Performance analysis of aseismic base isolation systems for a multi-story building

Performance analysis of aseismic base isolation systems for a multi-story building

F.-G. Fan and G. Ahmadi

Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13676, USA

N. Mostaghei

Department of Civil Engineering, University of Toledo, Toledo, Ohio 43606, USA

I. G. Tadjbaldash

Department of Civil Engineering, Rensselaer Polytechnic Institute, Troy, NY 12181, USA

A comparative study of the performances of several leading base isolation devices including the Rubber Bearing with and without lead core, the Sliding-Joint, the French System, and the Resilient-Friction isolator with and without upper sliding plate for a multi-story building under seismic ground accelerations is carried out. Several earthquake ground accelerations including E1 Centro 1940, Pacoima Dam 1971, and Mexico City 1985 earthquakes are considered. The acceleration, the base displacement and the structural deflection response spectra for the structure with different base isolation systems under various conditions are obtained and discussed. Several sensitivity analyses for variations in the parameters of the isolators and/or structure are also carried out. The effectiveness of various base isolators under a variety of conditions are studied and advantages and disadvantages of different systems are discussed. The results show that the acceleration transmitted and the column stresses of the structure can be effectively reduced by using properly designed base isolation systems. The results of the sensitivity analyses show the friction-type isolation systems are less sensitive to the variations in the amplitude and frequency content of the ground excitation in comparison to the Rubber Bearing base isolators. The study also shows that the peak accelerations transmitted by the friction-type isolators are not significantly affected by small variations in friction coefficient. Furthermore, variations in mass ratio and damping of the structure or the isolator do not significantly affect the peak responses.

INTRODUCTION

The conventional technique for aseismic design of structures is to strengthen the structural members in order to withstand strong earthquakes. However, this strengthen- ing strategy inevitably leads to higher masses and hence higher seismic forces. A structure designed in this way may survive a strong earthquake, while there could result intolerable damages to its members, as well as, to its sensitive internal equipment. Moreover, the econo- mical consideration limits the construction of a com- pletely safe structure within the bounds of traditional design methodology.

An alternative design strategy is to isolate the structure from the ground motion during the earthquake strong motion. The base isolation concept has been suggested a long time ago. According to Kelly ~.z, as early as 1909, a British physician had applied for a patent on

Paper accepted May 1989. Discussion closes September 1991.

© Computational Mechanics Publications 1991

separating a building from the ground by a layer of talc or sand. However, it was only in the last three decades that this design concept has received serious attentions. The base isolation design methodology appears to have considerable potential in preventing earthquake damages to structures and their internal equipment. A large number of base isolation systems for various types of structure have been suggested. Several of which have been developed and used to protect buildings, bridges, nuclear power plants, and other structures against earthquakes. Extensive reviews on historical developments and recent literature on the subject were provided by Kelly t.2. Therefore, only brief descriptions of several leading base isolation systems which are considered in this study are presented in this section.

A class of base isolation systems which has been extensively studied at the University of California by Kelly and co-workers ~'2.3 is the Laminated Rubber Bearing (LRB) base isolators. The system has been used in the four story Foothill Communities Law and

152 Soil Dynamics and Earthquake Engineering, 1991, Volume 10, Number 3, April

Performance analysis of aseismic base isolation systems: F.-G. Fan and G. Ahmadi

Justice Building in San Bernardino County, California and a number of buildings in Europe, Japan, and New Zealand. A LRB isolator is made of alternating layers of rubber and steel with the rubber being vulcanized to the steel plates. The LRB is rather flexible in the horizontal direction but quite stiff in the vertical direction. The horizontal stiffness of the bearing is also designed in such a way that it can resist the wind forces with little or no deformation. Figure l(a) shows a schematic diagram for a LRB isolator. The GERB system 4, which is composed of helical springs and viscodampers, behaves similar to the LRB system in the horizontal direction and its mechanical behaviour may also be represented by Fig. l(a).

The laminated rubber bearing base isolator with a lead core has found wide applications in New Zealand as well as other countries. This system is referred to as the lead core LRB or the New Zealand (NZ) base isolation system. The lead core is used to reduce the lateral displacement and to offer an additional mechanism for energy dissipation, while the flexibility and restoring force are provided by the rubber bearing. The performance of the NZ isolator (Lead core laminated rubber bearing) under a variety of conditions were reported in Refs 2, 3, 5. Figure l(b) displays the mechanical behavior of the NZ base isolation system. The mechanical behavior of hysteretic dampe r3"6-8 may also be schematically represented by this figure.

Base isolation systems in which the only isolation mechanism is sliding friction are Pure-Friction (P-F) or Sliding-Joint base isolation systems. In this class of base isolation systems, one or several friction plates or a layer of sand are used to isolate the structure from the ground. A schematic diagram for P-F base isolation systems is shown in Fig. l(c). There has been a large number of theoretical works on the performance of this class of

I. " I. ,I

(a) LRB System (b) NZ System

(c) P-F System

' I '

Y .I i- -!

(e) EDF System

Fig. 1.

v - - - - 1 ~ i- 9

(d) R-FBI System

Y I

I H

(f) SR-F System

Schematic diagrams of isolation systems

isolators under deterministic or stochastic ground excitations 9-16. In Refs 17 and 18, the use of a layer of sand as a simple P-F base isolator for a building in Bejin, China was described.

Recently, a base isolation system referred to as the Resilient-Friction Base Isolation system (R-FBI) was proposed by Mostaghe119-2~. This isolator consists of several layers of teflon coated friction plates with a cen- tral core of rubber. The rubber provides the restoring force for the system and hence control the relative displacement while energy is dissipated by the friction forces. An extensive study of the responses of a five- story building isolated by the R-FBI system was provided by Mostaghel and Khodaverdian 22. Figure l(d) illustrates the mechanical behavior of the R-FBI system. The Alexisismon base isolation system developed by Ikonomou 23 also makes use of the combined actions of sliding joint and rubber bearings. The rubber element in the Alexisismon system appears to act in bending while in the R-FBI isolator acts in shear. Although these designs are quite different, the mechanical behavior of the Alexisismon base isolator may also be schematically represented by Fig. l(d).

Another base isolation system which is used for base isolation of nuclear power plants in regions of high seismicity was developed under the auspices of Elec- tricite de France (EDF) 24. It has been used in the design of nuclear power plants in France, and Iran. The Kroeberg nuclear power plant in South Africa relies on the EDF base isolation system for protection against earthquake. An EDF base isolator unit consists of a laminated (steel-reinforced) neoprene pad topped by a lead-bronze plate which is in frictional contact with a steel plate anchored to the base raft of the structure. Whenever there is no sliding in the friction plate, the EDF system behaves as a LRB and the flexibility of the neoprene pad provides isolation for the structure. The presence of the friction plate serves as an additional safety feature for the system. Whenever the ground acceleration becomes very large, sliding occurs which dissipates energy and limits the acceleration transmitted to the superstructure. The behavior of the EDF base isolator is shown schematically in Fig. l(e).

A base isolation concept which combines the desirable features of the R-FBI and the EDF systems was proposed in Ref. 25. This system which is referred to as the Sliding Resilient-Friction (SR-F) base isolation system is a R-FBI unit with an additional upper friction plate. The behavior of the SR-F isolator is shown schematically in Fig. l(f). Whenever there is no sliding in the upper friction plate, the SR-F base isolator behaves as a R-FBI unit. For high ground accelerations, sliding in the upper friction plate occurs which provides an additional mechanism for energy dissipation and increases the overall effectiveness of the isolation system.

General design requirements for a base isolation system and design criteria for base-isolated building were described in Refs 2 6 - 2 8 . In these works, code- type criteria regarding allowable base displacement, peak transmitted acceleration, natural period and seismic coefficient were suggested. Guidelines regarding the design of the rubber bearing base isolation system with or without a lead core were also presented in Refs 2 6 - 2 8 . Recently, Mostaghel et al. 29"3° described the design procedure for the R-FBI system.

Soil Dynamics and Earthquake Engineering, 1991, Volume 10, Number 3, April 153


In spite of a large number of studies on performances of different base isolation systems, the advantages and disadvantages of various systems are not well under- stood. One difficulty here is the desired requirements are numerous. Hadjian and Tseng 3~ have pointed out eleven desired performance criteria related to safety and reliability of the isolated structure. Recently, S u e t al.25'32 have carried out several comparative studies of different base isolation devices for rigid and shear beam structures. Fan et al. 33.34 considered the performances of various base isolation systems for a multi-story building under a horizontal sinusoidal ground motion.

In this work, performances of several base isolation systems described earlier for a multi-story, shear frame subject to several seismic ground motions are studied. The equations of motion for various base isolation systems are described. The governing equations for frictional base isolation devices and the criteria for transition between different phases of motion are highly nonlinear. Considerable care is needed in formulation of the computational model for handling these rather stiff equations. Utilizing the fourth-order Runge-Kutta scheme, a computational algorithm for accurate numerical evaluation of the response of the base isolated structure is developed. The peak absolute acceleration of each floor, the peak base displacement, and the peak structural deflection for various base isolation systems are evaluated and the results are compared with each other and with those of the fixed-base structure. The acceleration responses both in time and frequency domains are examined. A series of sensitivity studies for variations in friction coefficient and natural period of the isolator, as well as, damping and mass ratio of the structure are also carried out. The effects of the velocity- dependence of friction coefficient is also studied and discussed.

The results show that the transmitted acceleration and the column stresses of the structure can be significantly reduced by using properly designed base isolation systems. The frictional systems generate high frequency peaks in the acceleration responses, however, these high frequency peaks do not lead to large structural deforma- tions. The results of the sensitivity analyses show the friction-type isolation systems are less sensitive to variations in the amplitude and frequency content of the ground excitation in comparison to the LRB, and the NZ base isolators. The study also shows that the peak accelerations transmitted by the friction-type isolators are not significantly affected by small variations in friction coefficient. Furthermore, variations in mass ratio and damping of the structure or the isolator only slightly affects the peak responses.

GOVERNING EQUATIONS

The equations governing the motion of various base isolation systems and the criteria for motion transitions of frictional systems have been described at length in Ref. 33. Therefore, only a brief description is needed here. For a multi-story, lumped-mass, shear building with different base isolation systems, the equations of motion and the criteria for motion transitions are summarized in this section.

