基于组合拱理论隧道锚喷支护稳定可靠度求解的一维积分方法

doi:10.13722/j.cnki.jrme.2015.0039

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摘要基于组合拱原理和剪切滑移破坏模型，导出隧道锚喷支护结构功能函数。该函数表现为高度非线性隐式特征，同时基本参数间存在相关性，导致其可靠度求解困难。首先，引入基于半解析的Nataf变换以消除基本参数相关性的影响，将原始随机变量导入到标准正态空间中。其次，根据统计矩点估计法原理，依靠基本随机变量统计特征导出功能函数统计特征的矩估计公式。最后，根据统计矩与其变量的关系，以功能函数的前四阶矩为约束，基于最大熵理论导出功能函数的概率密度函数。构建基于组合拱理论的隧道锚喷支护稳定可靠度求解的一维数值积分方法。通过数值算例验证其准确性，最后分析荆竹山公路隧道支护结构的稳定可靠度，展示该方法的应用前景。

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关键词 ：隧道工程, 隧道锚喷支护结构, 可靠度, 一维积分, 点估计法, 最大熵原理

Abstract：A function describing the performance of tunnel lining with the protection of rock bolts and shotcrete was derived based on the theory of build-up arches and the failure model of shear slip. Because of the high nonlinear and implicit characteristics of the function and the correlation between the basic parameters，the reliability was difficult to be obtained. In order to eliminate the influence of the correlation between the basic parameters，the semi analytical Nataf transform was introduced，and thus the original random variables were converted into the standard normal space. According to the point estimate method，the moment estimation formula of the performance function was established on the statistical characteristics of basic random variables. According to the relationship between the statistical moment and variables，the probability density function was derived based on the maximum entropy principle with the constraint of the first four moments of the performance function. A one-dimensional numerical integral method of reliability analysis was then developed for structural stability of tunnel lining consisting of rock bolts and shotcrete based on build-up arch theory. The accuracy of the proposed approach was verified using a numerical example，and the reliability analysis for Jingzhushan highway tunnel was conducted.

Key words： tunnelling engineering tunnel lining consisting of rock bolts and shotcrete reliability index one- dimensional integral method point estimation method maximum entropy principle

引用本文:

苏永华，梁斌，刘少峰，李帅. 基于组合拱理论隧道锚喷支护稳定可靠度求解的一维积分方法[J]. 岩石力学与工程学报, 2015, 34(12): 2446-2454.
SU Yonghua，LIANG Bin，LIU Shaofeng，LI Shuai. ONE-DIMENSIONAL INTEGRAL METHOD OF RELIABILITY ANALYSIS FOR STRUCTURAL STABILITY OF TUNNEL LINING CONSISTING OF ROCKBOLTS AND SHOTCRETE BASED ON BUILD-UP ARCH THEORY. , 2015, 34(12): 2446-2454.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2015.0039 或 https://rockmech.whrsm.ac.cn/CN/Y2015/V34/I12/2446

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