Development of DamDamage3D1.0. A MATLAB program for non-linear analysis of arch dams using a damage model

Abstract

The main goal of this report is to present DamDamage3D1.0, a 3D finite element-based program for non-linear static analysis of arch dams, developed using MATLAB. The non-linear simulations are performed using a damage law and an iterative numerical method based on the stress-transfer technique, considering the redistribution of unbalanced forces in each iteration due to material damage. The concrete’s non-linear behaviour up to failure is simulated using an isotropic damage model with softening, considering two independent scalar damage variables: d+ for tension damage and d- for compression damage. The implemented code was verified and optimized for a simple test structure, more specifically a concrete frame structure with three columns. According to the defined material properties for the structural elements, the concrete failure is expected to occur only at the central column without causing the collapse of the structure, which remains in equilibrium. DamDamage3D1.0 is used to evaluate the structural safety of Cabril arch dam (132 m high) for the concrete strength decrease scenario, considering the material deterioration under tension and compression. This failure scenario is usually considered in the scope of the safety control of dams, and the main goal is to obtain a global safety factor λs that indicates how many times the material’s resistance can be reduced without causing the dam’s structural collapse. This way λs is the maximum admissible multiplying factor of the applied loads. The non-linear behaviour of the dam is analysed for the load combination with the self-weight (SW) and the hydrostatic pressure (HP) at the upstream face (full reservoir), using a 3D finite element mesh with three elements in thickness. The numerical simulations are performed using two different constitutive damage laws to evaluate the influence of the compression softening phenomenon in the global resistant capacity of the dam. The main results include displacements and stress fields and the distributions of tension and compression damage in the dam body.