Abstract
A significant increase of the permeability of concrete upon micro-cracking and a good correlation between the evolution of damage (material stiffness) and permeability are observed experimentally. The present contribution investigates this correlation theoretically, with the help of lattice analyses. Scaling analysis of lattices which contain elastic brittle bonds has shown that the material degradation should be described by the evolution of the material stiffness, or compliance, in a continuum setting (damage models). This result is reviewed and further documented in the first part of the paper. In the second part, hydro-mechanical problems are considered with the construction of a hydraulic lattice, dual to the mechanical one. We observe that the average permeability upon micro-cracking is the lattice scale-independent controlling variable in the hydraulic problem. Additionally, results show that in a continuum poro-mechanical approach, the evolution of the material permeability ought to be related to the elastic unloading stiffness, described e.g. with the help of continuum damage variables. Copyright © 2005 John Wiley & Sons, Ltd.
Highlights
In large structures such as concrete nuclear vessels where the long-term safety is of high priority, durability is important for design
Simulations of such case studies, with the aim of estimating the increase of leakage rate that is induced by internal pressure in vessels, ought to rely on material models in which the evolution of material permeability is related to the non-linear mechanical response of concrete
What we intend to see is on which parameter of the mechanical problem the variation of permeability depends upon material damage growth, and by which moment of the hydraulic and mechanical problems the evolution of the fluid flow distribution in the lattice can be described in a sizeindependent way
Summary
In large structures such as concrete nuclear vessels where the long-term safety is of high priority, durability is important for design. Coupling between the non-linear response of concrete and its permeability can be achieved in a very standard way with the help of the theory of porous materials initially due to Biot (see e.g. References [7, 8]) This approach has become very popular in the literature for durability analyses involving mass transfer such as hydro-mechanical damage analyses [9], analysis of concrete at an early age [10], chemo-mechanical effects [11], and more generally environmentally induced degradations [12]. Two-dimensional lattice models consisting of beams [15] or springs [16] have been used, where the heterogeneity is captured by a random distribution of the failure thresholds of each beam/bar These lattices are very simple, and not capable of reproducing the exact features of the micro-cracking processes in brittle heterogeneous materials, the limit of a lattice of infinite size is related to the response of a material point in the continuum sense. We compare the results with experimental curves obtained by Picandet et al [19] from a qualitative point of view
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