The numerical simulation of cracking in large concrete structures can be made, in many cases, adopting the smeared cracking approach and using constitutive laws of continuous damage (with softening), in order to simulate the material tension ruptures.
The consideration of a tension softening branch that depends on the value of the material fracture energy, implies the localization phenomena and requires the use of some specific numerical procedures in finite element analysis. Namely, consistent formulations evolving the energy dissipated during the rupture process must be used in order to obtain numerical results that do not dependent on the mesh discretisation - mesh objectivity.
In this paper, a 3D finite element formulation and a constitutive law of isotropic damage, with two independent variables, conceived to model the tension and compression softening effects (independently), are presented. The finite element model is used in the analysis of the Cabril Dam (the largest Portuguese arch dam) when submitted to the self-weight and the hydrostatic pressure (water at crest level). Numerical results related with the cracks propagation for dif-ferent 3D finite element discretisations are presented, in order to analyze the solutions objectivity. These results consist of (i) the radial displacements, (ii) the principal stresses and (iii) the tensile damages at the dam (i) central cantilever and/or (ii) upstream and downstream faces (Fig.A).
Comparison of tensile damages for the two meshes