Synopses of Master Papers

Bulletin of IISEE, 47, 103-108, 2013

NUMERICAL SIMULATION OF BASE ISOLATEDBUILDINGS DURING THE GREAT EAST JAPAN
EARTHQUAKE AND A PROPOSAL FOR A DESIGNPROCEDURE OF BASE ISOLATION SYSTEM IN
PERURoy Ericksen REYNA SALAZAR 1
MEE11619

Supervisor:

Taiki SAITO 2

ABSTRACTA numerical simulation to evaluate responses of seismically isolated buildings during the Great East
Japan Earthquake in 2011 is carried out in this study. The numerical simulation includes non-linear
analyses of the base isolation system based on a Simple Bi-Linear Model and Modified Bi-Linear
Model, which take into consideration the degradation of the secondary stiffness.
From the result of those analyses, it was proved that the response of seismically isolatedbuildings is as follow: the base isolation system has non-linear behavior and the upper-structure
behaves in the elastic range, because the base isolation decouples the movement from the groundmotion, the displacement concentrates at the isolation level and the upper-structure behaves as a rigidbody.
A proposal for the design procedure for base isolated buildings in Peru is made in thisstudy. This procedure is based on the recommendation of CIB (International Council for Research andInnovation in Building and Construction), using the preliminary design procedure for seismicallyisolated buildings (CW2012) and taking into consideration the Peruvian seismic code.
Keywords: Base Isolation, Modified Bilinear Model, Design Procedure.

1.

INTRODUCTION

Peru is located in a high seismic hazard zone, the Ring of Fire, which defines the area with highest
seismic activity. The area includes some countries such as Japan, USA, Mexico, Chile and Peru, which
are affected mainly by earthquakes and aftershocks, as well as tsunamis which can be originated byearthquakes. In the case of Peru, earthquakes are caused mainly by sudden release of energy, which isgenerated by the subduction movement between the Nazca Plate and the South American Plate. In
addition to the subduction mechanism, there are earthquakes generated by geological fault mechanism
and volcanism.
The last March 11, 2011, Japan was struck by The Great East Japan Earthquake ofmagnitude 9.0Mw followed by a tsunami that affected the east coast of Japan, the epicenter of which
was located off the Pacific coast of Tohoku. The earthquake caused many casualties, economic losses,and damages on buildings, transportation facilities, and lifeline facilities among others due to the mainshock and aftershocks.
The lesson learnt from the past disasters: “It is necessary to improve the seismic responseof buildings against earthquakes”. The Base Isolation System, as a technology which permits tominimize the damage and reduce economic losses and casualties, will be a great choice.
12Japan-Peru Center for Earthquake Engineering Research and Disaster Mitigation (CISMID), Peru.
Chief Research Engineer, Building Research Institute, Japan

2.

THEORETICAL STUDY

The principle of the seismic-resistance design is based on: the energy dissipation capacity of thestructure must be higher than the demand of hysteretic energy. Moreover, the technologies to improve
the seismic behavior of the structures are based fundamentally on the reduction of the input energy as
well as in the increment of the energy dissipation of the structure. In that sense, the reduction of theinput energy is possible trough the seismic isolation system, whereas the energy dissipation devices
help to increase of the dissipation energy capacity.
There are several types of multi-layer rubber bearing device, such as Natural Rubber
Bearing (NRB), Lead Plug Rubber Bearing (LRB) and High Damping Rubber Bearing (HRB); themain difference among them is the energy-dissipation capacity through shear deformation.
Using the base isolation system, it can be expected that the response of the upperstructure will behave in elastic range, whereas the base isolation system should have a non-linear
behavior, which is represented by a hysteretic model (Bi-Linear Model or Modified Bi-Linear Model).
This study will focus in base isolation system using Lead Plug Rubber Bearing (LRB).
2.1

BI-LINEAR MODEL (BImod)

The Bi-Linear hysteresis of LRB is defined as
a combination of an elastic model derived fromthe lateral stiffness of rubber K r and theadditional stiffness K p derived from plastic
model of lead plug. See Equation ( 1 ) and ( 2 ).
Where: G r is the shear modulus of
the rubber, G p is the shear modulus of the lead,A r is the cross section area of laminated rubber,
A p is the cross section area of lead and H r isthe total height of rubber.
The Bi-Linear Model has an
initial elastic stiffness K 1 , a secondary stiffness
K 2 , See Equation ( 3 ) and ( 4 ).
Moreover, the equivalent stiffnessand equivalent damping ratio are shown inEquation ( 5 ) and ( 6 ) Equation respectively,
where D max is the displacement peak per loop.
2.2

MODIFIED BI-LINEAR MODEL (MBImod)

Modified Bi-Linear Model is based on BiLinear Model. The secondary stiffness of leadrubber bearing (K 2 = K d (γ)) depends on thestrain level, where C Kd (γ) is a modification
factor of the secondary stiffness. See Equation( 7 ).
Also, the yielding shear force isdefined as shown in Equation ( 8 ), whereC Qd (γ) is a modification factor of the yielding
shear force and σ p is the yielding shear stressof lead and A p is the cross section area of leadplug.

