Abstract Quantitative risk assessment of spalling damage needs to address three key tasks: risk probability estimation, loss estimation and risk level determination. Here, based on uncertainty analysis of the damage initiation and spalling limit method, a general risk assessment method for spalling damage in hard-rock tunnels is proposed. First, with a reliability-based design method, a probability reliability estimation model for spalling damage depth was established to determine the probability of roof and wall spalling damage based on the stochastic response surface of the Hermite polynomial chaos expansion. Second, the direct economic loss due to damage was calculated by using the spalling damage depth of a unit length tunnel section and the average loss cost; thus, the risk estimation of spalling damage was carried out. Last, a theoretical analytical formula for the spalling damage expected cost ratio was derived to determine probability level thresholds, and the risk grading criteria were calculated. The method was applied to the case of the Canadian deep geologic repository project for low- and intermediate-level nuclear waste. The risk levels of roof spalling damage, wall spalling damage and both types of spalling damage were obtained, and the influences of the commonly used empirical formula for depth estimation, the coefficient of variation and the correlation coefficients of random variables on the estimated probability of spalling damage depth were analysed. The method was shown to be feasible for accurate risk assessment of spalling damage, and the results can be used to guide dynamic risk prevention and control and to support design optimization for hard-rock tunnel construction.

中文翻译：

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深部硬岩隧道剥落损伤风险评估方法探讨与应用

摘要 剥落损伤的定量风险评估需要解决三个关键任务：风险概率估计、损失估计和风险水平确定。在此，基于损伤起裂和剥落极限方法的不确定性分析，提出了硬岩隧道剥落损伤的通用风险评估方法。首先，采用基于可靠性的设计方法，基于Hermite多项式混沌展开的随机响应面，建立剥落破坏深度概率可靠性估计模型，确定屋顶和墙体剥落破坏的概率。其次，利用单位长度隧道断面的剥落破坏深度和平均损失成本，计算直接破坏造成的经济损失；因此，进行了剥落损坏的风险评估。最后的，推导出剥落损伤预期成本比的理论分析公式，确定概率水平阈值，计算风险分级标准。将该方法应用于加拿大中低放核废料深层地质处置库项目。得到屋顶剥落破坏、墙体剥落破坏和两种类型剥落破坏的风险等级，以及常用的深度估计经验公式、变异系数和随机变量相关系数对估计剥落概率的影响损伤深度进行了分析。该方法被证明对于剥落损伤的准确风险评估是可行的，