Systematic study of the effects of mass and time scaling techniques applied in numerical rock mechanics simulations

作者：Heinze Thomas; Jansen Gunnar; Galvan Boris; Miller Stephen A

来源：Tectonophysics, 2016, 684: 4-11.

DOI：10.1016/j.tecto.2015.10.013

• Mass scaling
• Time scaling
• Computational density
• Artificial hardening
• Explicit time stepping

Numerical modeling is a well established tool in rock mechanics studies investigating a wide range of problems. Implicit methods for solving linear equations have the advantage of being unconditionally stable, while explicit methods, although limited by the time step, are often used because of their limited memory demand, their scalability in parallel computing, and simple implementation of complex boundary conditions. In numerical modeling of explicit elastoplastic dynamics where the time step is limited by the material density, mass scaling techniques can be used to overcome this limit and significantly reduce computation time. While often used, the effect of mass and time scaling and how it may influence the numerical results is rarely-mentioned in publications, and choosing the right scaling technique is typically performed by trial and error. To our knowledge, no systematic studies have addressed how mass scaling might affect the numerical results. In this paper, we present results from an extensive and systematic study of the influence of mass and time scaling on the behavior of a variety of rock-mechanical models. We employ a finite difference scheme to model uniaxial and biaxial compression experiments using different mass and time scaling factors, and with physical models of increasing complexity up to a cohesion-weakening frictional-strengthening model (CWFS). We also introduce a normalized energy ratio to assist analyzing mass scaling effects. We find the tested models to be less sensitive to time scaling than to mass scaling, so mass scaling has higher potential for decreasing computational costs. However, we also demonstrate that mass scaling may lead to quantitatively wrong results, so care must be taken in interpreting stress values when mass scaling is used in complicated rock mechanics simulations. Mass scaling significantly influences the stress-strain response of numerical rocks because mass scaling acts as an artificial hardening agent on rock deformation.

• 出版日期2016-8-2