Seismic Responses of an Isolated Long-span Bridge using Frequency Domain and Time Dependent Procedures

Year 2023, Volume: 34 Issue: 4, 45 - 70, 01.07.2023

Fevzi Sarıtaş , Zeki Hasgür

https://doi.org/10.18400/tjce.1208867

Abstract

Seismic behavior of an isolated bridge is analyzed in the frequency domain under the effects of nonstationary ground motions. For dynamic solutions, different ground environments are considered by simulating nonstationary quakes that can be represented from bedrock to soft ground level. In the simulations, power spectral functions and filtered white noise model are adopted for spectral densities of the earthquake excitations. Various computer algorithms have been developed for earthquake simulations, establishing the bridge finite element model and stochastic solutions. Twenty simulated ground motions are used for each soil profile and the parameters of Rayleigh dispersion are estimated by evaluating the system responses for each ensemble. A number of peak response factors dependent on soil conditions are presented for seismic responses. In addition, extreme value distributions of the responses are shown with the probability of exceeding functions and tables. The responses are discussed for the specific exceedance level of probabilities used in probabilistic design process. The stochastic analyses generally yielded responses consistent with time domain solutions. Exceedance probability functions of the peak responses were obtained in a close relationship. However, the probability distributions of the responses decomposed for the soft soil case and they displayed a wider dispersion even for low exceedance levels. The peak responses are expressed with some exceedance probabilities. In the estimation of response variations, this study showed the practicality of the frequency domain method and the results revealed higher peak response factors and variances for softer soil conditions. Furthermore, this study indicated that the frequency domain procedure is an effective tool in the obtaining of nonstationary seismic responses.

