ANALYTICAL SOLUTION FOR CIRCULAR TUNNELS WITH ROCK BOLTS
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摘要: 该文推导了锚杆支护前后圆形隧洞的应力、位移和塑性区半径表达式。首先考虑静水压力状态下,岩石表现为弹脆塑性材料模型,采用Mohr-Coulomb线性屈服准则以及非关联流动法则,推导了无支护状态下圆形隧洞的弹塑性解析新解。在此基础上,通过均匀化方法,从宏观尺度将锚杆高密度支护模式下的岩石和锚杆复合体考虑成均匀连续、强度参数增强的等效材料,定义能够反映隧洞支护参数的锚杆密度因子,推导出等效弹性模量,等效粘聚力和等效内摩擦角的表达式,然后通过该文得到的隧洞在无支护状态下的解析解可以得到锚杆支护圆形隧洞解析解。最后将该文结果与前人研究结果及数值结果进行了比较分析,对比了锚杆支护前后圆形隧洞的塑性区半径、塑性区位移和塑性区应力,结果表明锚杆支护对隧洞的加固效果明显,该文结果可为地下工程中圆形隧洞的稳定性分析提供参考。Abstract: Analytical expressions of stress, displacement, and plastic zone radius in circular tunnels with or without rock bolts are presented. Considering a circular tunnel in hydrostatic stress field, with elastic-brittle-plastic rock mass, a linear Mohr-Coulomb yield criterion, and a non-associated flow rule, a new elastoplastic analytical solution for unsupported circular tunnels was derived. Based on the homogenization method, considering the composite material of rock mass and rock bolts as a new homogeneous, isotropic, parameter-strengthened equivalent material, the bolt density parameter was defined to reflect the influence of a high density support pattern of rock bolts, thus an equivalent Young’s modulus, equivalent cohesion, and equivalent friction angle for supported circular tunnels can be derived. Then an analytical solution for circular tunnel with rock bolts can be derived based on the new elastoplastic analytical solution without rock bolts. Bolt support was shown to be effective in reducing plastic zone radius and displacement of circular tunnel by comparison with an unsupported tunnel, also comparative analysis was undertaken using existing results and numerical solutions; the solutions derived provide reference for circular tunnel stability analysis in underground engineering.
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