Biot's theory of poroelasticity has gained new prominence in rock mechanics to understand the hydro-mechanical (H-M) response of fluid flow and deformation in tunneling in deep saturated ground. Numerically, explicit coupling technique has been widely used for simulating this coupled interaction. However, the technique is conditionally stable and requires small time steps, making it inefficient for simulating large-scale H-M problems. To improve the efficiency, the unconditionally stable alternating direction explicit (ADE) scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain problems. Thus, it is impractical for large-scale domains and inapplicable for axisymmetric problems. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving the flow problem in an axisymmetric non-uniform grid. The new scheme is derived by performing a fourth-order finite difference approximation for the spatial derivatives of the axisymmetric fluid-diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps, giving rise to a new high-order axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code Fast Lagrangian Analysis of Continua (FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. When applied for simulating an advancing tunnel in deep saturated ground, SEA-4-AXI reduces computer runtime up to 42% that of FLAC's basic scheme without numerical instability while also producing high numerical accuracy with average differences of 0.6–1.8% for pore pressure and displacement.
Biot's theory of poroelasticity (Biot, 1941) has gained new prominence in rock mechanics to understand the coupled response of fluid flow and deformation in deformable porous media (i.e., soils and rocks). Consolidation and subsidence induced by fluid extraction from underground formations are the most common examples of this coupled hydro-mechanical (H-M) interaction. In these examples, the transient fluid flow affects deformation in the ground and vice versa (Wang, 2000; Gutierrez and Lewis, 2002; Neuzil, 2003). Thus, consideration of this H-M interaction is essential for the safe design of underground structures such as deep tunnel in saturated ground.
