Theoretical modelling of bowing in cracked marble slabs under cyclic thermal loading

In the first part of the present paper, a theoretical model to calculate the progressive bowing of marble slabs submitted to thermal cycles is presented. The model, developed within the framework of linear elastic fracture mechanics, takes into account the mechanical characteristics of the marble as well as the actual cyclic temperature field in the material. The slabs are subjected to a thermal gradient along their thickness (due to different values of temperature between the outer and inner sides of the slab) as well as to thermal fluctuation on the two sides of the slab due to daily and seasonal temperature excursions. This thermal action causes a stress field which can locally determine microcracks due to decohesion of grains. Stress intensification near the cracks occurs and leads to crack propagation in the slab. Such crack propagation under thermal actions is evaluated, and, considering different crack densities in the material and different boundary conditions in the slab, the corresponding deflection (bowing), which account for both elastic bulk deformation of the slab and for the deformation due to the crack presence, is calculated. In the second part of the present paper, the model is applied to the case study of the Pescara (Italy) court building.