Scale effect on concrete in tension

Parallel Implementation for Probabilistic Analysis of 3D Discrete Cracking in Concrete

“…The heterogeneity governs the overall cracking behavior and related size effects on concrete fracture. The probabilistic crack approach, based on the direct Monte Carlo method, developed by Rossi and co-workers ( Rossi et al [1], [2], [3], [4] ) takes this stochastic process into account by assigning in finite element analysis, randomly distributed material properties, such as tensile strength and Young's modulus to both the solid elements and the contact elements interfacing the former, that is, a discrete crack approach. This approach considers that all nonlinearities are restricted to contact elements modeling cracks.…”

“…The present probabilistic model involves a number of mechanical properties of the material to be determined, which constitutes the modeling data. From a large number of direct tensile tests, it was found that a normal law describes rather well the experimental distribution of the relevant material data (Rossi et al [2]). These characteristics are the means of the tensile strength ( ) and of the Young's modulus ( ); the standard deviations of the tensile strength ( ) and of the Young's modulus ( ).…”

“…These characteristics are the means of the tensile strength ( ) and of the Young's modulus ( ); the standard deviations of the tensile strength ( ) and of the Young's modulus ( ). The following analytical expressions were proposed (Rossi et al [2]): In these expressions, the compressive strength represents the quality of the concrete matrix, while the volume of the coarsest aggregate V , refers to the elementary material heterogeneity. Equations (1) to (3) show that the smaller the scale of observation, the larger the fluctuation of the local mechanical properties, and thus the (modeled) heterogeneity of the matter.…”

“…Following Rossi et al [2] findings, these individual local tensile strengths and Young's modulus are represented by normal distributions having the densities:…”

“…To handle with these characteristics, two basic approaches are generally used to model the mechanical behavior of the material: (i) the heterogeneous material is assimilated to a statistically equivalent homogeneous material and a deterministic approach together with a size effect law is used; (ii) homogeneity is no longer considered, at a certain scale, and the heterogeneity of the material, introduced by a stochastic approach, is the responsible for the scale effect. Regarding concrete, the second approach is quite recent, and in this paper we refer to Rossi's et al [1], [2], [3], [4] probabilistic model that seems to take into account size effects when the statistical parameters are well determined. This method uses Monte Carlo simulations to find the average behavior of the structure, which corresponds to the converged mean values of some typical results.…”