Surface flow boundary conditions in modeling land subsidence due to fluid withdrawal

Land subsidence due to subsurface fluid withdrawal is often predicted by either finite element or finite difference models based on tha coupled poroelastic theory, where the soil is represented as a semi-infinite medium bounded by the traction-free ground surface. One of the variables playing a most important role on the final outcome is the flow condition used on the traction-free boundary, which may be assumed as either permeable or impermeable. Although occasionally justified, the assumption of no-flow surface seems to be rather unrealistic. A permeable boundary where the pore pressure is fixed to the external atmospheric pressure appears to be more appropriate. This paper addresses the response in terms of land subsidence obtained with a coupled poroelastic finite element model that simulates a distributed pumping from a horizontal aquifer confined two relatively impervious layers, and takes either a permeable boundary surface, i.e., constant hydraulic potential, or an impermeable boundary, i.e., a zero Neumann flow condition. The analysis reveals that land subsidence is rather sensitive to the flow condition implemented on the traction-free boundary. In general, the no-flow condition leads to an overestimate of the predicted ground surface settlement, which could even be one order of magnitude larger than that obtained with the permeable boundary.