| Resumo : |
This study deals with a well-known problem in the field of civil engineering, which is the phenomenon of bowing, that occurs in marble slabs on the façades of buildings and causes damage to constructions all over the world. Laboratory studies have shown that marble slabs subjected to temperature oscillations suffer from non-uniform and permanent deformation, and that this problem is exacerbated in saturated marble. The understanding of this pathology is still incomplete, despite its importance for civil construction. Therefore, is a necessary object of study, in order to enable preventive measures and effective solutions. To facilitate a better comprehension of the bowing phenomenon, this problem is sub-divided into two particular cases along with their corresponding solutions. Also, the study consider the porous matrix, fluid and grains of the porous medium as compressible. In the first particular case it is assumed that the marble is in an undrained environment. In the formulation developed herein, heat transfer problem is modeled by sol-air formulation, in order to linearize radiation transfer and convective transfer. The fully lin-earized problem is then solved by trigonometric series specially developed for time-periodic problems, in order to represent the daily cycles of heating and cooling. This formulation is extended here to model saturated environment under undrained circumstances. This formulation is compared to a numerical formulation which involves transient heat transfer and stress-strain relations for the condition of dry marble. In the second case, still in a saturated environment, an analytical solution for a steady state profile of pore pressures is obtained for a slab which is cooled at a constant rate. The proposed solution is a quadratic polynomial in space and a linear function in time for the temperatures. The thermal load compensates exactly for the pore pressure dissipation which leads to a quadratic profile of pore pressure that is constant in time. Both particular solutions are applied for a study case of temperature readings at Pescara Justice Court's Carrara marble façade, that involves the sudden drop of weather temperature. |