Global weak solutions for coupled transport processes in concrete walls at high temperatures

TL;DR

This paper establishes the existence of global weak solutions for a nonlinear coupled hygro-thermal model of concrete at high temperatures, with practical implications for fire safety and structural integrity.

Contribution

It introduces a rigorous mathematical proof of global weak solutions for a complex coupled system modeling concrete behavior under fire conditions, using approximation and Leray-Schauder methods.

Findings

Model predicts pore pressure buildup during transient heating.

Analysis indicates potential for explosive spalling under certain fire scenarios.

Provides a mathematical foundation for safety assessments of concrete structures.

Abstract

We consider an initial-boundary value problem for a fully nonlinear coupled parabolic system with nonlinear boundary conditions modelling hygro-thermal behavior of concrete at high temperatures. We prove a global existence of a weak solution to this system on an arbitrary time interval. The main result is proved by an approximation procedure. This consists in proving the existence of solutions to mollified problems using the Leray-Schauder theorem, for which a priori estimates are obtained. The limit then provides a weak solution for the original problem. A practical example illustrates a performance of the model for a problem of a concrete segment exposed to transient heating according to three different fire scenarios. Here, the focus is on the short-term pore pressure build up, which can lead to explosive spalling of concrete and catastrophic failures of concrete structures.