A nonlinear elastic solution for 1-D subsidence due to aquifer storage and recovery applications

Applications of the aquifer storage and recovery (ASR) technology can cause land subsidence due to the net compression of one or more semi-pervious clay beds. In order to estimate the potential risk of aquifer system deformation in response to an injecting-pumping scheme, a one-dimensional analytical solution based on a conceptual sandwich model is solved. The analytical solution corresponds to boundary and initial conditions. The boundary condition comprises linear and periodic strains changing with time. The periodic strain is assumed to be a sinusoidal function of time. The solution is analyzed for a unit column of an idealized compressible semi-pervious layer. A complete mathematical description includes an initial condition, two sets of boundary conditions and a governing equation that is expressed directly in terms of the vertical displacement of the skeletal frame. The saturated aquifer system is assumed to behave like nonlinear poroelastic material (both recoverable and non-recoverable). The two idealized aquifers (one above the modeled semi-confining bed and the other beneath) can be pumped independently of each other. The analytical solution is analyzed and applied to estimate the potential risk of land subsidence caused by ASR applications at Las Vegas, Nevada, USA and the results are satisfactory. Estimate and prediction of land subsidence using the analytical solution provide a first-estimate type of guideline for city and regional planning and the exploration of water resources.