DIFFUSION OF A DAMAGING FLUID THROUGH A DAM-SHAPED BIDIMENSIONAL BODY FOR THE ESTIMATION OF ITS LIFETIME

The aging phenomena are often associated with the diffusion of certain particles which then activate internal chemical reactions. In this paper, the system of such particles is modelled with an damaging fluid and a hemi-variational method is proposed in order to describe damage and deformation of a dam-shaped two-dimensional body, where a key point is the introduction of the coupling between the damage and the damaging fluid concentration. Another important key point of the present model is the presence of energetic thresholds for damage activation, which are assumed to be different in tension (lower) and in compression (higher). In this work, the body is subjected not only to the self-weight of the two-dimensional dam body and to the left-hand side water pressure, and therefore to the distributed external loads, dual of the displacement field, but also to the dual of the concentration of the mentioned damaging fluid, called the external distributed damaging fluid influx pressure. The parametric analyses are carried out in terms of diffusivity and damage-concentration coupling. The influx pressure drives the incoming flow of the damaging fluid, which is coupled with the damage variable, which is induced to evolve until the failure event, which characterises the lifetime of the structure. In order to evaluate the reasonableness of the model two cases are analysed: in the first one the body is modelled having a rectangular shape. In the second one a realistic trapezoidal dam shape is considered. Both have the same area and height in order to compare the results. This comparison yields the following intuitive considerations. First of all, at the beginning of the time history, i.e., at the time at which the structure is assumed to be built, the tensile state, evaluated by the positive part of the trace of the deformation tensor, of the rectangular structure, is much higher then that of the trapezoidal one. The evolution of damage is faster in the rectangular model and, as expected, the present trapezoidal shapes for the design of the dams possess a longer lifetime and are valid not only for the structural response at the time of construction but also, within the presented model, for a better aging performance. It is worth noting that this is a standard result for dam engineers, and justifies the shapes that are used in the present dam design.