  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.