LRB system The schematic diagram for the Laminated Rubber

Bearing base isolation system is shown in Fig. l(a). The equations of motion of a multi-story frame with a LRB system are given as,

~' + 2g'o~0o$ + ~02s + ~ cti$~ = -j~g i=l

(1)

[m]le} + [c ] lx ] + [k]lx} = - ( ~ ' + ~ g ) [ m ] { l l

(2)

where s is the relative displacement between the base of structure and the ground, xi is the displacement of the ith floor relative to the base as shown in Fig. 2, yg is the horizontal ground acceleration, and [m ], [ c] , [k] represent mass, damping, and stiffness matrices, respectively. The natural circular frequency of the bearing O:o, and its effective damping ratio ~'o are defined as

2 ko 2~'°~°° = M ' O:o = ~ (3)

where Co and ko are the damping and the horizontal stiffness of the bearing, respectively. The mass-ratio parameter c~i is defined as

mi m b °li - M ' C~b = --~, M = mb + m~ (4)

i=l where mi is the mass of the ith floor, mb is the mass of the base and M is total mass of the structure. Here, [ 1 } is a column vector all of whose elements are unity and a dot on top of a letter denotes a time derivative. A natural period To of about 2 sec(% = 7r rad/sec) is commonly suggested for the LRB base isolation systems. The effective damping ratio of the isolator ~'o varies considerably with the strain of the rubber. Accor- ding to Refs 35 and 36, it may be as high as 0.3 for low strain and reduces to about 0.05 for high strain. Here, an intermediate value of 0.08 for ~'o is considered in

• za ~ ,~,.._~3 ~l "~ ard FLOOR

z~ ~ ~2nd FLOOR

Fig. 2. Structural model of a three-story building with a base isolation system


Performance analysis o f aseismic base isolation systems: F.-G. Fan and G. Ahmadi

most cases. Note also that the motion of the GERB system may also be described by equation (1).

NZ system The schematic diagram for the mechanical behavior of

the New Zealand system is shown in Fig. 1 (b). When a multi-story building is isolated by the NZ (or a hysteretic damper) base isolation system, the deflection of the structure is governed by equation (2), and the equation governing the base displacement is given as,

Equation (8) governs both the sliding and nonsliding ~ s of motion of the R-FBI system. The deformation of structure is governed by equation (2) which is coupled with equation (8) through the inertial forces. The nonsliding phase continues as long as

I.~g + 6o2 s + ~ Oti.~il < #g i=l

As soon as the condition,

(10)

N ~" + 2~oO~o ~ + O~:oS + ~1 Q + °liXi "~" -'~g (5)

i=1

where N is number of base isolators used, and M is total mass of the structure. The hysteretic restoring force Q which is generated by the lead core may be approx- imated by Wen S37 model as

F Q(s, ~) = tx - y s + (1 - ot)E,.Z (6)

Y

I£g + co 2 s + ~ c~i~i I = #g (11) i=1

is satisfied, the sliding motion starts. The natural period of 3 to 4.5 sec are suggested for the

R-FBI base isolation system in Refs 19-21. In this study, unless stated otherwise, To = 4 sec, # - 0.05 and ~'o = 0.08 are used. It is noted that equations (8)-(11) are also applicable to the Alexisismon system as long as the deformation in its rubber element remains small.

where the dimensionless hysteretic displacement Z satisfies

YZ= -3,1JIZIZt n-t - /3JIZl~ + 0~ (7)

P - F system Figure l(c) shows the schematic diagram for a Pure-

Friction base isolation system. The equation governing the displacement of the P - F isolator is given as,

In equation (6) and (7), F r and Y represent the force and the yield displacement of the equivalent hysteretic dampers, 13, 3', and 0 are dimensionless parameters, ~/is an integer which controls the smoothness of transition from elastic to plastic response, tx is the post to pre- yielding stiffness ratio.

In order that the predictions of this model may fit the experimental results, for certain lead-core laminated rubber bearings, the values of E, .=46 KN, Y = 7.7 mm, ot = 0.157,/3 = -0 .54 , 3' = 1.4, 0 = 1.0, and *1 = 1 were suggested in Ref. 7. These values together with the natural period To of 2 sec (COo = ~" rad/sec), a damping ratio ~'o of 0.08 and the mass per isolator ratio, M/N, of 200 tons are used in this study.

R - F B I system Figure l(d) shows the schematic diagram describing

the mechanical behavior of the Resilient-Friction Base Isolation system. The equation for the displacement of isolator is given as,

+ 2~oO~o~ + O~2oS + #gsgnl(~) + ~ oti£i = -£g (8) i=1

g + p.gsgnl (~) + ~.~ oti.~i = -£g i= l

(12)

where sgn~ (~) is defined by equation (9) with co o being zero for the P - F system. The deflection of the base isolated structure is governed by equation (2). With the definition of sgn~ (~) as given by equation (9), equations (12) and (2) govern both the sliding and the nonsliding motions. For the nonsliding phase (,¢ = 0), equation (12) reduces to g = 0, and the deformation of the structure is governed by equation (2).

The criteria for motion transitions are identical to those given by equations (10) and (11) with ~o m 0. Usually, a friction coefficient between 0.05 and 0.2 are used for the P--F (Sliding-Joint) base isolation systems 9-~6. In this study, # = 0.1 is used in most of the numerical experiments.

S R - F system The mechanical behavior of the Sliding Resilient-

Friction base isolation system is shown in Fig. 1 (f). The equations of motion of the S R - F base isolator are given a s

2 2~oO~o~ + OOoy + #jgsgn3(P) = #gsgn2(~ - y) (13)

where # and g are the friction coefficient and acceleration of gravity, respectively; and sgn~(J) is defined as

I ~ l ~ > 0 JCs + °~2s + ~ otiXi

sgnl(g) = t~g ~=1 ~ = 0 (9)

- 1 ~ < 0

+ 2~oO~o~ + o~2Y + #igsgn3(P) + ~ oti~i = -~8 i=1

(14)

where the relative displacements y and s are defined in Fig. l(f), and tz and #~ represent the friction coefficients of the upper and the body friction plates, respec-



tively. With the definitions

y "~ j~g "~ OlijC i

. . . . = .¢ - 5, = 0 (15) sgn: (~ y) Itg

~ - y < 0

The criterion for the nonsliding phase to continue is the same as that given by equation (18).

In practice, the laminated neoprene pad is designed to have a natural period of about 0.8 to 1.2 sec, and the friction coefficient of the friction plate is about 0.2. In the present study, unless stated otherwise the values of T,, = 1 sec (090 = 27r rad/sec), ~'o = 0.08, and # = 0.2 are used.

and

+ xg + 09:o5' + ~ ~xi

sgn3(Y)= Itlg i=1 19=0 (16)

~9<o

Equations (13) and (14) govern various sliding and nonsliding states of motion. In all these different phases of motion, the deformation of structure is governed by equation (2). Explicit equations of motion for fully sliding, partially sliding, and nonsliding conditions were given in Ref. 33.

The nonsliding condition in the body friction plates continues as long as

Is + Xg + 092y + E c~il < It/g (17) i=1

As soon as the lefthand side of (17) becomes equal to Itlg, the body friction plates begin to slide. Likewise, the nonsliding condition in the upper friction plate per- sists as long as the criterion

l Y + £g + ~ Oliff i I < #g i=1

(18)

holds. Sliding starts when the lefthand side of (18) becomes equal to Itg.

In the subsequent analysis, unless stated otherwise the values of It1 = 0.05, It = 0.1, ~'o = 0.08, and a natural period of To = 4 sec (090 = r /2 rad/sec) are used.

EDF system Figure l(e) shows the schematic diagram for the

behavior of the EDF base isolation system. The equations of motion of the EDF isolator for both sliding and nonsliding motions are given by

2~o090Y + JoY = Itgsgn2(J - Y ) (19)

MODELING

The formulation given in the previous section is for a general multi-story shear frame. In the subsequent analyses, a three-story building as shown in Fig. 2 is used as the structural model. It is assumed that the masses of different floors and the base raft are identical and the stiffness and damping of columns of various stories are also the same. For this particular structural model, the damping matrix is proportional to the stiffness matrix. The explicit expressions for mass, damping, and stiffness matrices are given in Appendix A. The equations of motion of the structure can be decoupled into three independent modal equations by the method of normal mode. The modal equations, the modal matrix and the relations between natural frequencies of the structure are also listed in Appendix A. Accordingly,

09: = 2.802091, 093 = 4.049091 (21)

and

~': = 2.802~'1, ~'3 = 4.049~'1 (22)

in which 09 is the natural circular frequency and ~" is the modal damping ratio. Here, subscripts 1, 2, and 3 identify the mode of vibration. In the subsequent analyses, the fundamental natural period /'1 = 27r/oh is varied between 0.1 to 1 sec to cover the range of stiff to flexible structures. Except for the section on sensitivity analysis on the effects of variation of ~'1, a damping ratio of 0.02 for the fundamental mode is used throughout this study.

The recommended values of natural periods To, damping ratios g'o, and friction coefficients It (or Its) of the isolators studied are summarized in Table 1. These values are used throughout this work except for the sec- tions on sensitivity studies.

Techniques of solution In this section, the procedure of numerical evaluation

is briefly described. Based on the fourth-order Runge- Kutta scheme, a double precision FORTRAN routine for

~t' + 2~'o09oy + 09:Oy + ~ otiXi = - Xg i = l

(20)

where y is the deflection of the rubber, s is the total relative displacement between the base raft of the structure and the ground, and the sgn2 function is given by equation (15). Equations (19) and (20) are identical to equations (13) and (14) with #1 equal to zero. For nonsliding phase, equation (19) vanishes and the EDF base isolator reduces to a LRB unit. As noted before, the deflection of the structure is governed by equation (2).

