of the intermediate principal stress on deep-buried circular tunnels, plane strain hypothesis is given and the new Drucker-Prager criterion compatible with the transversely isotropic materials is obtained. Then Mohr-Coulomb criterion is precisely matched to the new Drucker-Prager criterion. The analytical expression of the intermediate principal stress in plastic state for the transversely isotropic perfect elastoplastic materials with dilatancy is deduced based on the criterion. According to the expression of the intermediate principal stress, the analytical expressions of the displacement and stress in plastic area for a deep-buried circular tunnel in transversely isotropic rock masses can be obtained. A practical engineering case is given and the regularities that transversely isotropic parameters and dilation angle act on the displacements in the plastic area of the deep-buried circular highway tunnel in transversely rock masses are discussed. So, the elastoplastic solutions may provide a more reasonable theoretic basis for the calculation and design of the deep-buried circular traffic tunnels.