Fault stability changes induced beneath a reservoir with cyclic variations in water level

The stress and pore pressure changes produced by a steady periodic variation of water level on the surface of a uniform porous elastic half‐space are evaluated using the fully coupled (Biot) equations of elastic deformation and pore fluid flow. Diverse choices of material properties all give a coupled stress field differing from the elastic stress field by at most 0.035 p o , where p o is the water pressure at the bottom of the reservoir. Peak coupled pore pressure change can lag peak water level in the depth range 0 < (ω/2 c ) 1/2 z < π, where ω is frequency of the cyclic change in water level, c is diffusivity, and z is depth. The maximum lag increases as B decreases, where B is the ratio of pore pressure increase to mean compressive stress increase under undrained conditions. Directly beneath the reservoir, for example, peak pore pressure in an annual cycle can lag peak water level by at most 10 days if B = 0.80, but can lag by up to 122 days if B = 0.11. When cyclic water level changes are superimposed on the steady state reservoir level, the time during the cycle at which a fault is most destabilized depends on whether the weight of the reservoir stabilizes or destabilizes the fault, which, in turn, depends on its orientation and location relative to the reservoir. B and c also influence the timing of the greatest destabilization. If B and c are low, maximum destabilization at low water level is possible for faults that are stabilized by the weight of the reservoir; this mechanism may have operated at Lake Mead. The analysis suggests that induced seismic events should be separated into groups having a common focal mechanism and occurring in similar locations relative to the reservoir before studying the time at which the events occur relative to the water level. The fully coupled solution is compared with an uncoupled solution, with a solution that is coupled but which assumes incompressible solid and fluid constituents (consolidation) and with a decoupled solution in which the difference between the pore pressure field and B times the elastic mean compressive stress obeys a homogeneous diffusion equation. The uncoupled and consolidation solutions respectively underestimate and overestimate pore pressure during short‐term reservoir level fluctuations as well as at times short compared to that required to achieve steady state. In contrast, the decoupled solution agrees closely with the fully coupled solution for the problem studied here.