On a model simulating lack of hydraulic connection between a man-made reservoir and the volume of poroelastic rock hosting the focus of a post-impoundment earthquake

The idea that a direct hydraulic connection between a man-made reservoir and the foci of post-impoundment earthquakes may not exist at all sites is eminently credible on geological grounds. Our aim is to provide a simple earth model and related theory for use during investigations of earthquakes near new man-made reservoirs. We consider a uniform circular reservoir which rests on the top surface of a no-hydraulic-connection earth model (NHCEM). The model comprises a top elastic (E) layer, an intermediate poroelastic (P) layer, and a bottom elastic half space. The focus of a potential earthquake in the P layer is located directly under the reservoir. The E layer disrupts the hydraulic connection between the reservoir and the focus. Depth of water in the reservoir varies as H ^′ + hcos(ω t). Expressions for reservoir-induced stresses and pore pressure in different layers of the NHCEM are obtained by solving the boundary-value problem invoking full coupling between mean normal stress and pore pressure in the P layer. As an application of the derived mathematical results, we have examined and found that earthquakes on 60^° normal faults may occur in the P-layer of a selected NHCEM at epochs of low reservoir level if the reservoir lies mostly in the footwall of the fault. The exercise was motivated by observations of such earthquakes under the man-made Lake Mead after it was impounded.