Abstract:The determination of tunnel convergence patterns is a critical step in the analysis of strata deformation induced by tunnel excavation. However, due to their inherent concealment and complexity, tunnel convergence patterns are difficult to accurately determine through field monitoring and theoretical analysis. Existing convergence patterns are often derived from engineering experience and analogy-based methods, which limit the accuracy of strata deformation analysis. To develop a method for determining complex tunnel convergence patterns, a unified equation for the convergence patterns was established based on the transformation relationship of three independent coordinate systems and Fourier series, which enables an accurate description of such patterns. Subsequently, parameter sensitivity analysis was conducted based on stochastic medium theory to investigate the influence of different convergence pattern parameters on ground settlement. Then, a sample set was generated by discretizing the domain into a high-dimensional grid, and a data mapping was established using ground settlement as input and the parameters of the unified equation for the convergence patterns as output, thereby enabling the inversion of complex convergence patterns. Finally, the reliability of the method was validated via an engineering case study. The results indicate that although the non-uniform convergence pattern is widely adopted in engineering practice, its assumptions regarding tunnel contour deformation are oversimplified and may not accurately reflect actual conditions. Under complex geological and construction conditions, the deformed tunnel contour may not strictly remain within the excavation boundary, and the ground loss region may exhibit asymmetry, causing the peak of ground settlement to deviate from the tunnel centerline. In engineering practice, the factors influencing tunnel convergence patterns are highly complex. The proposed method can determine the tunnel convergence pattern using simple field-measured deformation data, thereby providing a basis for refined analysis and dual-engine prediction of strata deformation induced by tunnel excavation.