A free-boundary problem for concrete carbonation: Rigorous justification of the t-law of propagation
Abstract
We study a one-dimensional free-boundary problem describing the penetration of carbonation fronts (free reaction-triggered interfaces) in concrete. A couple of decades ago, it was observed experimentally that the penetration depth versus time curve (say s(t) vs. t) behaves like s(t)=Ct for sufficiently large times t > 0 (with C a positive constant). Consequently, many fitting arguments solely based on this experimental law were used to predict the large-time behavior of carbonation fronts in real structures, a theoretical justification of the t-law being lacking until now. %This is the place where our paper contributes: The aim of this paper is to fill this gap by justifying rigorously the experimentally guessed asymptotic behavior. We have previously proven the upper bound s(t)≤ C't for some constant C'; now we show the optimality of the rate by proving the right nontrivial lower estimate, i.e. there exists C">0 such that s(t)≥ C"t. Additionally, we obtain weak solutions to the free-boundary problem for the case when the measure of the initial domain vanishes. In this way, our mathematical model is now allowing for the appearance of a moving carbonation front -- a scenario that until was hard to handle from the analysis point of view.