Macroscopic probabilistic cracking approach for the numerical modelling of fluid leakage in concrete

Abstract

The article presents a numerical finite element study of fluid leakage in concrete. Concrete cracking is numerically modelled in the framework of a macroscopic probabilistic approach. Material heterogeneity and the re- lated mechanical effects are taken into account by defining the elementary mechanical properties according to spatially uncorrelated random fields. Each finite element is consid- ered as representative of a volume of heterogeneous ma- terial, whose mechanical behaviour depends on its own volume. The parameters of the statistical distributions defining the elementary mechanical properties thus vary over the computational mesh element-by-element. A weak hydro-mechanical coupling assumption is introduced to represent the influence of cracking on the variation of transfer properties: it is assumed that the mechanical cracking of a finite element induces a loss of isotropy of its own permeability tensor. At the elementary level, an ex- perimentally enhanced parallel plates model is used to re- late the local crack permeability to the elementary crack aperture. A Monte Carlo-like approach allows to statisti- cally validate the numerical method. The self-consistency of the proposed modelling strategy is finally explored through the numerical simulation of the hydro-mechanical splitting test, recently proposed by authors to evaluate the real-time evolution of the transfer properties of a concrete sample under loading

New continuous strain‐based description of concrete's damage‐permeability coupling

“…A comparison between the different matching laws is depicted in Figure A‐C: In literature, one can find a linear matching between the 2 modes where the increase of permeability, when damage exceeds 15%, is only due to the increase of the crack opening value. However, for values of damage between 15% and 90%, the effective crack opening remains quasinull, which leads to a constant permeability within that domain. Other linear models suggest a damage‐weighted addition of the 2 modes .…”

“…Indeed, for a complete unloading, the macrocrack can be considered fully closed whereas the network of microcracks around remains active. Such configuration favours the use of Darcy's law rather than Poiseuille's, which is valid for crack openings that are at least higher than 20 μm . Accordingly, the irreversibility of permeability is herein associated with concrete damage and not with a residual macrocrack opening.…”

“…Poiseuille's law is usually used to describe permeability through a macrocrack (Equation ). It consists of writing the apparent permeability k P (P in k P stands for Poiseuille) as a function of the squared crack opening value (which is unbounded in opposition with the damage variable): where ξ ≤ 1 is a factor to account for the roughness and shape effects of the through crack domain . When ξ = 1, the domain is supposed to be perfectly smooth.…”

“…When ξ = 1, the domain is supposed to be perfectly smooth. The expression suggested in Rastiello et al based on real‐time water permeability evolution through a localized crack during a splitting test (Equation ) seems more appropriate compared to others where ξ is considered constant (between 0.01 and 0.1 in Picandet et al). Indeed, as the crack opening becomes larger, the roughness effects are supposed to be relatively less and ξ should tend towards 1 (Figure ).…”

“…Poiseuille's mode: As the loading increases, those microcracks localize into macrocracks, which are descriptive of a high and spatially localized strain. The associated permeability in that case is due to the fluid's flow through the macrocracks' openings and is commonly described using the so‐called Poiseuille's law …”