Inelastic seismic response and damage analysis of a tall bridge pier

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1 Tailor Made Concrete Structures Walraven & Stoelhorst (eds) 28 Taylor & Francis Group, London, ISBN Inelastic seismic response and damage analysis of a tall bridge pier X. Zhu, J.-W. Huang & L.-Y. Song School of Civil Engineering and Architecture, Beijing Jiaotong University, Beijing, China ABSTRACT: The impulsive near-fault earthquake ground motions generally impose high demands on structures compared to ordinary ground motions. The seismic behavior of a reinforced concrete tall bridge pier is studied in this paper, using a realistic example of Huatupo bridge Pier #8. According to Park-Ang dual-parameter damage model, the maximum local damage index was obtained at the about height of 6 m, it is located at the medium to upper portion of this pier. The inelastic seismic response demands and seismic damage performance evaluation of reinforced concrete tall bridge pier subjected to pulse-type near-fault earthquake ground motions and corresponding equivalent pulses would be investigated. Except seismic behavior of tall bridge piers, this study was also intended to identify salient inelastic response and damage characteristics of tall bridge pier excited by near-fault ground motions, and to check whether pulse-type near-fault ground motions could be reasonably represented by simple equivalent pulses. 1 INTRODUCTION The impulsive near-fault ground motions generally impose the higher demands on structures compared to ordinary ground motions. Many scholars such as Alavi (2), Menun (22) & Makris (1997, 2, and 23) have proposed equivalent pulse models to represent the pulse-type near-fault ground motions with forward directivity. It is important to note that the use of equivalent pulses to describe near-fault ground motions is an approximation to a very complex problem. In this study, the inelastic response demands and seismic damage performance evaluation of reinforced concrete tall bridge pier subjected to pulse-type near-fault ground motions and corresponding equivalent pulses would be investigated by using nonlinear dynamic time-history analysis method. The goal of this study was intended to identify salient inelastic response and damage characteristics of tall bridge pier excited by near-fault ground motions, and to check whether pulse-type near-fault ground motions could be reasonably represented by simple equivalent pulses. velocity pulse model would be used to simplify the pulse-type near-fault ground motions. The amplitude of the velocity pulse v p was determined by applying the recommended method shown in reference (Li & Zhu 24), and the pulse period T p for a pulse-type nearfault record was identified from the location of a global and clear peak in the velocity response spectrum. The values of characteristic parameters of three near-fault pulse-type records and the equivalent pulse parameters were summarized in Table 1 for the fault-normal component of the recorded near-fault ground motions with forward directivity. Figure 1, and (c) illustrated plots of acceleration, velocity and displacement time history traces respectively of the fault-normal components of two typical near-fault records and NorthridgeNewhall#46 by a dashed curve, of responding equivalent pulses by a solid curve. It appeared to be reasonable to represent nearfault ground motions by the equivalent pulse used in this study. The near-fault records and their equivalent pulses would be applied into the inelastic time-history response demands and damage analysis for reinforced concrete tall bridge pier. 2 EQUIVALENT PULSE MODEL Makris (1997) & Somerville (1998) classified velocity pulses in near-fault ground motions into three types of pulses, namely, type A pulse, type B pulse and type C pulse represented by a unique set of closed-form tri-geometric functions. In this study, this equivalent 3 CALCULATING MODEL A long-span continuous girder railway bridge with tall piers was taken as an example. The longitudinal profile of Huatupo bridge was shown in Figure 2. The Pier #8, with height of 11 m, was the highest reinforced 947

2 Table 1. Pulse-type near-fault records and their characteristic parameters. Name of near-fault R Field PGA PGV PGD PGV/ T P v P T g1 T g2 records M w (m) condition (g) (cm/s) (cm) PGA (s) (m/s) (s) (s) Soil NorthridgeNewhall# Soil NorthridgeParkinglot Soil Tg1, Tg2-characteristic period of ground motions, Tg1 = 6.28 Sv/Sa, Tg2 = 6.28 PGV/PGA[1]; Sv, Sa-the peak value of velocity and acceleration response spectrum; PGV, PGA-the peak value of velocity and acceleration time history ( Erzincan-EW) ( pulse) ( NorthridgeNewhall46) ( pulse) acc (g) -.5 acc (g) vel (m/s) type-c 1 v p =.7 m/s Tp =1.8 s acc (g) vel(m/s) type-b v p =.93 m/s T p =1.92 s t(s) vel (m/s) 1. Figure 2. Huatupo bridge..2.5 dis (m) dis (m) (c) dis (m) Figure 1. Comparison of acceleration, velocity and displacement time histories of record, NorthridgeNewhall#46 and their equivalent pulses. concrete pier with hollow circle-nosed sections shown as Figure 3. The fixed hinge bearing of the continuous girder was set on the Pier #8, and the slipped bearings were set on other piers. So Pier #8 almost took the whole horizontal seismic force along the bridge longitudinal axes. The nonlinear time history analysis was performed to estimate the seismic response and the elasto-plastic seismic behaviors. The Takeda degrading trilinear hysteretic model was adapted as the skeleton model of each element. The bending moment-curvature relationships of the hollow circle-nosed sections of this bridge pier at different height levels was shown as Figure 5. Figure 3. Section of 8# pier. The corresponding skeleton curves were shown in Figure 5, and the initial stiffness K e, cracking stiffness K f and yielding stiffness K q could be expressed as: 948

