Fundamentals of Seismic Base Isolation

Wang, Yen-Po1

1 Professor, Dept. of Civil Engineering, National Chiao-Tung University, Hsinchu, Taiwan Director, Large-Scale Structural Lab, NCTU

1、、、、Introduction Over the past decades, earthquake resistant design of building structures has been largely

based on a ductility design concept worldwide. The performances of the intended ductile structures during major earthquakes (e.g. Northridge, 1994; Kobe, 1995; Chi-Chi, 1999…etc.), however, have proved to be unsatisfactory and indeed far below expectation. High uncertainty of the ductility design strategy is primarily attributed to:

(1) The desired “strong column weak beam” mechanism may not form in reality, due to existence of walls.

(2) Shear failure of columns due to inappropriate geometrical proportions or short-column effect.

(3) Construction difficulty in grouting, especially at beam-column joints, due to complexity of steel reinforcement required by the ductility design.

To enhance structural safety and integrity against severe earthquakes, more effective and reliable techniques for aseismic design of structures based on structural control concepts are desired. Among the structural control schemes developed, seismic base isolation is one of the most promising alternatives. It can be adopted for new structures as well as the retrofit of existing buildings and bridges.

Strategies to achieving seismic isolation include:

(1) Period-shifting of structures (2) Cutting-off load transmission path

The spring-like isolation bearings with considerable lateral flexibility help in reducing the earthquake forces by changing the structure’s fundamental period to avoid resonance with the predominant frequency contents of the earthquakes, as indicated by Fig. 1. Whereas the sliding-type isolation bearings filter out earthquake forces via the discontinuous sliding interfaces, between which the forces transmitted to the superstructure are limited by the maximum friction forces, regardless of earthquake intensity.

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International Training Programs for Seismic Design of Building Structures Hosted by National Center for Research on Earthquake Engineering

Sponsored by Department of International Programs, National Science Council

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Fig.1 Typical acceleration response spectra

Conventional Isolated

Fig. 2 Effects of Base Isolation

During earthquakes, the conventional structure without seismic isolation is subjected to substantial storydrifts, which may lead to damage or even collapse of the building. Whereas the isolated structure vibrates almost like a rigid body with large deformations or displacements endured by the isolation bearings, as illustrated in Fig 2.The lateral forces of the isolated building are not only reduced in magnitude but also fairly redistributed over the floors, which further mitigates the overturning moment of the structure.

Fig. 3 Construction of LRB

Fig. 4 Construction of HDRB

Lead core

Rubber coverLaminated rubber and steel plates

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The spring-like bearings that have seen widespread applications include the lead-rubber bearing (LRB) and the high-damping rubber bearing (HDRB). The sliding-type bearings, on the other hand, are impractical due to lack of restoring capability. To overcome this drawback, the friction pendulum system (FPS) originated from the sliding-type bearings is developed by introducing a spherical sliding interface to provide restoring stiffness, while the friction between the sliding interfaces helps in dissipating energy. As a result, the FPS is functionally equivalent to LRB and HDRB in lengthening structure’s fundamental period, with additional advantageous features such as period-invariance, torsion-resistance, temperature-insensitivity and durability. Although the rubber bearings have been extensively adopted for seismic isolation, the FPS has recently found increasing applications (Buckle et al., 1990; Zayas et al., 1987; Kawamura et al., 1988 ). The friction pendulum bearings provide strength and stability that exceed those of rubber bearings. Its properties are not affected by aging or temperature. The bearing’s low profile, high strength, and high vertical stiffness reduce installation costs. These bearings offer versatile properties which can satisfy the diverse requirements of buildings, bridges and industrial facilities. This article will address the basic mechanical properties of FPS, status of its development as well as a preliminary design procedure based on static analysis.

Fig. 5 Construction of FPS

2、、、、Mechanical Properties of FPS The friction pendulum bearings are stainless steel seismic isolators consisting of a

concave surface, an articulated slider, and a cover plate. The slider is coated with self-lubricating composite liner (e.g. Teflon). During an earthquake, the articulated slider within the bearing slide along the concave surface, causing the supported structure to move with gentle pendulum motions. The motions of the FPS are illustrated in Fig. 6.

