In the case of quasi-homogeneously applied tensile loads, the intrinsic scattering of concrete properties leads to spatially random strain localization, crack initiation and propagation. The modelling of such spatial randomness, in the case of Equivalent-Homogeneous-Material Finite Elements based approaches, can be achieved thanks to the use of Random Fields. However, when aiming at probabilistic analyses, numerous realizations are required which induces a hefty computational time and restricts their applicability to the modelling of large concrete structures. In this contribution, an original probabilistic coupling strategy is provided based on non-intrusive Stochastic Finite Elements Methods. It consists of defining an explicit Surface Response of the cracking patterns expressed in terms of the most influential inputs using an Adaptive Surface Response Method combined to a Polynomial Chaos Expansion Method. Direct Monte Carlo Method is then applied—to the explicit Surface Response of the cracking patterns—to achieve Global Sensitivity Analysis, Uncertainties Quantification and probabilistic modelling at a reasonable cost. The defined strategy is validated based on a Representative Structural Volume of a 1:3 scaled experimental Containment Building at early age using a weakly coupled thermo-mechanical model. As a result, the study quantifies the effect of the most influential parameters (the Young’s modulus—the tensile strength—the coefficients of thermal expansion and autogenous shrinkages) on concrete cracking at early age and provides accurate numerical prediction of the cracking patterns (cracks’ number, opening and spacing values) observed on site and their frequencies.

中文翻译：

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使用随机有限元方法对混凝土开裂进行概率分析：在早期核安全壳建筑中的应用

在准均匀施加拉伸载荷的情况下，混凝土特性的固有散射导致空间随机应变局部化、裂纹萌生和扩展。在基于等效均质材料有限元方法的情况下，可以通过使用随机场来实现这种空间随机性的建模。然而，当针对概率分析时，需要大量的实现，这会导致大量的计算时间并限制它们对大型混凝土结构建模的适用性。在这个贡献中，提供了一种基于非侵入式随机有限元方法的原始概率耦合策略。它包括使用自适应表面响应方法与多项式混沌扩展方法相结合，定义以最具影响力的输入表示的开裂模式的显式表面响应。然后将直接蒙特卡罗方法应用于开裂模式的显式表面响应，以合理的成本实现全局灵敏度分析、不确定性量化和概率建模。使用弱耦合热机械模型，在早期根据 1:3 比例的实验收容大楼的代表性结构体积对定义的策略进行了验证。因此，