Earthquake Engineering & Structural Dynamics Volume 19 Issue 1 1990 [Doi 10.1002%2Feqe.4290190104] Lin Su; Goodarz Ahmadi; Iradj G. Tadjbakhsh -- A Comparative Study of Performances

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, VOL. 19.21-33 (1990)

A COMPARATIVE STUDY OF PERFORMANCES OF VARIOUS BASE ISOLATION SYSTEMS, PART 11: SENSITIVITY

ANALYSIS

LIN SU A N D GOODARZ AHMADI Department of Mechanical and Industrial Engineering, Clarkson University, Potsdam. N Y 13676, U.S.A.

A N D

IRADJ G. TADJBAKHSH Department of Civil Engineering, Rensselaer Polytechnic Institute, Troy. N Y 12181, U.S.A.

SUMMARY A series of numerical experiments on the performance of different base isolation systems for a non-uniform shear beam structure is carried out. Several base isolation systems are considered and the peak relative displacements and the maximum absolute accelerations of the base-isolated structure and its base raft under a variety of conditions are evaluated. Several sensitivity analyses for variations in properties of the base isolator and the structure are carried out. A number of different earthquake excitations are also used in the study. The results show that performances of the base isolation systems are not sensitive to small variations in their natural period, damping or friction coefficient. The presence of a frictional element in the isolators reduces their sensitivity to severe variations in frequency content and amplitude of the ground acceleration. In particular, the resilient-friction base isolators with or without sliding upper plate perform reasonably well under a variety of loading conditions. The rubber bearing type, however, leads to the lowest peak transmitted accelerations for moderate intensity earthquakes.

INTRODUCTION

Using base isolation systems for aseismic design of relatively stiff structures has attracted considerable interest in the recent years. The concept is to isolate the structure from ground during earthquake strong motions. Excellent reviews on the subject were provided by Kelly.'*2 The base isolation system which has found wide applications is the laminated rubber bearing (LRB).' - ' The four-storey Foothill Communities Law and Justice Building in San Bernardino County, California, which is the largest base-isolated building in the world, uses laminated rubber bearings. This system was also used in a number of buildings in Europe, Japan and New Zealand. A LRB with a lead core (lead-rubber or NZ) was used extensively in New Zealand.2 - 4 The pure-friction (P-F) or sliding-joint the resilient-friction base isolator (R-FBIX7 the French system (EDF)* and the Alexisismon9 system are among the leading base isolation systems which are considered to have considerable potential for wide applications. A new base isolator design was proposed in Reference10 which combines the desirable features of the EDF and the R-FBI systems. This isolator was referred to as the sliding resilient-friction (SR-F) base isolation system.

In spite of numerous studies on base isolation systems, the advantages and disadvantages of various systems are not fully understood." In Part I of this work" (from here on referred to as Part I), a number of comparative studies on performances of various base isolation devices for non-uniform shear beam structures were carried out. Several base isolation systems, including the pure-friction, the laminated rubber bearing with and without lead core, the EDF system and the resilient-friction base isolator with and without sliding upper plate were considered. The method of expansion by normal modes for obtaining the response of the elastic shear beam structure was used, and the effectiveness of different base isolation devices under a variety of conditions was studied.

OO98-8847/90/01OO2 1-1 3$06.50 0 1990 by John Wiley & Sons, Ltd.

Received 15 July 1988 Revised 6 April 1989

22 L. SU, G. AHMADI AND I. G. TADJBAKHSH

In this Part I1 of the study, sensitivities of peak responses to variations in the properties of the base isolator and the structure are analysed. The accelerograms of El Centro 1940, Pacoima Dam 1971, Taft 1952, Olympia 1965 and Mexico City 1985 earthquakes are used. The peak responses of the base-isolated shear beam structure are evaluated and sensitivities to variations in natural period of the isolator, damping ratio of the structure and the isolator, friction coefficient of the isolator, mass ratio, and shape of the structure are studied. The results show that properly designed base isolation systems are highly effective in attenuating the acceleration transmitted to the superstructure and in reducing the generated column stresses. Furthermore, the friction type isolation systems are less sensitive to unexpected variations in frequency content and amplitude of the ground excitation than the non-friction types. The rubber bearing types, however, transmit the lowest peak accelerations for moderate intensity earthquakes. The results also show that the base isolation systems are generally quite reliable devices and their performances are not sensitive to small variations in their natural period, damping or friction coefficient. It is also shown that the velocity-dependence of the friction coefficient has no noticeable effects on peak responses for the R-FBI system, and using a constant friction coefficient is a reasonable approximation.