Fig.6 Motions of FPS

Center position Displaced position

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The natural period (T ) of the friction pendulum bearing is selected simply by choosing the radius of curvature of the concave surface ( R ) as

gRT /2π= (1) where g is gravitational acceleration. It is independent of the mass of the supported structure. The lateral stiffness ( bK ) of the bearing providing the restoring capability of the system is RWKb /= (2) where W is the weight of the structure. As a result, the torsional motions of the structure are minimized since the center of stiffness of the bearings coincides with the center of mass of the supported structure.

The movement of the slider generates a dynamic friction force that provides the required damping for absorbing the energy of the earthquake. The lateral loads (i.e. the base shear), V , transmitted to the structure as the bearing slides to a distance, u , away from the neutral position include the restoring forces and the friction forces as

WRuV )( µ+= (3)

where µ is the coefficient of friction. Typical hysteretic loops of the lateral force of FPS in cyclic motion are shown in Fig. 7. The energy ( DE ) dissipated for one cycle of sliding with amplitude D is estimated as

WDED µ4= (4)

The coefficient of friction is dependent on the contact pressure between the Teflon-coated slider and the stainless steel surface. The coefficient decreases as the pressure increased. The value of µ between 3~10% is considered reasonable for the FPS to be effective.

Fig. 7 Hysteresis of Lateral Load

3、、、、Design Procedure Based on Static Analysis

Design of the seismic isolation system includes determination of the base shear, bearing displacement, etc., in accordance with the site-specific conditions by code provisions, at desired bearing properties ( e.g. friction coefficient, µ , and radius of curvature of the concave surface, R , for FPS). In this section, a simple design procedure based on static analysis is introduced for the preliminary design of isolation systems. This procedure alone is sufficient for building structures with fair geometrical regularities. However, a more complex

dissipated energy

displacement

lateral load

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nonlinear dynamic analysis is desired for those with geometrical irregularities.

The hysteresis of the base shear against sliding displacement of an FPS can be idealized by a rigid-plastic linear-hardening model, as depicted in Fig. 8. The characteristic constant (Q ) of the isolation system is the maximum friction force defined as

WQ µ= (5)

while the effective stiffness ( effk ) of the isolation system as a function of the expected largest bearing displacement ( D ) with given µ and R is determined by

WDR

keff

+= µ1 (6)

As a result, the equivalent natural period ( eT ) of the isolated building can be approximated as

gk

WTeff

e π2= (7)

by taking the superstructure as a rigid body, and this equivalent natural period is again dependent on D .

Q kb

Bearing displ.

Base shear

keff

D

Vmax

1

1

Fig. 8 Idealized Hysteresis of FPS

On the other hand, the maximum base shear ( maxV ) of the isolation system can be obtained by spectral analysis using the elastic spectrum as

WZICCV D=max (8)

where Z is the seismic-hazard-based PGA of the design earthquake, I is the important factor of the structure, C is the site-specific normalized (PGA=1g) 5% elastic acceleration response spectrum specified in the code, and DC is the modification factor for structures with a damping factor other than 5%. It is defined as

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5.0140

5.1 ++

=e

DCς

(9)

where the equivalent damping factor, eς , is in turn determined by

= 22

1Dk

E

eff

De π

ς (10)

where DE is again the dissipated energy defined in Equ. (4). The maximum base shear is equivalent to the mass of the structure ( gW / ) times the spectral acceleration, aS , therefore,

gZICCS Da = (11)

Using the spectral relation

( ) DTDS ea22 /2πω == (12)

and taking the important factor I as unity for seismic isolated buildings, the spectral displacement ( D ) turns out to be

2

2

4πgTZCCD eD= (13)

The above equation suggests that D is a function of eT and DC which in turn are functions of D implicitly. Therefore, an iterative procedure is required until convergence of the spectral displacement, D , is achieved.

The base shear is then estimated by

DkV eff= (14)

Distribution of the lateral force at the i-th floor is suggested as

∑

=

= N

kkk

iii

uw

uwVF

0

(15)

where kw represents the weight of the k-th floor of the N-storey building; ku is the lateral displacement of the k-th floor due to lateral loads at each floor proportional to its weight, that is

Nkw

wf N

jj

kk ,...,0,

0

==∑

=

(16)

With the lateral force determined, the superstructure is then designed in a manner similar to conventional structures in accordance with the building codes.

