Numerical Simulation of Shake-table Tests of a Full-Scale Building Seismically
Isolated with Lead-Rubber Bearings
Qingyuan DONG
Candidate for the Degree of Master of Engineering
Supervisor: Mitsumasa MIDORIKAWA
Division of Architectural and Structural Design
Keywords: base isolation, lead-rubber bearing, shake-table test, numerical simulation, seismic response.
Z
(a) Y
1.2
0.6
SW-CLB
-0.6
-1.2
1.2
0.6
Y
0
-0.6
-1.2
0
50
(a)
100
150
200
Time (s)
1.2
0.6
W-LRB NW-CLB
X
-0.6
SE-CLB
C-CLB
E-LRB
N-LRB
NE-CLB
5,000
S-LRB
Acceleration [g]
-1.2
Steel Plates
1.2
0.6
W
Y
(b)
Y
0
-0.6
-1.2
1.2
0.6
E
X
0
0
7,000
15,835
900 3,815 3,035 3,000 3,000 3,000
12,000
7,000
5,000
460
2. E-Defense test
In August 2011, a full-scale, base-isolated steel moment-frame
building was tested using the E-Defense shake table [1]. As
shown in Fig. 1(a), the two-by-two bay, five-story building was
10-m and 12-m wide in the X and Y-directions, respectively,
and 15.8-m tall. The building had a total weight of W = 542
tons. Steel plates weighing 54 ton were placed on the roof to
introduce a mass eccentricity ratio of 2% (the distance between
the mass center and geometric center divided by the floor-plan
dimension) in the Y-direction of the isolation layer.
As shown in Fig. 1(b), the isolation system comprised four
lead-rubber bearings (LRBs) and five cross-liner bearings
(CLBs) between the shake table and the building. The LRBs
were placed under the four edge columns, and the CLBs were
placed under the four corner columns and the center column.
Fig. 2 shows the dimensions of the LRB. The LRB had a first
shape factor S1 of 23.8, and a second shape factor S2 of 2.8. The
initial vertical stress on four LRBs ranged from 0.66 to 2.1
N/mm2. The CLBs comprised two linear bearings oriented
orthogonally to each other, and had negligible horizontal
stiffness and very large vertical stiffness compared to the LRBs.
Fifteen excitations were conducted. This paper focuses on
three excitations. The Iwanuma motion from the 2011 Tohoku
earthquake was a long-duration motion. The Rinaldi motion,
obtained from the 1994 Northridge earthquake, featured very
large vertical acceleration. Fig. 3 shows the time history of the
two excitations, 100%-XY Iwanuma and 88%-XYZ Rinaldi.
Another excitation, 88%-XY Rinaldi, had the same X and Y
acceleration as the 88%-XYZ Rinaldi, but did not include
vertical acceleration.
The same building was also
673
lead core
102
tested with the isolation layer
steel shim 3
removed and its base fixed to
total thickness 119
the shake table. The building in
rubber layer 6
total thickness 240
fixed-base configuration was
subjected to reduced-scaled
Iwanuma and Rinaldi motion
Figure 2. LRB Dimensions.
to enable comparison between
(in mm)
the isolated and fixed-base
building.
Acceleration [g]
1. Introduction
Numerical simulation of a full-scale five-story building base
isolated by a system of lead-rubber bearings (LRBs) and crossliner bearings (CLBs) was performed. The structure was
subjected to a number of bidirectional and bidirectional-plusvertical ground motions using the E-Defense shake table. A
three-dimensional nonlinear model of the structure was
established and subjected to ground motion measured on the
shake table. The behavior of LRBs, response of the building,
vertical loads, and the effectiveness of the LRB-CLB isolation
system are discussed.
Z
0
Shake Table
X
5,000
-0.6
5,000
Figure 1. Outline of the building: (a) North elevation;
(b) Location of bearings. (Unit: mm)
-1.2
0
(b)
10
Time (s)
Figure 3. Input motions: (a) 100%-XY Iwanuma;
(b) 88%-XYZ Rinaldi.
20
4. Validation of analysis
The fundamental period of the building with its base fixed was
0.69 s in the analysis, which is very close to the experimental
value of 0.7 s identified through white noise excitation.