3 Figure 4. Calculating model. Figure 5. Moment-curvature curves and Skeleton curves of #8 bridge pier at different altitude h. 4 DAMAGE MODEL According to Park-Ang dual-parameter damage model (Park & Ang 1985a, b), the damage index can be defined as: Where and u are respectively the actual and ultimate rotations; Ek represents the dissipated hysteretic energy; Mu is the yielding bending moment; β is an empirical constant which depends on structural characteristics, and it is taken as.15 in this study. The damage index of each structural member can be expressed as: Figure 6. Comparison of damage time-history response of each element under three different near-fault ground motions (ag,max =.3 g). The global damage index can be obtained by weighting average damage indices of individual structural member, and the weights are the local damage indices: 949

4 5 RESULTS ANALYSIS Except the ground motions listed in Table 1, a reference far-fault record El Centro (SE) was utilized for comparison purposes, and the value of peak ground acceleration (PGA) a g,max of those four records was uniformly adjusted to.1 g,.2 g,.3 g and.4 g so that inelastic time-history analysis results for the Pier #8 under different ground motions could be compared with each other. In the following process, the inelastic time-history response demands and damage analysis results of the pier subjected to pulse-type record, record NorthridgeNewhall#46 and corresponding equivalent pulses were compared in order to check the reasonability of equivalent velocity pulse model used in this study. It was shown from Figure 6 that time-history damage response value of the 5th element located at the height of 51.8 m to 66.8 m of #8 high-rise bridge pier Figure 7. Comparison of maximum bending moment of each section over the height of bridge pier under different ground motions. a g,max =.3 g. a g,max =.4 g. was generally larger than that of other elements under three pulse-type near-fault ground motions. The timehistory damage analysis results of Pier #8 subjected to three near-fault excitations indicated that yielding would start at the height of 6 m located in medium NorthridgeNewhall#46 NorthridgeParkinglot El-centro(SE) (Far-fault) NorthridgeNewhall#46 NorthridgeParkinglot36 El-centro(SE) (Far-fault) t /s Figure 1. Comparison of time-history damage response of the 5th element under different ground motions. a g,max =.3 g. a g,max =.4 g. Figure 8. Comparison of maximum curvature of each section over the height of bridge pier under different ground motions. a g,max =.3 g. a g,max =.4 g. 1 8 NorthridgeNewhall#46 NorthridgeParkinglot36 El-centro(SE) (Far-fault) NorthridgeNewhall#46 NorthridgeParkinglot36 El-centro(SE) (Far-fault) 4 NorthridgeNewhall#46 NorthridgeParkinglot36 2 El-centro(SE) (Far-fault) Displacement (cm) Displacement (cm) Figure 9. Comparison of maximum joint displacement over the height of bridge pier under different ground motions. a g,max =.3 g. a g,max =.4 g. Figure 11. Comparison of local damage index of each section over the height of pier under different ground motions (a g,max =.4 g). 95

5 portion of pier, not at the lower portion or bottom of pier, and the location of plastic hinges determined by inelastic dynamic time history analysis agreed well with that by the capacity spectrum method performed in references (Zhai 21, Seismic-resisting research institute 21). Figure 12 and Table 2 showed the comparison of global damage index of pier subjected to different ground motions when a g,max was adjusted from.1 g Global damage index NorthridgeNewhall#46 NorthridgeParkinglot36 El-centro(SE) (Far-fault) a g,max (g).35.4 Figure 12. Variation of global damage index with the values of a g,max under different ground motions. to.4 g. As shown in Figure 12 and Table 2, the global damage index increased with the increasing value of a g,max, and the values of global damage index of pier subjected to near-fault pulse-type ground motions were larger than those obtained under far-fault ground motion. Those were shown from above figures that inelastic response and damage analysis results of Pier #8 subjected to the pulse-type near-fault records and their equivalent pulses agreed well with each other. 6 CONCLUNG REMARKS On the basis of results for inelastic response and damage analysis, the summary concluding remarks can be drawn as following: (1) The equivalent velocity pulse model proposed by Makris could represent the near-fault pulse-type ground motions with sufficient accuracy. (2) The near-fault ground motions tend to impose larger inelastic response demands such as roof displacement, bottom bending moment, etc., than far-fault ground motions on tall bridge piers. (3) The critical section could be located at the medium to upper portion of tall bridge pier with variety Table 2. Comparison of roof displacement, bottom bending moment and global damage index at different levels of peak acceleration a g,max under different ground motions. Bottom bending moment Roof displacement (cm) (MN m) Global damage index Name of records.1 (g) NorthridgeNewhall# NorthridgeParkinglot El-centro (SE) (Far-fault) Pulse 15 1 Pulse Displacement(cm) -2-4 M (MN.m) Figure 13. Comparison of roof displacement time-history response. Comparison of bottom bending moment time-history response under record and its equivalent pulse. 951

