A novel analytical method for describing ground motion behaviour caused by tunnel excavation

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.