Dynamic Modelling of Induced Seismicity by Using Seismic Efficiency Constraints and a New Scaling Law for Slip-Weakening Distance

In the numerical simulation of induced seismicity, much attention is generally paid to the calibration of the frictional resistance of the causative fault to obtain a seismic moment consistent with that of the actual event, whereas sufficient investigation is not made in the estimation of the slip-weakening distance D_c as well as in the calibration of seismically radiated energy. The present study addresses this problem by numerically and analytically investigating the relation between D_c and seismic source parameters. First, this study performs the dynamic simulation of an induced seismic event caused by a decrease in the effective normal stress. The analysis demonstrated that seismic efficiency η can be used to improve the accuracy of estimating the critical slip-weakening distance and the coefficient of kinetic friction µ_d whilst considering not only seismic moment but also radiated energy in the calibration. This gave insight into the development of the new calibration method for induced seismicity that considers energy-related seismic source parameters. Furthermore, a new scaling law of the slip-weakening distance was derived from the theoretical expression of seismic efficiency η, considering seismic moment M_o and scaled energy $\hat{e}$. The proposed scaling law can yield the relation between D_c and M_o, which is shown to be similar to that obtained from a previous study, but additionally considers the relation between seismically radiated energy and D_c. The dependency of D_c on seismically radiated energy implied from the proposed scaling law has been verified from the dynamic analyses where η = 0.06 was used to place a constraint on D_c for seismic events with different magnitudes. The developed numerical simulation methodology of induced seismicity as well as the scaling law considering the energy indices significantly contributes to improving the accuracy of back-analysis, thus leading to a more accurate estimation of the mechanical properties of faults and/or shear zones in seismically active regions of deep underground mines or reservoirs composed of discontinuous hard rock masses.