Structural nominal concrete strength derived by statistical mechanics

The purpose of this paper is to model the effects of the structural size and temperature on the nominal strength of concrete structures. on thermodynamics of irreversible processes, concrete damage theory and statistical mechanics, a constitutive behaviour of concrete was first derived. Then, generalized Boltzmann entropy was calculated by using the number of failure surfaces defined in the concrete microstructure. The number of states is defined as the number of possible failure surfaces. It was shown that states are correlated. This gives a nonadditive entropy for small structures. A theoretical nominal strength taking into account the structural size and temperature effects was deduced. fter, a one parameter rigid failure mechanism was considered to model experimental tests performed on concrete structures. The theoretical approach was applied to experimental tests performed on notched beams. A lower size effect is highlighted for lower temperatures. Theoretical results were compared with experimental test results performed on notched beams under bending. Comparison showed a good agreement.