TECHNIQUE OF ANALYSIS

The equations of motion of a non-uniform shear beam structure with different base isolation systems subject to an earthquake excitation were described at length in Part I" and hence need not be repeated here. As noted in Part I, consideration of the first ten modes of vibration of the structure is sufficient for an accurate response analysis. The computer program developed in Part I for numerical integration of equations of motion is modified and is used for the present sensitivity analyses. For several major earthquake excitations, variations of the peak responses of the base-isolated shear beam structure for a range of values of structural and isolator parameters are evaluated and discussed.

As in Part I, it is assumed that the cross sectional area of the shear beam structure varies exponentially as A = A, exp { - 2ax}, where x is the dimensionless height and a is the spatial non-uniformity coefficient. For sensitivity analysis, one parameter is varied while the other parameters are kept fixed. The fundamental natural period for the structure is taken to be Tl. =- 0.4 sec, and the modal damping coefficients of [. = 0.02 and u = 0.1 are usually used. Unless stated otherwise, the recommended values of parameters for various base isolators as summarized in Table I are employed. The corrected accelerograms of the NOOW component of El Centro 1940, the S16E component of Pacoima Dam 1971 and three other major earthquakes are used as seismic excitations. The peak relative displacements and the maximum absolute accelerations of the shear beam structure at its base raft and its roof are evaluated and discussed. Sensitivities of the peak responses of the structure to variations in different parameters of the base isolator and the structure are studied in detail.

COMPARATIVE STUDIES FOR DIFFERENT EARTHQUAKES

As indicated in Part I, the intensity of an earthquake can affect strongly the performances of different base isolation systems. In this section, five earthquake records, namely, El Centro 1940 (NOOW, 0*348g), Pacoima

Table I. Values of parameters used for various base isolators

Natural Damping Friction Friction Mass period coefficient coefficient coefficient ratio

Isolator To(=) To Pl P R ~ ~

- - - 0 1 0.75 P-F R-FBI 4.0 010 0.04 - 0.7 5 LRB 2.0 0.10 - - 075 EDF 1 .o 0.10 - 0.2 0.75 NZ 2.0 0.10 - - 0.7 5 S-RF 4.0 010 0.04 0.1 075

A COMPARISON OF BASE ISOLATION SYSTEMS 23

Dam 1971 (S16E, 1.17g), Taft 1952 (S69E, 0*178g), Olympia 1965 (S86W, 0.198g) and Mexico City 1985 (N90W, 0*17g), are used as ground excitations. These earthquake records have a variety of peak ground accelerations ranging from 0.179 to 1.179 and cover various forms of frequency content. In particular the Mexico City 1985 earthquake had considerable energy at low frequencies of about 0.5 Hz. Maximum relative displacements and peak absolute accelerations of the structure at its base raft and its roof for various base isolation systems and different earthquake excitations are evaluated and the results are summarized in Tables 11-V. The recommended values of parameters for different base isolation systems as listed in Table I are used in these analyses. The corresponding peak responses for the fixed-base structure are also reproduced in these tables for comparison.

Maximum deflections at the roof of the structure for various base isolators are listed in Table 11. This table shows that, for all earthquakes with the exception of the Mexico City 1985 earthquake, the peak deflections of the base-isolated structures are generally much lower than that of the fixed-base one. It is also observed that the peak deflections for the R-FBI system and the SR-F base isolator coincide except for the Pacoima Dam and Mexico City earthquakes. This is because, for low or moderate intensity excitations, no sliding in the upper friction plate of the SR-F isolator occurs and, hence, it behaves exactly as a R-FBI unit. However, for high intensity earthquakes such as the Pacoima Dam earthquake or for earthquakes which have considerable energy at low frequencies such as the Mexico City earthquake, sliding occurs and the peak responses of the R- FBI and the SR-F base isolators are somewhat different. Table I1 also shows that the rubber bearing type isolators (the LRB and the NZ systems) are more effective in reducing the peak deflection of the shear beam structure for moderate intensity earthquakes. The friction type isolators, on the other hand, lead to lower peak deflections when compared to the rubber bearing type isolators for high intensity earthquakes.

