Systematic study of the effects of mass and time scaling techniques applied in numerical rock mechanics simulations
Systematic study of the effects of mass and time scaling techniques applied in numerical rock mechanics simulations
复制标题
DOI：
10.1016/j.tecto.2015.10.013
复制
发表时间：
2016-08
期刊：
影响因子：
2.9
通讯作者：
T. Heinze;G. Jansen;B. Galvan;S. A. Miller
中科院分区：
文献类型：
--
作者：
T. Heinze;G. Jansen;B. Galvan;S. A. Miller
数值模拟是岩石力学研究中的一种成熟工具，可以研究各种各样的问题。求解线性方程组的隐式方法具有无条件稳定的优点，而显式方法虽然受到时间步长的限制，但由于其有限的内存需求，其在并行计算中的可扩展性以及复杂边界条件的简单实现而经常被使用。在显式弹塑性动力学的数值模拟中，时间步长受到材料密度的限制，质量缩放技术可以用来克服这个限制，并显着减少计算时间。虽然经常使用，但质量和时间缩放的效果以及它如何影响数值结果在出版物中很少提及，并且通常通过试验和错误来选择正确的缩放技术。据我们所知，没有系统的研究已经解决了如何质量缩放可能会影响数值结果。在本文中，我们提出了一个广泛的和系统的研究质量和时间尺度的影响，各种岩石力学模型的行为的结果。我们采用了有限差分格式来模拟单轴和双轴压缩实验，使用不同的质量和时间比例因子，并与物理模型的复杂性增加到一个凝聚力减弱摩擦加强模型（CWFS）。我们还引入了一个归一化的能量比，以协助分析质量标度效应。我们发现测试的模型是不敏感的时间缩放比质量缩放，所以质量缩放有更大的潜力，降低计算成本。然而，我们也表明，质量缩放可能会导致定量错误的结果，所以必须小心解释应力值时，质量缩放用于复杂的岩石力学模拟。质量缩放显着影响数值岩石的应力-应变响应，因为质量缩放作为一个人工硬化剂对岩石变形。
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.