𝐾𝑟 = 𝐺𝑟𝐾𝑝 = 𝐺𝑝

𝐴𝑟
𝐻𝑟

(1)

𝐴𝑝
𝐻𝑟

(2)

𝐾2 = 𝐾𝑟 + 𝐾𝑝

𝐾1 = 𝛽𝐾2,

𝐾𝑒𝑞 = 𝐾2 +𝛽 = 10~15
𝑄𝑑
𝐷𝑚𝑎𝑥

𝑄𝑑
2 𝑄𝑑 �𝐷𝑚𝑎𝑥 − (𝛽 − 1)𝐾2 �ℎ𝑒𝑞 =𝜋𝐾𝑒𝑞 𝐷𝑚𝑎𝑥 2
𝐾𝑑 (𝛾) = 𝐶𝐾𝑑 (𝛾)(𝐾𝑟 + 𝐾𝑝 )𝑄𝑑 (𝛾) = 𝐶𝑄𝑑 (𝛾)𝜎𝑝 𝐴𝑝0.779𝛾 −0.43
𝐶𝐾𝑑(𝛾) = � 𝛾 −0.25
𝛾 −0.122.036𝛾 0.41
𝐶𝑄𝑑(𝛾) = �1.106𝛾 0.145
1→→→→→→

𝛾 < 0.250.25 ≤ 𝛾 < 1.01.0 < 𝛾 ≤ 2.5𝛾 ≤ 0.1
0.1 < 𝛾 < 0.5
0.5 < 𝛾

(3)
(4)
(5)

(6)

(7)
(8)
(9)

( 10 )

To understand how it works the hysteresis loop shown in Figure 1, three rules are
introduced as follows:•Rule1:The

initialelasticstiffness

Shear Force2

corresponds to the 5% of strain of the•3Rule 2: The stiffness can be equal or less

1
dmax2

than stiffness in the previous loop but neverdmax2
dmax2

can be greater.
•2

4skeleton curve using parameters type 1 or 2.

d(γ=5%)

dmax1

Disp.

3
3Rule 3: The force should be equal or less4

respect to the skeleton curve.
2

Figure 1. Hysteresis Loop of MBImod
Following the rules described above, the levels which defines the hysteresis loop (SeeFigure 1) are shown below:•Level 1 – Elastic Stage (Loading):•If d ≤ d(γ=5%)  K 1 = β*K d (γ=5%)
Level 2 – Plastic Stage (Loading):•

Level 4 – Plastic Stage (Unloading):•

If: d < (d max1 - 2dy) K 2 = K 2
If: |d max2 | ≤ |d max1 |:•If: d < d max1  K 2 = K d (γ)
1st Peak: d max1  γ max1•

K 1 = K 1 , K2 = K 2
If: |d max2 | > |d max1 |  Level 2 continues•

K 2 = K d (γ max1 ), K 1 = βK d (γ max1 )Level 3 – Elastic Stage (Unloading):•K 2 = K d (γ), K 1 = βK 1
2nd Peak: d max2  γ max2If: d < d max1  K 1 = K 1
3.

K 2 = K d (γ max2 ), K 1 = βK d (γ max2 )NUMERICAL SIMULATION AND COMPARISON WITH RECORDED DATA

Two buildings in Japan were selected to conduct this research; either of buildings implemented a baseisolation system. Also, the buildings were equipped with strong motion sensors to register the seismic
response of those buildings; the buildings chosen are: H-Building and T-Building.
H-Building is located in Aomori Prefecture. The building is steel reinforce concrete(SRC) structure, has 10 stories above the ground, 1 story penthouse, 1 story Basemen and a Base
Isolation System composed of LRB. T-Building is located in Ibaraki Prefecture. The building isreinforce concrete (RC) structure, and it has 7 stories and a Base Isolation System composed of NRB,LRB and Steel Damper.
The analysis was carried out using BImod and MBImod. The results presented in thispaper, corresponds to the analysis of H-Building and T-Building in X and Y direction respectively.
Figure 2 shows the comparison of the maximum response displacement for both buildings. The shear
force – displacement relationship of the base isolation system is shown in Figure 3.
H-Building has strong motion sensors at B1F, 01F and 10F. T-Building has strong motionsensors at B1F, 01F and 06F. The comparison of the response acceleration from the analysis and therecorded data during the Tohoku Earthquake is shown in Figure 4 and Figure 5.