The computed response is compared against the test results
for the 100%-XY Iwanuma and 88%-XY Rinaldi motions in
terms of the hysteresis of the S-LRB (Fig. 8), maximum story
drift (Fig. 9), maximum floor acceleration (Fig. 10) and
translation and twist angle of the isolation layer (Fig. 10 and 11).
MSS-4 spring
MSS-6 spring
MSS-8 spring
MSS-12 spring
350
175
Disp-Y [mm]
3. Model of the structure
A 3-D nonlinear model of the structure was produced. The
model included all columns and girders of the building and
each LRB and CLB. Members of the superstructure were
modeled as linear elastic. An end zone was added at every
girder-to-column joint to consider the stiffness of the joints. To
simulate rigid floor diaphragms, the relative horizontal
distances between the nodes in each floor were fixed.
Composite beam effect was accounted for by multiplying the
flexural stiffness by 2 for girders with concrete slab at two sides,
and multiplying by 1.5 for girders with concrete slab on one
side only. Masses were lumped to the girder-to-column joints
according to the gravity load distribution of the building and the
mass moment of inertia of each floor.
As shown in Fig. 4, a multiple shear spring (MSS) model
was used to simulate the bidirectional horizontal response of
LRBs [2]. The MSS model comprised horizontal springs
placed evenly in a circular configuration. As shown in Fig. 6(a),
each horizontal spring behaved bilinearly. Based on production
test, the target bilinear model had an initial stiffness K0 of 6.5
kN/mm, post-yielding stiffness KF of 0.65 kN/mm, and yield
strength FU of 73 kN. Fig.5 shows the bidirectional
displacement response of an LRB subjected to 4 cycles of slow,
circular forces. The figure compares MSS models with
different number of horizontal springs. While models with 4and 6-springs showed oscillation, models with 8- and 12springs moved smoothly along a circular orbit. Therefore,
based on a convergence study, the 8–spring model was deemed
sufficient. Fig. 6 shows that the 8-spring MSS model agreed
with monotonic target response. The vertical response of the
LRBs was modeled by a bilinear model, as shown in Fig. 6(b),
with a compressive stiffness KC of 1500 kN/mm and tensile
stiffness K T of 150 kN/mm. From the formula, σ cr =
 /( 2 2) S1S2, the critical compressive stress σcr of the LRB
was 30.6 MPa.
The CLBs were modeled as bidirectional rollers.
In the isolation layer, the horizontal restoring force was
derived from the four LRBs only. Fig. 7 shows the unidirectional force versus displacement relationship of the LRBCLB isolation system. The bracketed values in the ordinate are
the restoring force, V, normalized by the total weight of the
building, W. The bracketed values in the abscissa are the
horizontal strain assuming that the four LRBs deform equally.
The isolation system provided a yield strength of V/W=0.055
and a strength of V/W=0.34 at 250% strain, which is the design
limit specified for the specimen. From the formula, Teff =
2π(M/Keff)0.5 [3], and Keff =3.0 kN/mm (the effective stiffness at
250% strain), the effective period is evaluated as Teff = 2.66 s,
which is four times the fundamental period of the building
when its base was fixed, 0.7 s.
Rayleigh damping was specified by assigning 2% critical
damping for the period of 0.7 s and 2.5% for the period of 2.66
s. Analysis was performed with a time increment of
0.01s.Recorded acceleration of the shake table was used as
ground motion.
0
-175
-350
-350
-175
0
175
Disp-X [mm]
350
Figure 5. Displacement orbit of
MSS model under dynamic
force.
Figure 4. Outline of the
MSS model: (a) Elevation
view; (c) Plan view.
(a)
Force
(b)
KT
Disp.
KC
Figure 6. Skeleton curve of LRB: (a) horizontal; (b) vertical.
1823
(0.34W)
Restoring force (kN)
(0.054W)
292
11mm
(4.6%)
Horizontal
deformation (mm)
600mm
(250%)
K eff =3.0 kN/mm
Figure 7. Force vs. deformation relationship of LRB-CLB
isolation system.
Analy.
Exper.
5
4
4
3
3
2
Floor
5
1
0
2
(a)
200
400
600
RF
1
0
RF
5
5
4
4
3
3
2
1
0
400
200
400
2
(c)
200
(b)
600
1
0
Disp.-X (mm)
600
(d)
200
400
600
Disp.-Y (mm)
RF
5
5
4
4
3
3
2
Floor
RF
Analy.
