Abstract Numerical simulations of concrete fracture performed with a probabilistic mesoscale discrete model are presented. The model represents a substantial part of material randomness by assigning random locations to the largest aggregates. The remaining part of randomness is introduced by causing material parameters to fluctuate randomly via a homogeneous random field. An extensive numerical study performed with the model considers prisms loaded in uniaxial tension with both fixed and rotating platens, and also beams with and without a notch loaded in three point bending. The results show the nontrivial effect of (i) autocorrelation length and (ii) variance of the random field on the fracture behavior of the model. Statistics of the peak load are presented as well as the size and shape of the fracture process zone at the moment when the maximum load is attained. Local averaging within the fracture process zone and weakest-link are identified as underlying mechanisms explaining the reported results. The companion paper, Part II (Vořechovský and Elias, 2020), introduces an analytical model capable of predicting the distribution of the peak load obtained with the probabilistic discrete model via the simple estimation of extremes of a random field obtained as moving average of local strength.

中文翻译：

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随机准脆性介质中的断裂：I. 承载能力和断裂过程区的离散中尺度模拟

摘要 介绍了用概率中尺度离散模型进行的混凝土断裂数值模拟。该模型通过将随机位置分配给最大的聚集体来代表材料随机性的很大一部分。随机性的剩余部分是通过均匀随机场使材料参数随机波动来引入的。使用该模型进行的广泛数值研究考虑了在固定和旋转压盘上以单轴张力加载的棱镜，以及在三点弯曲中加载和不加载凹口的梁。结果显示了 (i) 自相关长度和 (ii) 随机场方差对模型断裂行为的重要影响。给出峰值载荷的统计数据以及达到最大载荷时断裂过程区的大小和形状。断裂过程区和最弱链接内的局部平均被确定为解释报告结果的潜在机制。配套论文第二部分（Vořechovský 和 Elias，2020 年）介绍了一种分析模型，该模型能够通过简单估计随机场的极端值来预测使用概率离散模型获得的峰值载荷的分布，该随机场的极值作为局部强度的移动平均值获得.