The Onset of Depletion‐Induced Seismicity in Slip‐Weakening Faults With Interacting Peaked Shear Stresses: Uenishi and Rice Extended

Abstract Depletion‐induced fault slip and seismicity in the Groningen natural gas field are known to be caused by compaction of reservoir rock, most likely at locations in faults where reservoir rock juxtaposes non‐reservoir rock leading to severely‐peaked shear stresses at the reservoir‐fault corners. The resulting fault slip is probably initially aseismic until a critical nucleation length is reached. Under the assumption of slip‐weakening friction, the nucleation length can be approximated with a classic stability criterion developed by Uenishi and Rice (U&R) in 2003 for a single‐peaked stress distribution. Earlier work revealed that the validity of this criterion breaks down when the fault offset exceeds approximately 70% of the reservoir height because interaction effects between neighboring stress peaks can no longer be ignored. We therefore extended the U&R criterion to cope with such a double‐peaked shear stress. The key mathematical innovation involves a singular functional form of the slip gradient which allows for the formulation of slip‐patch end conditions that can be directly extended to multiple patches. We derived an exact double‐patch eigenvalue criterion and an approximate closed‐form “Extended Uenishi and Rice (EU&R) criterion” that is dependent on a parameter representing the scaled distance between the slip patches. For examples with parameter values roughly based on those of the Groningen field, we found a good agreement between our approximate EU&R criterion and an exact eigenvalue‐based approach. Our results can serve as a robust code‐independent termination criterion during numerical simulation of depletion‐induced onset of seismicity resulting from natural gas or geothermal energy production.