FEM modeling requirements for accurate analysis of highly nonlinear shallow tunnels

Modern tunnel design in urban areas heavily relies on numerical modeling to assess excavation stability and predict ground movement. Recent advancements in soil modeling, hardware, and software have facilitated the development of sophisticated 3D models within tight schedules. Urban tunnels are often shallow and excavated in challenging ground conditions, with proximity to existing structures and infrastructure. Consequently, numerical modeling of such tunnels involves highly nonlinear analyses with complex boundary conditions. Despite the widespread use of numerical modeling in tunnel research and design, there is a lack of publications addressing modeling procedures to ensure accurate and reliable results for highly nonlinear shallow tunnel analyses. This paper investigates the requirements for accurate results for highly nonlinear shallow tunnel analyses. The Finite Element Method (FEM) is employed with different mesh refinements and element types. The study focuses on the hypothetical excavation stability scenario explored by Carranza-Torres et al. (2013). Tunnel stability is assessed using Caquot’s analytical solution based on the lower bound theorem of plasticity, as well as FEM modeling with the strength reduction method. The FEM numerical solution, which approaches the exact solution for the problem, provided a factor of safety slightly larger (2.3%) than Caquot’s lower-bound solution. The results of the FEM modeling indicate that a significantly less refined mesh is required to achieve accurate results for highly nonlinear shallow tunnel analyses when adopting 2nd-order elements (i.e., quadratic interpolation) instead of 1st-order elements (i.e., linear interpolation). This study improves our understanding of FEM modeling requirements and provides practical insights regarding the numerical modeling of highly nonlinear shallow tunnels in urban areas.