Table I. Values of parameters used for various base isolators

Base Isolation System

Natural Damping Friction Period Ratio Coefficient To (sen) ~'o ~(~/~,)

Laminated Rubber Bearing (LRB) 2 New Zealand (NZ) 2 Pure-Friction (P -F) Resilient-Friction (R-FBI) 4 Electricite de France (EDF) 1 Sliding Resilient Friction (SR-F) 4

0.08 0.08

0.08 0.08 0.08

0.1 0.05 0.2 0.05/0. i



numerical evaluation of responses of the base isolated multi-story shear frame was developed in Ref. 33. This program is adapted for use in the present analysis. A time step of At = 0.00025 sec is used during the con- tinuous phases of motion away from the transitions. The accuracy of the results is verified by comparing the results with those obtained by finer time steps for several cases. For frictional systems, the precise evaluation of the time of phase transitions are crucial to the accuracy of response analysis. Therefore, a successive time-step- reducing procedure is used to approach each of these transitions with an accuracy of 10-1°m/sec 2 in evaluating the stick-slip criteria and an accuracy of 10 -1° m/sec in evaluating the zeros of ~ (or ~ -3> and for the EDF and the S R - F systems). In this fashion, the time of transition is accurately determined, and based on the appropriate criteria, the equations governing the subsequent phase are specified.

Responses of the three-story structure with various base isolators subject to several earthquake ground accelerations including El Centro 1940 N00W, Pacoima Dam 1971 S16E, and Mexico City 1985 N90W are evaluated. The first 20 sec record of E1 Centro and Pacoima Dam earthquakes and the first 80 sec record of Mexico City earthquake are used in this study. The peak absolute accelerations for various floors, (~8 + g + • ; ) 1 . ~ , the maximum deflection, X3lmax, and the maximum relative base displacement, S lma x, for a range of natural period of 0.1 < TI < 1 sec are evaluated and discussed. Sensitivity studies on the effects of variations of parameters of the isolators and the structure for El Centro 1940 earthquake are carried out. To understand the effects of variation in intensity of ground excitation, the magnified accelerogram of El Clentro 1940 earthquake is used and the peak responses are evaluated. The results are compared with those for the original E1 Cen- tro earthquake record and discussed. Unless stated otherwise a structure with a fundamental natural period of 0.3 sec and the parameters of isolators as listed in Table 1 are used in the sensitivity analysis.

RESPONSES TO EL CENTRO EARTHQUAKE

In this section, responses of the base isolated and the fixed-base three-story frame subject to the accelerogram of El Centro 1940 earthquake are studied. The base isolation systems described earlier are considered and the sample as well as the peak responses are obtained and discussed.

Sample responses The characteristics of acceleration response time

histories of the structure for various base isolation systems and for the fixed-base one are quite different. In certain respects, these characteristics are important for performance analyses of base isolation systems. Prior to analyzing peak structural responses under different conditions, it is desirable to examine the response time histories in order to identify the behaviors of various base isolation systems. In this section, several sample response time histories and their Fourier decompositions are presented and discussed. A structure with a fundamental natural period of 0.3 see and the recommended values of the parameters for various isolators as listed in

Table 1 are used in these analyses. The IMSL Fast Fourier Transform routine FCOST 38 is used for the frequency analysis of approximate the first 20 sec of the acceleration responses.

Figure 3 shows the sample absolute acceleration time histories at the top of structure, '(~t'e + ~" +~3), for various base isolation systems and fro: the fixed-base (F-B) structure. The ground acceleration, .fg, is also plotted in this figure, It is noticed that the fixed-base structure significantly amplifies the ground acceleration while the base isolation systems generally reduces the acceleration transmitted to the structure. Figure 3(a) shows that the fixed-based structure amplifies the ground acceleration of El Centro 1940 earthquake to about lg. The acceleration response time history of the fixed-based structure shows a narrow-band oscillation which is essentially a random amplitude sinusoidal time variation with a dominant period of 0.3 sec (corresponding to the fundamental natural period of the structure). This is due to the wide-band nature of ground excitation and the light daming of the structure. It is .perhaps of interest to point out that in the earlier study ~, where a sinusoidal ground excitation was used, the acceleration response time history at the third floor of structure also

v

Z o

W . J Lid C.~ C.~ <

I

0

- - I

(o)

LR8

R-FBI/SR-F

l l l I i

1 2 3 4 5 6 7 8 ~) I0 11 t ( sec )

12

v

Z 0

J W

<

(b) P-F

EDF

~g

0 ~ ½ 3 4 ~3 6 "/ 8 ~) 1'0 1'1 12 t ( sec )

Fig. 3. Sample absolute acceleration responses at the top o f structffre for El Centro 1940 earthquake



showed a sinusoidal time variation, however, with a period of that of the ground excitation.

From Fig. 3 it is observed that the acceleration ._. response for a structure with a LRB system shows a ~, rather smooth low amplitude sinusoidal time variation "-" with a period of about 2 sec which is the natural period _o of the base isolated structure. The acceleration response time history of the NZ system has similar features to those of the LRB system, and therefore, is not shown in o here. The acceleration time histories of a structure with frictional base isolation systems contain many high frequency sharp peaks. This is because the non-linear stick- slip and slip-reversal transitions exert discontinuous forces on the base of structure. For El Centro 1940 earthquake ground excitation considered here, no sliding in the upper friction plate of the S R - F system occurs. Therefore, the response of the S R - F system coincides with that of the R - F B I system. It is perhaps of interest to mention that the acceleration time history patterns ._. observed here for the R-FBI , the P - F , and EDF systems are similar to those for the sinusoidal ground excitation studied in Ref. 33. z _o

The sample absolute acceleration time histories at various floors for different base isolation systems are shown in Fig. 4. Figure 4(a) displays the acceleration o"' time histories at various floors of structure for the LRB ~ 0.5 system. The ground acceleration time history shown by 0.0 dash line is also plotted in this figure for reference. It is observed, the LRB system filters out the high frequency -0.s accelerations contained in the ground acceleration. It is also noticed that the shape of the acceleration responses for various floors are approximately the same. This implies that the structure vibrates essentially as a rigid body.

Figure 4(b) shows the acceleration time histories for .-. the P - F system. It is observed that the response at the base floor contains some sharp peaks which are due to the slip-stick transitions of the P - F system. It is known that at the slip-stick and the slip-reversal transitions, the absolute accelerations at the base of structure change

lad

discontinuously due to the shock loadings of friction ~ 0.5 force. It is noticed that for certain short time durations, the solid line and dash line coincide. These indicate the 0.0 stick phases for the P - F isolator. Upon examining the -o.s acceleration time histories for various floors, it is observed that as the accelerations are transmitted through the floors, the sharp peaks become broader and the amplitudes are slightly modified due to the damping and the amplifying effects of structure. Figure 4(b) shows that for 6 < t < 8 sec, for which the amplitude of ground acceleration is small and the base of structure "" essentially sticks to the foundation, the amplifying effect ... of structure is quite significant, z

The acceleration time histories at various floors for o the R - F B I / S R - F systems are presented in Fig. 4(c). The general features of these acceleration time histories ,., are similar to those for the P - F system; however, the ~ 0.5 amplitudes of vibration for the R-FBI/SR--F systems are smaller than those for the P - F system. A careful 0.0 examination of base floor response shows that the dura- -0.5 tions of stick phase for the R - F B I / S R - F systems are much shorter than those for the P - F system.

Figure 4(d) shows the acceleration time histories of various floors for the EDF system. It is observed that the acceleration time histories exhibit approximate sinusoi-

Z

hi

o s

0.0

-0.5 0

i i i i 1 i i i i i i 1 1 2 3 4 :5 6 7 8 9 10 11 12

t ( s e c )

(o) LRB

3rd FL

2rid FL

1 st FL

BASE

(b) P-F 3rd FL

2rid FL

BASE

, , , , , , , ; , ~ , I 0 1 2 3 4 5 6 7 8 9 10 11 12

t ( s e c )

~ (c) R-FBI

3rd FL

2rid FL

BASE

t ( s e c )

(¢) EDF

3rd FL

2nd FL

o I R g . I

BASE

t ( s e c )

Fig. 4. Sample absolute acceleration responses at various floors for different base isolation systems for El Centro 1940 earthquake



dal variations with a period of about 1 sec which corresponds to the natural period of the EDF system when there is no slip in its friction plate.

Fourier decomposition of the acceleration time histories are shown in Fig. 5. Frequency contents of the acceleration responses may be clearly observed from this figure. Figure 5(a) shows the Fourier spectra of acceleration responses at various floors for the fixed- base structure. The Fourier spectrum for the base shown in this figure is that of the accelerogram of El Centro 1940 earthquake. It is observed that the ground acceleration has a broad spectrum and peaks at frequencies of about 1 to 1.5 Hz. As the acceleration is transmitted to the upper floor, it develops a sharp peak at frequency of about 3.33 Hz corresponding to the fundamental frequency of the structure. It is also observed that the peak of the Fourier spectrum increases rapidly as the acceleration is transmitted to the higher floors.

The Fourier spectra of acceleration response at various floors for the LRB base isolation system are shown in Fig. 5(b). It is observed that the Fourier spectra of various floors are almost identical. This implies that the structure vibrates essentially in its rigid body mode. This figure also shows that the dominant frequencies for the LRB systems is about 0.5 Hz which cor-

responds to the natural frequencies of the base isolated structure.

Figure 5(c) displays the Fourier spectra of various floors for the R - F B I system. It is observed that the acceleration response of the base floor contains many high frequency components which are generated by the discontinuous shock loadings; furthermore, frequencies in the range of 0.3 to 2 Hz and 5 to 8 Hz contain substantial energy. As the acceleration is transnfitted to the higher floors, the amplitude of the Fourier spectra at high frequencies decay, and the energy containing frequencies are somewhat modified. For example, the acceleration response at the third floor contains essentially no energy at frequencies higher than 12 Hz.

Figure 5(d) shows the Fourier spectra of various floors for the EDF system. It is observed that the Fourier spectra are peaked at about 1 Hz. Furthermore, similar to the LRB system, the Fourier spectra of various floors are almost identical.

The present results show that the base isolation systems reduce the acceleration transmitted to the superstructure to a significant extent. The acceleration responses for the R - F B I system have broad band spectra and contain high frequency components. The Fourier spectra for the LRB system show sharp peaks at the

(/1

v

bJ a

F-"

- -J

<

(o) F - B

. . . . . 3rd FL

2rid FL

0.01'01.~.~.1__..%... T • , 0 2 4 6 8 10

FREQUENCY

I

1 2 I'4 ( H z )

1 st FL

BASE 1~6 ll8

o~

=<

0.25

0.00

(b) LRB

3rd FL

~ . 2rid FL

1 st FL

BASE

1 , 16 20 0 2 4 6 8 110 ll2 ll4 1 ll8 20 FREQUENCY ( Hz )

0

LO r~

..J n

<

0.25

0.00

F/g.

