Abstract
Manuscript Reference: Ufuk Yazgan and Alessandro Dazio, Earthquake Spectra, vol. 27, no. 4 (November 2011): 1187–1202.
The main goal of this study was to investigate different numerical models using a finite element computer program, OpenSees (2010), to determine peak and residual displacements of RC structures. As indicated in the paper, the peak displacements can be accurately predicted by the analytical model, but estimating the residual displacements is difficult and needs further investigations. While some important aspects of the problem are discussed in the article, six key elements and considerations are missed:
(1) We appreciate the authors' effort and the good correlation they obtained between the calculated and measured peak displacements for the shake table test model. But the paper offered no unique approach to improve the accuracy of the residual displacement estimation. For example, in the last section of the paper, it is not clear why authors are more interested in the displacement-based fiber elements than force-based fiber elements while the findings in the previous sections of the paper indicate that the latter model is slightly better than the former in terms of estimating the residual displacements.
(2) Two relevant studies available at the time of submission of this paper were missed. These studies showed that it was possible to use OpenSees to match the calculated and measured displacement history of a RC bridge column tested on a shake table with large residual displacements. First, Lee (2007) (and later Lee and Billington, 2010) developled a new constitutive concrete material in OpenSees labeled “Concrete01WithSITC” to improve estimation of the residual displacement. He used a force-based element called “beamWithHinges” that lumps the nonlinearity along the plastic hinge length at the ends of the element represented as a fiber section with linear-elastic element elsewhere. He successfully simulated both the peak and residual displacements of a run out of eight runs of a bridge column tested on the shake table. The column labeled “A1” in the paper (Table 1) is the same model but different run.
Second, Jeong et al. (2008) used a similar element to simulate residual displacement response of several bridge RC columns one conventional and onthers incorporating innovative methods tested on shake tables using “Concrete02,” which considers linear tension softening for concrete fibers. For the RC column, they simulated the displacement history of all four runs with good accuracy.
(3) The authors have considered only the first dynamic test in which inelastic deformations were developed. Considering that residual displacements are mostly due to nonlinear material behavior, critical residual displacements do not develop until significant nonlinear action takes place. The level of nonlinearity in systems that barely pass the yield point is not sufficient to put the adequacy of analytical models to test. For example, column “A1” has been tested on the shake table under eight runs. The authors selected run 2 for analyses with the peak drift ratio of 5.1% and the residual drift ratio of 0.55%. The residual drift ratio after run 8 in this column was 1.68% (Hachem et al. 2003). The maximum residual drift ratio in all test runs that the authors used was 0.62% or less. While there are no established criteria for the critical limit of residual displacement, this drift ratio is not generally considered to be significant.
(4) Seven out of twelve test units in this study were wall structures. Note that shear wall structures do not generally experience large residual displacements since a large portion of wall remains elastic and brings back the structure close to its at-rest position. The maximum residual drift ratio for the wall structures selected for this study was 0.21%.
(5) The authors selected the constitutive materials and elements that were previously shown not to be suitable for capturing residual displacements. They used “Steel02” as the fibers for the mild reinforcements. It is shown in Jeong et al. (2008) that “Reinforcing-Steel” is superior to the “Steel02” in terms of simulating the residual displacements. It is not clear which concrete model they used for the analyses. However, it appears that “Concrete01” was used because tensile strength of concrete was neglected. Lee (2010) has shown that this model has poor potential to simulate the displacement history especially after the peak displacement has reached. For force-based element, the authors used “nonlinearBeamColumn” element. Jeong et al. (2008) have shown that this element can estimate the displacement history with high accuracy under low levels of shaking. But for severe earthquakes, the residual displacement is appreciably underestimated. Since the authors analyzed only runs with relatively small displacement, they were not able to observe this shortcoming.
(6) The authors have presented a graph to adjust the simulated nonlinear responses by random correction factors to match the measured data. There are two shortcomings in using this graph: (i) limited number of the test data and, (ii) simulations with a model that is not adequately described in the paper. Rather than using the graph to enhance estimation of the residual displacements, it is appropriate to use better modeling approaches such as those in the references included in this discussion.