Experimental validation of an anisotropic delay damage model for impact on reinforced concrete structures

International audienceImpact problems on reinforced concrete structures are usually computed with models coupling plasticity and isotropic damage. The induced damage anisotropy observed for quasi-brittle materials such as concrete is often reproduced considering different variables for tension and compression (not consistent with the thermodynamic framework). Introducing viscosity for both damage and plasticity evolutions enables to reproduce the strength enhancement due to rate effects. Such kinds of models present the main advantage to describe precisely each phenomenon locally observed (different rate effects in traction and compression, compaction under confined loadings ...) but require a large number of parameters. Anisotropic damage is quite relevant to describe the micro-cracking pattern and the failure conditions of quasi-brittle materials and structures. In concrete, a state of micro-cracks orthogonal to the loading direction in tension and parallel to it in compression is easily described by a second order damage variable. This anisotropic delay-damage model, used in this work, introduces only few parameters (7 including elasticity parameters E and ν) compared to the ones mentioned higher. The efficiency and the validation of such an approach is illustrated with its application on impacted reinforced concrete beams and dynamic Brazilian tests. The test has been performed with the drop-weight tower ORION of the CEA Saclay for two kinds of beam geometries in order to exhibit flexion and shear rupture. 1 INTRODUCTION The challenge of understanding the behavior of civil engineering structures under dynamic loading is usually linked to security issues but also some economic problems. Advances in instrumentation continue to improve our understanding on these subjects, so one continues around the world to develop impact tests on reinforced concrete structures. The civil engineering is one area where the tests are the most numerous. Indeed, it's only repeating the experiments and varying the parameters that we managed to understand the behavior of structures. But few cases where experiments are conducted on real structures with the stresses actually envisaged, are available. Moreover these experiments do not always provide more information than mockup models. Therefore, we find in the literature a large number of tests on simple structures such as slabs or beams. The philosophy of these kind of tests is to demonstrate on simple structures (beams, slabs) a number of local and global phenomena to allow modeling of more complex cases. Tests developed in the Dynamics Laboratory (DYN) of the CEA Saclay during this work include in this perspective. Two types of tests on a drop-weight tower were made: dynamic Brazilian tests and impact tests on beams. The dynamic Brazilian tests are relatively uncommon in the literature ((Tedesco, Ross, and Kuennen 1993) made the first dynamic Brazilian tests on split Hopkinson bars), but very interesting. A fast digital camera has been used in addition to more traditional, but precise and efficient, instrumentations (accelerometer, displacement measurement by camera, force sensors). The recorded images are analyzed by Digital Image Correlation with the software CORRELI developed at the LMT Cachan (Besnard, Hild, and Roux 2006). The impact tests on beams were designed to study the transition from a ductile failure mode (flexural) to a brittle fracture mode (shear cone). The two factors influencing this study are the slenderness of the beam and the transverse reinforcement (stirrups). An anisotropic delay-damage model has been developed during this work and it is presented in the last section. Finally this model is used to model the tests realized on the drop-weight tower