Exper.
1
0
2
(a)
0.5
1
RF
1
0
0.5
1
RF
5
5
4
4
3
3
(c)
2
1
0
(b)
0.5
Acce.-X (g)
(d)
2
1
1
0
0.5
1
Acce.-Y (g)
Figure 10. Maximum floor acceleration: (a), (b) X-dir. and Ydir. from 88%-XY Rinaldi;
(c), (d) X-dir. and Y-dir. from 88%-XY Rinaldi.
Force-Y [kN]
(a)
-200
Force-X [kN]
400
200
0
(c)
-200
400
200
0
(b)
-200
-400
-400 -200
0
200
Disp-Y [mm]
400
Force-Y [kN]
Force-X [kN]
0
-400
-400 -200
0
200
Disp-X [mm]
400
200
0
(d)
-200
-400
-400 -200
0
200
Disp-Y [mm]
400
Figure 8. Hysteretic loop of S-LRB: (a), (b) X-dir. and Y-dir. from
100%-XY Iwanuma; (c), (d) X-dir. and Y-dir. from 88%-XY Rinaldi.
400
(a)
200
Exper.
Analy.
Exper.
Analy.
0
-200
-400
0
400
50
100
150
(b)
200
200
0
-200
-400
0
1
50
100
150
200
Exper.
(c)
Analy.
0
-1
0
50
100
150
200
Time (s)
Figure 11. Translation and twist angle of isolation layer for 100%-XY
Iwanuma motion: (a) X - translation; (b) Y -translation; (c) Twist Angle.
Disp.-X [mm]
Figure 9. Maximum floor acceleration: (a), (b) X-dir. and Ydir. from 100%-XY Iwanuma;
(c), (d) X-dir. and Y-dir. from 88%-XY Rinaldi.
200
400
Analy.
Exper.
-400
-400 -200
0
200
Disp-X [mm]
400
Twist Angle [degree] Disp.-Y [mm]
RF
400
Disp.-X [mm]
RF
Fig. 11 and 12 compares the translation and twist angle of the
isolation layer represented by the center column location. The
computed translation and twist angle showed good match with
the test result when the translation was large (especially near
300-mm), but did not match when the translation was small.
The MSS model is calibrated to production test conducted to a
maximum displacement of 300-mm, and was not suited to
represent the range of smaller translation.
Twist Angle [degree] Disp.-Y [mm]
As shown in Fig. 8, for both motions, the computed
maximum displacement was similar to that from the test.
However, test loop was notably more slender near the center
due to the pinching (typical for a lead-rubber bearing). The
pinching of the loop near zero displacement is not included in
the MSS model used in this study. And the test loop was
somewhat larger and more unsmooth than the computed.
Fig. 9 suggests that the analysis provided a good match with
the experiment for maximum story drift. A nearly uniform
displacement profile along the height of the building was
obtained because the base-isolation system was effective. For
both motions, the maximum story drift ratio was smaller than
1/200, which is the limit for building frames, in analysis and
test. In Fig. 10, the maximum floor acceleration in the analysis
matched the test in one direction but showed some discrepancy
in the other direction. The discrepancy may be due to the
limitation of the MSS model mentioned above. For these two
motions, the maximum floor acceleration was smaller than
0.6g from both analysis and test.
As previously noted, the isolation layer had a mass
eccentricity ratio of 2% in the Y-direction. The mass-stiffness
eccentricity ratio (the distance between the mass center and
stiffness center divided by the floor-plan dimension) was 6% in
the isolation layer.
400
200
(a)
Exper.
Analy.
Exper.
Analy.
0
-200
-400
0
400
200
5
10
15
(b)
20
0
-200
-400
0
1
5
10
15
(c)
20
Exper.
(c)
Analy.
0
-1
0
5
10
Time (s)
15
Figure 12. Translation and twist angle of isolation layer for 88%-XY
Rinaldi motion: (a) X - translation; (b) Y -translation; (c) Twist Angle.
