The damage and fracture mechanisms of concrete are complicated due to the material’s inherent meso-scale heterogeneities. In this study, continuous random fields for selected properties, such as the tensile strength, are first generated on the basis of real microscale X-ray Computed Tomography (CT) images of concrete, using statistical reconstruction algorithms and the Karhunen-Loève expansion technique. The random fields are then assigned to finite element models with mesoscale crack initiation and propagation simulated by a phase-field regularized cohesive zone model (PF-CZM) with softening laws. The proposed two-step modelling method is validated by Monte Carlo simulations of a square test-piece under uniaxial tension and an L-shaped panel under mixed-mode fracture. It is found that the method can capture the variability of mesoscale fracture processes, crack paths and load-displacement curves, in good agreement with measured experimental variations. The method holds promise for the efficient evaluation of structural reliability by Monte Carlo simulations taking into account stochastic microstructural variability, thanks to the fast generation of a large number of random samples, through the high-fidelity representation of real materials’ microstructures, and flexible simulation of complicated nonlinear fracture of phase-field models without the need for remeshing or mesh enrichments.

由于材料固有的介观尺度异质性，混凝土的破坏和断裂机理变得复杂。在这项研究中，首先使用统计重建算法和Karhunen-Loève膨胀技术，在混凝土的真实X射线计算机断层扫描（CT）图像的基础上，生成选定特性（例如拉伸强度）的连续随机场。然后，将随机场分配给具有中尺度裂纹萌生和扩展的有限元模型，并由具有软化律的相场正则化粘结带模型（PF-CZM）模拟。提出的两步建模方法通过蒙特卡洛模拟对单轴拉伸下的方形试件和混合模式断裂下的L形板进行了验证。结果发现，该方法可以捕获中尺度断裂过程，裂纹路径和载荷-位移曲线的变化，与实测的实验变化非常吻合。该方法为通过考虑随机微观结构变异性的蒙特卡洛模拟进行结构可靠性的有效评估提供了希望，这要归功于通过真实材料微观结构的高保真表示可以快速生成大量随机样本，并且可以进行灵活的模拟无需重新网格化或网格富集，即可完成相场模型的复杂非线性断裂。