PLASTIC STRAIN ENERGY BASED DAMAGE INDICES FOR CONCRETE STRUCTURES

Evaluating the degree of damage and the remaining strength of structures after an earthquake is an extremely important task. Finite element method (FEM) is useful for simulating the nonlinear behavior of concrete structures up to their maximum strength. Actually, FEM provides much information, even on a microscopic level, for phenomena such as stress, strain, and cracks in concrete. However, evaluating the degree of damage in concrete structures from various responses of respective elements obtained from FEM is not easy. A damage index that represents the degree of damage of the target structure derived from analysis results would be extremely useful for evaluating the remaining strength of the structure on a macroscopic level. Earthquake-induced damage to concrete structures is roughly classifiable into cracking of concrete, compressive deterioration of concrete, and yielding of steel. This study proposes two indices for the damage evaluation of concrete structures. They are defined using element responses obtained from a nonlinear finite element analysis. One is a weighted damage index that reflects the condition of concrete in compression. The index is calculated based on the plastic strain energy of each concrete element normalized by the absorbed plastic strain energy at the point of compressive strength of concrete. The index of each concrete element is weighted by its minimum principal strain and volume of the element. Then the indices of all concrete elements are averaged to obtain a unique damage index that represents the degree of damage to concrete in compression. The other index reflects the yielding and plasticization of steel. In the same manner as that for concrete, the index is calculated based on the plastic strain energy of each steel element normalized by the absorbed plastic strain energy at the point where the equivalent plastic strain becomes 0.01. The index of each steel element is weighted by its second deviatoric strain and the volume of the element. Then those indices are averaged to obtain a unique damage index representing the degree of steel damage. Each index represents no damage with a value of 0.0 and severe damage with a value of 1.0 or greater. To investigate the applicability of the proposed damage indices, nonlinear finite element analyses were conducted for a steel-embedded concrete column specimen and reinforced concrete test specimens of several types. Plane stress analysis and three-dimensional analysis are applied f