th
5 International Advanced Technologies Symposium (IATS’09), May 13-15, 2009, Karabuk, Turkey
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
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
© IATS’09, Karabük University, Karabük, Turkey
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.
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
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].
Y
X
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:
kD
GA
tr
(1)
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):
Figure 1. Typical floor plan
3rd Floor
0.5 0.19635
0.25
0.3927 MN/m
(2a)
1.0 0.19635
0.25
0.7854 MN/m
(2b)
kD HDR
A
2nd Floor
k D HDR
B
1st Floor
The total effective stiffness of the isolation system is
obtained as
16k D HDR
kD
Seismic
Isolator
Base
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
A
9k D HDR
B
13351.8 kN/m
(3)
providing an effective isolation period of
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
A
HDR A
D
D
kD HDR
B
HDR B
D
kD
0.127 (5)
around 0.05~0.15. Therefore,
lies in the typical range.
Q/W=660.8/12556.8=0.052
F
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].
Fy
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]:
4
2
K1
CVDTD
0.242 m
BD
DD 1 y
12e
b d2
2
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
DD
D
Figure 3. Force-Displacement relationship of a highdamping rubber bearing.
0.278 m
(7)
Kef
1
Dy
(6)
Finally, the total design displacement including additional
displacement due to accidental torsion is calculated
according to the UBC97 [20] as follows:
DTD
K2
Q
1
g
DD
1
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.
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:
P1
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
Velocity [cm/s]
EL CENTRO
50
0
-50
-100
0
5
10
15
20
25
Time (s)
30
35
40
45
50
100
Velocity [cm/s]
KOBE
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
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 )
max t ( Vb )
Performance
Criteria
(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.
EL CENTRO
KOBE
Fixedbase
Baseisolated
Fixedbase
Baseisolated
-
6.51
-
25.34
P2 (x10-3) [-]
2.57
0.60
9.74
1.25
P3 [m/s2]
8.24
2.06
29.56
3.02
P4 [kN]
5532
878
21206
3399
P3/ag [-]
2.41
0.60
3.61
0.37
P1 [cm]
(10)
where a3 is the total acceleration of the third floor. Finally,
peak base shear is given by
P4
Table 1. Performance Criteria
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
EL CENTRO
Base-Isolated
Fixed-Base
Base Shear [kN]
4000
2000
0
-2000
-4000
-6000
0
5
10
15
20
25
Time [s]
30
35
40
45
50
25000
20000
KOBE
Base-Isolated
Fixed-Base
Base Shear [kN]
15000
10000
5000
0
-5000
-10000
-15000
-20000
-25000
0
5
10
15
20
25
Time [s]
30
35
40
45
50
Figure 5. Base Shear under El Centro and Kobe Earthquakes
40
100
HDR-A
HDR-B
50
Force [kN]
Force [kN]
20
0
-20
0
-50
-40
-10
-5
0
5
Displacement [cm]
-100
-10
10
-5
0
5
Displacement [cm]
10
Figure 6. Force-Displacement curves for rubber bearings under El Centro Earthquake
100
200
HDR-A
100
Force [kN]
Force [kN]
50
0
0
-100
-50
-100
HDR-B
-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
Alhan, C. and Altun, M.
Force [kN]
20
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.