Evaluation of Rockburst Hazard by Accelerated Numerical Modeling of Stressed State and Induced Seismicity - RASIM2022

Joined modeling of stressed state and induced seismicity is a means to join geomechanics with seismic observations. When applied to quantifying rockburst hazard, it provides, on one hand, estimations in terms of mechanics, such as stress concentration, and, on the other hand, in statistical terms of the risk analysis developed in mining seismology. The modeling became possible due to progress in computers and numerical methods. However, despite tremendous increase of computational abilities, the joined modeling is still quite time expensive. To make it available for wide use and real time simulations, there is need to reduce the time cost of its key stages: calculation of stresses, caused by mining, and simulation of seismic events, induced by these stresses. The present work aims to decrease the time cost. The stages are time costly because of the same reason, which is a very large number N (up to millions) of elements, representing rock structure, openings and flaws. This leads to immense computational complexity (roughly of order N2) of conventional accounting for pairwise interactions between the elements. The complexity may be notably reduced, when employing the fact that interactions decrease with growing distance between elements. Specifically, the fast multipole methods (FMM) avoid the complexity N2, by employing translations of far-fields from whole collections of sources. This reduces the complexity to the order 𝑝𝑝2𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑚𝑚2, where p is the number of terms involved in a single translation, 𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 is the number of translations, and 𝑚𝑚 is the dimension of the quantity translated. Still, for conventional FMM, the complexity remains too high to routinely perform joined modeling of stresses and seismicity.