New developments of an in-house hybrid code, named Modified Discrete Element Method (MDEM) are presented in the paper. The new developments are on the treatment of pre-existing and propagating fractures in quasi-brittle materials. These developments are the embedment of Linear Elastic Fracture Mechanics (LEFM) and elastic-softening crack band model -based methodologies in the MDEM and their application in lab and reservoir scale. Using the first methodology, MDEM can calculate stress intensity factors, $$K^{\text{I}}$$ K I and $$K^{\text{II}}$$ K II using the internal contact forces of particles. $$K^{\text{I}}$$ K I and $$K^{\text{II}}$$ K II are calculated independent of boundary conditions and geometrical configuration with acceptable accuracy level. The methodology has been also used in reservoir scale to study the rupture likelihood of faults and fractures due to fluid injection. This methodology enables the code to model mode I and mode II failures and propagation direction based on the fracturing model proposed by Rao et al. (Int J Rock Mech Min Sci 40(3): 355–375, 2003). Using the second methodology, the MDEM can model nonlinear behavior of quasi-brittle materials including or excluding preexisting cracks based on fracture energy. A model was verified against an experiment of a three point bend test with a notch. The numerically obtained force-crack mouth opening curve was reasonably comparable to the experimental test. The analysis was repeated for three other mesh sizes and the results are less mesh size dependent. Finally, it was shown that MDEM has the potential in studying fracture mechanics of quasi-brittle materials both in lab and large-scale investigations.

中文翻译：

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改进离散元法模拟的准脆性岩石断裂评价

论文中介绍了内部混合代码的新发展，称为修改离散元方法 (MDEM)。新的发展是关于准脆性材料中预先存在和扩展的裂缝的处理。这些发展是线弹性断裂力学 (LEFM) 和基于弹性软化裂纹带模型的方法在 MDEM 中的嵌入及其在实验室和储层规模中的应用。使用第一种方法，MDEM 可以使用粒子的内部接触力计算应力强度因子 $$K^{\text{I}}$$ KI 和 $$K^{\text{II}}$K II。$$K^{\text{I}}$$ KI 和 $$K^{\text{II}}$$ K II 的计算与边界条件和几何配置无关，精度水平可以接受。该方法也已用于储层规模，以研究由于流体注入引起的断层和裂缝破裂的可能性。这种方法使代码能够基于 Rao 等人提出的压裂模型对模式 I 和模式 II 故障和传播方向进行建模。(Int J Rock Mech Min Sci 40(3): 355–375, 2003)。使用第二种方法，MDEM 可以模拟准脆性材料的非线性行为，包括或排除基于断裂能的预先存在的裂纹。模型根据带缺口的三点弯曲试验进行了验证。数值获得的力-裂纹嘴张开曲线与实验测试相当。对其他三种网格尺寸重复分析，结果与网格尺寸的相关性较小。最后，