The results for the Mexico City 1985 earthquake show that the N Z and the LRB systems generate peak deflections which are two to three times that of the fixed-base structure, while the SR-F, the R-FBI and the

Table 11. Peak deflection (cm)

Earthquake El Centro Pacoima Dam Taft Olympia Mexico City 1940 1971 1952 1965 1985

Isolator (NOOW) (S16E) (S69E) (S86W) (N90W)

Fixed-base 4.14 20.23 2.45 1.87 1.26 P-F 1.40 2.78 1.38 1.33 1.17 R-FBI 0.84 1.35 0.68 0.70 0.86 LRB 0.80 2.28 037 0.38 3.28 EDF 1.30 1.78 0.79 0.68 1.06 NS 0.74 3.29 0.45 0.37 2.46 SR-F 0.84 1.29 068 0.70 0.77

Table 111. Peak acceleration (9)

Earthquake El Centro 1940

Isolator (NOOW)

Fixed- base 1.330 P-F 0.703 R-FBI 0.4 19 LRB 0.162 EDF 0.32 1 NZ 0.170 SR-F 0.4 19

Pacoima Dam 1971

(S16E)

Taft 1952

(S69E)

0 1 y m p i a 1965

(S86W)

Mexico City 1985

(N90W)

6.07 1 1.381 0585 0.488 0.532 0.718 0.561

0.696 0604 0.331 0.08 1 0.180 0.107 0.33 1

0-642 0.586 0.373 0088 0.172 0.085 0.373

0.276 0.345 0.372 0.665 0.334 0.503 0.378

24 L. SU. G . AHMADI A N D I. G. TADJBAKHSH

Table IV. Peak base raft displacement (cm)

Earthquake El Centro Pacoima Dam Taft Olympia Mexico City 1940 1971 1952 1965 1985

Isolator (NWW) (S16E) (S69E) (S86W) (N90W)

P-F 4.73 4027 2.52 1.92 14.68 R-FBI 5.57 40.57 2.24 2.35 33.84 LRB 14.96 41.12 6.10 6.84 63.48 EDF 7.45 3064 3.30 2.70 6.18 NZ 8-16 4040 4.09 3.19 32.80 SR-F 5.57 43.23 2.23 2.35 31.33

Table V. Peak base raft acceleration (9)

Earthquake

Isolator

El Centro 1940

(NOOW)

Pacoima Dam 1971

(S16E)

Taft 1952

(S69E)

Olympia 1965

(S86W)

Fixed-base P-F R-FBI LRB EDF NZ SR-F

0.348 0.368 0-232 0.153 0270 0.131 0.232

1.170 0869 0.413 0.436 0.402 0.590 0.393

0179 0.365 0184 0.062 0128 0.090 0.184

0.198 0.359 0.165 0077 0.117 0.070 0.165

Mexico City 1985

(N90W)

0171 0.255 0.181 0-636 0.263 0463 0.181

EDF systems still provide a certain amount of protection. For the earthquake excitations considered, Table I1 shows that the peak deflection for the fixed-base structure varies from 1.26 to 20.23 cm. Peak deflections for the rubber bearing type isolators vary from 0.37 to 3.29 cm while those of the friction type base isolators remain between 0.68 and 2.78 cm. In particular, for the R-FBI and the SR-F systems, the range of variation is only between 0.68 and 1.35 cm. Based on these results it may be concluded that the peak deflections of friction type base isolators are less sensitive to substantial variations in the frequency content and the intensity of earthquake excitations. Since the stresses generated in the shear beam structure are directly proportional to the deflection, Table I1 implies that for friction type base isolation systems, peak stresses in the structure do not vary significantly even when the intensity of ground acceleration is increased to a high level or when the ground excitation contains severe frequency distribution.

Peak absolute accelerations at the roof of the structure for different base isolation systems are listed in Table 111. It is observed that peak accelerations for the base-isolated structure are reduced by a factor of two to eight when compared with the fixed-base one for the El Centro earthquake. For the Pacoima Dam earthquake, the reduction is about eight to twelve times except for the P-F isolator. However, owing to the severe low frequency energy content of Mexico City earthquake, all base isolation systems amplify the peak acceleration by a factor of 1.2 to 2.4. Similar to peak deflection responses, peak acceleration responses for friction type isolators do not vary to a significant extent with severe variations in the frequency content and the intensity of the earthquake excitation. Table I11 also shows that the LRB leads to the least amount of peak accelerations for all earthquakes except the Mexico City 1985 earthquake.

Table IV compares the peak relative displacements at the base raft of the structure produced by different base isolation systems. It appears that the peak relative displacement of the LRB system is higher than those of other base isolation systems for all earthquakes considered. The exception is the Pacoima Dam earthquake for which the peak base displacements of all isolation systems become comparable with the SR-F system, leading to a somewhat larger peak base displacement. Table IV also shows that for the El Centro, Taft and

25 A COMPARISON OF BASE ISOLATION SYSTEMS

Olympia earthquakes, the P-F, the R-FBI and the SR-F systems lead to the lowest peak base displacement. For the Mexico City and Pacoima Dam earthquakes, the EDF system produces the least amount of peak base displacement.

