A unified empirical method for predicting both vertical and horizontal ground displacements induced by tunnel excavation

An empirical model for describing the soil movements induced by tunneling is proposed, then the mathematical relationship between horizontal displacement and vertical displacement is obtained. By analyzing 25 sets of data from field engineering and 35 sets of data from model tests, the formula for the maximum settlement Sv,max(z) is optimized to adapt to different ground conditions. The10modified Gaussian function is developed by introducing the existing width coefficient of the settlement trough i(z) and the optimized11Sv,max(z) to describe the surface and subsurface vertical displacement. Subsequently, the formula for the horizontal displacement is12derived based on the Modified Gaussian function. H(z) representing the position of the oriented point of the soil movement is a variable13in the formula for horizontal displacement. Based on measured results, a logarithmic function and a quadratic polynomial function are14proposed to describe the variation of H(z) with depth in the clay stratum and sand stratum, respectively. Then, the rationality of the15proposed method is validated by 4 sets of in-situ data and 4 sets of test data. Finally, the implementation process of the proposed method16is illustrated, and the inversion results of the ground displacement field in Beijing Metro Line 12 are presented.