Seismic performance and effect of curved geometry on isolation system in horizontally curved bridge

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1 Seismic performance and effect of curved geometry on isolation system in horizontally curved ridge *Nitin P. Kataria 1) and R. S. Jangid 2) 1), 2) Department of Civil Engineering, Indian Institute of Technology Bomay, Mumai , India 1) 2) ABSTRACT Seismic response of horizontally curved concrete ox girder ridge isolated y the Elastomeric Ruer Bearings (ERBs) is carried out. The effect of curved geometry on the performance of isolation system is studied under excitation with four different ground motions of different frequency spectrum characteristic, and each ground motion contains three-directions. The selected ridge consists of three span continuous concrete ox girder superstructure supported on piers and autments. In the modeling of the ridge, the deck is modeled as a single spine eam, made up of small straight eam elements with 6 DOF at each node. The coupled equations of motion for isolated system are derived and solved in the incremental form using Newmark s step-y-step method. In addition, comparison is made etween the response of curved isolated ridge with straight isolated ridge (having the same cross section and material property) in order to study the effect of curved geometry on the response of the isolation system. It is oserved that ERBs system is effective for controlling the seismic response of curved ridge and effect of curved geometry makes no significant difference in peak response of ERBs system. 1. INTRODUCTION In past various devastating earthquakes inflicted heavy damage to ridges resulting into heavy casualties and economic losses. It is oserved that the damage to ridges in the earthquakes is mainly due to shear failure of piers and due to excessive displacement of ridge deck and earings. Additionally, ridges with curved configurations may sustain severe damage owing to rotation of the superstructure or displacement toward the outside of the curve line during an severe earthquake (Galindo et al. 2009). Failure of ridges during a seismic event will seriously hamper the relief and rehailitation work, as they serve as major access and evacuation routes during and after catastrophic events, so ridges come under the category of lifeline structures. Therefore, there is a need of finding more rational and sustantiated solutions for protection of ridges from severe earthquake ground motion. 1) Research Scholar 2) Professor 1934

2 The traditional way to improve performance of ridge during earthquake y reducing viration due to seismic event is done y making its memer stronger and more ductile. This approach, ased on ensuring of strength-ductility comination, provides the strong seismic action as ultimate loads, accepting a certain numer of structural or nonstructural degradations. This indicates that, ridges designed with traditional methods are still vulnerale in strong seismic event. The performance of ridges during earthquakes can e improved y making use of suitale energy dissipation devices in the ridge system. In the case of ridges, those usually have a simple structural configuration, made from a continuous deck supported on the top of the pier y simple earings only with the function of supporting gravity loads, the seismic isolation earings, can e replace conventional ridge earings, decouple the superstructure from piers and autments during earthquakes. This significantly reduces the seismic forces induced in the ridge structure, and lowers the strength and ductility demands on the ridge (Kunde and Jangid 2003). Lei and Chien (2004) shown that the isolation performance on ase shear reduction of curved ridge will e closely related to the content of the earthquake and the curvature angle of the structure. They concluded that the use of the isolator with smaller stiffness in lead ruer earing series or with lower frictional coefficient in the friction pendulum system series would induce a etter performance on ase shear reduction. Liu et al. (2011) estalished the three-dimensional computational model of a doule-pier curved continuous girder ridge and viscous dampers were added at the positions of sliding earings y them. Ates and Constantinou (2011a, ) studied the effects of the earthquake ground motions on the seismic response of isolated and nonisolated curved ridges including soil structure interaction using response history analysis and response spectrum analysis. The aove review indicates that very few studies are reported on the ehavior of isolated horizontally curved concrete ox girder ridge. Therefore, it will e interesting to study the dynamic ehavior of isolated curved concrete ox girder ridge and effect of curved geometry on the performance of isolation system. The present study signifies the seismic response of horizontally curved concrete ox girder ridge isolated y the ERBs system. Parametric study of ERBs is carried out for otaining etter response under different earthquake ground motion. Using different evaluation criteria effectiveness of ERBs is studied. Also, the effect of curved geometry on the performance of ERBs system is studied y comparing the response of curved isolated ridge with the response of straight isolated ridge. 2. MODELLING OF CURVED BRIDGE The ridge model used for the present study is that of Federal Highway Administration Seismic Design Course, Design Example No. 6, prepared y BERGER/ABAM Engineers (Berger / Aam Engineers 1996), and also used y (Ates and Constantinou 2011a and ) for getting seismic response of isolated curved ridge with some modification. The selected ridge is three spans, cast-in-place concrete ox girder superstructure supported on reinforced concrete columns as shown in Fig. 1. The span length of curved ridge along the centerline is m, 33.5 m, and m 1935