Peak absolute accelerations at the base raft of the structure are listed in Table V. It is observed that the peak accelerations are lower than the peak ground accelerations for all the earthquakes with the exception of the Mexico City earthquake and for all base isolation systems with the exception of the P-F one. The P-F system transmits the largest peak acceleration to the base of the structure and the LRB system generally transmits the lowest one. For the Pacoima Dam earthquake, the lowest peak acceleration is transmitted by the SR-F base isolator. All isolators, except for the P-F one, transmit only about one half to two-third of the peak ground acceleration to the base raft of the structure for the El Centro and Pacoima Dam earthquakes.

Comparison of Tables 111 and V shows that the base-isolated structure, generally, behaves as a rigid body and does not amplify the transmitted acceleration to an appreciable extent. In contrast, the fixed-base structure amplifies the ground acceleration by a factor of 3 to 6.

Based on the results presented in Table 11-V, i t may be concluded that, under moderate to high intensity earthquake excitations, all base isolation systems considered here effectively reduce the structural peak responses. The only exception is the Mexico City earthquake with considerable energy at low frequencies for which the isolators do not function properly. These tables also show that friction type base isolation systems are, generally, less sensitive to severe variations in the frequency content and the intensity of earthquake excitations.

VARIATIONS IN NATURAL PERIOD OF ISOLATORS

One important property of most base isolation systems is to shift the natural period of the structure to higher values and away from the energy containing range of earthquake ground excitations. Therefore, the parameters of different base isolation systems must be selected carefully to achieve this goal. In this section, the sensitivity of peak responses to variations in natural period of the isolator, To, is analysed. The accelerogram of the Pacoima Dam earthquake is used as the ground excitation. A shear beam structure with a fundamental natural period of TI =04 sec and modal damping ratio of 002 is used throughout this analysis. The variations of peak responses of the structure with To for various isolators are shown in Figure 1.

Figure 1 shows the peak responses of the structure with various base isolation systems subject to the S16E component of the Pacoima Dam 1971 earthquake. Maximum deflections at the roof of the structure are shown in Figure l(a). For this high intensity earthquake, sliding on the upper friction plates of the SR-F and the EDF systems occurs and their responses are quite different from those of the R-FBI and the LRB systems, respectively. Figure l(a) shows that, for To < 3.0 sec, the peak structural deflections for the LRB, the NZ and the R-FBI systems decrease sharply with increasing To. It is also observed that the peak deflections for the SR-F and the EDF base isolators are much lower than those of the R-FBI and the LRB systems for To < 3.0 sec, respectively. From Figure l(a), it is noticed that the peak structural deflections for the SR-F and the EDF systems do not vary appreciably for the entire range of To considered.

For different base isolation systems, variations of the peak absolute accelerations at the roof of the structure are shown in Figure l(b). It is observed that, for the SR-F system, the peak acceleration remains at the same level for the entire range of To considered. On the other hand, those for the NZ, the LRB and the EDF systems decrease as To increases. The peak acceleration for the R-FBI system varies slightly for To > 2.0 sec. Figure l(b) also shows that the EDF system leads to the lowest peak acceleration among the base isolators considered.

Figure l(c) displays peak relative base raft displacements for different base isolation systems. It is observed that the peak base displacements for the LRB, the NZ and the R-FBI systems increase rather sharply with To for To < 2.0 sec. The displacement response spectrum for the SR-F base isolator shows the opposite trend and decreases in this range. For To > 2.0 sec, variations of peak base raft displacements with To are rather mild. Figure l(c) also shows that the R-FBI system generally leads to the lowest peak base raft displacement.

Peak absolute accelerations transmitted to the base raft of the structure for various base isolation systems are compared in Figure l(d). It is observed that, for the SR-F and the EDF base isolators, peak transmitted

26 L. SU. G. AHMADI A N D I. G. TADJBAKHSH

h

W i l 3 30 PACOIMA DAM

_..- ....... ..

....... '\ EDP R-FBI

( C l . I

20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 0.5 1.5 2.5 5.5 4.5

To (sec)

1.0 - '..\'. PACOIMA DAM h

Y M . ..,'\ clo.ll - \.'%\ w . u u 4 0.6 - w . v) 2 0 . 4 -

3 0 . 2 - EDF

R-FBI \'. .. .I! .......

-.,NZ - - - _ _

(4 0.0 ~ . . . . . . . . . . . . . . . . . . . . 'rrm

0.5 1.5 2.5 5.5 4 To (sec)

Figure 1. Variations of the peak responses of the structure with the natural period of isolator for Pacoima Dam 1971 earthquake

accelerations vary slightly with To. This figure shows that the peak accelerations for the NZ and the LRB systems decrease as To increases. A similar trend is observed for the R-FBI system for To -= 2.3 sec. For To > 2.5 sec, the peak transmitted acceleration for the R-FBI system increases to a maximum then decreases for To > 3.0 sec. It is also noticed that the EDF system leads to the lowest peak acceleration transmitted to the base raft of the structure.