Keywords

Nonstationary, simulated earthquakes, peak responses, power spectrum, isolator

References

• Shinzouka, M., Jan, C.M., Digital Simulation of Random Processes and its Applications, Journal of Sound and Vibration, 22(1), 111-128, 1972.
• Zhu, D.Y., Zhang, Y.H., Kennedy, D., Williams, F.W., Stochastic Vibration of The Vehicle–Bridge System Subject to Nonuniform Ground Motions, Vehicle System Dynamics. 52(3), 410–428, 2014.
• Pagnini, L.C., Solari, G., Stochastic Analysis of The Linear Equivalent Response of Bridge Piers with Aseismic Devices, Earthquake Engineering and Structural Dynamic, 28, 543-560, 1999.
• Der Kiureghian A., Neuenhofer, A., A Response Spectrum Method for Multiple-Support Seismic Excitations, UCB/EERC-91/08. University of California, Berkeley, 1991.
• Der Kiureghian, A., Structural Response to Stationary Excitation, Journal of the Engineering Mechanics Division. 106(10), 1195-1213, 1980.
• Vrouwenvelder, T., Stochastic Modeling of Extreme Action Events in Structural Engineering, Probabilistic Engineering Mechanics, 15, 109-117, 2000.
• Yang, L.F., Leung, A.Y.T, The Stochastic Finite Segment in the Analysis of the Shear-Lag Effect on Box-Girders, Engineering Structures, 23, 1461-1468, 2001.
• Ettouney, M., Hapij, A., Gajer, R., Frequency-Domain Analysis of Long-Span Bridges Subjected to Nonuniform Seismic Motions, Journal of Bridge Engineering, 6(6), 577-586, 2001.
• Hasgür, Z., Stochastic Analysis of Bridge Piers with Symmetric Cantilevers under the Base Accelerations, Bulletin of the Technical University of Istanbul, 48(3-4), 657-667, 1995.
• Ates S., Bayraktar. A., Dumanoglu, A.A., The Effect of Spatially Varying Earthquake Ground Motions on the Stochastic Response of Bridges Isolated with Friction Pendulum Systems, Soil Dynamics and Earthquake Engineering, 26, 31-44, 2000.
• Jangid, R.S., Equivalent Linear Stochastic Seismic Response of Isolated Bridges, Journal of Sound and Vibration, 309, 805-822, 2008.
• Marona, G.C., Sgobba, S., Stochastic Energy Analysis of Seismic Isolated Bridges, Soil Dynamics and Earthquake Engineering, 27, 759-773, 2007.
• Dicleli, M., Karalar, M., Optimum Characteristic Properties of Isolators with Bilinear Force–Displacement Hysteresis for Seismic Protection of Bridges Built on Various Site Soils, Soil Dynamics and Earthquake Engineering, 31, 982–99, 2011.
• Sarıtaş, F., Performance-Based Seismic Assessment of a Base-isolated Bridge-pier, European Journal of Environmental and Civil Engineering, 26(1), 21-38, 2022.
• Sarıtaş, F., Seismic Performance Assessment of an Isolated Multispan Bridge, Arabian Journal of Science and Engineering, 47(10), 12993-13008, 2022.
• Qiang, H., Jianian, W., Xiuli, D., Nonlinear Response of Continuous Girder Bridges with Isolation Bearings under Bidirectional Ground Motions, Journal of Vibro engineering, 7(2), 816-826, 2015.
• Davenport, A.G., Note on The Distribution of Largest Values of Random Function with Application to Gust Loading, Proceedings of the Institution of Civil Engineers, 28, 187–196, 1964.
• Vanmarcke, E.H., Lomnitz, C., Rosenbleuth, E., Structural Response to Earthquakes. Chapter 8, In Seismic Risk and Engineering Decision, Elsevier, New York, USA, 1976.
• Mahmoud, S., Austrell, P.E., Jankowski, R., Simulation of The Response of Base-Isolated Buildings under Earthquake Excitations Considering Soil Flexibility, Earthquake Engineering and Engineering Vibration, 11(3), 359-374, 2012.
• Sarıtaş, F., Hasgür, Z., Dynamic Behavior of Bridge Pier with Elastomeric Bearings under Earthquake Effects for Different Soil Layers and Support Conditions, Technical Journal of Turkish Chamber of Civil Engineers, 1733-1756, 2014.
• Jia, H.Y., Zhang, D.Y., Zheng, S.X., Xie W.C., Pandey, M.D., Local Site Effects on a High-Pier Railway Bridge under Tridirectionally Spatial Excitations, Nonstationary Stochastic Analysis, Soil Dynamics and Earthquake Engineering, 52, 55–69, 2013.
• Jiao, C., Dong, X., Zhou, G.D., Wu, X.P., Seismic Response of Long-Span Triple-Tower Suspension Bridge under Random Ground Motion, Mathematical Problems in Engineering, 1-17, 2017.
• Adanur, S., Altunışık, A.C, Soyluk, K., Bayraktar, A., Dumanoglu, A., Contribution of Local Site-Effect on The Seismic Response of Suspension Bridges to Spatially Varying Ground Motions, Earthquakes and Structures, 10(5), 1233-1251, 2016.
• Schueller, G.I., Developments in stochastic structural mechanics, Archive of Applied Mechanics. 75(10-12) (2006) 755-773.
• Konaklı, K., Seismic Response Analysis with Spatially Varying Stochastic Excitation, Risk and Reliability Analysis; Theory and Applications. (Springer series in reliability engineering, 199-225, 2017.
• Clough R.W., Penzien, J., Dynamics of Structures, Second edition, Mc-Graw Hill Book Company, New York, 1993.
• Rofooei, F.R., Mobarake, A., Ahmadi, G., Generation of Artificial Earthquake Records with a Stationary Kanai-Tajimi Model, Engineering Structures, 23, 827-837, 2001.
• Kanai, K., Semi-Empirical Formula for the Seismic Characteristics of the Ground Motion, Bull Earthq. Res, Inst. University of Tokyo, 35, 309–325, 1957.
• Tajimi, H.A., Statistical Method of Determining the Maximum Response of a Building Structure, Proceedings of the 2nd World Conference Earthquake Engineering, 2, 1467–1482, 1960.
• Liu, S.C., Jhaveri, D.P., Spectral Simulation and Earthquake Site Properties, ASCE, J Eng Mech Div., 95, 1145–1168, 1969.
• Hasgür, Z., Obtaining of the Simulated Earthquake Ground Motions Depending on Soil Conditions, PhD Dissertation, Istanbul Technical University, Turkey, 1981.
• Penzien, J., Lee, M.C., Stochastic Analysis of Structures and Piping Systems Subjected to Stationary Multiple Support Excitations, Earthquake Engineering and Structural Dynamics. 11, 91-110, 1983.
• Ohsaki, Y., Introduction to Spectral Analysis of Earthquake Waves, Translated by Muzaffer İpek, TMMOB, İstanbul, Turkey, 1991.
• Jennings, P.C., Housner, G.W., Tsai, N.C., Simulated Earthquake Motions for Design Purposes, Proceedings of the 4th World Conference Earthquake Engineering. Chile, 1(a-1), 145–160, 1969.
• Housner, G.W., Jennings, P.C., Generation of Artificial Earthquakes, Probabilistic Engineering Mechanics, 90, 113-150, 1964.
• Şafak, E., Mueller, C., Boatwright, J., A Simple Model for Strong Ground Motions and Response Spectra, Earthquake Engineering and Structural Dynamics, 16, 203-215, 1987.
• Lee, S.C., Latha, V., Rajaserkan, S., Generation of Artificial Earthquake Motion Records using Wavelets and Principal Component Analysis, Journal of Earthquake Engineering, 10, 665-691, 2006.
• Sarıtaş, F., Stochastic Dynamic Analysis of Box-Girder Bridges, PhD Dissertation, Istanbul Technical University, Turkey, 2007.
• DIN 4141-14. Structural Bearings, Laminated Elastomeric Bearings Design and Construction. Deutsche Institut für Normung. 1985.
• AASHTO, LFRD Bridge Design Specifications, American Association of State Highway and Transportation Officials, Joints and Bearings, Washington D.C., 2007.
• Naeim, F. and Kelly, J.M. Design of Seismic Isolated Structure. John Wiley & Sons, U.S.A. 1999.
• CSI Computer & Structures Inc. SAP2000, Linear and Nonlinear Static and Dynamic Analysis of Three-Dimensional Structures. Computer & Structures, Inc., Berkeley, California. 2004.