Hindered thermal warping triggers tensile cracking in the cores of compressed columns of a fire-loaded tunnel segment structure: Efficiency and accuracy of beam theory prediction, compared to FEM

The nonlinear Finite Element Method (FEM) is the current gold standard for the thermo-mechanical analysis of reinforced concrete structures. As an alternative, this paper is devoted to a model reduction strategy which reduces the CPU time by a factor of 500. This strategy combines Fourier series-based solutions for the thermal conduction problem, and thermo-elastic Timoshenko beam theory. Temperature histories known to be relevant for fire accidents enter series solutions quantifying the conduction of heat into a closed cell frame consisting of slabs, walls, and columns. Corresponding temperature profiles are translated into thermal eigenstrains. The latter are represented as the sum of three portions: (i) their cross-sectional averages (called thermal eigenstretches); (ii) their cross-sectional moments (called thermal eigencurvatures); and (iii) the remaining eigenstrain distributions (called eigenwarping). The latter portion is hindered at the cross-sectional scale, giving rise to non-linearly distributed self-equilibrated thermal stresses. The eigenstretches and eigencurvatures, in turn, are constrained at the scale of the frame structure. Together with external mechanical loads, they enter the exact solutions of thermo-elastic Timoshenko beam theory with equivalent cross-sections accounting for the different material properties of concrete and steel. Axial normal stresses, quantified from beam-theory-related normal forces and bending moments, are superimposed with the hindered-warping-induced stresses. These stresses agree well with corresponding results obtained by the nonlinear FEM. As regards the load carrying behavior of the columns, excessive thermal tensile strains at the periphery of the columns trigger, in the core of the columns, large tensile stresses which even exceed the strength of concrete. Respective cracking events are considered through reduced effective columnar cross-sections. Right after initiation of cracking, around 12 min after the start of the heating process, the cracks propagate for some 30 sec quite rapidly, and very much slower thereafter. If the initial cross-sections of the columns are increased, more pronounced hindered thermal warping, together with less quickly evolving compressive forces, results in earlier cracking. Overall, it is concluded that tensile cracking is the key material non-linearity, at least during the first 30 min of the fire test, with maximum temperatures up to 300 °C.