Figure 1 shows that the deflection and acceleration response spectra usually decrease as the natural periods of base isolators increase, while the peak base raft displacements generally increase with To. Furthermore, the peak responses for various base isolation systems are insensitive to small variations of To in the neighbourhood of their recommended natural periods. However, substantial variations in natural periods of base isolation systems could significantly affect the peak responses of the base-isolated structure.

VARIATIONS IN DAMPING O F ISOLATORS

For a range of damping ratio of various base isolators, the peak responses of the base-isolated shear beam structure subject to the Pacoima Dam earthquake are evaluated and the results are shown in Figure 2. Maximum deflections at the roof of the structure versus damping ratio for various base isolation systems are displayed in Figure 2(a). It is observed that the peak deflections decrease slightly with an increase in c0 for the NZ, the LRB and the EDF systems; however, the peak deflections of the R-FBI and the SR-F systems remain constant and are the lowest among the isolators considered.

In Figure 2(b), variations of the peak absolute accelerations at the roof of the structure with T o are shown. It is observed that the peak accelerations for various base isolation systems remain almost at the same level of about 0.59 to 069. The peak acceleration for the NZ system is somewhat higher at small c0 and decreases with an increase in damping ratio.

Peak relative displacements at the base raft of the structure produced by different base isolation systems are shown in Figure 2(c). It is noticed that the peak base displacements decrease with an increase in damping ratio of the isolator for the rubber bearing type base isolation systems. For the friction type isolation systems, peak

A COMPARISON OF BASE ISOLATION SYSTEMS

( C ) 25 . , , , . , , , , , , , , ~,

27

(d) 0 . 0 , I I I , , 3 . 7 1 I I . . I

SR-F'

E (4 o . o , . . , , 1 1 , , , , , , , , ,

0.04 0.08 0.12 0.10 0.20 ISOLATOR DAMPING -

2 4 5

w m y 35 i41 3 30

-1.0

PACOIU DAM M v

I ~ , o . o ' . . 1 I 1 I I I I I I . I 1 0.64 0.68 0.12 0.16 0.40

ISOLATOR DAMPING

- 2 0 . 6 - I-1 w . V V C0.4 - W v l . C m

PACOIMA DAM - - - - _ _ _ _ _

Figure 2. Variations of the peak responses of the structure with the damping ratio of isolator for Pacoima Dam 1 9 7 1 earthquake

displacements remain about the same. Furthermore, the EDF system leads to the lowest base displacement of about 30 cm.

Figure 2(d) displays peak absolute accelerations transmitted to the base raft of the structure. Similar to the acceleration response spectra at the roof of the structure, the damping ratio of the isolator does not affect appreciably the peak transmitted acceleration, which remains around 0.49. For the NZ system, the base acceleration is somewhat higher (about 0.69) and decreases slightly with i0.

Based on the results presented in Figure 2, it may be concluded that the peak responses are not sensitive to a small variation in damping ratio of the base isolator. The increase in damping ratio of the isolator will somewhat reduce the peak responses for the rubber bearing type isolators. On the other hand, for the friction type base isolation systems a substantial increase in to only slightly reduces the peak base raft displacement while the peak deflection and the maximum acceleration responses remain the same.

VARIATIONS IN FRICTION COEFFICIENTS

For the friction type base isolation systems, the friction coefficient is indeed an important parameter. The sensitivity of peak responses to variations in friction coefficient is studied in this section. The accelerogram of the El Centro earthquake is used as the ground excitation. The peak structural responses for a range of values of friction coefficient are evaluated and discussed. In most earlier studies a constant coefficient of friction, in accordance with Coulumb's law, was used. However, recent experimental data 12* l 3 suggest that the friction coefficient is not a constant and varies with velocity, normal pressure and other parameters. In the subsequent section, the effects of velocity-dependence of friction coefficients on the performance of frictional base isolation systems will be studied.

Velocity-dependent friction In this section, a shear beam structure with a R-FBI system subject to the El Centro 1940 earthquake is

considered, and the data for frictional characteristics of teflon-steel interfaces as obtained by Constantinou

28 L. SU, G. AHMADI A N D I. G. TADJBAKHSH

et al .I3 are used. The following two expressions for the velocity-dependence of the friction coefficient given as

p = 002 + c , (u/n) p = c2(u/n) + ~ ~ ( u / n ) ~ + c4(u/nI3

( 1 )

(2)

are fitted to the data of Constantinou et al. as shown in Figure 3. Here, u is the slip velocity, n is the number of friction plates used in the R-FBI system (n = 8 is used in the analysis) and the values of the cs are given by

c1 = 1.0762 x sec/cm, c2 = 2.5086 x sec/cm - c 3 = -3.1316 x lo- sec2/cm2, c4=2.2545 x lo- sec3/cm3 (3)

Equation (1) assumes a linear relationship between p and the slip velocity with a static friction coefficient of 0.02. Constantinou et a l l 3 have also reported that continuous non-stick sliding occurred in their experiments, which implies that p=O for u = O . Equation (2) satisfies this condition and leads to a zero static friction coefficient .