. . . . 3rd FL

~ , . i ~ . . . . I 2rid FL

~ , 1st FL

0 l b 1'2 1'4 1'6 1'8 FREQUENCY ( Hz )

(c) R-FBI

.

LO

=<

0.25

0.00

(d) EDF

3rd FL

Fourier decompositions

0

~ = ~ 2rid FL

I st FL

2 4 6 8 10 12 1 4 1 6 FREQUENCY ( Hz )

r o T " " - -

20 1 8 2 0

of acceleration responses at various floors for El Centro 1940 earthquake

Soil Dynamics and. Earthquake Engineering, 1991, Volume 10, Number 3, April 159

Performance analysis of aseismic base isolation systems." F.-G. Fan and G. Ahmadi

natural frequency of the isolators but do not have high frequency component.

Response spectra In this section, the N00W component of El Centro

1940 earthquake is used as the ground excitation. Parameters of base isolation systems as shown in Table 1 and a structural damping of ~'1 = 0.02 are considered. The peak absolute acceleration at the top of structure, (£g + # + -~3) I . . . . the peak base displacement, s I . . . . and the peak deflection of structure, x31 . . . . for various /'1 and for different base isolation systems and for the fixed-base structure are evaluated. The resulting response spectra curves are plotted in Fig 6 - 8 . For this level of ground excitation, no sliding in the upper friction plate of the S R - F system occurs. Therefore, it behaves exactly as a R - F B I base isolator.

Figure 6 shows the peak acceleration responses at the top floor for various base isolation systems and for the fixed-base structure. It is observed that the peak accelerations for the base isolated structure are less than half of that for the fixed-base one. The peak acceleration of the fixed-base structure is about lg which is approx- iamtely three times that of the ground excitation. The structure with the P - F system experiences a peak acceleration response of about 0.4g, while that with the R - F B I / S R - F or the EDF systems lead to peak acceleration responses of about 0.3g. From Fig. 6, it is also observed that the LRB and the NZ systems lead to the lowest peak acceleration responses of the order of 0.15 to 0.2g for the ground acceleration considered.

The peak base displacement responses for various base isolation systems are compared in Fig. 7. It is observed that a structure with the LR system experiences the highest base displacement (about 15 cm), while that with the P - F system generally experiences the lowest base displacement (about 4 cm). It is also noticed that except for the P - F system, the peak base displacement responses for all isolators remain almost constant for the entire range of/'1 considered. That is, the base isolated structure behaves essentially as a rigid body.

"-'- 0 .30 E

v

0.25

Z t , i

:~ 0 .20 W

~0.15

~o.~o < m

0.05 m n

0.00

LRB . . . . . . . . . . .

. . . . . . . . . . . . / i : ! EDF

R-FBI /SR-F N Z : :~ //

P -F . . . . . . "'", ,,- . . . . . . . . . . . . . . . . .,,, '°",%..,,""-'"

i i

0 ~~ T; ( sec )

Fig. 7. Variations of peak base displacements of structure with its natural period of El Centro 1940 earthquake

Figure 8 shows the peak deflection response spectra for the base isolated structures and the fixed-base one. It is observed, the fixed-base structure leads to a peak deflection which is much higher than those of the base isolated structures. For a structure with a fundamental natural period of 0.3 sec (which corresponds to a typical three-floor building), fixed-base structure leads to a peak deflection response of about 2 cm. The R - F B I / S R - F , the LRB, and the NZ systems lead to the lowest peak deflections of only about 0.4 cm. It is perhaps of interest to point out that the peak acceleration responses for the R - F B I / S R - F systems are about twice that of the LRB system; however, Fig. 8 shows that the peak deflection responses for these base isolators are comparable. This result indicates that the short duration sharp pulses observed in the acceleration response time histories of the R - F B I / S R - F systems do not contain sufficient energy to generate high levels of deformation and/or stresses in the structure.

v

10

Z _0 F-B

w 1 _J

EDF w p-F R-FBI/SR-F 0

LRB ~"

NZ

1 0 -' . . . . . . . 10 -I

T1 ( see )

Fig. 6. Variations of peak absolute accelerations at the top of structure with its natural period for El Centro 1940 earthquake

.--,,

E v

10 "" Z _o F- rO W

It. l.iJ ra

v

n

I 0 -L

I 0 -~ I 0 -~

/SR-F

T1 ( sec )

Fig. 8. Variations of peak deflections of structure with its natural period for El Centro 1940 earthquake



The present results show that the base isolation systems effectively reduce the peak transmitted acceleration and column stresses. For E1 Centro 1940 earthquake, the LRB and the NZ systems lead to the lowest peak acceleration responses among the isolators considered. The R - F B I / S R - F together with the LRB, the NZ systems generate the lowest peak deflections of structure. Furthermore, the frictional systems lead to the lowest peak base displacements. These results are in agreement with those of Ref. 32.

SENSITIVITY ANALYSIS

It is of importance to understand the sensitivity of peak responses of base isolated structures to the variations in the parameters of the isolators and the structure. In the following, such sensitivity analyses for El Centro 1940 earthquake are carried out. The parameters of the isolators and the structure including friction coefficient, damping ratio, natural period, and mass ratio are varied. The peak responses of the base isolated structure and the fixed-base one are evaluated and their sensitivities are analyzed. The effects of variations in the intensity and

frequency content of seismic excitation are also studied and discussed.

Effects of friction coefficient of isolation system Due to the construction imperfection and ageing pro-

cess, a certain degree of deviation in friction coefficient from its nominal design value may be expected. There- fore, it is desirable to understand the effects of variations in friction coefficient on the peak responses of the superstructure. In this section, such a study is under- taken. A structure with a fundamental natural period of 0.3 sec and ~', = 0.02 is considered, and the N00W component of El Centro 1940 earthquake is used as the ground excitation. The peak responses for a range values of friction coefficient are evaluated and the results are presented in Figs 9 and 10.

Figure 9(a) shows the variations of peak acceleration with # for the P - F , the R - F B I , and the EDF systems. It is observed that, in general, the peak acceleration response increase as # increases for the systems shown in this figure. For example, the peak acceleration responses for the P - F and R - F B I systems increase from about 0.2g to about 0.45g as/~ increases from 0.03 to 0.1. For the EDF system, the peak acceleration

v

Z 0

i . i - . I h i 0 o<

0..

(o)

. .°.

R- I ,/' EDF

/ "

/ 10 -~ o.oo o.&5 o. o o. s o. o 0.25

FRICTION COEFFICIENT,

"'-0.30 E

"-" 0.25 I-,- Z

m 0.20 uJ 0

a- 0.15 (/3 5

~ 0 . 1 0 < m

v 0.05

(o)

0.00 0.00

/.,/,oF

0.65 0. 0 0. 5 0. 0 0.25 FRICTION COEFFICIENT,

v

Z _o

n~ iii

iiiJ 0 0 <

%-

(b) SR-r

SR-F2 o.-o . . . . . . . . . . . . . . . . . . . . . . . . . . .

/ / "

.oooo° SR-F1 o°."

10 -' 0 . 0 0 0 . 6 5 0 . 1 0 1 O. 15

FRICTION COEFFICIENT, /~ (or #1)

Fig. 9. Variations of peak absolute accelerations at the top of structure with friction coefficient

" - ' 0 .20 E

v

~z 0.15 uJ

LLJ (.J

5 a_ 0.10 0'1 a

hi U3 < m 0.05

0.00 0.00

Fig. 10.

(b) SR-F

SR-F1

. . . . . . . . . " ' . SR-F2 "~ . . . . . . . . . . . . . . . . . . . . . . . . . . .

o.6s o. o o. s FRICTION COEFFICIENT, /~ (o r /~ )

Variations of peak base displacements with friction coefficient



response increases from about 0.15g for # = 0.1 to about 0.25g for # = 0.2. Figure 9(a) also shows that the peak acceleration responses for the P - F and the R - F B I sysems are almost identical in the entire range of # considered.

Figure 9(b) displays the variations of peak acceleration versus friction coefficients of the upper and the body friction plates of the S R - F systems. In this figure, S R - F 1 stands for a Sliding Resilient- Friction system for which the friction coefficient of the body plates is 0.05, while that of the upper plate is varying. Similarly, S R - F 2 denotes a S R - F system for which the friction coefficient of the upper friction plate is kept fixed at 0.1, while that of the body plates is varied. Figure 9(b) shows that, for small friction coefficient, the peak acceleration response for the S R - F 1 system increases with #. For # > 0.07, the peak acceleration becomes a constant. The reason is that, for relatively larger #, no sliding in the upper friction plate occurs during the entire duration of ground excitation. Similarly, the peak acceleration response for the S R - F 2 system increases as #j increases for small #t. A slight decrease in the peak acceleration in the range of 0.09 < #, < 0.1 is noticed. For #, > 0.1, the body friction plates of the S R - F 2 system stick to each other, the system reduces to a P - F unit and the peak acceleration remains a constant.

Figure 10(a) shows the effect of variation of friction coefficient on the peak base displacement responses for the P - F , the R - F B I and the EDF systems. It is observed that the peak base displacement responses generally decrease as # increases. The exception is the EDF sysem for which the peak displacement response first increases to a peak of about 19 cm at/z = 0.05, and then decreases with further increase in/z. For the P - F and R - F B I systems, a 50% decrease in their peak displacement responses are observed as ~ varies from 0.03 to 0.1. The effects of variations in friction coefficients of the body and the upper friction plates on the peak base displacement responses for the S R - F systems are displayed in Fig. 10(b). This figure shows that as # increases, the peak base displacement of the S R - F 1 system first decreases, and remains a constant for ~ > 0.07. Similarly, for the S R - F 2 system the peak base displacement decreases with an increase in #, up to #, = 0.1 and remains a constant for large #1.

The sensitivity of peak deflection responses for various frictional base isolation systems are also studied. Trends of variations of peak deflections with changes in friction coefficient are quite similar to those of the peak acceleration responses. Additional details may be found in Ref. 39.

