From local to global probabilistic modeling of concrete cracking

Abstract

The description of cracks in concrete is crucial when dealing with life expectancy of structures such as dams, nuclear power plants vessels, waste (nuclear or not) storage structures, tunnels, etc. The main objective is not only to describe the growth of a preexisting flaw, but also to predict the genesis and formation of cracks in an initially flaw-free structure (at least at the macroscopic level) subjected to tension. The presented paper provides a macroscopic model for tensile cracking (i.e., a model adequate for describing the behavior at the structure level), capable at the same time of providing information on the local response (i.e., cracks). The model takes into account scale effects as well as the heterogeneous nature of concrete via appropriate, experimentally validated, size effect laws and via a statistical distribution of mechanical properties. Results are provided and validated via a 2D comparison with an original experimental test.

Numerical modeling of the cracking behavior of a steel fiber‐reinforced concrete beam on grade

“…At this stage, the stiffness of the interface element becomes equal to zero (perfect brittle behavior). The critical value of the tensile stress is treated as a random number using a Weibull distribution function (commonly used for brittle failure of heterogeneous materials) . This choice is based on a previous experimental study (performed at IFSTTAR) concerning a statistical analysis of the tensile strength of different concretes …”

“…The critical value of the tensile stress is treated as a random number using a Weibull distribution function (commonly used for brittle failure of heterogeneous materials). 11 This choice is based on a previous experimental study (performed at IFSTTAR) concerning a statistical analysis of the tensile strength of different concretes. 12 As previously mentioned, the critical value of the tensile stress depends on the total volume of the two volumetric elements connected to the considered interface element.…”

Finite-element modelling of SFRC members in bending

“…Finite-element modelling of SFRC members in bending de Montaignac, Massicotte and Charron Another approach would be to use variable material properties dispersed randomly according to the actual distribution of material properties (Tailhan et al, 2010). Crack localisation in the model is then much more representative of the actual mechanical behaviour of the structural member, particularly if it is combined with multiple calculations (Monte Carlo simulations).…”

3D numerical modelling of concrete structural element reinforced with ribbed flat steel rebars

“…This numerical modelling takes into account: -Cracking of concrete through a probabilistic discrete cracking model 3D numerical modelling of concrete structural element reinforced with ribbed flat steel rebars [1,2] and recently improved by Tailhan et al [3]. The feature of this model is its ability to take into account two major characteristics of concrete: heterogeneity on the one hand and its sensitivity to scale effects on the other [2].…”

“…In terms of numerical modelling (within the scope of FEM), this physical evidence can be taken into account as follows: -The tensile strength is initially randomly distributed over all elements of the mesh following a probability distribution whose parameters depend on [1,2,3]:…”