For p given by equations (1) and (2), as well as a constant value of 002, the peak responses of the structure versus its natural period T , are shown in Figure 4. It is observed that the peak responses for p given by equation (1) are almost the same as those for a constant friction coefficient. That is, the velocity-dependence of the friction coefficient as given by equation ( 1 ) does not affect the peak responses. Figure 4 also shows that peak responses obtained by using equation (2) differ significantly from those obtained for a constant p. The peak deflection and the peak acceleration are lower by a factor of 2 to 4 and the peak base displacement is higher by about 10 to 30 per cent.

From the results presented in Figure 4, it may be concluded that the response spectra of the structure with the R-FBI system are not sensitive to the velocity-dependence of p for a non-zero static friction coefficient. However, should it be proved that continuous non-stick sliding with zero static friction coefficient occurs for certain interfaces, then the velocity-dependence of p can significantly affect the peak responses of the friction type base isolators. The effects, in this case, are generally favourable and result in significant reductions in the peak deflection and acceleration of the structure. At the present time, however, the available meager data are inconclusive and it is more acceptable to consider a non-zero friction coefficient at u = 0. That is, equation (l), perhaps more realistically, describes the velocity-dependence of p compared to equation (2). Thus, the results imply that the velocity-dependence of the friction coefficient does not affect significantly the peak responses of the friction type base isolators and using a constant friction coefficient is a reasonable approximation.

Sensit iuit y In this section, the velocity-dependence of the friction coefficient is neglected and sensitivities of the peak

responses of various friction type base isolation systems to variation in p are studied. A shear beam structure with a natural period of 0.4 sec is considered and the NOOW component of the El Centro 1940 earthquake is used as the base excitation. Two sets of results for the SR-F system are shown in this figure in order to display

0 10 20 30 40 50 60 VELOCITY (cm/sec)

Figure 3. Velocity-dependence of frication coefficient

A COMPARISON OF BASE ISOLATION SYSTEMS

. v

4 C L -

f i z .

29

EL CENTRO

................... ......................

p=0.02 ,,: ',

....... E4.(2) _.

-0.4

3 1 EL CENTRO

r 0.2 r=O.oz __/- ...<

_.a- ................. E'4.W .........

(bl 0.0 A , L , * , . , ,

0.0 0.2 0.4 0.0 0.8 TI (sec)

^M I ELCEhTRO I v

u go.z 4 1 4 0.1 m ...............

/\ E4.W

(4 0.0 1 , I , 1 , 1

0.0 0.2 0.4 0.0 0.h 1.0 T1 (sec)

Figure 4. Variations of the peak responses of the structure with its natural period for R-FBI systems with velocity-dependent friction coefficient

the effects of variations in friction coefficient of the body friction plates, pl, and the upper friction plate, p. In the following discussion, SR-F1 and SR-F2 denote the SR-F system with p=O.l and varying pl, and with pl = 0.04 and varying p, respectively.

Figure 5(a) shows the maximum deflections at the roof of the structure versus the friction coefficient for different base isolators. It is observed that the increase in friction coefficient of the isolator, generally, leads to an increase of peak deflections. The exception is the SR-F system for which the peak deflection remains constant for certain ranges of p and pl . For the P-F and the R-FBI systems, the peak deflections are almost the same and increase rapidly with an increase in friction coefficient. For p < 0.06, the EDF system leads to the lowest deflection among the friction type base isolators considered. For the SR-F1 system (with constant p=O.l), the peak deflection is identical to that of the R-FBI system for pl < p and remains a constant for pl >pL. This is because, when p1 is greater than p, sliding occurs almost exclusively on the upper friction plate and the SR-F1 system behaves essentially as a P-F system with p=O*l. Likewise, p > p l , the peak deflection response for the SR-F2 system (with constant pl =0.04) remains a constant, and the SR-F2 system behaves essentially as a R-FBI unit. It is also observed from this figure that the SR-F2 system leads to the lowest peak deflection of only about 0.8 cm.

