Three-Dimensional Stress-Free Assumption 3-DOF FE-LEM for Tunnel Face Stability

Abstract

Currently, existing three-dimensional limit equilibrium methods (LEM) for calculating the limit support pressure of the tunnel face discard the drawbacks of the inter-slice force assumptions in the traditional LEM. They assume that the potential failure body in front of the tunnel face is a wedge, thereby transforming the problem from a statically indeterminate to a statically determinate one, with only one degree of freedom for optimization. This approach fails to accurately reflect the true failure pattern of the tunnel face and the ultimate support pressure, leading to less precise results. In this paper, no assumptions are made regarding the normal stress on the slip surface. Instead, σ is treated as the primary variable, and finite element method (FEM) interpolation is used for approximation. A 5th-order parameter vector a is employed to construct σ, ensuring that it satisfies the limit equilibrium condition of the entire slip mass. A new FE-LEM calculation method is thus proposed. At the same time, the failure mode of the tunnel face is modeled as a quarter-ellipsoid, and the degree of freedom for optimization is increased from 1 to 3, making the failure shape more consistent with the actual sliding body. The accuracy of the proposed calculation method was verified through typical examples of homogeneous stratigraphy, composite layered stratigraphy, and numerical calculation results. Finally, the calculation model was extended to account for the spatial variability and anisotropy of geotechnical properties. By comparing the optimization results from random field calculations with model test results, it was found that the optimized ellipsoid radius parameters can effectively cover the collapse area in front of the tunnel face. Additionally, the mean value of the limit support pressure (T) obtained is largely consistent with the model test results.