Based on the results presented in this section, it may be concluded that an increase in the value of friction coefficient (# or ~,) generally produces higher peak acceleration and peak deflection, and lower peak displacement responses. However, small variations in (or #,) lead only to slight changes in the peak responses of the structure.

Effects of velocity-dependent friction model It is well known that the Coulomb law of friction is

only an approximation and the friction coefficient between surfaces vary with velocity, normal force and

etc 4°. The recent data of Ref. 41 suggests that the friction coefficient for teflon-steel interfaces increases with the slip (relative sliding) velocity and decreases with the interface pressure. In this section, the effects of velocity- dependence of friction coefficient on the performance of the R - F B I , the P - F , and athe EDF systems are studied. The N00W component of E1 Centro 1940 earthquake is used as the ground acceleration. A friction model with linear velocity dependence is considered. That is, it is is assumed that the dynamic friction coefficient is given as

# = #o + ~lzl (23)

in which #o is the static friction coefficient, ~ is the slip velocity between surfaces in contact, and ~ is a parameter which is the rate of variation of/~ with the sliding velocity. Equation (23) with a range of values of

between 0 to 0.5 s/m is used for analyzing the sensitivity of performances of frictional base isolation systems to velocity-dependence of friction coefficient. The values of friction coefficient as listed in Table 1 are used for/zo in the analysis.

Figure 11 shows the peak acceleration responses at the top of structure and the peak slip velocity versus ~. It is observed that the accelerations and the sliding velocities are not sensitive to the variations in ~. The exception is the peak sliding velocity of the EDF system which shows a 50% decrease as ~ increases form zero to 0.5 s/m.

The variation of maximum base displacement with are shown in Fig. 12. The peak slip displacement, (s -Y)lmax, for the EDF system is also shown in this figure. It is observed that both the total base displacement, s I m~x, and the slip displacement of the EDF system are not sensitive to the variations in ~. The results for the R - F B I and the P - F systems show gradual reduction in the peak base displacement responses as ~ increases. Sensitivities of peak deflection responses of frictional base isolation systems to velocity dependence of friction coefficient are also studied. The results (which are not shown here due to space limitation but may be found in Ref. 39) show that the variations of

do not have a significant effect on the peak deflection responses.

1

v

Z o

t , i , .d h i r O

n

1 0 - ' [

1 Peak Accellrotion

...... Peak Sliding Velocity

P-F"

......... .Epr ~-re,

i i I i i i

0.0 0.1 0.2 0.3 0.4 0.5 (see/m)

Fig. 11. Effects o f velocity - dependent friction coefficient on peak acceleration and peak sliding velocity responses

E

G S t~J >

0 Z

Y < t,i

10 -,eL



"- '0.10 E

v

0.08 I,,-, Z bJ

0.06 5 D_ U~

0.04 hl U') < rn v 0.02

(3.

0.00 0.0

EDF (Totol)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~ FBI

........... . ===================================== ................

0.1 0.2 0.3 0.4 0.5 (sec/m)

Fig. 12. Effects of velocity - dependent friction coefficient on peak base displacement responses

R-F Z "I ~ l ~ x / C R B _o

COOILIL~' 2 . ~ , ~ R-FBI/SR-r

< S R - F

v ~ /LRB/EDF o_ i5 ,, ~.

10 "' . . . . . I i o.o 1.o 2.b 4.0 5.b 6.0

To ( sec )

Fig. 13. Variations of peak absolute accelerations at the top of structure with natural period of isolation system

Considering the peak slip velocities for various systems as shown in Fig. 11, the amount of variations in friction coefficient for the R - F B I , the P - F , and the EDF systems are about 0.05 to 0.07, 0.1 to 0.25, and 0.2 to 0.275, respectively. (Note that for the R - F B I system, eight friction plates are considered and the slip velocity is divided by eight in equation (23).) Although these are rather substantial variations in friction coefficient, the results show that the peak acceleration and the peak deflection responses remain almost unchanged. Thus, it may be concluded that the peak responses of the base isolated structure are not sensitive to the variation of friction coefficient with slip velocity. The Coulomb law of friction with a constant # (equal to the static coefficient of friction) appears to be capable of describing the performances of frictional base isolators satisfac- torily. A similar observation was noted in Ref. 32.

Effects of natural period of isolation system The importance of selecting appropriate values of

natural period for the base isolation system is well known. In this section, the effects of variations in natural periods of various isolators on the peak responses of structure are studied. A three-story building described earlier with a fundamental natural period of 0.3 sec and damping of 0.02 is considered and the accelerogram of El Centro 1940 earthquake is used. The resulting peak responses are plotted versus the natural period of the base isolation system, To, in Fig. 13-15 .

Figure 13 shows the acceleration response spectra for various base isolation systems. It is observed that for natural periods of isolation system below 1 sec, the peak acceleration responses for all systems are quite high. The exception is the S R - F system for which the peak acceleration remains less than 0.3g. For To > 1.8 sec, the acceleration response spectrum for the S R - F system coincides with that for the R - F B I system and takes an almost constant value of about 0.25g. The peak accelerations for the EDF system are identical to those for the LRB system for To > 1.5 sec. In this range the peak acceleration for the LRB/EDF and the NZ systems decrease rapidly with an increase in To.

Figure 14 shows the peak base displacements for various base isolation systems versus To. It is observed,

for To < 1.5 sec, the peak base displacement responses are less than 10 cm for all base isolation systems considered. As To increases, the peak base displacement for the LRB/EDF system increases sharply, and reaches a maximum of about 25 cm at To = 2.5 sec. The peak base displacements for the R - F B I and the S R - F systems coincide for To > 2 sec and increase only slightly with To.

The variations of the peak deflections of the structure with To for different base isolation systems are shown in Fig. 15. It is noticed that the peak deflections for the LRB, the NZ, and the R - F B I systems are quite large for To < 1.5 sec, while that for the EDF system is about 0.5 to 1 cm. The S R - F base isolation system is the only system which appears to be insensitive to a large variation in To. It is also observed that the S R - F system leads to the lowest structural deflections for To < 1.5 sec. For To > 2 sec, the peak deflection responses for the R - F B I and the S R - F systems become identical and remain approximately a constant

" ' 0 . 3 0 E

v

0.25

Z hl m 0.20 bJ 0 5 n 0 . 1 5 u3

~o.~o < m

~ 0.05 w n

0.00 0.0

Fig. 14.

r-~, LRB/EDF / ' \ . / f~. \

\ \ \

LR8 / NZ ~- ~ - - - - - - - - - - EOF I / SR-F ~... . / / . -

_~?'~J, ~ / R-FBI/SR-F ..-

R-FBI

1.'0 2.'0 4.'0 6.0 To ( sec )

Variations of peak base displacements with natural period of isolation system



10 -~

L , R-FBI

.J

w EDF \ R-FBI/SR-F

Y < SR-F --""~... . . . . . . ..NZ (3..

\ ' \ I..RB/EDF

10 -~ I i ~ I J 0.0 1.0 2.0 ..3.0 4.0 5.0 6.0

T o ( sec )

Fig. 15. Variations of peak base deflections with natural period of isolation system

v

Z 0

Ld Ld ¢,.) (..) < :

(3-

10

10 -~

................. ] . . - ~ - : ~ - ~ - . . . . . . . . . . -_- : - _ -

0.00 0.05 O. 10 O. 15 0.20 STRUCTURAL DAMPING, ~'l

Fig. 17. Variations of peak absolute accelerations at the top of structure with structural damping

of about 0.4 cm. The peak deflection for the LRB/EDF system decreases sharply for To > 2.5 sec.

The results presented in this section show that the peak acceleration and the peak deflection responses for the R - F B I / S R - F , the NZ, and the LRB systems are not sensitive to variation in To in the neighborhood of the recommended values for their natural period. However, the peak responses for the EDF system appear to be rather sensitive to variation in natural period near To = 1 sec. The peak acceleration and the peak deflection responses for the S R - F system remain almost constant for the entire range of To considered.

Effects o f dampings o f isolation systems and structure In this section, effects of dampings of the base isola-

tion system and the structure on the peak responses of a structure with TI = 0.3 sec are studied. In the first phase, the damping of the structure is kept fixed at ~'~ = 0.02 and ~'o is varied. The entire range of ~'o from zero to 0.5 are studied for the sake of com- pleteness, although, in practice ~'o is always more than 0.05. In the second phase, the damping of the isolator is kept at ~'o = 0.08 and the structural damping is

v

Z o_

if2

. d

V

13-

EDF R~/~BI/SR-F

. x LRB

10 " 't 0.0 0.'I 0.12 0.13 0.4 0.5

~o

Fig. 16. Variations of peak absolute accelerations at the top of structure with damping of isolation system

changed. The N00W component of El Centro 1940 earthquake is used and the resulting peak acceleration responses are shown in Fig. 16 and 17.

Figure 16 shows the peak acceleration responses for various base isolation systems. It is observed that the R - F B I / S R - F and the EDF systems are insensitive to variation in damping coefficients of the isolation system and lead to almost constant peak acceleration responses of about 0.3g. For small ~'o, the peak acceleration responses for the LRB and the NZ systems first decrease with an increase in ~'o, and reaches a minimum value of about 0.13g occurring at ~'o = 0.4 for the LRB system and ~'o = 0.2 for the NZ system. The peak acceleration then increases with further increase in ~'o. The reason is that as damping increases the energy dissipation capacity of the isolator increases; however, for vary large damping ratios, the isolator becomes rather stiff and the transmitted acceleration increases.

The corresponding results for the peak base displacement and the peak deflection responses (not shown here but may be found in Ref. 39) show that for practical range of ~'o, variations in the damping of isolation system produce only slight variations in the peak structural responses for the LRB and the NZ systems. Fur- thermore, the effects of variations in damping ratio are negligible for the frictional systems for the entire range of ~'o considered.

Figure 17 shows the peak acceleration responses versus ~'1 for different base isolation systems. The results for the fixed-base structure is also shown in this figure for reference. It is observed that the peak accelerations for the fixed-base structure, the P - F , and the R - F B I / S R - F systems decrease as ~'~ increases. Those of the structure with the LRB or the NZ base isolation systems, however, remain approximately constant with magnitude of less than 0.2g for the entire range of ~'1 considered. The EDF system also leads to a roughly constant peak acceleration response of about 0.3g.