Peak absolute accelerations at the roof of the structure are shown in Figure 5(b). It is observed, similar to the peak deflection responses, that peak accelerations generally increase as the friction coefficient increases. Furthermore, the EDF system provides the lowest peak acceleration response for the entire range of p considered. This figure shows that, for p>O*O6, the EDF and the SR-F2 systems generate constant peak accelerations of about 03s and 049, respectively. Figure 5(b) shows that the peak acceleration responses for the R-FBI and the P-F system are almost the same. The peak accelerations for the SR-F base isolators become similar to the R-FBI and the P-F systems for p>pl and pl >p, respectively.

Figure 5(c) compares the peak relative displacements at the base raft of the structure. This figure shows that the peak base displacements generally decrease with an increase in friction coefficient. Furthermore, the EDF system leads to the highest base displacement among the isolators studied here. When friction coefficients are less than 0.04, all isolators lead to relatively high base displacements; furthermore, peak displacements

30 L. SU, G. AHMADI AND I. G. TADJBAKHSH

-1.0 , I h E L C E N T R O /

-2.0 ,/-

2 1.0 P

(b) 0.0 I I I I 1 1 1 . I , , 1 1 I , , . , ,

(4 0.0 1 1 I I , r 1 1 1 , I I I I , 8 1 1 I

0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20 FRICTION COEFF FRICTION COEFF

W v) 4

EL CENTRO I 1 1 a \ u, SR-FZ, SR-PI, I

(C) 0 . . . . , . . . . , . , . . , ~ . . . 0.00 0.05 0.10 0.15 0.20

FRICTION COEFF

0.6 , I h

a

(4 0.0 . . , I , , , . , , . , , , , , , , ,

0.00 0.05 0.10 0.1s 0.20 FRICTION COEFF

Figure 5. Variations of the peak responses of the structure with the friction coefficient of isolator for El Centro 1940 earthquake

become sensitive to variations in friction coefficient. When p (or pl) is greater than 0.05, all isolators, with the exception of the EDF system, limit the base displacement to under 6.0 cm and among them the R-FBI system leads to the lowest peak base displacement.

Figure 5(d) displays the peak transmitted accelerations to the base raft of the structure. It is observed that the peak base acceleration increases with friction coefficient. This figure also shows that the peak base accelerations for the SR-F2 and the EDF systems are the lowest (about 0.29). The other features of the variations of the peak base accelerations are quite similar to those of the peak accelerations at the roof described earlier.

The results presented in Figure 5 show that the peak accelerations and the peak deflections of frictional base isolators increase with the friction coefficient while their peak base raft displacements decrease. It is also observed that the peak responses are not sensitive to a small variation in the friction coefficient.

VARIATION IN DAMPING O F STRUCTURE

The accelerograms of the El Centro and Pacoima Dam earthquakes are used as ground excitations to analyse the sensitivity of the peak responses to variations in structural damping. The resulting peak responses for these earthquakes show the same trend; therefore, only the results for the El Centro earthquake are presented in Figure 6 and discussed here. Peak responses for the fixed-base structure are also plotted in Figure 6 for reference. This figure shows that the peak deflections and the maximum base raft displacements of the base- isolated structure remain constant for various base isolation systems. Peak accelerations, however, decrease with an increase in structural damping for the friction type base isolation systems. The peak deflection and acceleration of the fixed-base structure, however, decrease considerably with an increase in structural damping. These results further show that the base-isolated structure behaves as a rigid body and the peak responses do not vary substantially with structural damping.

A COMPARISON OF BASE ISOLATION SYSTEMS

(dl

31

. , 0 . 0 ; . I I , 1 I I I 1 I

0.00 0.02 0.04 0.06 0.08 0.10 STRUCTURAL DAMPING

h

w 3 \ EL CENTRO M1.S

. . 0 . 0.h 0.62 0.64 0.06 0.08 0.10

STRUCTURAL DAMPING

0

0.5 - Y M EL CENTRO

(4 0 . 0 , r , . , 1 0.00 0.08 0.04 0.61 0.68 0.10

STRUCTURAL DAMPING

Figure 6. Variations of the peak responses of the structure with its damping ratio for El Centro 1940 earthquake

-6.0 8 EL CENTRO v F-8 .

