Effects of Excavation Loading Conditions on Ground Deformation and Stress Evolution in Plane-Strain Tunnel Simulations

The construction of tunnels in urban areas typically affects a large number of buildings and infrastructure. The interaction between ground deformations induced by tunnel excavation and buildings or buried infrastructure is highly complex, and often requires numerical modeling for damage assessment. Despite recent advances in three-dimensional tunnel modeling, two-dimensional (2D) plane-strain analysis remain widely used in practice, particularly for TBM tunneling, because they are substantially simpler, computationally faster, and provides satisfactory results when the plane-strain simplification approximates the problem geometry. This paper investigates and compares three common loading conditions for simulating tunnel excavation using 2D plane-strain analysis: (1) the stress relief method (SR), (2) applied displacements at the tunnel perimeter promoting tunnel convergence while maintaining the invert position (AD), and (3) hydrostatic pressure applied at the tunnel perimeter (HP). The first two, SR and AD, are the most common excavation loading conditions in 2D numerical modeling of tunnels, whereas HP is commonly adopted in centrifuge modeling of tunnels. Centrifuge modeling results presented by Farrell (2011), Marshall (2009), and Zhou (2015) were used as reference data. These experiments encompass cover-to-diameter ratios (C/D) of 1.33, 2.0, and 2.44, relative densities of sand of 50% and 90%, and tunnel diameters of 4.67 m, 7.2 m, and 6.1 m. The centrifuge tunnel modeling results, conducted with HP excavation loading conditions, were satisfactorily replicated by all three excavation loading conditions using the Hardening Soil Model and the soil properties reported in Celestino et al. (2025). It was observed that: (1) for small tunnel volume losses (≈ 1%), the three excavation loading conditions provide essentially the same results; (2) for larger tunnel volume losses (≈ 2 to 4%), HP loading induces larger deformations at the tunnel crown, more pronounced dilatancy above the tunnel, and a narrower subsidence trough than SR and AD; and (3) SR and AD produce practically identical ground deformations above the tunnel, rendering the two excavation loading conditions equivalent for ground displacement predictions in the scenarios explored in this study. Thus, SR loading is recommended because it does not require prescribing tunnel convergence as an input for modeling and results in a more realistic radial stress redistribution around the tunnel perimeter compared to AD loading.