The results for variations of the peak base displacement and peak deflection responses for various base isolation systems with structural damping 39 show that an increase in structural damping leads to a slight decrease in peak deflection respsonses for the fixed-base



structure and the structure with the P - F and the R - F B I / S R - F systems. However, variations in structural damping has negligible effets on the peak deflection responses for the LRB, the NZ, and the EDF systems. Furthermore, the peak base displacements for all the systems considered are insensitive to variations in

Effects of intensity To understand the effects of increase in intensity of

ground excitation on performances of various base isolation systems, the N00W component of E1 Centro 1940 earthquake is magnified by a factor of two and is used as the ground excitation. Thus, the intensity is increased while the 'frequency content of the ground excitation remains unchanged. The peak responses for the base isolated structure and the fixed-base one under the magnified El Centro 1940 earthquake are evaluated and the results are described in this section.

Figure 18 shows the acceleration response spectra for various base isolation systems and for the fixed-base structure. It is observed that the base isolated structure experiences much lower peak accelerations when compared with the fixed-base one. It is also noticed that the peak accelerations of the base isolated structure do not vary appreciably with variation in T.. The exception is the EDF system for which the peak acceleration increases somewhat as TI increases. For this level of excitation, still the response of the S R - F system is identical to that of the R - F B I system due to the absence of sliding in the upper plate of the S R - F system. Com- paring Fig. 18 with Fig. 6, it is observed that the peak acceleration responses for the fixed-base structure, the LRB, and the NZ systems are doubled when the ground acceleration is doubled; however, those of the frictional system have increased only by 25%. For the P - F system, an increase of about 45 % in the peak acceleration responses is noticed. These figures also show that the peak accelerations for the LRB and the NZ systems are about one half of that for the R - FBI /SR-F systems for the El Centro 1940 ground excitation; however, these becomes comparable for the magnified El Centro earthquake.

" ' 0 . 4 0

E v 0.35

0 .30 L,J ' 5 w 0.25 (...) 5 (3..

5

v

a .

0.20

0 .15

0 .10

0 .05

0 .00 10 -~

s

LRB .........

EDF - - ---~---""~"" ".":T;'-r-.

NZ _ .,_',,

R - F B r / S R - F

r 1 i t , |

T1 ( s e c )

Fig. 19. Variations of peak base displacements of structure with its natural period for the magnified El Centro 1940 earthquake

Figure 19 compares the peak base displacement responses for various base isolation systems under the magnified E1 Centro earthquake ground excitation. It is observed that the peak base displacement responses remain almost constant for the entire range of TI. The exception is the P - F system for which the peak base displacement varies between about 12 and 24 cm. This figure shows that the base displacement is lowest (about 15 cm) for the R - F B I / S R - F systems and highest (about 30 to 35 cm) for the LRB system. Comparing Fig. 19 with Fig. 7, it is observed that the peak base displacement responses for the LRB, the NZ, and the R - F B I / S R - F systems are roughly doubled when the intensity of the ground acceleration is doubled.

Figure 20 displays the peak structural deflections for various base isolation systems and the fixed-based structure under the magnified accelerogram of E1 Centro 1940 earthquake. It is observed that the R - F B I / S R - F systems lead to the lowest deflections among the base isolation systems considered; the peak deflections for the P - F , the LRB, the NZ and the EDF systems are

lO

v F - 8

__Q

W 1 P - F R - F B I / S R - F LRB

.~. . . . . . . . . . , . . . . . . . . . . . . . . . . . , , ' " " . , . . . . . . . >..<.'.:i". 0 - . . ( J ~o . . . . < y

n NZ EDF

1 0 -~ . . . . . . . . 10 -~

T1 ( s e c )

Fig. 18. Variations of peak absolute accelerations at the top of structure with its natural period for the magnified El Centro 1940 earthquake

1 0 -" /" Z NZ 0 F - 0

10 -2_

-FBI/SR-F

1 0 -5 , ,

10 - ' TI ( sec )

Fig. 20. Variations of peak deflections of structure with its natural period for the magnified El Centro 1940 earthquake


Performance analysis of aseismic base isolation systems." F.-G. Fan and G. Ahmadi

comparable in the entire range of TI considered. The peak deflections of the base isolated structure are much lower than that of the fixed-base one. For example, for a structure with a fundamental natural period of 0.3 sec, the base isolated structures lead to peak deflections which are about five to ten times lower than those for the fixed-base structure. A comparison of Fig. 8 and 20 shows that the peak deflection responses for the fixed- base structure, the LRB, and the NZ systems are approximately doubled when the intensity of the ground ~ - - acceleration is doubled; however, those of the frictional ~ 1 systems have increased by only about 25 %.

Based on the presented results, it may be concluded 0 that the frictional base isolation systems are relatively

- 1 insensitive to variations in the intensity of ground excitation. As the intensity of the ground excitation is doubled, the peak responses of the LRB, the NZ, and the fixed-based structure increase by about 100%. However, an increase of only about 25 % in the peak acceleration and peak deflection responses are observed for the frictional systems under the same variation of ground I excitation. I R-FBI

It should be pointed out that the results for the effects L -.,,,~,~¢~ of mass ratio (Ctb) on the peak structural responses are "-" not presented in here due to the space limitation.

v

However, it was shown in Ref. 39 that, for practical range of ab, variations in mass ratio have no significant effect on the peak responses of the base isolated structure.

RESPONSE TO PACOIMA DAM EARTHQUAKE

To understand the effects of extremely high intensity ground excitation on the performances of various base isolation systems, the accelerogram of the S 16E component of Pacoima Dam 1971 earthquake is used in this section. The peak ground acceleration for this record is about 1.17g. The recommended values of parameters as listed in Table 1 for various base isolation systems are considered in these analyses.

0

(0)

F - B

b

1 2 3 4 5 6 7 ~ 9 I'0 I !2 '1 I t ( s e c )

Z _o

tY t , I - A W

,<

0

-1

SR-F

0 1 2 3 4 5 6 7 8 9 10 11 12 t ( sec )

Fig. 21. Sample absolute acceleration responses at the top of structure for Pacoima dam 1971 earthquake

Sample responses For a structure with a natural period of 0.3 sec,

several absolute acceleration time histories at the top of structure for various base isolation systems and for the fixed-base structure are shown in Fig. 21. The ground acceleration is also plotted in this figure for reference. It is observed that the fixed-base structure amplifies the ground acceleration more than three times to about 3.5g. The acceleration time history for the fixed-base structure is essentially a narrow-band random process with a dominant period of 0.3 sec. The acceleration time history for the LRB system shows a sinusoidal time variation with a period of about 2 sec. This figure shows that the acceleration time histories of the R - F B I or the P - F systems contain many high frequency peaks. It is also observed that the acceleration responses for the R - F B I and the EDF systems are generally lower than those for the LRB, the P - F systems. Figure 21 also shows that there are small amplitude high frequency oscillations superposed on the low frequency sinusoidal variation of the acceleration time history for the EDF system.

Using IMSL Fast Fourier Transform routine FCOST, approximately the first 20 sec acceleration response time histories at the top of structure are frequency analyzed. The resulting Fourier spectra for various base isolation systems together with those of the fixed-base structure and the accelerogram of Pacoima Dam 1971 earthquake are shown in Fig. 22. It is observed that fre- quenoes between zero and 5 Hz of the ground excitation contain considerable energy. It is also observed that the fixed-based structure amplifies the ground acceleration to a significant extent, and its Fourier spectrum is sharply peaked at the frequency of about 3.33 Hz. The Fourier spectra of the LRB and the EDF systems are peaked, respectively, at 0.5 Hz and 1 Hz which corres- pond to the natural frequencies of these systems. The Fourier spectrum of the R - F B I system, however, shows a low amplitude broad-band feature with no distinguishable peak. This is the characteristic of acceleration responses of the sliding systems for which the friction force scatters the energy into high frequency regions.



0 Q)

I,.iJ

_.1 n

<

0.5 0.0

F-B

LRB

R-FBI

EDF

~g 0 2 4 6 8 10 12 14 16 18 20

FREQUENCY ( Hz )

Fig. 22. Fourier spectra of acceleration response at the top of structure for various base isolation systems for Pacoima dam 1971 earthquake

" - "0 .70 E

0.65

0.60 {.,.

Z w 0.55

o 0.50 5 0. 0.45 O9

F~ 0 .40 Ld

<~ 0.35 m • ,,, 0 . 3 0 ,,(

0.25

0.20 10 -'

SR-F P-F ," ,,1 . . . . . . . . . . ,,, ,,.,, / '

~':a" " ; = : 7 " . . . . . '4.. . .# -":,', .,'" " v '

~ ° 7 EDF

, , r , ,

T1 ( sec )

Fig. 24. Variations of peak base displacement of structure with its natural period for Pacoima dam 1971 earthquake

Response spectra Figure 23 compares the acceleration response spectra

at the top of structure for various base isolation systems under Pacoima Dam 1971 earthquake. It is observed that the peak acceleration response for the fixed-base structure varies between 1 to 5g; while those for the base isolated structure are 0.3 to 0.9g. Among the base isolation system considered, the R - F B I , the S R - F , and the LRB systems, generally, lead to the lowest peak acceleration. All base isolation systems, except the EDF system, lead to almost constant peak acceleration responses. For the EDF system, the peak acceleration increases as /'1 increases. For /'1 < 0.4 sec, its peak acceleration is is about 0.25 to 0.4g which is the lowest among the base isolators considered. This figure also shows that while sliding occurs in the upper friction plate of the S R - F system, no significant difference in the peak acceleration responses between the S R - F and the R - F B I systems is observed.

Figure 24 shows the peak base displacement responses for various base isolation systems under Pacoima Dam earthquake. It is observed that the peak base displacements for different systems are comparable and vary between 35 and 50 cm for T, less than 0.8 sec. This figure also shows the peak base displacement responses are almost constant for the entire range of T, considered. The exception is the P - F system for which the peak base displacement response varies between 37 to 60 cm as T, increases from 0.5 to 1 sec. It is also observed that sliding on the upper friction plate of the S R - F system occur, and the peak base displacements for the S R - F system are about 5 to 8 cm larger than those for the R - F B I system.

