Determination of the required supporting pressure is the premise of tunnel support design. Only when the support design meets the requirements can the tunnel be safe and stable during construction and operation. This paper focuses on a shallow tunnel in layered rock strata and proposes a method for predicting the required supporting pressure. In this method, the 2D and 3D failure mechanisms are constructed, respectively. The analytical solutions of the supporting pressure corresponding to the two cases are derived on the basis of upper bound theorem and Hoek–Brown failure criterion. Then, the proposed method is validated by comparing with the results of existing research studies. Furthermore, a shallow tunnel in two-layer rock strata is chosen to illustrate the difference between the two solutions. The comparison shows that the supporting pressure in the 2D case is greater than that in the 3D case in general and it tends to be conservative for tunnel design. Conversely, the 3D solution may help to reduce the support cost. Furthermore, the change laws of the supporting pressure and failure range corresponding to varying parameters are obtained. These results may practically provide theoretical references for tunnel support design in layered rock strata.

中文翻译：

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基于2D和3D上限分析的层状岩层浅埋隧道所需支护压力预测

确定所需的支护压力是隧道支护设计的前提。只有在支架设计达到要求时，隧道才能在施工和运营过程中安全稳定。本文重点研究了层状岩层中的浅埋隧道，并提出了一种预测所需支护压力的方法。在这种方法中，分别构造了2D和3D失效机制。根据上限定理和Hoek-Brown破坏准则，推导了两种情况下相应的支撑压力的解析解。然后，通过与现有研究结果进行比较来验证所提出的方法。此外，选择了两层岩层中的浅隧道来说明两种解决方案之间的差异。比较表明，通常情况下2D情况下的支撑压力要比3D情况下大，并且在隧道设计中倾向于保守。相反，3D解决方案可以帮助减少支持成本。此外，获得了与变化的参数相对应的支撑压力和破坏范围的变化规律。这些结果可为层状岩层隧道支护设计提供实用的理论参考。