Analysis of tunnel-support system stability with uncertain rock mass properties is conducted in this paper. A horseshoe shaped tunnel driven in weak rock mass is analyzed through deterministic, random variable and random field approaches. Performance of the tunnel in probabilistic analysis was assessed by defining three limit states which ensure that tunnel convergence remained below a safe threshold level, the rock bolts installed are embedded sufficiently beyond the depth of yielded rock mass and load induced on liner support does not exceed its capacity. Both unsupported and supported tunnels were analyzed with deterministic, random variable and random field approaches. Fourier series method was applied to discretize the random fields, and random finite difference analysis was conducted using Monte Carlo simulations. Scale of fluctuation (SOF) for isotropic random fields and horizontal and vertical SOF ratios for anisotropic random fields were varied to study their effect on performance of the tunnel and failure mechanisms involved. It was found that SOF significantly influences the output statistics and $P_f$ of the limit states. It was observed that, random variable approach underestimates the performance of the tunnel-support system; however, it can be adopted as conservative option in absence of data required for random field characterization.

本文对不确定岩体特性的隧道支护系统稳定性进行了分析。通过确定性、随机变量和随机场方法分析了在软弱岩体中开挖的马蹄形隧道。通过定义三个极限状态来评估隧道在概率分析中的性能，这些状态确保隧道收敛保持在安全阈值水平以下，安装的岩栓充分嵌入超过屈服岩体的深度，并且衬砌支架上引起的载荷不超过其容量。使用确定性、随机变量和随机场方法分析了无支撑和有支撑的隧道。应用傅里叶级数方法离散随机场，并使用蒙特卡罗模拟进行随机有限差分分析。各向同性随机场的波动尺度 (SOF) 和各向异性随机场的水平和垂直 SOF 比率是变化的，以研究它们对隧道性能和所涉及的破坏机制的影响。发现 SOF 显着影响输出统计和${磷}_F$极限状态。据观察，随机变量方法低估了隧道支护系统的性能；然而，在没有随机场表征所需的数据的情况下，它可以作为保守的选择。