The peak deflection responses for various base isolation systems are displayed in Fig. 25. This figure shows that the R - F B I and the S R - F system lead to the lowest peak deflection responses among the base isolation systems considered. For a structure with T, = 0.3 sec,

v

10

Z o_

n- w I .J LaJ 0 0 <

v

P-F' NZ / / . . . . .

-

-I- " .

SR-F

I 0 -'

10 "' T1 ( see )

Fig. 23. Variations of peak absolute accelerations at the top of structure with its natural period for Pacoima dam 1971 earthquake

v

oZ 1 0 - I . ~ / ~ " ~ ' ' / / ~'~ ,:...,,,

b.l . . . . - _ / .

,, / N~. ,-.-..y-y__L,./ sR-~

Q 10 -L <: P-F ~x, / " °"

1 0 -~ . . . . . . . . 10 "'

TI ( sec )

Fig. 25. Variations of peak deflections of structure with its natural period for Pacoima dam 1971 earthquake



a peak structural deflection of about 0.6 cm for the R - F B I and the S R - F systems is observed. The EDF system generates a peak deflection of about 0.7 cm. The P - F and the LRB systems lead to a peak deflection of about 1 cm, and the NZ system leads to a peak deflection of about 1.8 cm. The peak deflection of the fixed- base structure is 8 cm which is about 4 to 14 times those z O

of the base isolated structure. ,~ The present results show that the base isolation

_ J systems are highly effective in reducing the peak "' transmitted accelerations to the structure and the peak <~ structural deflections under the high intensity earthquakes. Furthermore, the frictional systems such as the R - F B I , the S R - F and the EDF systems generally lead to the lowest peak acceleration and peak deflection responses.

(o) ,I F-B ]

LRB \ A /'~ ./~ ;

vv v VVi 1

0

-1 40 415

R-FBI

I

5'0 5'5 6'0 t ( sec )

65

RESPONSES TO MEXICO CITY EARTHQUAKE

To study the effects of severe frequency content of ground excitation, the performances of different base isolation systems subject to the N90W component of Mexico City 1985 earthquake are evaluated in this section. This earthquake which had a peak acceleration of 0.17g contained considerable energy at low frequency of about 0.5 Hz. A structure with a natural period of 0.3 sec and a damping ratio of 0.02 is considered. The parameters of base isolation systems as listed in Table 1 are used throughout this analysis.

Sample responses Figure 26 shows several acceleration response time

histories at the top of structure for different base isolation systems as well as for the fixed-base structure for the time duration of 40 < t < 65 sec. It is observed that the ground acceleration of Mexico City earthquake shows a dominant sinusoidal time variation with a rather long period of about 2 sec. Figure 26 also shows that the fixed-base structure does not amplify the ground acceleration to a significant extent. This is due to the disparity of the dominant frequency of the ground excitation from the fundamental natural frequency of the structure. It is also noticed that the LRB system amplifies the ground acceleration due to the resonance. Figure 26 also shows that the response time histories for the R - F B I and the P - F systems contain energy at high frequency due to the shock loadings; however, the peaks of these records are rather low. It is of interest to point out the peculiar sliding behavior of the R - F B I and the P - F isolators. It is observed that the isolator slides in one direction for about 1 sec and then slides in the opposite direction for another 1 sec. The acceleration response time history for the EDF system is a smooth time function with its amplitude being of the same order as that of the ground excitation. It should be mentioned that in this case sliding occurs in the upper friction plate of the S R - F system and the acceleration response time histories of the S R - F system are not identical to those of the R - F B I system. Nevertheless, the general characteristics of these two systems are quite similar. There- fore, the acceleration response time history of the S R - F system is not shown in here.

To understand the frequency content of these acceleration time histories, the responses approximately between

(b) P-F

Z EDF o_

uJ _,J

(.)

0,

- - 1 I ' 40 45 5b 5'5 6b 65

t ( sec )

Fig. 26. Sample absolute acceleration responses at the top of structure for Mexico City 1985 earthquake

35 and 75 sec are Fourier analyzed. The IMSL Fast Fourier Transform routine FCOST is used in these analyses. The resulting Fourier spectra are presented in Fig. 27. The Fourier spectrum of the N90W component of Mexico City 1985 earthquake is also presented in this

t ) ILL LRB

O3

v . . . . ~.-dL- F-B

{.d

I--- _J t2.

<

1.0 0.5 0.0

R-FBI

L~ EDF

Xg a~" " l o 2 1'o

FREQUENCY ( Hz ) 14

Fig. 2Z Fourier spectra of acceleration response at the top of structure for various base isolation systems for Mexico City 1985 earthquake



figure for reference. It is noticed that the ground acceleration of Mexico City 1985 earthquake has a narrow- band spectrum which is sharply peaked at about 0.5 Hz. For this peculiar seismic ground acceleration, the Fourier spectra of all systems also have peaks at the frequencies of about 0.5 Hz. In particular, the Fourier spectrum of the LRB system contains a very high peak at this frequency due to the resonance. It is also observed that the Fourier spectrum of the fixed-based structure has a secondary peak near its natural frequency of 3.33 Hz. Similarly the spectrum of the EDF system shows a peak at frequency of about 1 Hz. Figure 27 also shows that the Fourier spectra for the R - F B I system has a certain amount of energy in the frequency band of 5 to 7 Hz.

Response spectra For the accelerogram of Mexico City 1985 earth-

quake, the peak absolute accelerations at the top of structure, the peak base displacements, and the peak deflections for the base isolated structure and the fixed- base one are evaluated and the results are shown in Fig. 28-30 .

Figure 28 displays the variations of peak acceleration responses for various base isolation system with T~. It is observed that the LRB and the NZ systems considerably amplify the ground acceleration, and lead to peak acceleration responses of about 0.7 and 0.45g, respectively. The peak acceleration response of the fixed-base structure is about 0.2g for small T~, and varies between 0.3 to 0.6g for/'1 > 0.5 sec. Figure 28 also shows that the peak acceleration response for the S R - F system is slightly higher than that for the R - F B I system and these lead to the lowest peak acceleration of about 0.2g for the entire range of T~ considered. The peak acceleration for the EDF system increases with TI but it is generally lower than that of the fixed-base structure.

Figure 29 shows the peak base displacement responses for various base isolation systems. It is observed that all of the base isolation systems considered apparently lead to constant base displacement for the entire range of T].

"-'1.0 E 0.9

v

0.8 p .

Z ~0.7

~ 0 . 6

cL 0 . 5 CO

~0.4 bJ

o.s m

v

12.

0.2

0.1

O 0 10 " '

LRB . . . . . . . . . . . -

F/R-FBI _~-_=_-- . ' . . " "

.............. P - F . . . . . . . . . . . . . . . . . . . . .' /

. . . . . . . . . . . . . . . . . . . . . . . . . . . E OF___ . . . . . . . "~ I / J i i i i i J ~ |

t T1 ( sec )

Fig. 29. Variations of peak base displacements of structure with its natural period for Mexico City 1985 earthquake

The LRB system generates the highest base displacement response of about 70 cm. The NZ, the R-FBI , and the S R - F systems lead to a base displacement of about 30 cm. It is also observed that the P - F and the EDF systems lead to peak base displacement responses of only about 10 cm.

The deflection response spectra for various base isolation systems and for the fixed-base structure are plotted in Fig. 30. It is observed that the amplitude of the deflection spectra for the LRB and the NZ system are very high due to resonance. These peak deflections are several times of that of the fixed-base structure. Figure 30 also shows that the S R - F system leads to the lowest peak deflection response among the base isolation systems considered. The peak deflection for the R - F B I system is somewhat higher than that for the S R - F system. The peak deflections of the EDF and the P - F systems are comparable with that of the fixed-base structure. This figure also shows that for a structure with fundamental natural period of 0.3 sec, the peak deflection

1 LRB . . . . . . . . . . .

- - F-B / ' N - - Z -- -- 7-: 7 ~ //'~X, ~ . _o

~A ~ P - F / . .

<

v ,<

n R-FBI

1 0 "~ . . . . . . . . 10 -'

T1 ( sec )

Fig. 28. Variations of peak absolute acceleration at the top of structure with its natural period for Mexico City 1985 earthquake

E

"J I o -' EOF . -5 : Z ~x~ ~ I .: I-.- C.) -~. .. ~ / ~...>~,4.. X . LO

v

CL .- ," ~ / "" - " " . R-FBI

F

I 0 -~ 10 "'

T1 ( sec )

Fig. 30. Variations of peak deflections of structure with its natural period for Mexico City 1985 earthquake



for the fixed-base structure is about 0.7 cm, while those for the S R - F , the R-FBI , the P - F , and the EDF systems are about 0.3 to 0.5 cm. Peak deflections of about 1 cm and 2 cm are observed for the NZ and the LRB systems, respectively.

The presented results show that, for earthquakes with considerable energy at low frequency, most base isolators, do not perform very well. In particular the LRB and the NZ systems amplify the ground excitation to a significant extent. The S R - F and the R - F B I isolators are the only systems which appear to provide a certain amount of protection.

CONCLUSIONS

Responses of a multi-degree-of-freedom shear frame with and without base isolation system under several seismic ground excitation are analyzed. The peak acceleration, the peak base displacement, and the peak deflection of structure under a variety of conditions are evaluated and the results are used for comparison of performance of various base isolation systems. Sensitivities of performances of different systems to variations in the parameters of the isolation systems and the structure and the intensity and frequency content of the excitation are studied. Based on the presented results, the following conclusions may be drawn:

preliminary selection of the most suitable base isolation system for a specific structure and site condition. For example, for sites with histories of earthquakes with long period energy contents, the use of a rubber bearing type base isolation system should be avoided. The presence of a frictional element in the base isolator system, generally, provides a safety measure against unpredicted severe variations in intensity and frequency content of earthquake ground excitations. Furthermore, frictional elements provide rigidity for the base isolation system which alleviates the uncomfortable oscillation of base-isolated structure in winds during normal use. However, these additional protection features are at the expense of generation of high frequency excitations at higher floors during earthquake strong motion which could be quite damaging to the secondary systems and equipment housed in the structure.

ACKNOWLEDGEMENT

This work is supported by the National Center for Earth- quake Engineering Research, State University of New York at Buffalo under the Grants No. NCEER 86-3021F, and 87-2007.

