中文摘要：

通过采用均匀化方法,研究了圆形隧洞的锚杆支护特性,将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,简化了岩石和锚杆间复杂的力学耦合问题。通过定义锚杆密度参数来反映不同支护模式的特性,建立锚杆密度参数与Mohr-Coulomb屈服准则中主要参数之间的关系,推导出等效弹性模量、等效黏聚力和等效内摩擦角的表达式,并分析比较了隧洞在支护前后的位移情况。结合可靠性理论,采用容许极限位移量作为失稳判据,分析了隧洞在支护前后的可靠性指标与破坏概率,结果表明,文中提出的方法简单可靠,锚杆支护对隧洞的位移限制效果明显,可显著提高隧洞的可靠性。

英文摘要：

A homogenization method to analyze circular tunnel with rock bolts is presented, which can simplify this kind of complex mechanical coupling problem through considering the composite material of rock mass and rock bolts as a new homogeneous, isotropic, parameters strengthened equivalent material. Rock bolt density parameter is defined to reflect the influence of high density rock bolt support pattern; Mohr-Coulomb criterion is applied to the new equivalent material; the increasement of key coefficients for Mohr-Coulomb criterion is considered to related to rock bolt density parameter; thus equivalent Young’s modulus, equivalent cohesion and equivalent friction angle for circular tunnel with rock bolts can be derived. Displacements of tunnel with and without rock bolts are compared through the existed displacement solution. Based on this solution, the reliability index and failure probability of tunnel are calculated by considering allowable ultimate displacement as instability criterion. The results show that the tunnel with rock bolts is much reliable. It is shown that the proposed method is simple and feasible and the rock bolt can improve the stability and reliability of tunnel.