3 respectively and width of deck is 11.8 m. The alignment of road way over the ridge is sharply horizontally curved (104 o ). The two intermediate ents consist of rectangular columns with cross section area 1.7 m 2 and 6.4 m height from ground surface. The super structure consists of three cell deck with 10% slope with horizontal. The geometry of the ridge and section properties is the same as in the original ridge in the FHWA example. It is presumed (without any checks) that the original ridge design is enough to sustain the loads and displacement demands when seismically isolated as descried herein. The ridge is isolated with two isolators at each autment and pier location for a total of eight isolators. The isolators are directly located aove the cap of the rectangular columns and the autments. The properties of the ridge deck and pier are as given in Tale 1. The following assumptions are also made for seismic analyses of the ridges under consideration: 1) Bridge superstructure and piers are assumed to remain in the elastic state during the earthquake excitation, 2) The autments of ridge are assumed as rigid and Piers are considered as fixed at ground level, 3) The effect of soil structure interaction is not taken in consideration, 4) The ridge deck is modeled as single spin eam made up from small straight eam element. Each adjacent element is connected y a node, 5) The mass of each element is assumed to e distriuted etween the two adjacent nodes in the form of point masses and, 6) Stiffness contriution of non-structural elements such as side walk and parapet is neglected. The selected ridge is modeled as a multi degree of freedom (MDOF) system. Based on the detailed drawings of the curved ridge, a 3D evaluation model is made in MATLAB. As the central angle of curved concrete ridge is etween 12 o and 46 o etween supports, the deck is modeled as single spine eam, which is made up from small straight eam element with included angle less than 3.5 o as specified in American Association of State Highway and Transportation Officials (AASHTO), Tale 1. Properties of ridge deck and piers Properties Deck Piers Cross-sectional area (m 2 ) Moment of Inertia (m 4 ) Young s modulus of elasticity (m 2 ) 3.2* x10 10 Mass Density (kg/m 3 ) 2.5x x10 3 Length/height (m)

4 (a) () (c) Fig. 1 a) The curved ridge plan, ) developed elevation, c) section of the superstructure, and d) horizontal sections of the pier. (d) 1937

5 load and Resistance Bridge design specification reported in National Cooperative Highway Research Program (NCHRP) report 620 (Redfield et al. 2008). The numer of elements considered in the ridge deck and piers are 32 and 4, respectively. The idealized mathematical model of ridge is as shown in Fig.2. Fig. 2 Mathematical model of isolated ridge 3. GOVERNING EQUATIONS OF MOTION The general equation of motion for a structural system sujected to seismic loads is express as MU(t) CU(t) KU(t) MηU g (t) F(t) (1) where, U (t) is the second time derivative of the displacement response vector U(t), M, C and K are the mass, damping and stiffness matrices of the structure, F(t)is the vector of control force inputs, U g (t) [m/s 2 ] is the ground acceleration, is a vector of zeros and ones, relating the ground acceleration to the ridge degrees of freedom (DOF), and is a vector relating the force produced y the control device to the ridge DOFs. Firstly, individual elemental stiffness matrix of each element is formed and using transformation matrix it converted in to gloal matrix. Gloal Stiffness matrix of structure is assemled using elemental gloal stiffness matrices. Similarly, gloal mass matrix for structure is assemled. Thus, response of the structure is evaluated step-ystep at successive increments of time. It is assumed that the properties of the system remain constant during the time increment. Incremental equations of motion are solved using the Newmark-eta method. The gloal damping matrix C is a comination of the distriuted 5% inherent Rayleigh damping in the first two modes. 4. ELASTOMERIC RUBBER BEARING (ERBs) ERBs consist of thin layers of ruer and steel plates uilt in alternate layers as shown in Fig. 3(a). The internal steel plates, referred to as shims. The vertical stiffness of the earing is several hundred times the horizontal stiffness, which is due to the presence 1938

of internal steel shims and horizontal stiffness of the earing is controlled y the low shear modulus of elastomer. The steel shims also prevent the ulging of ruer.

6 of internal steel shims and horizontal stiffness of the earing is controlled y the low shear modulus of elastomer. The steel shims also prevent the ulging of ruer. The damping in the earing is increased y adding extra-fine caron lock, oils or resins and other proprietary fillers (Naeim and Kelly 1999). The dominant features of ERBs system are the parallel action of linear spring and viscous damping. Schematic diagram of the ERBs system is shown in Fig. 3(), which represents the linear ehavior with viscous damping. The restoring force developed in the earing, F is given y F c x k x (2) where, c and k are damping and stiffness of ERBs system, respectively. The stiffness and damping of ERBs system are selected to provide the specific values of the two parameters namely the isolation time-period ( T ) and damping ratio ( ) as T M 2 (3) k c 2M (4) where, ( M m md ) is the total mass of the ridge deck; and 2 / T is the isolation frequency. Fig. 3 a) Elastomeric Ruer Bearing and ) its schematic diagram 5. NUMERICAL STUDY The seismic response of curved ox girder ridge using ERBs is investigated for the four real earthquake ground excitation namely,,, Loma prieta (1989) and Koe (1995) earthquakes. The important features of earthquake ground motion are shown in Tale 2. For analysis east-west component of all earthquake are applied in chord direction, north-south component in radial direction of ridge. All the earthquakes are used at the full intensity for the evaluation of the performance of the proposed control strategy. To facilitate direct comparison and to evaluate the ERBs system, a set of 10 evaluation criteria has een developed. The evaluation criteria J 1 - J 4 are defined to 1939

7 Tale 2.Earthquake Data for Numerical Simulation Earthquake Recording Station Total Time (s) PGA (g) Vertical N-S E-W 117 El Centro Array # LGPC Sylmar Olive View Med FF Koe (1995) KJMA measure the reduction in peak response quantities as peak ase shear, peak overturning moment, peak mid-span displacement and peak mid-span acceleration of the curved ox girder ridge. The evaluation criteria evaluated y normalizing the peak response quantities of controlled ridge y the corresponding peak response quantities for the uncontrolled ridge; J 6 -J 9 are ased on the norm responses, calculated y normalizing the norm response quantities y the corresponding norm response of the uncontrolled ridge, and J 5 and J 10 are related to the peak and norm displacement of earing. To investigate the roustness of the isolation systems on the seismic response of curved ox girder ridge, the responses are otained y varying important parameter of ERBs, as damping ratio ( ), from 5 to 30% and considering isolation time period ( T ) equal to 2 sec. The variation of ase shear, ase moment, midspan displacement and midspan acceleration for different damping ratio of ERBs is shown in Figs It can e oserved that, all responses are decreasing with increase in the damping ratio of the ERBs for all earthquakes; whereas vertical displacement and acceleration are remain constant for variation of damping ration. Hence, from the Figs. 4-7, it can e concluded that a higher amount of damping is eneficial in reducing the seismic responses of the curved ox girder ridge. Further, for equal to 15%, the T is varied from 1.25 sec to 3.5 sec. Figs show variation of different response quantities for different isolation time period. From Fig. 8 and 10 it is oserved that the ase shear response and overturning moment at pier ase reduces with increasing time period of ERBs system. It is also oserved that more reduction in ase shear and overturning moment in chord direction compared to radial direction. From Figs. 9 and 11, it is oserved that with increase in isolation time period mid span displacement get increase and mid span acceleration decreases slightly. Hence, lower value T is ideal for efficient displacement response, whereas higher T is preferred for etter midspan acceleration response. Considering the value of the T as 2 sec and equal to 15% for overall etter response control for all earthquakes. Tale 3 shows the values of different evaluation criteria for all earthquakes at equal to 15% and T equal to 2 sec. The results of time history analyses along the chord and radial direction for reduction in ase shear of pier 1 are presented in Fig. 12 under the Koe (1995) earthquake. From the figure 12, it is oserved that due to use of ERBs system huge amount of reduction in ase shear of piers compared to uncontrolled structure. 1940

8 In order to study the effect of curved geometry on the response of the isolation system, comparison etween the responses of curved isolated ridge with straight isolated ridge is done. A straight isolated ridge modal with same cross section and material property as that of curved ridge, isolated with ERBs with parameter property equal to 15% andt equal to 2 sec is made and time history analysis is carried out. From analysis result, peak displacement and norm displacement of isolation system otain and compared with curved isolated ridge for different ground motions as shown in Tale 4.From results, it is found that there is no significant difference in peak response in radial and chord direction. Tale 3.Evaluation criteria J 1 -J 4 and J 6 to J 9 for ERBs ( T =2 Sec, =15%) Peak Value J1 J2 J3 J4 J6 J7 J8 J9 Location Pier 1 Pier 2 Pier 1 Pier 2 Deck Deck Pier 1 Pier 2 Pier 1 Pier 2 Deck Deck Earthquake Direction El Centro (1940) Loma Prieta (1989) Northridge (1994) Koe (1995) Chord Radial Chord Radial Chord Radial Chord Radial Chord Radial Vertical Chord Radial Vertical Chord Radial Chord Radial Chord Radial Chord Radial Chord Radial Vertical Chord Radial Vertical

9 (J 1 ) along chord of pier (J 6 ) along chord of pier Koe (1995) (J 1 ) along radial of pier (J 6 ) along radial of pier (J 1 ) along chord of pier (J 6 ) along chord of pier (J 1 ) along radial of pier (J 6 ) along radial of pier Damping ratio ( ) Fig.4 Effect of variation of damping ratio ( ) on peak ase shear (J 1 ) and norm ase shear (J 6 ) for ERBs ( T = 2 sec). 1942

10 (J 2 ) aout chord of pier (J 7 ) aout chord of pier Koe (1995) (J 2 ) aout radial of pier 1 (J 7 ) aout radial of pier 1 (J 2 ) aout chord of pier 2 (J 7 ) aout chord of pier (J 2 ) aout radial of pier (J 7 ) aout radial of pier Damping ratio ( ) Fig.5 Effect of variation of damping ratio ( ) on peak overturning moment (J 2 ) and norm overturning moment (J 7 ) for ERBs ( T = 2 sec). 1943

11 (J 3 ) along chord (J 8 ) along chord Koe (1995) (J 3 ) along radial (J 8 ) along radial (J 3 ) along vertical (J 8 ) along vertical Damping ratio ( ) Fig.6 Effect of variation of damping ratio ( ) on peak mid span displacement (J 3 ) and norm mid span displacement (J 8 ) for ERBs ( T = 2 sec). The results of time history analyses along the chord and radial direction of earing 1 (left autment top one earing) for variation of displacement are plotted for straight and curved ridge in chord and radial direction as shown in Fig. 13. From figure, it is oserved that displacement of earing in radial direction in curved ridge is lesser than that of the straight one and the pattern of displacement of earing is slightly changes in case of curved ridge compared to straight one. 1944

12 (J 4 ) along chord (J 9 ) along chord Koe (1995) (J 4 ) along radial (J 9 ) along radial (J 4 ) along vertical (J 9 ) along vertical Damping ratio ( ) Fig.7 Effect of variation of damping ratio ( ) on peak mid span acceleration (J 4 ) and norm mid span acceleration (J 9 ) for ERBs ( T = 2 sec). 1945

13 (J 1 ) along chord of pier 1 (J 6 ) along chord of pier Koe (1995) (J 1 ) along radial of pier 1 (J 6 ) along radial of pier (J 1 ) along chord of pier 2 (J 6 ) along chord of pier 2 (J 1 ) along radial of pier (J 6 ) along radial of pier Isolation Period, T (sec) Fig.8 Effect of variation of isolation time period on peak ase shear (J 1 ) and norm ase shear (J 6 ) for ERBs ( = 15%). 1946

14 (J 2 ) aout chord of pier 1 (J 7 ) aout chord of pier Koe (1995) (J 2 ) aout radial of pier 1 (J 7 ) aout radial of pier 1 (J 2 ) aout chord of pier (J 7 ) aout chord of pier (J 2 ) aout radial of pier (J 7 ) aout radial of pier Isolation Period T (sec) Fig.9 Effect of variation of isolation time period on peak overturning moment (J 2 ) and norm overturning moment (J 7 ) for ERBs ( = 15%). 1947

15 (J 3 ) along chord 3 2 (J 8 ) along chord 3 2 Koe (1995) (J 3 ) along radial (J 8 ) along radial (J 3 ) along vertical (J 8 ) along vertical Isolation Period, T (sec) Fig. 10 Effect of variation of isolation time period on peak mid span displacement (J 3 ) and norm mid span displacement (J 8 ) for ERBs ( = 15%). 1948

16 1.0 (J 4 ) along chord Koe (1995) (J 9 ) along chord (J 4 ) along radial 0.6 (J 9 ) along radial (J 4 ) along vertical (J 9 ) along vertical Isolation Period T (sec) Fig. 11 Effect of variation of isolation time period on peak mid span acceleration (J 4 ) and norm mid span acceleration (J 9 ) for ERBs ( = 15%). 1949

17 Base shear along chord (N) Base shear along radial (N) 4.0x x x x x x x10 7 Uncontrolled ERB Time (Sec) Fig. 12 Time variation of ase shear of pier 1 along the chord and radial direction of ridge isolated with ERBs ( = 15% and T = 2 sec) under Koe (1995) earthquake. Displacement (m) Chord direction Straight ridge Curved ridge Displacement (m) Radial direction Time (sec) Fig. 13 Time variation of displacement of earing along the chord and radial direction for straight and curved ridge isolated with ERBs ( = 15% and T = 2 sec) under Koe (1995) earthquake. 1950

18 Tale 4.Peak displacement and norm displacement of earings for straight and curved isolated ridge ( = 15% andt = 2 sec). Earthquake Koe (1995) Type of Bridge Peak displacement of earings (J 5 ) Bearing 1 Bearing 2 Bearing 3 Bearing 4 Chord Radial Chord Radial Chord Radial Chord Radial Curved Straight Curved Straight Curved Straight Curved Straight Norm displacement of earings (J 10 ) Koe (1995) Curved Straight Curved Straight Curved Straight Curved Straight CONCLUSION The analytical seismic response of a horizontally curved concrete ox girder ridge isolated y ERBs is investigated. The seismic response of the ridge with ERBs is evaluated using standard numerical technique under two horizontal and one vertical component of the four different earthquake ground motions. The effectiveness of the ERBs studied under different system parameters for assessment of its performance. From the trend of the results of the present study, the following conclusions are drawn: 1. With the installation of ERBs in the horizontally curved concrete ox girder ridge the ase shear and overturning moment under different ground motions can e controlled within a desirale range, 1951

19 2. All responses J 1 to J 4 are decreasing with increase in the damping ratio of the ERBs for all considered earthquake ground motions, 3. The effect of curved geometry makes no significant difference in peak response mainly peak isolator displacements of ERBs system where as pattern of displacement in radial and chord direction changes slightly and 4. The ERBs found to e effective for controlling the seismic response of curved ridge. REFERENCES Ates, S., and Constantinou, M. C. (2011a). "Example of application of response history analysis for seismically isolated curved ridges on drilled shaft with springs representing soil." Soil Dynamics and Earthquake Engineering, 31, Ates, S., and Constantinou, M. C. (2011). "Example of application of response spectrum analysis for seismically isolated curved ridges including soil-foundation effects." Soil Dynamics and Earthquake Engineering, 31, Berger / Aam Engineers, I. F. H. A. S. D. C. (1996). "Design Example No.6." Pulication no. FHWA-SA and Barcode no. PB Galindo, C. M., Hayashikawa, T., and Belda, J. G. (2009). "Damage evaluation of curved steel ridges upgraded with isolation earings and unseating prevention cale restrainers." World Academy of Science, Engineering and Technology, 59, Kunde, M. C., and Jangid, R. S. (2003). "Seismic ehavior of isolated ridges:a-stateof-the-art review." Electronic Journal of Structural Engineering, 3(3), Lei, Y.-H., and Chien, Y.-L. (2004). "Applications of LRB and FPS to 3-D curved ox ridges." Tamkang Journal of Science and Engineering, 7(1), Liu, Y., Qi, X., Wang, Y., and Chen, S. (2011). "Seismic mitigation analysis of viscous dampers for curved continuous girder ridge." Applied Mechanics and Materials, 90-93, Naeim, F. and Kelly, J.M., (1999). Design of Seismic Isolated Structures: From Theory to Practice, John Wiley and Sons, Inc., New York, USA. Redfield, N., Valentine Orangevale, i. a. w., David Evans & Associates, I., and Zocon Consulting Engineers, I. (2008). "Development of design specifications and commentary for horizontally curved concrete ox-girder ridges." T. R. Board, ed., National Cooperative Highway Research Program, Washington, D.C. 1952

Suhasini N. Madhekar

Seismic Control of Benchmark Highway Bridge Installed with Friction Pendulum System Suhasini N. Madhekar Associate Professor, Applied Mechanics, College of Engineering Pune, Pune 411005, India suhasinimadhekar@gmail.com