Probabilistic analysis of underground rock excavations using response surface method and SORM
Probabilistic analysis of underground rock excavations using response surface method and SORM
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DOI：
10.1016/j.compgeo.2011.07.003
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发表时间：
2011-12-01
影响因子：
5.3
通讯作者：
Low, Bak Kong
中科院分区：
文献类型：
--
作者：
Lu, Qing;Low, Bak Kong
采用响应面法和二次二阶矩法（SORM）对地下岩石开挖进行概率分析，其中使用含交叉项的二次多项式来逼近设计点处的隐式极限状态面。通过迭代算法确定响应面，并使用一阶和二阶可靠度方法（FORM/SORM）评估失效概率。选择U空间中的独立标准正态变量作为基本随机变量，并将其转换为原始随机变量空间中的相关非正态变量以构建响应面。首先针对分别考虑莫尔 - 库仑（M - C）和霍克 - 布朗（H - B）屈服准则且有解析解的圆形隧道对所提方法进行说明。根据FORM/SORM估算关于塑性区准则和隧道收敛准则的失效概率，并与蒙特卡罗模拟得到的结果进行比较。结果表明，支护压力对两种失效模式的失效概率有很大影响。对于M - C模型，与抗剪强度参数负相关的情况相比，摩擦角和黏聚力不相关的假设会产生更高的失效概率。还对涉及非正态分布的可靠度分析进行了研究。最后，给出一个马蹄形公路隧道的实例，以说明所提方法在需要数值程序计算功能函数值的实际应用中的可行性和有效性。（C）2011爱思唯尔有限公司。保留所有权利。
Probabilistic analysis of underground rock excavations is performed using response surface method and SORM, in which the quadratic polynomial with cross terms is used to approximate the implicit limit state surface at the design point. The response surface is found using an iterative algorithm and the probability of failure is evaluated using the first-order and the second-order reliability method (FORM/SORM). Independent standard normal variables in U-space are chosen as basic random variables and transformed into correlated non-normal variables in the original space of random variables for constructing the response surface. The proposed method is first illustrated for a circular tunnel with analytical solutions considering Mohr-Coulomb (M-C) and Hoek-Brown (H-B) yield criteria separately. The failure probability with respect to the plastic zone criterion and the tunnel convergence criterion are estimated from FORM/SORM and compared to those obtained from Monte Carlo Simulations. The results show that the support pressure has great influence on the failure probability of the two failure modes. For the M-C model, the hypothesis of uncorrelated friction angle and cohesion will generate higher non-performance probability in comparison to the case of negatively correlated shear strength parameters. Reliability analyses involving non-normal distributions are also investigated. Finally, an example of a horseshoe-shaped highway tunnel is presented to illustrate the feasibility and validity of the proposed method for practical applications where numerical procedures are needed to calculate the performance function values. (C) 2011 Elsevier Ltd. All rights reserved.