. I

O ' I I I , 1 I I , ! I 0.b 0.2 0.4 0.6 0.8 1.0

SHAPE FACTOR

-2.0

2 ! E L C E N T R O

h

w M0.4

cl W

U g 0.3 W

m y 0.2

3 0.1

0

1 EL CENTRO 1

Figure 7. Variations of the peak responses of the structure with its shape non-uniformity factor for El Centro 1940 earthquake

VARIATION IN SHAPE OF STRUCTURE

The effects of variation in non-uniformity of the shear beam structure on peak responses are studied in this section. Parameter a identifies the non-uniformity of the shear beam structure (see Part I), and a zero value of

32 L. SU, G. AHMADI A N D 1. G. TADJBAKHSH

I' P-P / I

B I

Figure 8. Amplification of the peak responses along the structure for El Centro 1940 earthquake

a corresponds to a uniform one. Peak responses of the structure subject to the El Centro 1940 earthquake versus a for different base isolators are shown in Figure 7. It is observed that the peak deflection and the peak acceleration of the fixed-base structure increase as a increases, while those of the base-isolated structure with different base isolation systems are almost independent of the shape of the structure and/or increase slightly with a. Figures 7(c) and (d) show that the peak base displacements and the maximum base accelerations for various base isolation systems also remain constant or vary slightly with a.

AMPLIFICATION ALONG THE STRUCTURE

Figure 8 shows variations of the peak deflections and the peak absolute accelerations along the structure for the base-isolated and the fixed-base structures. It is observed that the peak deflections of the structure increase monotonically from the base to the roof and have the same shape as the first mode of vibration of a shear beam. Furthermore, the magnitudes of peak deflections for the base-isolated structure are much lower than that of the fixed-base one. Figure 8(b) shows that the peak accelerations for the base-isolated structure remain the same or vary slightly along the structure. The fixed-base structure, however, amplifies the base acceleration. These results further show that the base-isolated structures respond in their rigid body mode.

CONCLUSIONS

Results of several sensitivity analyses of the peak responses of a base-isolated non-uniform shear beam structure are presented. A number of base isolation systems are considered, and peak deflections, maximum absolute accelerations and peak base raft displacements and accelerations of the structure for several major earthquakes with various frequency contents and different intensities are evaluated and discussed. The results are compared with each other and with those of the fixed-base structure. The sensitivity of the peak responses to variations in parameters of the isolation system and the structure is analysed. Based on these results, the following conclusions may be drawn.

1. Properly designed base isolation systems are highly effective in attenuating the ground acceleration

2. The base-isolated structures generally respond in their rigid body modes. 3. The LRB, the NZ, the R-FBI and the SR-F base isolation systems lead to comparable peak structural

deflections, which are about five times lower than that of the fixed-base one. The peak accelerations are lowest for the LRB and the NZ base isolators, while the base raft displacements are lowest for the frictional systems.

4. For the Pacoima Dam earthquake, the R-FBI and the SR-F systems generate the lowest peak deflections. The peak accelerations at the roof of the structure are comparable for the friction type and the rubber bearing type systems and are about twelve times less than that of the fixed-base structure.

transmitted to the superstructure and in reducing the structural deflection.

A COMPARISON OF BASE ISOLATION SYSTEMS 33

5.

6.

7.

8.

9.

10.

1 I .

12.

The response of base-isolated structures is sensitive to severe variations in the frequency content of earthquakes. Thus, use of base isolation systems in regions which have the potential of generating an earthquake with considerable energy in low frequencies should be avoided. The presence of frictional elements in base isolators makes their performances less sensitive to changes in frequency content and intensity of earthquake ground excitations. The peak responses are, generally, insensitive to small variations in the natural period of various base isolators in the neighbourhood of their recommended values. Substantial changes in the natural period, however, significantly alter the performance of a base isolation system. The peak responses of the base-isolated structure are insensitive to variations in damping ratio of the isolator. The exception is the peak base acceleration for the LRB which reduces slightly with an increase in the damping. The response spectra of the structure with a R-FBI system are insensitive to the velocity-dependence of p for a non-zero static friction coefficient. Thus, using a constant friction coefficient for response analysis is a reasonable approximation. Small variations in the friction coefficient lead only to slight change in the response spectra for all frictional base isolators. Substantial variations in firction coefficient will, however, significantly affect the peak responses of the P-F and the R-FBI systems. The peak responses of the EDF and the SR-F systems appear to be insensitive even to significant changes in friction coefficient. The peak acceleration of the structure with a frictional base isolation system decreases slightly as structural damping increases; however, variations in the damping ratio have no noticeable effects on the peak deflection and the peak base displacement responses. The deflection of the structure is dominated by the first mode of vibration. The acceleration along the structure remains almost a constant for various base isolation systems. Peak responses for the base-isolated structure are insensitive to shape non-uniformity of the structure.

ACKNOWLEDGEMENT

Thanks is given to Dr N. Mostaghel for many helpful discussions. This work is supported by the National Center for Earthquake Engineering Research, State University of New York at Buffalo under the Grants No. NCEER 86-3021 F and 872007.

1. 2. 3.

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5. 6.

7.

8.

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12. 13.

REFERENCES

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