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Application of high-order axisymmetric ADE scheme for efficient hydromechanical simulation of deep tunnel in saturated ground

Prassetyo S.H.a, Gutierrez M.S.b

a Institut Teknologi Bandung, Bandung, Indonesia
b Colorado School of Mines, Golden, United States

[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2018 ISRM & SRMEG (Singapore)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.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Alternating directions,Axisymmetric,Deep tunnels,Fast Lagrangian analysis of continuum,Finite difference approximations,Hydro-mechanical interactions,Saturated Ground,Unconditionally stable[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Axisymmetric Fluid Flow,Deep Tunnel,Hydro-Mechanical Interaction,Saturated Ground[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text]The authors gratefully acknowledge support from the University Transportation Center for Underground Transportation Infrastructure at the Colorado School of Mines for funding this research under Grant No. 69A3551747118 of the Fixing America’s Surface Transportation Act (FAST Act) of U.S. DoT FY2016.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]