A numerical homogenization method for the determination of the thermal bowing of a masonry wall exposed to fire: Application to natural stone masonry

Thermal bowing is one of the major concerns when analysing the structural behaviour of masonry walls in fire conditions, along with the loss of resistance due to material degradation. This contribution proposes a new homogenization method aimed at determining the thermal deformed shape of a masonry wall exposed to fire. First, the homogenized thermo-elastic characteristics of a natural stone masonry wall are determined taking into account the material properties of stone and mortar as functions of temperature increase, as well as the geometrical characteristics of their assembly. As a result, membrane and bending stiffness coefficients, as well as thermal-induced efforts, of the wall modelled as a homogenized plate are obtained. Such homogenized thermo-mechanical characteristics make it possible to determine the deformed shape of the wall after a certain time of fire exposure, through the formulation and the resolution of a finite element plate problem, making use of the previous homogenized stiffness characteristics. Numerical simulations show that the presence of joints has little influence on the deformed shape of the masonry wall compared to a homogeneous stone-only wall. They appear to be in rather good agreement with previous full-scale experimental tests carried out on limestone masonry walls, therefore providing a first validation of the proposed method, even though further improvements could be envisaged as regards a more reliable determination of the temperature gradient across the wall thickness.