(1) The transmitted acceleration and column stresses generated in the structure can be significantly reduced by the use of properly designed base isolation systems.

(2) An increase in friction coefficient generally leads to higher peak accelerations and peak deflections, and lower peak base displacements. However, small variations in friction coefficient lead only to slight changes in the peak responses of structure.

(3) The peak acceleration and the peak deflection responses for the frictional base isolators are insensitive to the velocity-dependence of friction coefficient.

(4) The peak responses are, in general, insensitive to small variations in the natural period of base isolation systems in the neighborhood of the recommended values except for the EDF system for which the peak responses vary somewhat with To.

(5) Variations in the structural damping, and damping of isolators have no significant effect on the peak acceleration and the peak deflection responses.

(6) The peak responses for the LRB and the NZ systems vary in direct proportion to the intensity of earthquakes.

(7) The LRB and the NZ systems are sensitive to the low frequency energy content of earthquakes.

(8) Frictional systems are less sensitive to severe variations in the intensity and frequency content of earthquakes.

As noted before, general design criteria for base isolation systems and base-isolated structures were described in Refs 26-28. The presented study provides detailed information concerning peak structural responses for different base isolation systems for a number of different earthquakes. Thus, the results may be helpful for the

REFERENCES

1 Kelly, J. M. Aseismic base isolation, Shock Vib. Dig., 1982, 14, 17-25

2 Kelly, J. M. Aseismic base isolation: review and bibliography, Soil Dyn. Earthquake Engng., 1986, $, 202-216

3 Kelly, J. M. and Hodder. S. B. Experimental study of lead and elasto- meric dampers for base isolation systems in laminated neoprene bearings, Bulletin of New Zealand National Society for Earthquake Engineering, 1982, 15. 53-67

4 Huffmann, G. R. Full base isolation for eanhqnake protection by helical springs and viscodampers, Nuclear Engng. and Design, 1985, 84, 331-338

5 Buckle, 1. G. New Zealand Seismic base isolation concepts and their application to nuclear engineering, Nuclear Engng. and Design, 1985, 84, 313-326

6 Skinner, R. J., Kelly, J. M. and Heine, A. J. Hysteretic dampers for earthquake-resistant structures, Earthquake Engng. Struct. Dyn., 1975 3. 287-296

7 Constantinou, M. C. and Tadjbakhsh, I. G. Hysteretic dampers in base isolation: random approach, ASCE, J, Structural Engng., 1985, Ill, 705-721

8 Robinson, W. H. and Tucker, A. G. A lead-rubber shear damper, Bull. New Zealand Nat. Soci. Earthquake Engng.. 1977. 10. 151 - 153

9 Chert, D. and Clough, R. W. Earthquake response of structures with friction sliding motion, Earthquake Engineering Research Center, University of California, Berkeley, CA. 1981

10 Mostaghel, N. and Tanbakuchi, J. Response of sliding structures to earthquake support motion, Earthquake Engng. Struct. Dyn., 1983, 11, 729 - 748

I I Kelly, J. M. and Beucke, K. E. A friction damped base isolation system with fail-safe characteristics, Earthquake Engng. Struct. Dyn., 1983, 11, 3 3 - 5 6

12 Ahmadi, G. and Mostaghel, N. On Dynamics of a structure with a frictional foundation. J. De Mecanique Theorique et Appliquee, 1984, 3, 271-285

13 Younis, C. J. and Tadjbakhsh, I. G. Response of sliding rigid structure to base excitation, ASCE, J. Engng. Mech., 1984, 110, 417 -432

14 Ahmadi, G. Stochastic earthquake response of structures on sliding foundation. Int. J. Engng. Sci., 1983, 121, 93-102

15 Constantinou, M. C. and Tadjbakhsh, I. G. Response of a sliding



structure to filtered random excitation, J. Structural Mech., 1984, 12, 401-418

16 Su, L., Orabi, 1. I. and Ahmadi, G. Nonstationary earthquake response of a sliding rigid structure, Int. J. Engng. Sci., 1988, 26, 1013-1026

17 Li, L. Base isolation measure for aseismic building in China, Proc. 8WCEE, San Francisco, July 21-28, Vol. VI, 791-798, 1984

18 Li, L. Advances in base isolation in China, Presented at the 3rd International Conference on Soil Dynamics and Earthquake Engineering, June 22-24, Princeton University, Princeton, NJ, 1987.

19 Mostaghel, N. Resilent-friction base isolator, Report No. UTEC 84-097, The University of Utah, 1984

20 Mostaghel, N., Hejazi, M. and Khodaverdian, M. Response of structures supported on resilient-friction base isolator, Proceed. Third U.S. National Conference on Earthquake Engineering, Charleston, South Carolina, August 1986, 1993-2003

21 Mostaghel, N. and Khodaverdian, M. Dynamics of resilient- friction base isolator (R-FBI), Earthquake Engng. Struct. Dyn. 1987, 15, 379-390

22 Mostaghel, N. and Khodaverdian, M. Seismic response of structures supported on R-FBI system, Report No. UTEC 87-035, The University of Utah, September 1987

23 Ikonomou, A. S. Alexisismon seismic isolation levels for transla- tional and rotational seismic input, Proc. 8WCEE, San Francisco, July 21-28, 1984, Vol. V, 975-982

24 Guerand, R., Noei-Leroux, J.-P., Livolant, M. and Michalopoulos, A. P. Seismic isolation using sliding-elastomer bearing pads, Nuclear Engng. and Design, 1985, 84, 363-377

25 Su, L., Ahmadi, G. and Tadjbakhsh, I. G. A comparative study of base isolation systems, ASCE J. Engng. Mech. 1989, 115, 1976- 1992

26 Tentative seismic isolation design requirements, Base Isolation Subcommittee of Seismology Committee. Structural Engineers Association of Northern California (SEAONC), September 1986

27 Mayes. R. L., et al., Design guidelines for base-isolated buildings with energy dissipators, Earthquake Spectra, November 1984, 1, 4111-4174

28 Kariotis, J. C. and Ewing R. D. Tentative guidelines for the design of buildings with base isolators, ASTM, PVP-V.127, Seismic Engineering, Recent Advances in Design, Analysis, Testing, and Qualification Methods, 1987, 501-510

29 Mostagbel, N., Kelly, J. M. and Mortazavi, A. R. Design procedure for R-FBI Bearings, Report No. UEC 88-031, The Univer- sity of Utah, March 1988

30 Mostagbel, N., Lo, S. H. and Buman, E. Design of R-FBI bearings for seismic isolation, PVP-Vol. 147 Seismic, Shock, and Vibration Isolation - 1988, edited by H. Chung and N. Mostaghel, June 1988

31 Hadjian, A. H. and Tseng, W. S. A comparative evaluation of passive seismic isolation schemes, ATC-17, Seminar on Base Isola- tion and Passive Energy Dissipation, California, March, 1986

32 Su, L., Ahmadi, G. and Tadjbakhsh, I. G. A comparative study of performances of various base isolation systems, Part I: Shear beam structures, Earthquake Engng. Struct. Dyn., 1989, 18, 11-32

33 Fan, F.-G., Ahmadi, G. and Tadjbakhsh, I. G. Multi-story base- isolated buildings under a harmonic ground motion - Part I: A comparison of performances of various systems, Nuclear Engng. Design. 1990, 123, 1-16

34 Fan, F.-G., Ahmadi, G. and Tadjbakhsh, I. G. Multi-story base- isolated buildings under a harmonic ground motion - Part II: sensitivity analysis, Nuclear Engng. Design. 1990, 123, 17-26

35 Derham, C. J. Nonlinear natural rubber bearings for seismic isolation, ATC-17, Seminar on Base Isolation and Passive Energy Dissipation, California, March. 1986

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38 International Mathematics and Statistics Library, IMSL Inc., 1987 39 Fan. F.-G. Base isolation of a Multi-Story Structure - A com-

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characteristics of teflon-steel interfaces under dynamic conditions, Earthquake Engng. Struct. Dyn., 1987, 15, 751-759

A P P E N D I X A

In this append ix , the pa rame te r s o f the s t ructural moda l used in this s tudy are desc r ibed . F u r t h e r m o r e , the cor- r e spond ing moda l ma t r ix and moda l equat ions are a lso presen ted . As men t ioned be fo re , the s t ructura l mode l cons ide red is a th ree - f loor bu i ld ing w i t h ident ical mass for each f loor , m, and ident ical co lumn st i ffness , k. The equat ion o f mot ion o f the bu i ld ing is g iven by equat ion (2) with the mass , da mp ing and st iffness mat r ices g iven as, i1001 [m] = m 0 1 0 ,

0 0 1

2 - 1 0 1 [cl = c - 1 2 - 1 ,

0 - 1 1

i 2 - 1 0 1 [k] = k - 1 2 - 1 (A1)

0 - 1 1

where c is the da mp ing coeff ic ient . The co r r e spond ing natura l f requencies , o~i, and the

moda l mat r ix , [ ¢ ] , are g iven by ,

~01 J 0 . 1 9 8 0 6 k J k = - - , o~ 2 = 1 . 5 5 4 9 6 - - , m m

/

o~ 3 = , , / 3 . 24698 --k (A2) m

and

[ ~ ] =

0.59100

- 0 . 7 3 6 9 7

0.32798

0.73697 0.32798

0.32798 0.59100 / -0.59100 0.73697 J

(A3)

Using the transformation {x} = [q~] Iql , the equations of motion in terms of modal coordinates qi may be restated as

k c ii3 + 3 .24698 //3 + 3 .24698 - - - - q3 = - - ~ . - ~ - ~ - v ¢ + ~ g , - ( ~ I R ? N I ( ¢ ~

m m

(A4)

ii2 + 1.55496 c //2 + 1 .55496 k - - - - q2 = - 0 . 4 7 3 9 5 ( g + . ~ ) m m

(A5)

iil + 0 . 1 9 8 0 6 c //I + 0 . 1 9 8 0 6 k - - - - ql = - 1.65595(g +Xg) m m

(A6)

where the subscr ip ts 1, 2, and 3 indicate the modes o f v ibra t ion .


Performance analysis of aseismic base isolation systems for a multi-story building

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