On the relationship between small amplitude vibration dynamic properties and the past maximum displacement in reinforced concrete structures

Damage detection in structural health monitoring is usually done by correlating the level of damage in a structure to its dynamic parameters estimated from vibration records. In buildings such correlations are not well established. A vibration-based damage detection technique that is able to identify the structural condition of the system based on small amplitude vibrations is desirable because such kind of data are typically available. This study focuses on the relationships between small-amplitude vibration dynamic properties and past levels of displacement in reinforced concrete structures. Small displacements are defined as displacements below an overall drift ratio of 0.03%. Laboratory tests on a full-scale flat-plate structure and a series of small-scale beams were done. It is observed that natural frequency and equivalent viscous damping ratio are displacement-dependent parameters even at small displacement levels. Such displacement-dependency of dynamic parameters was captured by using an elastic single-degree-of-freedom (SDOF) system with variable stiffness and variable equivalent viscous damping, i.e., nonlinear-elastic SDOF, to represent the small-amplitude vibration response of the reinforced concrete structures. It is found that change in the dynamic parameters with past maximum displacement is tracked best using tests done at identical displacement. Observations from tests are compared to those extracted from experiments done by other researchers. In the small-scale beams, the equivalent viscous damping ratio measured at small displacements found to increase from the as-built level with displacement initially but then decrease once the past maximum drift reaches approximately the yield level. A similar behavior is observed in a full-scale 7-story structure. A condition based on relative change in fundamental frequency and equivalent viscous damping ratio is suggested to define, and identify, a characteristic displacement associated with yield in reinforced concrete buildings. However, more data from full-scale building tests are necessary to justify the extension of the observations made from small-scale test for use in structural health monitoring of actual buildings. Nonlinear-elastic SDOF model representation has encountered difficulties when applied on currently existing data sets from full-scale buildings. A practical finding of this study is that the fundamental frequency in a typical reinforced concrete building reduces to approximately 2/3 of that measured at as-built condition after the structure is subjected to approximately 1.5% maximum drift ratio level