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It is noted that, torsional effect due to accidental eccentricity on the bearing displacement should be accounted for, especially for those to be placed at the corners of the building. Moreover, to ensure bearing stability at critical conditions, a safety factor of 1.5 is further imposed when sizing the bearings. Stability verification of the prototype bearings prior to implementation is based on this factored displacement demand.

Although the above discussions emphasize on the friction pendulum systems, the design procedure described in this section is in fact common for structures isolated with any type of seismic isolators, regardless of FPS, LRB or HDRB.

4、、、、FPS in Buildings, Bridges and Industrial Applications The friction pendulum bearings have been specified for many seismic isolation projects

in buildings, bridges and industrial storage tanks. Among which, the U.S. Court of Appeal; San Francisco Airport International Terminal; Greece’s LNG tanks; and the Benicia-Martinez Bridge are the world’s largest seismic isolation projects to date. (Earthquake Protective Systems, Inc., 1998).

The seismic retrofit of the U.S. Court of Appeals building in San Francisco, upon its completion in 1994, was the largest building in the world to have been retrofitted with seismic isolators. The advantages of the friction pendulum bearings- its novel technical approach, supported test results and other analysis, are found to be more effectively enhance the buildings survivability in the event of an earthquake.

Fig. 9 U.S. Court of Appeals

The San Francisco Airport International Terminal is the largest new building in the world constructed using seismic isolation. It has dramatic architectural features, including: expansive interior spaces, 80 feet tall columns, 700 feet long roof trusses, and glass exterior walls. The building was designed to resist a magnitude 8 earthquake occurring on the San

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Andreas fault. Seismic isolation provides the lowest construction cost for achieving the desired seismic performance. Moreover, the use of friction pendulum bearings, as compared to rubber bearings, allowed for a further reduction in column and beam sizes and saved an additional 680 ton of structural steel.

Fig. 10 San Francisco Airport Int’l Terminal

Greece’s centralized liquefied natural gas (LNG) storage tanks are located just outside of Athens. These tanks contain 38 million gallons of flammable LNG, and are situated within one of Europe’s highest seismic regions. The bearing performance requirements for this project were the mosstringent in the history of seismic isolation. The isolation bearings were required to maintain their design properties while fully accommodating the effects of: 35 years of aging in a marine environment; simultaneous lateral and vertical earthquake motions; temperatures ranging from 10 to 86 °F. Friction bearings were selected over elastomeric bearings after tests of full size bearings showed that they were best able to satisfy these demanding performance requirements, and would thereby achieve the safest tank performance.

The Benicia-Martinez bridge is one of the largest bridges to date to undertake a seismic isolation retrofit, and uses the largest seismic isolation bearings ever manufactured. The friction pendulum bearings for this project have a 5 second period, a lateral displacement capacity of 53 inches, a 5 million lg. Design vertical load, measure 13 feet in diameter, and weigh 40,000 lbs.

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Fig. 11 LNG Tank in Revithoussa, Greece

Fig. 12 Benicia-Martinez Bridge in San Francisco

5、、、、Reference Buckle, I. G., and Mayes, R. L. “Seismic isolation history: application and performance - a

world review.” Earthquake Spectra, 6, 161-201, (1990).

Earthquake Protective Systems, Inc., DM of August, 1998.

Elsesser, E., Jokerst, M. and Naaseh, S. “Historic Upgrades in San Francisco”, Civil Engineering, ASCE, p.50-57, October, (1997).

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Kawamura, S., Kitazawa, K., Hisano, M., and Nagashima, I. “Study of a sliding-type base isolation system－system composition and element properties.”, Proc. 9th WCEE, Tokyo-Kyoto, Vol. V, 735-740, (1988).

Zayas, V., Low, S. S. and Main, S. A. “The FPS earthquake resisting system, experimental report,” Report No. UCB/EERC-87/01, Earthquake Engineering Research Center, University of California, Berkeley, CA., June, (1987).