12BImodMBImod10StoryStory

864
20012349876543210MBImod
Bimod

052

Displacement (cm)46810

Displacement (cm)Figure 2. Comparison of the Maximum Response Displacement.
Left: H-Biulding (X-direction). Right: T-Building (Y-direction)
2000
Shear Force (tonf)

Shear Force (tonf)

1000
5000-500
BImod
MBImod-1000-6-4-20241000
0-1000-2000

BImod
MBImod-3000
6-10-8

Displacement (cm)-6-4-20246

Displacement (cm)150

254-01F
MBImodBImod100

Response Acceleration (gal)Response Acceleration (gal)Figure 3. Comparison of Shear Force – Drift Relationship of Base Isolation System
Left: H-Biulding (X-direction). Right: T-Building (Y-direction)

500-50-100-150050100150200250150004-01F
BImod
MBImod100500-50-100-150300050100Time (sec)150200250300

Time (sec)200
150100500-50-100-150-200254-10F
MBImodBIMod050100150
Time (sec)

200

250

Response Acceleration (gal)Response Acceleration (gal)Figure 4. Comparison of Response Acceleration.
Left: 01F-H-Biulding (X-direction). Right: 01F-T-Building (Y-direction)

300

150004-06F
BImod
MBImod100
500-50-100-150050100150200

Time (sec)Figure 5. Comparison of Response Acceleration.
Left: 10F-H-Biulding (X-direction). Right: 06F-T-Building (Y-direction)

250300

4.

A PROPOSAL FOR A DESIGN PROCEDURE OF BASE ISOLATION IN PERU

The proposal for a design procedure of seismically isolated buildings in Peru presented in this researchis based on the recommendation of CIB (International Council for Research and Innovation inBuilding and Construction) using the preliminary design procedure for seismically isolated buildings(CW2012) and taking into consideration the Peruvian seismic code.
This research presents the design procedure using an equivalent linear analysis method.
The limitations for this method are:•••••

Building height: Less than 45m.
Type of soil: Medium and hard soil, Type S1 and S2.
Location of seismic isolated layer: Base isolation.
Special case: For masonry buildings, the height limitation is 15m
For other case Time History Analysis is recommended.

The design procedure of base isolated buildings and convergence procedure following theEquivalent Linear Method (ELM) is shown in Figure 6.
BASE ISOLATION DESIGN PROCEDURE
Target Building – Select Parameters(Z, U, S,Tp, R=1)

Calculate: WT, Wmax
Estimate Qd

DESIGN SPECTRUM
Define Target Period TH, TV
Calculate:
C, FH, Sa, δ, δmax

Selection ofRubber Material
Gr, E0, E∞, kDefine Target Maximum Strain γ

DIMENSIONOF RUBBERDIMENSION
OF LEAD

Calculate:
D0, n, tr, S1, Hr, Ar

CalculateAp, Dp, Qd

BI-LINEAR PARAMETERS
Kr, Kp, Kd, Keq, KV, Teq

CHECKING
S2, δmax, γ1, γ2, σi = i+1

Convergence|δ(i)-δ(i-1)| < εEND

Figure 6. Base Isolation Design Procedure

Selection of Lead
Material
Gp, σp5.

CONCLIDING REMARKS

The expected response of two buildings during the Tohoku Earthquake is a non-linear behavior on theisolation system and a linear behavior in the upper-structure.
Using a Modified Bi-Linear Model to model the H-Building, the simulation has moreaccurate response of the building. On the other hand, the analysis of the T-Building using MBImod
has higher response in comparison with the analysis using BImod.
The parameters used in the analysis should be checked to get better response accuracy inorder to predict the response recorded during the Tohoku Earthquake and further earthquakes.
The proposal for a design procedure of base isolation buildings in Peru is based on
Equivalent Linearization Method (ELM), taking into consideration the Peruvian Design Spectrum.
Base Isolation System can be applied for designing new buildings or as a retrofitting
technique in Peruvian buildings, even for masonry buildings and also to protect old buildings, such as
historical heritage in Peru.

6.

FURTHER STUDIES

Further studies are needed to get the parameters of a hysteretic model to predict the non-linear
response of base isolated buildings, because the parameters used in this research depends on themanufacturer of base isolation devices.
For base isolated building in Peru, the mechanical characteristics and non-linear
properties of isolation devices manufactured with different materials should be researched, also taking
into account damper devices.
A proposal for a design procedure is presented in this research, expecting to be theinitiative for developing Seismic Isolation Code for seismically isolated buildings in Peru

7.

ACKNOWLEDGEMENT

I would like to express gratitude to Dr. Carlos Zavala, Director of Japan-Peru Center for Earthquake
Research Engineering and Disaster Mitigation (CISMID) for his support and collaboration.

8.

REFERENCES

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