6 Displacement(cm) NorthridgeNewhall#46 NorthridgeNewhall#46Pulse M (MN.m) NorthridgeNewhall#46 NorthridgeNewhall#46Pulse Figure 14. Comparison of roof displacement time-history response. Comparison of bottom bending moment time-history response under record NorthridgeNewhall#46 and its equivalent pulse Element 5 Record.6 Element 5 pulse Element 6 Record.4 Element 6 pulse Element 7 Record.2 Element 7 pulse Cracking moment Yielding moment Pulse Ultimate moment M (MN.m) Figure 15. Comparison of damage time-history response of partial elements. Comparison of bending moment of each section over the height of pier under record and its equivalent pulse Element 5 Record Element 5 pulse.4 Element 6 Record.2 Element 6 pulse Element 7 Record Element 7 pulse Cracking moment NorthridgeNewhall#46 NorthridgeNewhall#46Pulse Yielding moment Ultimate moment M (MN.m) Figure 16. Comparison of damage time-history response of partial elements. Comparison of bending moment of each section over the height of pier under record NorthridgeNewhall#46 and its equivalent pulse. Figure 17. Comparison of maximum curvature of each section over the height of pier. under record and its equivalent pulse. under record NorthridgeNewhall#46 and its equivalent pulse. 952

7 Pulse NorthridgeNewhall#46 NorthridgeNewhall#46Pulse Displacement(cm) Figure 18. Comparison of maximum joint displacement over the height of pier under near-fault ground motions and their equivalent pulses Pulse NorthridgeNewhall#46 NorthridgeNewhall#46Pulse Figure 19. Comparison of local damage of each section over the height of pier under near-fault ground motions and their equivalent pulses. cross-section in seismic design. The results evaluated by inelastic dynamic time history analysis are agreed well with that by the capacity spectrum method. ACKNOWLEDGEMENTS This study is sponsored by National Nature Science Foundations of China Grant No This support is gratefully acknowledged. REFERENCES Somerville Development of an improved ground motion representation for near fault ground motions. Report, SMIP98 Seminar on Utilization of Strong-motion Data, Oakland, CA. Menun, C. & Fu, Qiang. 22. An analytical model for nearfault ground motions and the response of SDOF systems. presented the 7th National Conference of Earthquake Engineering, Boston, Reference No. 11. Alavi, B. 2. Effects of near-fault ground motions on frame structures. Ph.D Dissertation, Department of Civil and Environmental Engineering, Stanford University. Makris, N Rigidity-plasticity-viscosity: can electrorheological dampers protect base-isolated structures from near-source ground motions? Earthquake Engineering and Structural Dynamics, 26: Makris, N. & Chang, S.P. 2. Effect of viscous, viscoplastic and friction damping on the response of seismic isolated structures. Earthquake Engineering and Structural Dynamics, 29: Makris, N. & Black, C. 23. Dimensional analysis of inelastic structures subjected to near fault ground motions. Report, College of Engineering, University of California, Berkeley, CA. Seismic-resisting research institute. 21. Ductility performance and seismic response analysis of high-rise bridge structures. Report, School of Civil Engineering andarchitecture, Beijing Jiaotong University, PRC. Zhai, Dongwu & Zhu, Xi Elasto plastic seismic behavior of reinforced concrete gravity bridge pier. Journal of Northern Jiaotong University, 23(4): Zhai, Dongwu. 21. Nonlinear seismic behavior of high-rise bridge structures and displacement-based seismic design method. PH. D. Dissertation, Beijing Jiaotong University, PRC. Li, Xinle & Zhu, Xi. 24, Velocity pulse for near-fault ground motions and its effect on seismic response of pier. Journal of Northern Jiaotong University, 28(1): Jiang, Jingbei, et al. 22. Determination method of characteristic period of ground motions, presented at the 6th National Conference of Earthquake Engineering, PR.China, Park, Y.J. & Ang, A.H-S. 1985a. A mechanistic seismic damage model for reinforced concrete. Journal of Structural Engineering, ASCE. Park, Y.J. & Ang. A. H-S. 1985b. Seismic damage analysis of reinforced concrete buildings. Journal of Structural Engineering, 112(2): Fajfar, P. et al The N2 method for the seismic damage analysis for RC buildings. Earthquake Engineering and Structural Dynamics, 25:

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