A proposed damage model for R/C bridge elements under cyclic loading

Analytical damage models provide a way to have an index to create a single measure that fairly represents the damage sustained under seismic loading in reinforced concrete structures. Damage indices are important tools to quantify the consequences of a structural decision. A damage model is proposed for reinforced concrete elements. The model yields a damage index at a point in the time history for the load on the element, based on the predicted monotonic response from the point in time to failure. The model takes into account the parameters that describe the hysteretic behavior: stiffness degradation, strength deterioration, and ultimate displacement reduction. The model is cumulative and it combines energy, ductility, and low-cycle accumulation. The model is based on the work needed to fail the element monotonically after it experiences cyclic loading and takes the energy under the monotonic load-deformation envelope for the virgin state of the element as a reference capacity. The model modifies the ultimate displacement that the element can achieve, due to low-cycle accumulated damage at the longitudinal reinforcement using the Coffin-Manson rule in combination with Miner's hypothesis. Most of this study is applied specifically to reinforced concrete columns and column-like elements, but the application is also demonstrated for a coupling beam in a coupled shear wall system. A layers analysis program is written to predict the monotonic force-displacement envelope based on plane sections remaining plane, accounting for concrete confinement, elastic shear deformation, elastic and inelastic flexural deformation, and bond slip deformation. The proposed model is applied to 12 bridge columns tested by others. The proposed model gave a realistic prediction o f the damage throughout the loading cycles for the test specimens investigated. The results are also compared to two existing damage models; the Park and Ang (1985) and the low-cycle damage model by Mander and Cheng (1995). An experimental test for a full-scale coupling beam is conducted in this study in order to observe the damage due to cyclic loading. A theoretical prediction of the monotonic force-displacement response of a diagonally reinforced coupling beam is proposed based on a truss model. The model considers the confined concrete between the diagonal reinforcement in the compression direction in addition to the diagonal reinforcement, while only the diagonal reinforcement is considered in the tension direction. The proposed damage model is applied to predict the damage and is compared to the observed damage and to other existing models. The damage prediction of the proposed model compared very well with the observed damage and showed the ability of the proposed model in describing the damage of elements other than bridge columns. The proposed damage model is applied to two existing bridges in Vancouver area. The piers of these bridges consist of a spread footing, a single column and a cap beam. The bridge piers are modeled as cantilevers with lumped mass. A bilinear monotonic force-displacement response for each pier was predicted using the layer analysis program. A nonlinear dynamic analysis is performed using the CANNY structural program (CANNY-E, 1996). CANNY sophisticated hysteresis model is used to model stiffness degradation, strength deterioration and pinching behavior. A series of nonlinear dynamic analyses were performed using records from the 1971 San Fernando, 1989 Loma Prieta, 1978 Miyaki-Oki (Japan), and 1999 TW (Taiwan) earthquakes fitted to Vancouver firm ground spectrum with 2% probability of exceedance in 50 years. A comparison between the proposed model, the Park and Ang model, and the low-cycle damage model by Mander and Cheng is performed. This study showed that the proposed model is applicable to real bridge columns under real seismic loading. A risk-based retrofit decision is briefly demonstrated for an existing bridge in Vancouver using the proposed damage as a tool. This is done to demonstrate how the damage index can be useful as a measure of consequences.Applied Science, Faculty ofCivil Engineering, Department ofGraduat