Comparative Analysis of Simplified and Finite Element Method Approaches for Seismic Forces in Circular Tunnels

This paper presents a comparative analysis between simplified and Finite Element Method (FEM) approaches for evaluating seismic forces in circular tunnels, with a specific focus on the Algiers Metro as a practical case study, considering the Boumerdes earthquake in 2003. The FE modeling was carried out under plane strain conditions, using the contraction method to phase the performed model and incorporating the Volume Loss coefficient (VL). The behavior of soil and tunnel elements was considered linear elastic. Based on the maximum strain rate of the soil medium, various simplified approaches existing in the literature were adopted in this study, including solutions proposed by Wang (1993), Penzien (2000), Bobet (2003, 2010), and Park et al. (2009). The maximum shear strain rate was determined by plotting the cumulative horizontal displacement of the soil profile and then using this value to deduce the vertical strain rate. Results indicate that increasing VL values initially reduce axial thrust, followed by an increase. Shear force and bending moment proportionally increased with the VL ratio, remaining within the practical range of simplified solutions. The best agreement between the simplified and FEM approaches was observed when VL ranged between 1 and 2. Additionally, the total principal stresses around the tunnel increased with the VL ratio. This study highlights the importance of estimating the appropriate maximum strain rate and VL ratio to achieve accurate results while using both simplified and FEM approaches.