20
5. Effect of LRB-CLB isolation system
Fig. 13 compares the maximum floor acceleration of the baseisolated case and base-fixed case. The maximum of the vectorsum acceleration aiF,max, normalized by the maximum vectorsum table acceleration aT,max, is taken for the abscissa. The
maximum measured table acceleration for the Iwanuma and
Rinaldi motion were 0.57g and 1.14g, respectively. The factor
aiF,max / aT,max increased along the building height in the basefixed case. The factor aiF,max / aT,max of the base-isolated case
was smaller than unity for both motions, reaching at the roof
0.63 and 0.49 in the test, and 0.71 and 0.34 in the analysis.
Therefore, the test and analysis agrees that the LRB-CLB
system worked effectively to reduce floor acceleration.
7. Conclusions
The MSS model captured the fundamental behavior of the
LRB and the computer model captured the response of the fullscale base-isolated building specimen. Both test and analysis
indicated that floor acceleration and story drift ratio were
reduced effectively by the LRB-CLB isolation system.
Isolated-Exper.
Fixed-Exper.
Isolated-Analy.
RF
RF
5F
5F
4F
4F
3F
3F
2F
2F
1F
1F
Table
0
1
2
3
4
Table
0
1
Fixed-Analys
2
3
4
(a) Iwanuma motion
(b) Rinaldi motion
Figure 13. Ratio of horizontal max-vector-sum value between
response acceleration and table acceleration
Vertical Force [kN]
0
(a)
Exper.
Analy.
-1000
-2000
0
0
4
8
12
Exper.
(b)
Analy.
-1000
-2000
0
4
8
12
Time (s)
Figure 14. Vertical force in LRBs for 88%-XY Rinaldi: (a) NLRB; (b) S-LRB.
σ = 1.0 MPa
0
Vertical Force [kN]
6. Vertical load in isolation layer
Fig. 14 and 15 compares the time history of the vertical force
(tension as positive) in N-LRB and S-LRB for the 88%-XY
Rinaldi and 88%-XYZ Rinaldi motion. The load applied to the
LRBs at stationary condition was different between test and
analysis, because in the test, the superstructure could not be
placed perfectly evenly on the nine bearings.
For the 88%-XY Rinaldi motion, the vertical force on the
bearings was caused primarily by overturning moment in the
superstructure. As shown in Fig. 14, in instants when the NLRB saw increase in compression, the opposite S-LRB saw
decrease in compression, and vice versa. Aside from the
difference in initial vertical force, the computed response was
smaller than the test when the vertical force approached zero.
For the 88%-XYZ Rinaldi motion, the vertical force on the
bearings was caused by both the overturning moment and
vertical table acceleration. As shown in Fig. 15, similar to the
XY case in Fig. 14, the force was smaller in the analysis than in
the test when the vertical force approached zero or exceeded
zero. This phenomenon is likely due to the difference in how
vertical forces were redistributed between LRBs and CLBs.
The roller models were infinitely stiff in the vertical direction
and hence drew larger forces than the actual LRBs, especially
when the dynamic vertical force was in tension.
As shown in Fig. 15, in the 88%-XYZ Rinaldi motion test,
the largest measured stress in N-LRB and S-LRB was -5.5
N/mm2 in compression and 1.02 N/mm2 in tension. The
compressive stress in LRBs was quite small compared with the
critical compressive stress σcr = 35.4 MPa. The safety of LRBs
was satisfied under combined action of the compressive force
and large horizontal deformation.
REFERENCES
[1] Sasaki T, et al. (2012). NEED/E-Defense base-isolation
tests: Effectiveness of friction pendulum and lead-rubber
bearings systems. 15th World Conference of Earthquake
Engineering, Lisbon, Portugal, September 24-28, 2012.
[2] Furukawa T, et al. (2005). System Identification of BaseIsolated Building using Seismic Response Data. Journal of
Engineering Mechanics, ASCE, Vol. 131, No3.
[3] Architectural Institute of Japan (2001). Recommendation
for the Design of Base Isolated Structures. Maruzen, Tokyo.
Third Edition (in Japanese).
(a)
Exper.
Analy.
-1000
-2000
0
0
6
(b)
12
Exper.
Analy.
-1000
-2000
0
σ = -5.5 MPa
6
Time (s)
Figure 15. Vertical force in LRBs for 88%-XYZ Rinaldi: (a)
N-LRB; (b) S-LRB.
12