Probabilistic analysis of concrete cracking using stochastic finite element methods: application to nuclear containment buildings at early age

• Published in: Materials and structures Vol. 53; no. 4
• Main Authors: Bouhjiti, D. E.-M., Baroth, J., Dufour, F., Briffaut, M., Masson, B.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.08.2020; Springer Nature B.V; Springer Verlag
• Subjects: Age; Building construction; Building Materials; Civil Engineering; Computer simulation; Computing time; Concrete; Concrete structures; Containment; Containment vessels; Cost analysis; Crack initiation; Crack propagation; Cracks; Engineering; Engineering Sciences; Fields (mathematics); Finite element method; Machines; Manufacturing; Materials Science; Modulus of elasticity; Monte Carlo simulation; Numerical prediction; Original Article; Polynomials; Probabilistic analysis; Probability theory; Processes; Randomness; Sensitivity analysis; Solid Mechanics; Stochastic processes; Tensile strength; Tensile stress; Theoretical and Applied Mechanics; Thermal expansion; Non-intrusive stochastic finite elements method; Surface response method; Monte Carlo; Containment buildings; Polynomial chaos expansion; Early age; Concrete cracking
• ISSN: 1359-5997; 1871-6873
• DOI: 10.1617/s11527-020-01519-3

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.