New modeling approach for tunnels under complex ground and loading conditions

Rock masses may present pronounced stress and material anisotropy. Stress measurements in rock masses show that stress anisotropy may be highly pronounced, as shown by McGarr & Gay (1978). Also, the data compiled by Brown & Hoek (1978) show that large horizontal stresses are common at shallow depths. According to Brady & Brown (2006), the major horizontal stress (σH) and the minor horizontal stress (σh) rarely have the same magnitude. Large and highly anisotropic horizontal stresses were reported by Haimson et al. (2003) and Park et al. (2014) in gneissic and granitic rock masses in South Korea. Those stresses were associated with the intense tectonic activity in the area. Rock masses may present pronounced fabric structure; thus, anisotropic mechanical behavior is expected. The data compiled by Worotnicki (1993) in metamorphic rocks showed that the ratio between the Young modulus perpendicular to the rock structure and parallel to the rock structure was larger than 2 for more than 50% of the rocks tested (e.g. schists, slates, quartzites, mudstones and phyllites), and the largest stiffness ratio was 6. This is relevant because anisotropic rock properties strongly affect the behavior of tunnels and should be considered in tunnel design (Fortsakis et al., 2012; Wittke, 1990; Armand et al., 2013; Bobet, 2011, 2016; Bobet & Yu, 2016; Vitali et al., 2020a, b, c; Vitali, 2020; Goricki et al., 2005; Schubert & Mendez, 2017, Klopčič & Logar, 2014). In anisotropic rock masses, the tunnel alignment with one of the principal directions of stress and material anisotropy is unlikely. In this case, asymmetric displacements are induced near the face and anti-symmetric axial displacements occur far-behind the face of the tunnel (Vitali et al. 2019b, 2020a, c; Vitali, 2020). The asymmetric displacements near the face affect the performance of the support and rock surrounding the excavation and may produce asymmetric plastic deformations around the tunnel (Vitali et al., 2019b, c, 2020a). Further, asymmetric displacements and asymmetric failure at the tunnel walls are commonly observed (Schubert & Budil, 1995; Goricki et al., 2005; Schubert et al., 2005; Schubert & Moritz, 2011; Klopčič & Logar, 2014; Lenz et al., 2017). 2D analyses cannot capture the 3D face effects that occur in tunnels during construction and, in particular, when the tunnel axis is not one of the principal directions of material anisotropy or a principal far-field stress; thus, 3D analyses are required. Because of recent advances in hardware and software, 3D FEM modeling is nowadays possible in the practice of engineering. However, the numerical modeling of tunnels not aligned with one of the principal directions of material anisotropy may be cumbersome and time consuming. Abstract The behavior of tunnels in anisotropic rock masses is highly complex and heavily dependent on the orientation of the tunnel axis with respect to the geostatic principal stress directions and to the rock structural planes. 2D solutions cannot capture the 3D face effects of such complex scenario; thus, 3D numerical modeling is required. The modeling of such tunnels using conventional boundary conditions may be cumbersome since the tunnel may not be parallel to the boundaries. The issue is further complicated if the principal far-field stresses are not parallel to the principal axes of material anisotropy. In this case, the use of conventional boundary conditions may be problematic. In this paper, a new approach is presented to impose the boundary conditions and the far-field stresses on 3D numerical models of tunnels under complex ground and loading conditions. With the proposed approach, it is possible to easily simulate any orientation of the tunnel with respect to the principal directions of stress and material anisotropy. The numerical results obtained with the proposed approach were validated with an analytical solution and with numerical results using traditional boundary conditions.