This paper proposes a probabilistic‐based framework to assess the failure probability of the existing shield tunnel owing to undercrossing tunnelling. A novel deterministic model using the two‐phase analysis method is presented to evaluate the longitudinal behaviours of the in‐service shield tunnel. First, the tunnelling‐induced settlement is estimated using the Loganathan and Poulos’ method; second, the longitudinal beam‐spring model (LBSM), which can explicitly consider the circumferential joints, is applied to reflect the performances of the existing shield tunnel. Two well‐documented case histories are selected to validate the effectiveness of the deterministic analysis model. The predictions are also compared with previous analytical methods. Afterward, to improve the computational efficiency, a surrogate model is then established to replace deterministic model and perform the global sensitivity analysis (GSA). A probabilistic analysis is further performed to explore the tunnelling‐induced deformation characteristics of the shield tunnel by means of Monte Carlo simulation (MCS) method. Parametric analyses are further performed to explore the influences of key variables on the failure probabilities of the existing shield tunnel. The results show the proposed deterministic model gives a satisfactory prediction in tunnelling‐induced responses of the existing shield tunnel. The LBSM can reflect the segmental ring and joint deformations more realistically. The uncertainties in the ground elastic modulus, joint rotation stiffness and the joint shearing stiffness dominate the tunnel settlement, joint opening and dislocation, respectively. The failure probability of tunnel settlement is more sensitive to volume loss than that of the joint opening and dislocation. The whole system failure probability is identical to that of the tunnel settlement failure mode. By increasing the coefficient of variation (COV) of random variables, probability density function (PDF) curves for neutral and pessimistic conditions become lower and wider, and the maximum joint opening and dislocation positions corresponding to the peaks of PDF apparently deviate from that of the determinate results. Increasing the two tunnel clearances, the allowable volume loss for opening and dislocation increase linearly, but it has insignificant influence on the tunnel failure mode. However, enlarge the new tunnel diameter leads to rapid decrease in the allowable volume loss for all failure modes.

中文翻译：

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现有盾构隧道纵向对隧道开挖响应的概率评估

本文提出了一种基于概率的框架来评估现有盾构隧道因下穿隧道而失效的概率。提出了一种使用两阶段分析方法的新型确定性模型来评估在役盾构隧道的纵向行为。首先，使用 Loganathan 和 Poulos 方法估算隧道开挖引起的沉降；其次，采用可以明确考虑周向接缝的纵梁弹簧模型（LBSM）来反映现有盾构隧道的性能。选择两个有据可查的案例来验证确定性分析模型的有效性。这些预测还与以前的分析方法进行了比较。随后，为了提高计算效率，建立代理模型来代替确定性模型并进行全局敏感性分析（GSA）。进一步采用蒙特卡罗模拟（MCS）方法进行概率分析，探讨盾构隧道的掘进变形特征。进一步进行参数分析，探讨关键变量对现有盾构隧道破坏概率的影响。结果表明，所提出的确定性模型对现有盾构隧道的隧道诱发响应给出了令人满意的预测。 LBSM可以更真实地反映节段环和节理变形。地面弹性模量、节理旋转刚度和节理剪切刚度的不确定性分别主导隧道沉降、节理张开和错位。隧道沉降的破坏概率比节理张开和错动的破坏概率对体积损失更敏感。整个系统失效概率与隧道沉降失效模式相同。通过增加随机变量的变异系数（COV），中性和悲观条件下的概率密度函数（PDF）曲线变得更低更宽，并且PDF峰值对应的最大关节张开和位错位置明显偏离确定的结果。增大两个隧道净空，开洞和错位的允许体积损失呈线性增加，但对隧道破坏模式影响不显着。然而，扩大新隧道直径会导致所有失效模式的允许体积损失迅速减小。