The use of 3D modeling for the prediction of the seismic demands on the gravity dams

Abstract

Summary Seismic behavior of gravity dams has long been evaluated using a representative two‐dimensional (2D) system. Formulated for the gravity dams built in wide canyons, the assumption is nevertheless utilized extensively for almost all concrete dams due to the established procedures as well as the expected computational costs of a three‐dimensional model. However, a significant number of roller‐compacted concrete dams, characterized as such systems, do not conform to the basic assumptions of these methods by violating the conditions on canyon dimensions and joint‐spacing/details. Based on the premise that the 2D modeling assumption is overstretched for practical purposes in a variety of settings, the purpose of this study is to critically evaluate the use of 2D modeling for the prediction of the seismic demands on these systems. Using a rigorous soil–structure interaction approach, the difference between the two and three‐dimensional response for gravity dams was investigated first in the frequency domain for a range of canyon widths and foundation to dam moduli ratios. Then, the time domain differences between the crest displacements and the maximum principal stress were obtained using 70 different ground motions in order to show the possible bias introduced into the analysis results due to the modeling approach. The results of the study show that even for relatively wide canyons, the 2D analysis can lead to misleading predictions. Copyright © 2017 John Wiley & Sons, Ltd.

Structure‐soil‐structure interaction of adjacent buildings subjected to seismic loading

“…The base shear for a structure, an important global demand quantity for a building, was chosen as the second EDP. For the calculation of the story drifts, first, the story displacements were obtained from the inverse FFT of the multiplication of the displacement FRFs at each story with the FFT of the ground motions . For the calculation of base shear time histories, a similar approach was followed using the base shear FRFs (as given in Section ).…”

“…For the calculation of the story drifts, first, the story displacements were obtained from the inverse FFT of the multiplication of the displacement FRFs at each story with the FFT of the ground motions. 28 For the calculation of base shear time histories, a similar approach was followed using the base shear FRFs (as given in Section 3). The envelope of the aforementioned quantities was obtained to get the maximum base shear.…”

Direct finite element method for nonlinear earthquake analysis of concrete dams: Simplification, modeling, and practical application

“…In contrast, the current practice of specifying a viscous damping ratio of 5% for the concrete dam alone and a similar value for the foundation domain is likely to lead to damping in the range of 10% to 15% in the overall dam‐water‐foundation system for “common” system parameters. A wider range of 6% to 30% overall damping was identified in Bybordiani and Arıcı for 2D and 3D idealizations of a gravity dam‐water‐foundation system covering several values for the foundation stiffness and different ratios of the canyon width to the height of the dam. Thus, the current practice of choosing damping values should be abandoned because it will likely underestimate the earthquake response of dams.…”

“…Limiting the overall damping to less than 5% in 2D numerical models is very difficult because of the large amount of radiation damping associated with 2D homogeneous, semi‐unbounded foundation models (Figure 17). The additional damping erroneously introduced to the system by using a 2D idealization to represent a 3D gravity dam system can be significant, unless the canyon is very wide . Presented in Table are examples of total damping in a 2D model of Pine Flat Dam computed by the substructure method for several values of the parameters that characterize energy loss in the system: material damping in the dam, ζ s ; material damping in the foundation, ζ f ; the moduli ratio of the foundation to the dam concrete, E f / E s ; and the reservoir bottom reflection coefficient α , which is computed here based on rock properties alone to approximately account for water‐foundation interaction in the substructure method (see Appendix ).…”

“…The additional damping erroneously introduced to the system by using a 2D idealization to represent a 3D gravity dam system can be significant, unless the canyon is very wide. 54 Presented in Table 1 are examples of total damping in a 2D model of Pine Flat Dam computed by the substructure method 12 for several values of the parameters that characterize energy loss in the system: material damping in the dam, ζ s ; material damping in the foundation, ζ f ; the moduli ratio of the foundation to the dam concrete, E f /E s ; and the reservoir bottom reflection coefficient α, which is computed here based on rock properties alone to approximately account for water-foundation interaction in the substructure method (see Appendix A). As an example, specifying 2% damping in the dam and 2% for the foundation domain (case 2 in Table 1) leads to overall damping of approximately 10% in the 2D numerical model, which is much higher than the 2% to 4% damping "measured" at Pine Flat Dam during forced vibration tests.…”