Voids behind linings may affect the safety and performance of structures. In this paper, the applicability of the extended finite element method for simulating crack propagation was verified firstly through comparisons between numerical simulations and model tests. Moreover, the mechanical behavior of double-arch tunnels under effects of voids on the top of the middle wall was investigated numerically. Two factors, including void size and tunnel shape, were mainly investigated. The main results obtained were explored including internal forces, deformation and fracturing of the liner. The results showed that voids produced adverse effects on the liner. Internal forces on the liner experienced significant changes and the deformation of the liner increased. Besides, larger crack depth was observed at the crown and the connection between the spandrel and middle wall, indicating a significant decrease in bearing capacity of the structure compared with tunnels without voids.

A reliable prediction of the characteristics of roof collapse in deep tunnels is still one of the most important and challenging tasks in tunnel engineering. To investigate the collapse mechanisms and possible shapes of the collapsing blocks in deep tunnels, an analytical solution of shape curves for collapsing blocks is derived based on the nonlinear Hoek-Brown failure criterion by using the functional catastrophe theory. The obtained formulas are extremely simple. Furthermore, a judging criterion is proposed to distinguish whether the roof collapses of deep tunnels will occur or not. The effects of rock mass parameters used in the proposed method on the collapsing block shapes of deep tunnels are also discussed. The proposed analytical solution is verified by both the empirical method and the model test. 分析深埋隧道的塌方机制并推导塌方体形状曲线的解析表达式。 基于霍克-布朗准则, 采用泛函突变理论推导得到了深埋隧道塌方体形状曲线的解析表达式, 并据此分析了围岩参数变化对塌方体形状的影响规律。 通过理论分析建立深埋圆形隧道的解析模型(图1), 采用泛函突变理论推导基于霍克-布朗准则的隧道塌方体形状曲线解析表达式, 并研究围岩参数变化对塌方体形状的影响规律(图3 和4, 表2)。 通过与自然拱理论和模型试验结果的对比(图5–7)验证本文解析解的正确性。 采用泛函突变理论推导了基于霍克-布朗准则的深埋隧道塌方体形状曲线解析表达式。 该解析表达式简洁直观, 不仅可以预测无支护条件下隧道的塌落体尺寸, 还可以估算塌落围岩作用于衬砌上的荷载。

This article proposes a new 3D failure mechanism to analyze the stability of the tunnel face driven by a closed shield in cohesive-frictional soils. The failure mechanism consists of a single block in the lower part defined by logarithmic-spiral and a distributed force caused by the weight of a half-ellipsoid in the upper part. The logarithmic-spiral surface represents the shear band and the distributed force is applied to simulate the arch effect. The arch effect and rotational mechanism are considered simultaneously. Comparisons among the proposed mechanism, numerical simulation and existing mechanism are conducted. The results show that the proposed mechanism provides improved limit support pressure values, and the failure patterns of the proposed mechanism agree well with those of the numerical simulation and experimental tests. This verifies that the proposed mechanism is effective and reasonable.