A model is proposed to describe the soil movement caused by tunnel excavation. The mathematical relationships for soil displacement in both the horizontal and vertical directions are established. An optimized Gaussian function is developed to accommodate various ground conditions for describing vertical displacement, then, a formula for horizontal displacement is derived on this basis, providing a unified calculation method for both vertical and horizontal displacements. Utilizing the principles of elastic–plastic mechanics, the vertical and horizontal strains of soil are obtained by solving the first-order partial derivative of the displacement formulas. Subsequently, formulas for volume strain and engineering shear strain are derived using the Mohr strain circle. The validity of the displacement and strain formulas is confirmed through comparison with measured results from sandy strata (4 sets) and clay strata (2 sets). In conclusion, a comprehensive empirical framework for analyzing ground disturbance caused by tunnel excavation is established. The method relies on just two parameters and four known quantities, making it convenient for practical engineering.

中文翻译：

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一种描述隧道开挖引起的地震动行为的新型分析方法


提出了一个模型来描述隧道开挖引起的土体运动。建立了水平和垂直方向上土壤位移的数学关系。为了适应描述垂直位移的各种地质条件，开发了一个优化的高斯函数，并在此基础上推导出水平位移公式，为垂直和水平位移提供了统一的计算方法。利用弹塑性力学原理，通过求解位移公式的一阶偏导数获得土体的垂直和水平应变。随后，使用 Mohr 应变圈推导出体积应变和工程剪切应变的公式。通过与砂质地层（4 组）和粘土层（2 组）的测量结果进行比较，证实了位移和应变公式的有效性。综上所述，建立了分析隧道开挖引起的地面扰动的综合实证框架。该方法仅依赖于两个参数和 4 个已知量，便于进行实际工程设计。