Damage Measures for Performance-based Seismic Evaluation of Rc Frame Structures

In performance-based earthquake engineering, deformation based methods such as member plastic rotation and inter-story drift ratio are recommended in guideline documents such as FEMA-356 for evaluating structural performance. Such response quantities, however, don’t provide insight into the state of damage in the structure. Yet, damage at a certain local level in the system can result in unexpected structural damage which may lead to partial failure or structural collapse – a condition that may not be immediately evident from standard deformation measures. Local damage is associated with many parameters at the element and constitutive level. Therefore this study introduces a material-based structural damage model to evaluate the performance of RC frame structures subjected to strong ground motions. Introduction Growing interest in performance-based seismic engineering due to both economic considerations and safety concerns has led to the need to develop more precise methods to measure structural damage. While several efforts to define component and system damage has appeared in the literature (Chung et al, 1989; Krawinkler and Zohrei, 1983; Legeron et al, 2005; Park et al, 1985, 1988), very few damage models have been implemented in performance-based seismic assessment. Current guideline documents such as FEMA356 (REF) utilized inter-story drift ratio and plastic rotation to establish building performance levels such as immediate occupancy, life safety, and collapse prevention. While these measures provide information on the deformation of elements and the displaced profiles at critical states, they are inadequate in themselves to provide an assessment of the state of damage or proximity to collapse. An alternative methodology to measure structural damage based on material response states is proposed in this paper. Material-Based Structural Damage Since the response of common structural engineering materials such as steel and RC from the elastic state to failure is represented by yielding, plastic or irreversible behavior, crack growth, and fatigue during monotonic and cyclic loading, it is possible to represent such deterioration 1 Graduate Student Researcher, Dept. of Civil and Environmental Engineering, University of California, Davis, CA 95616 2 Professor, Dept. of Civil and Environmental Engineering, University of California, Davis, CA 95616 Proceedings of the 9th U.S. National and 10th Canadian Conference on Earthquake Engineering Compte Rendu de la 9ième Conférence Nationale Américaine et 10ième Conférence Canadienne de Génie Parasismique July 25-29, 2010, Toronto, Ontario, Canada • Paper No 545 phenomena by a numerical model which can be incorporated in fiber-based discretization of a section for material-based damage estimation at the element level. Damage Modeling at Constitutive Level In this section, a damage model is introduced at the material level that is related to the response of the section deformation. This deformation is characterized by the stress and strain in the fibers of the cross-section. Damage in Concrete Fiber Strains at the threshold of damage initiation, attainment of compressive strength, and residual strength of crushed concrete are defined as damage parameters. In the present study, damage is considered only in the core concrete because it was determined that calibrating the damage state to the compression damage in the core was a better indicator of section damage than incorporating deterioration in both core and cover concrete. Other measures of concrete damage such as tensile cracking was found to be inessential since the corresponding response in the unconfined concrete fiber is reflected in reinforcing steel. Moreover, the response in compression governs the section damage in the concrete core. The constitutive model proposed by Mander et al. (1988) is used to evaluate the stress-strain response of the confined concrete. Damage in concrete is initiated when bond and mortar micro cracks occur under loading. It usually happens quite early since concrete is a brittle material, so the strain at the damage initiation will generally be small. In compression, damage evolution is suspended when the cracks close during unloading. Upon reloading, damage accumulation continues when the previous unloading point is reached. However, an examination of cyclic stress-strain response of plain concrete suggests that a simple model based on the monotonic stress-strain curve is feasible. Ignoring the damage resulting from tensile cracking, a simple bilinear model is proposed in Eq. 1 and 2 assuming that the damage index is 1.0 when accumulated plastic strain reaches the strain at the residual strength: ( ) ( ) cu cd ci cu cd D f f D f f − = − for cu ε ε ≤ (1) (1 )( ) 1 ( ) cu cf ci cf cu D f f D f f − − = + − for cu ε ε > (2) where ci D is the concrete damage index at the th i concrete fiber, cu D denotes the damage index at the corresponding compressive strength, cd f is the strength at damage initiation, cu f is the concrete compressive strength, cf f is the residual strength, and cu ε denotes strain at concrete compressive strength. As shown in Figure 1, the damage rate changes at the peak compressive strength according to cu D which can be determined by the ratio of the degraded strength at the failure ( cu cf f f − ) to the compressive strength ( cu f ) denoted by cu D as follows: cu cd cu cf cd D ε ε ε ε − = − (3) Figure 1. Stress-strain response of confined concrete and corresponding damage evolution The proposed bilinear model is an idealization of the nonlinear damage evolution process, but it is expected that ongoing calibration and validation studies will serve to improve the model. Damage in Reinforcing Steel Fiber While the response of reinforcing steel beyond the elastic phase is described through yielding, hardening, softening, and fracture under monotonic loading, these monotonic parameters are inadequate to incorporate random cyclic effects such as strength degradation because steel is vulnerable to fatigue damage under seismic loads. It is more efficient to consider damage due to cyclic fatigue since it encompasses the combined effect of multiple damage parameters. Buckling of reinforcing bars is an important phenomenon that occurs under both monotonic and cyclic loading however, a cyclic fatigue model can also include buckling effects. Therefore Miner’s (1945) linear damage rule shown in Eq. 3 is applied to compute damage in reinforcing steel fiber: