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5 International Advanced Technologies Symposium (IATS'09), May 13-15, 2009, Karabuk, Turkey

th

PERFORMANCE OF NON-LINEAR BASE ISOLATION SYSTEMS DESIGNED ACCORDING TO UNIFORM BUILDING CODE

Cenk Alhana and Metin Altun b

a

b

Department of Civil Engineering, stanbul University, stanbul, Turkey E-mail: [email protected] Department of Civil Engineering, stanbul University, stanbul, Turkey E-mail: [email protected]

Abstract

For the safety and welfare of the public, industrial facilities and public structures must remain functional at all times. Consequently, they have to remain essentially elastic even after major earthquakes. This could be achieved via seismic base isolation which is an advanced technology used in earthquake-resistant design. Rubber isolation pads with low horizontal stiffness placed between the columns and the foundation lengthen the period of a structure and thereby reduce floor accelerations and inter-story drifts. A challenge that base isolated structures may face is the near-fault earthquakes which contain long-period velocity pulses that may coincide with the period of base isolated structures resulting in excessive deformation and rupture of isolators. Uniform Building Code (UBC97) is widely used in design of base isolation systems which contains provisions accounting for near-fault earthquake effects. In order to investigate the performance of base isolation systems designed according to UBC97 under near-fault and far-fault earthquakes, bi-directional non-linear time history analyses of a 4-story base isolated benchmark building, located close to an active fault, are carried out. The isolation system is composed of high damping rubber bearings and the force-displacement behavior of the bearings is modeled as bi-linear. Design displacements are estimated using UBC97 parameters. The building is subjected to the far-fault 1940 El Centro Earthquake and the near-fault 1996 Kobe Earthquake. Results show that UBC97 predicts isolator displacements successfully. Floor accelerations and inter-story drifts of the subject baseisolated building are significantly reduced when compared to its fixed-based counterpart. Keywords: Seismic isolation, earthquake engineering, non-linear isolation system, Uniform Building Code

technology that could provide such desired behavior [3, 4, 5, 6, 7]. Seismic isolation can be achieved by lengthening the natural period of vibration of a structure via use of rubber isolation pads between the columns and the foundation [3, 8]. Consequently, the seismic effects are reduced which leads to significant reductions in seismic response variables such as floor accelerations, inter-story drifts, and base shear [9, 10]. On the other hand, as the flexibility of the isolation system increases, base displacements become larger [11, 12]. Since all isolation systems have a deformation capacity, the peak isolator deformations should not exceed a certain design value [13]. In case the deformation capacity of the isolators exceeded, rupture or buckling of the isolators may come into scene which would be a major safety problem [14, 15, 16]. Therefore, it is vital to accurately estimate the peak base displacements in case of major earthquakes, particularly if the base isolated building is likely to be struck by near-fault earthquakes. Near-fault earthquakes may contain long-period velocity pulses which may coincide with the period of the base isolated structures. In such a case, the isolators may deform excessively [2, 17, 18, 19]. Uniform Building Code (UBC97) [20] is a seismic code that is widely used in the design of base isolation systems which contains special provisions to account for the near-fault earthquake effects depending on the closest distance to an active fault [2, 13]. In this study, bi-directional non-linear time history analyses of a 4-story base isolated building are carried out in order to investigate the performance of base isolation systems designed according to UBC97 [20]. The building is assumed to be located close to an active fault and the design displacements of high damping rubber bearings used in the isolation system are estimated using parameters defined in UBC97 [20]. The building is subjected to the 1940 El Centro Earthquake which can be classified as a typical far-fault earthquake and the 1996 Kobe Earthquake which can be classified as a near-fault earthquake.

1. Introduction

The basic philosophy of the seismic codes is to save lives by requiring that structures are designed such that any partial or total collapse is prevented in case of major earthquakes [1]. In conventional earthquake-resistant design, this is provided by ductility whereby the structure is allowed to deform beyond the elastic range. This consequently means that even though the collapse of the structure can be prevented, significant structural damage may be sustained in case of major earthquakes. However, for the safety and welfare of the public, structures such as hospitals, fire departments, and industrial facilities must remain completely functional [2]. Therefore, these structures have to remain essentially elastic even after major earthquakes. Seismic base isolation is an advanced

2. Mathematical Modeling

Typical floor plan and elevation of the base-isolated threestory reinforced concrete building, which is used as the subject structure in this study, are shown in Fig 1 and Fig 2, respectively. All columns are 45 cm x 45 cm, all beams are 30 cm x 55 cm, and the floor heights are 3.00 m. There are 4 bays of 5.00 m in each direction, i.e. plan dimensions are 20.00 m x 20.00 m. The total mass of the building is 1280 tons corresponding to a total weight of W=12556.8 kN. All structural members are of concrete class C30 with an elasticity modulus of 32000 MPa. Each floor has three

© IATS'09, Karabük University, Karabük, Turkey

Alhan, C. and Altun, M.

degrees of freedom, X and Y translations and rotation about the center of mass of the floor. These degrees of freedom are attached to the center of mass of each floor which is at the geometric center. The centers of mass and centers of rigidity of each floor coincide and therefore there exists no eccentricity. The fixed-base periods of the superstructure in each translational direction are 0.34 seconds and the super-structure modal damping ratios are assumed to be constant for each mode as 5%. The superstructure is placed on an isolation system consisting of high-damping rubber bearings (HDR) placed under each column. Since the weight transferred to the bearings located on the corners and sides of the building is less than the weight transferred to the inner ones, two types of bearings are designed. The outer (corner and side) and inner bearings are labeled as HDR-A and HDR-B, respectively. There exists a rigid slab at the base level that connects all isolation elements. The three-dimensional model of the base-isolated building and the non-linear time-history analyses are made using a well-known finite element analysis program SAP2000n [21].

closest distance to a known fault that is capable of producing large magnitude events and that has a high rate of seismic activity (Class A seismic source according to Table 16-U of the UBC97 [20]) is assumed to be 5 km. Since the building is in the vicinity of an active fault, it is likely to be subjected to the near-fault effects. The UBC97 [20] takes these effects into account by defining the nearsource factor Nv. Based on the closest distance to the known seismic source, which is 5 km, the near-source factor Nv is obtained from Table 16-T of the UBC97 [20] as 1.6. Based on the seismic zone factor and the soil profile type, which is assumed as SB that corresponds to rock profile, the seismic coefficient CVD=Cv is obtained from Table 16-R of the UBC97 [20] as CVD=Cv=0.4Nv=0.4x1.6=0.64. High damping rubber bearings are composed of rubber layers and thin steel sheets. The damping is increased by adding oils, resins, or other fillers and a damping around 10%~15% can be obtained. The stiffness of the bearing is high in case of small displacements and low in case of high displacements. This is very advantageous since large movements are prevented under wind load. On the other hand long periods and therefore isolation under strong ground motion are obtained. Following the standard design procedure for high damping rubber bearings [4, 22, 23] target design level effective isolation period TD and target design level effective damping ratio D are selected, which are TD=2 s and D= 0.13 in this study. Horizontal stiffness of an individual rubber isolation bearing is given by:

Y X

kD

GA tr

(1)

Figure 1. Typical floor plan

where G is the shear modulus of the rubber, A is the crosssectional area of the bearing, and tr is the total thickness of the rubber layers in the bearing. Selecting the total thickness of the rubber layers in each bearing as tr=25 cm =50 cm, the and the diameter of each bearing as horizontal stiffness for HDR-A (G=0.5 Mpa) and HDR-B (G=1.0 Mpa) with cross sectional areas of A= x0.52/4=0.19635 m2 are calculated following (1):

3rd Floor

kD HDR

k D HDR

A

0.5 0.19635 0.25

1.0 0.19635 0.25

0.3927 MN/m

(2a)

2nd Floor

B

0.7854 MN/m

(2b)

1st Floor

Seismic Isolator

The total effective stiffness of the isolation system is obtained as

kD

16k D HDR

A

9k D HDR

B

13351.8 kN/m

(3)

Base

providing an effective isolation period of

Figure 2. Elevation The building is assumed to be located in a high-seismicity region, i.e Zone 4, and assigned a seismic zone factor Z=0.4 according to Table 16-I of the UBC97 [20]. The

TD

2

W kD g

1.95 sn

(4)

which is very close to the target period. Here, g is the gravitational force and taken as 9.81 m/s2. The design level damping ratio of the isolation system is obtained by:

Alhan, C. and Altun, M.

k D HDR

D

A

HDR A D

kD HDR kD

B

HDR B D

0.127 (5)

around 0.05~0.15. Therefore, lies in the typical range. F

Q/W=660.8/12556.8=0.052

where DHDR-A and DHDR-B are damping ratios of individual bearings and are chosen as 0.10 and 0.15, respectively. The damping coefficient corresponding to D=0.127 is BD=1.28 according to Table A-16-C of the UBC97 [20]. The design displacement of the isolation system along each main horizontal axis at design basis earthquake (DBE) level is calculated according to the UBC97 [20]:

Fy Q K1 1 1

1

K2

Kef D

g DD 4

2

CVDTD BD 0.242 m

(6)

Dy

DD

Finally, the total design displacement including additional displacement due to accidental torsion is calculated according to the UBC97 [20] as follows:

Figure 3. Force-Displacement relationship of a highdamping rubber bearing.

DTD

(7)

DD 1 y

12e b d2

2

0.278 m

3. Earthquake Data

The 18 May 1940 El Centro Earthquake and the 17 January 1995 Kobe Earthquake data are used in the bidirectional time history analyses. The NS and EW components of the earthquakes are applied in X and Y directions, respectively. However, since the NS components are the larger components of these earthquakes, only the results in X-direction will be presented and discussed here. The velocity records of the NS components are shown in Fig 4. As it can be seen from the figure, while there exists no significant pulse in the El Centro record, there exists a significant velocity pulse with amplitude of 91.33 cm/s in the Kobe record. While El Centro is a typical far-fault earthquake, the Kobe Earthquake can be classified as a near-fault earthquake. The peak ground accelerations for the NS components of the El Centro and Kobe Earthquakes are 3.42 m/s2 and 8.18 m/s2, respectively.

where b=20 m is the shortest plan dimension of the structure measured perpendicular to the longest plan dimension of the structure, which is d=20 m. Here, y is the distance between the center of rigidity of the isolation system and the isolation bearings placed at the sides of the plan, measured perpendicular to the direction of seismic loading under consideration, thus y=b/2=d/2=10 m in this study. Finally, e is the actual eccentricity plus the accidental eccentricity which is taken as 5 percent of the maximum building dimension perpendicular to the direction of force under consideration. Since the structure at hand is symmetrical, the actual eccentricity is zero and therefore e=0.05x20=1.00 m. The total design displacement calculated above satisfies the UBC97 [20] minimum criteria; DTD=0.278 m > 1.10xDD=0.266 m. Force displacement relationship of a high-damping rubber bearing, which is modeled as bi-linear, is shown in Fig 3. Shown in the figure are the yield force, Fy, the yield displacement, Dy, the design displacement, DD, the preyield stiffness, K1, the post-yield stiffness, K2, the effective stiffness, Kef, and characteristic force, Q. Post-yield to preyield stiffness ratio ( =K2/K1) depends on the material used and typically attains values around 0.05~0.15. In this study, is chosen as 0.10 for both HDR-A and HDR-B and the design displacement values for both isolators are the same (DD=0.242 m). In order to achieve effective stiffness values of kDHDR-A=392.7 kN/m and kDHDR-A=785.4 kN/m, other parameters of the curves are calculated as K1=3296.8 kN/m, K2=329.7 kN/m, Fy=16.9 kN, Q=15.2 kN, and Dy=5.1 mm for HDR-A and K1=5934.5 kN/m, K2=593.5 kN/m, Fy=51.6 kN, Q=46.4 kN, and Dy=8.7 mm for HDR-B. For high damping rubber bearings, typically, yield displacements attain values around 5 mm~15 mm and the yield displacements calculated in this study lie in this typical range. In this study, the total characteristic force is Q=16x15.2+9x46.4=660.8 kN. Typically, Q/W would be

4. Performance Criteria

Displacements, accelerations, and base shear discussed here are all in X-direction. In order to assess the performance of the structure when subjected to near-fault and far-fault earthquakes, a performance criteria is established. These include peak base displacement (P1), peak roof-drift ratio (P2), peak 3rd floor acceleration (P3), and peak base shear (P4). Since there exists a rigid slab at the base level that connects all isolation elements, relative displacement of the base with respect to the ground also represents the deformations of the isolators:

P 1

max t ( db )

(8)

where t is time, db is the relative displacement of base with respect to the ground. As a measure of the inter-story drifts, a roof-drift ratio is defined as the difference between

Alhan, C. and Altun, M.

100

EL CENTRO

Velocity [cm/s] 50 0 -50 -100 0 5 10 15 20 25 Time (s) 30 35 40 45 50

100

KOBE

Velocity [cm/s] 50 0 -50 -100 0 5 10 15 20 25 Time (s) 30 35 40 45 50

Figure 4. Velocity records for NS components of the El Centro and the Kobe Earthquakes the displacement of the third floor (roof) and the base floor divided by the total height of the building. Thus, peak roofdrift ratio is defined as Table 1. Performance Criteria Performance Criteria P1 [cm] P2 (x10-3) [-] P3 [m/s2] EL CENTRO Fixedbase 2.57 8.24 5532 2.41 Baseisolated 6.51 0.60 2.06 878 0.60 KOBE Fixedbase 9.74 29.56 21206 3.61 Baseisolated 25.34 1.25 3.02 3399 0.37

P2

max t ( (d3 db ) / H )

(9)

where d3 is relative displacement of the roof with respect to the ground and H is total height of the building. Peak 3rd floor acceleration is

P3

maxt ( a3 )

(10) P4 [kN] P3/ag [-]

where a3 is the total acceleration of the third floor. Finally, peak base shear is given by

P4

max t ( Vb )

(11)

where Vb is the base shear of the structure. .

5. Results

Fig 5 shows the X-direction base shear time history of base-isolated building and its fixed-base counterpart for both El Centro and Kobe Earthquakes. As it can be seen from the figure, the period of the base-isolated building is much longer and the base shear is much smaller. Evidently, the seismic effects are reduced significantly. A complete list of the performance criteria is presented in Table 1. The peak base shear (P4) of the base-isolated building is only 16% of its fixed-base counterpart in case of both El Centro and Kobe Earthquakes. The peak 3rd floor acceleration is reduced from P3=8.24 m/s2 to P3=2.06 m/s2 in case of El Centro Earthquake and from P3=29.56 m/s2 to P3=3.02 m/s2 in case of Kobe Earthquake. The peak 3rd floor acceleration is only 60% and 37% of the peak ground acceleration (ag) in case of El Centro and Kobe Earthquakes, respectively showing the success of isolation.

Likewise, the roof-drift ratio is reduced to P2=0.0006 in case of El Centro Earthquake proving that the superstructure moved almost like a rigid-body above the isolation system. In case of Kobe Earthquake, the roof-drift ratio for the fixed-base building is 0.00974 which would be unacceptable. With the aid of base isolation, this value is reduced to an acceptable level, i.e P2=0.00125. The force-displacement curves for the two types of bearings, HDR-A and HDR-B are presented in Figs 6 and 7 in case of El Centro and Kobe Earthquakes, respectively. It is seen that the bi-linear behavior assumption made in the design stage according to the UBC97 [20] is appropriate. A close inspection of the curves shows that the characteristic force, yield displacement, pre-yield stiffness and post-yield stiffness for the HDR-A and HDR-B bearings appear as designed and modeled. The peak displacement is P1=6.51 cm in case of the far-fault El Centro Earthquake which is much smaller than the predicted total design displacement of 27.8 cm. However, this prediction included the likelihood of the building to be subjected to a near-fault earthquake and corresponding near-source factor was included in the design displacement calculations. The peak displacement in case of the near-fault Kobe Earthquake shows the importance of taking this near-source factor into account.

Alhan, C. and Altun, M.

6000 4000 Base Shear [kN] 2000 0 -2000 -4000 -6000

EL CENTRO

Base-Isolated Fixed-Base

0

5

10

15

20

25 Time [s]

30

35

40

45

50

25000 20000 15000 Base Shear [kN] 10000 5000 0 -5000 -10000 -15000 -20000 -25000 0 5 10 15 20 25 Time [s] 30 35 40 45 50 KOBE Base-Isolated Fixed-Base

Figure 5. Base Shear under El Centro and Kobe Earthquakes

40 HDR-A 20 Force [kN]

100 HDR-B 50 Force [kN]

0

0

-20

-50

-40 -10

-5 0 5 Displacement [cm]

10

-100 -10

-5 0 5 Displacement [cm]

10

Figure 6. Force-Displacement curves for rubber bearings under El Centro Earthquake

100

200

HDR-A

HDR-B

50 Force [kN]

Force [kN]

100

0

0

-50

-100

-100

-200

-20

0 20 Displacement [cm]

-20

0 20 Displacement [cm]

Figure 7. Force-Displacement curves for rubber bearings under Kobe Earthquake

40 HDR-A 20 Force [kN]

Alhan, C. and Altun, M.

The peak base displacement in case of Kobe Earthquake jumps to P1=25.34 cm which is 91% of the total design displacement calculated according to the UBC97 [20].

5. Conclusions

Seismic base isolation can reduce the seismic effects and therefore floor accelerations, inter-story drifts, and base shear by lengthening the natural period of vibration of a structure via use of rubber isolation pads between the columns and the foundation. However, in case the deformation capacity of the isolators exceeded, isolators may rupture or buckle. Therefore, it is vitally important to accurately estimate the peak base displacements in case of major earthquakes, particularly if the base isolated building is likely to be struck by near-fault earthquakes. Near-fault earthquakes may contain long-period velocity pulses which may coincide with the period of the base isolated structures. In such a case, the isolators may deform excessively. Uniform Building Code [20] is widely used in design of base isolation systems which contains provisions accounting for near-fault earthquake effects. In order to investigate the performance of base isolation systems designed according to UBC97 [20] under nearfault and far-fault earthquakes, bi-directional non-linear time history analyses of a 4-story base isolated benchmark building, located close to an active fault, are carried out. Based on the simulations carried out, it is concluded that seismic base isolation is a successfull technique that can be used in earthquake-resistant design. A major improvement in the super-structure performance is achieved as the floor accelerations, inter-story drifts and base shear can be significantly reduced alltogether. However, inclusion of near-source effects defined in the UBC97 [20] in calculating the total design displacement is crucial since the peak base displacement is significantly bigger when a base-isolated building is hit by a near-fault earthquake containing a long-period and large amplitude velocity instead of a far-fault earthquake.

References

[1] Dowrick, D.J., Earthquake Resistant Design For Engineers and Architects, 2nd Ed., John Wiley & Sons, Great Britain, 1987. [2] Ramallo, J.C., Johnson, E.A., and Spencer Jr., B.F., Smart base isolation systems, Journal of Engineering Mechanics, vol 28, 1088-1099, 2002. [3] Deb, S.K., Seismic base isolation ­ an overview, Current Science, vol 87, 1426-1430, 2004. [4] Kelly, J.M., Earthquake-resistant design with rubber, Springer-Verlag, London, UK, 1997. [5] Komodromos, P., Seismic isolation for earthquakeresistant structures, WITPress, Southampton, UK, 2000. [6] De la Llera, J., Lüders, C., Leigh, P., and Sady, H., Analysis, testing, and implementation of seismic isolation of buildings in Chile, Earthquake Engineering and Structural Dynamics, vol 33, 543-574, 2004. [7] Nagarajaiah, S. And Xiaohong, S., Response of baseisolated USC hospital building in Northridge Earthquake, Journal of Structural Engineering, vol 126, 1177-1186, 2000.

[8] Naeim, F. and Kelly, J.M., Design of seismic isolated structures from theory to practise, John Wiley & Sons, USA, 1999. [9] Morales, C.A., Transmissibility concept to control base motion in isolated structures, Engineering Structures, vol 25, 1325-1331, 2003 [10] Skinner, R.I., Robinson, W.H., and McVerry, G.H., An intoduction to seismic isolation, John Wiley & Sons, UK, 1993. [11] Alhan, C. and Gavin, H., A parametric study of linear and non-linear passively damped seismic isolation systems for buildings, Engineering Structures, vol 26, 485-497, 2004. [12] Su, L. And Ahmadi, G., A comparative study of performances of various base isolation systems Part II: Sensitivity analysis, Earthquake Engineering and Structural Dynamics, vol 19, 21-33, 1990. [13] Kelly, J.M., The role of damping in base isolation, Earthquake Engineering and Structural Dynamics, vol 28, 3-20, 1999. [14] Koh, C.G. and Balendra, T., Seismic response of base isolated buildings including P-Delta effects of isolation bearings, Earthquake Engineering and Structural Dynamics, vol 18, 461-473, 1989. [15] Nagarajaiah,S. and Ferrell, K., Stability of elastomeric seismic isolation bearings, Journal of Structural Engineering, vol 125, 946-954, 1999. [16] Nagarajaiah,S. and Ferrell, K., Stability of elastomeric seismic isolation bearings: Experimental study, Journal of Structural Engineering, vol 128, 3-11, 2002. [17] Heaton, T.H., Hall, J.F., Wald, D.J., and Halling, M.W., Response of high-rise and base-isolated buildings to a hypothetical Mw 7.0 blind thrust earthquake, Science, vol 267, 206-211, 1995. [18] Jangid, R.S. and Kelly, J.M., Base isolation for nearfault motions, Earthquake Engineering and Structural Dynamics, vol 30, 691-707, 2001. [19] Yoshioka, H., Ramallo, J.C., and Spencer Jr., B.F., Smart base isolation strategies employing magnetorheological dampers, Journal of Engineering Mechanics, vol 128, 540-551, 2002. [20] International Code Council, Uniform Building Code, Vol. 2, USA, 1997 [21] Computers and Structures Inc., SAP2000N Static and dynamic finite element analysis of structures, Version 10.0.1, Berkeley, USA, 2005. [22] Tezcan, S.S. and Cimilli, S., Seismic base isolation, Yüksek Ö renim E itim Ve Ara rma Vakf , Yay n No:KT004/02, Cenkler Matbaac k, stanbul, 2002. [23] Ba tu , B.K., Yap sistemlerinde depreme kar sismik izolatör kullan lmas , Yüksek Lisans Tezi, Y ld z Teknik Üniv., Fen Bilimleri Enst., aat Mühendisli i Anabilim Dal , Mekanik Program , stanbul, 2004.

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