Hydro-mechanical analysis of tunneling in saturated ground using a novel and efficient sequential coupling technique

Abstract

In 1941, Belgian-born physicist Maurice Anthony Biot (1905-1985) developed the first equations that govern the coupled interactions between fluid flow and deformation in elastic porous media. This hydro-mechanical (H-M) interaction has started to receive wide attention in the field of tunnel engineering. In urban areas, the induced H-M interaction due to surface loading over an existing shallow tunnel can have a severe impact on short- and long-term tunnel stabilities, the degree of which remains unclear. Likewise, advancing tunnel in deep saturated ground causes time-dependent consolidation that is invoked by the transient nature of the coupled interaction. Yet, deep tunnel advance is still commonly simulated in one excavation step and under a steady state condition, oversimplifying the excavation-induced H-M interaction as proposed by Biot. Explicit coupling techniques have been widely used for H-M analysis of such tunnel problems. However, explicit techniques are conditionally stable, requiring small time steps to maintain numerical stability. To improve the efficiency of H-M analysis, an unconditionally stable explicit finite difference scheme such as the alternating direction explicit (ADE) scheme could be used to solve the flow problem. Yet, the standard ADE scheme is only moderately accurate and restricted to uniform grids and plane strain conditions. This thesis presents the derivation of novel high-order ADE schemes for non-uniform grids to solve the flow problems in plane strain and axisymmetric conditions. For each condition, the resulting pore pressure solutions from the new ADE scheme were sequentially coupled with a geomechanical simulator in Fast Lagrangian Analysis of Continua (FLAC), resulting in a novel and efficient sequentially-explicit coupling technique called SEA-4 for the plane strain problem and SEA-4-AXI for the axisymmetric problem. This thesis will show that by using SEA-4 and SEA-4-AXI, the H-M simulations of tunneling in saturated ground can be performed efficiently without numerical instability and yet still retain high numerical accuracy. Verifications from well-known consolidations and tunnel problems have shown that SEA-4 and SEA-4-AXI reduced the computer runtime to 20-66% that of FLAC’s basic flow scheme. They also maintained maximum absolute errors of < 6% for the pore pressure and < 1.5% for the displacement solutions, demonstrating their future application for producing efficient H-M simulations. The H-M analysis also showed that under surface loading, tunnel stability in addition to ground strength was largely influenced by liner permeability and the long-term H-M response of the ground. The step-wise excavation in deep advancing tunnel caused a non-monotonic behavior of pore pressure, temporarily confining the advanced core, leading to a new insight for the convergence-confinement method (CCM) in saturated ground. Recognizing this transient coupling effect, this thesis proposed: (1) theoretical relationships between the extrusion and convergence and preconvergence of the face and the advance core, (2) an extended CCM using proposed transient unloading factors and (3) new semi-analytical equations for predicting the transient longitudinal displacement profile (LDP) of a deep saturated tunnel taking into account the transient coupling effect induced by the consolidation process. In addition to the H-M analysis of tunneling, the thesis made two additional contributions to further explicate the role of H-M interaction in rock engineering in other applications. First, it presented the role of the coupled two-phase flow and geomechanical interaction of CO2 sequestration into deep underground reservoirs. Second, the thesis presented a newly developed constitutive model for predicting the nonlinear shear behavior of rock joints using the linearized implementation of the Barton-Bandis joint model. When this model is coupled with either SEA-4 or SEA-4-AXI, it can be potentially used for H-M analysis of tunneling in fractured saturated rock.