Numerical strategy for developing a probabilistic model for elements of reinforced concrete

This paper introduces a new approach to model cracking processes in large reinforced concrete structures, like dams or nuclear power plants. For these types of structures it is unreasonable, due to calculation time, to explicitly model rebars and steel–concrete bonds. To solve this problem, we developed, in the framework of the finite element method, a probabilistic macroscopic cracking model based on a multiscale simulation strategy: the probabilistic model for (finite) elements of reinforced concrete (PMERC). The PMERC’s identification strategy is case-specific because it holds information about the local behavior, obtained in advance via numerical experimentations. This information is then projected to the macroscopic finite element scale via inverse analysis. The numerical experimentations are performed using a validated cracking model allowing a fine description of the cracking processes. The method used in the inverse analysis is inspired from regression (supervised learning) algorithms: data on the local scale—the training data coupled with working knowledge of the mechanical problem—would shape the macroscopic model. Although the identification phase can be relatively time-consuming, the structural simulation is as a result, very fast, leading to a sensitive reduction of the overall computational time. It is proposed a first validation of this multiscale modeling strategy on a reinforced concrete slab-beam subjected to three-point bending. We achieved promising results in terms of global behavior and macrocracking (mainly crack openings), and an important reduction in calculation time—up to 99% reduction! So we believe this is a promising approach to solve bigger and more complex structures in shorter time.