Calculation Method for the Ultimate Face Support Pressure of Shield Tunnels in Highly Permeable Sandy Soils

To address the face stability issue of shield tunnels constructed in highly permeable sandy soils, a calculation method for the ultimate support pressure at the tunnel face is developed based on the upper bound theorem of limit analysis. A three-dimensional rotational failure mechanism is constructed using a spatial discretization technique. By comparing the proposed method with existing analytical solutions and further validating it through numerical modeling, a sensitivity analysis of key parameters is conducted. The results indicate that: (1) the discrepancy between the proposed method and the existing analytical solutions is within 7%, while achieving significantly higher computational efficiency; (2) although the difference from numerical simulation results is approximately 20%, the proposed method provides a reference for effectively controlling seepage at the tunnel face; (3) groundwater level exerts the most pronounced influence on the ultimate support pressure, followed by internal friction angle, while soil unit weight has the least effect. A case study from an actual metro shield tunnel project further verifies the reliability of the proposed calculation method.