EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, VOL. 22, 261-273 (1993)

BASE ISOLATION BY FREE' ROLLING RODS UNDER BASEMENT

TSUNG-WU LIN* AND CHAO-CHI HONE' Department of Civil Engineering, National Taiwan University, 1, Roosevelt Road, Sec. 4 , Taipei, Taiwan 10764

SUMMARY A new base isolation method is proposed for the protection of structures. Because of the efficiency of the isolation devices, the isolated structure may be made to remain elastic throughout major earthquakes. This device consists of two sets of mutually orthogonal free rolling rods under the basement of the structure. Since the coefficient of rolling friction of the rods is very small in practice, the structure can be isolated excellently from the support excitation. In this paper, the analytical method and the response of the isolated system for different parameters, such as the periods of the structure, the coefficient of rolling friction and the masses of rolling rods, are presented. The results indicate that the proposed method is excellent in isolating the structure from support excitations, as expected.

INTRODUCTION

Many practical base isolators proposed in the past have been demonstrated to be effective in the reduction of seismic response of structures. The well-known pure-friction (PF) base isolation system can dissipate the energy of excitation by sliding,'-7 the laminated rubber bearing (LRB) consists mainly of alternating layers of rubber and steel with the rubber being vulcanized to the steel platesa-" and the resilient-friction base isolator (R-FBI), composed of a set of teflon coated flat rings with a central rubber core and/or peripheral rubber cores, can slide on each other."*12

The base isolation system can separate the structure from the ground excitation during a major earth- quake. As such, the structure may be subjected to smaller external forces due to earthquakes compared to unisolated structures. In our imagination, we thought that the best technique of isolation is to disconnect the structure from the ground completely when the earthquake occurs. Free rolling rods under the basement (Figure 1) is a new method of base isolation specifically designed for this purpose. It is easy to see that the maximum forces of excitation transmitted to the superstructure by earthquakes are the rolling friction in this device. In general, the friction resistance to the rolling motion is so small that it can be neglected as usual. According to Noonan and Strange,13 the friction force is Ff = W(k + k') /d , where W is the vertical load on the rollers, and d is the diameter of the roller in inches. The values of k and k , the respective parameters of friction from experiment for the upper and lower surfaces that are in contact with the roller, are O~ooO5-0401 in. for steel, assuming that the surfaces of the steel rollers and steel plates are well finished and clean. For example, if d = 4 in and k = k' = 0001 in, the coefficient of rolling friction is p = (0001 + 0.001)/4 = 0.0005, that is, the friction force is 09005 W, a very small value.# Because the friction force is

small, it is necessary to implement a useful apparatus between the rollers and the foundation. The principle of the design is that it must fix the roller most of the time so as to sustain the wind load, ambient vibration from the ground and the internal movement of occupants. When an earthquake occurs (and exceeds a certain intensity), the apparatus may release the fixed force and the rollers can roll free, resulting in the isolation of the superstructure. Unquestionably, this apparatus is easy to design and manufacture at the present time. As for the problem of ground subsidence, either a well-designed foundation to prevent the exceedingly uneven

'Professor. 'Graduate Student. # 1 in = 0.0254 m.

OO98-8847/93/030261-13$11~50 0 1993 by John Wiley & Sons, Ltd.

Received 11 February 1992 Revised I September 1992

262 T.-W. LIN AND C.-C. HONE

settlement should be carefully considered, or an added counterweight (W,) to balance the horizontal force caused by the uneven settlement can be arranged as shown in Figure 1.

The responses of a three-storey frame subjected to an earthquake of the SMART-I array in Taiwan (station COO, 1986) (Figure 3) with a dominant period of 0.16 sec are calculated and shown graphically. There are great differences between the responses of time history for the isolated structure and those for the fixed-base structure. In order to evaluate the characteristics of the seismic responses of the isolated structure, the response spectra are calculated and plotted for the absolute accelerations and relative-to-basement dis- placements of the roof, the absolute accelerations, relative-to-ground displacements and residual dis- placements of the basement for different parameters and for two earthquakes of different periods.

ANALYTICAL FORMULATION

The primary horizontal input force to the structure is the friction force between the roller and the basement, Ff . Assume that the resultant of the friction force and the vertical normal force passes through the centre of the roller, so that they do not make any contribution to the acceleration of the roller. As shown in Figure 2, the inertia forces of the rolling roller are balanced by F b and F,, where F b is the force between the roller and the basement, and F, is the force between the roller and the foundation. Therefore, the total horizontal force between the roller and the basement is Ff + F b , and that between the roller and the foundation is Ff + F,. The equation of motion of the superstructure relative to the basement is

[ M I {ii} 4- [C] { u } + [ K ] { u } = - [ M I { I } i ib (1)

HI '"T Fixed frame U S

I Figure 1. Structure with free rolling rods under basement

I I

Basement

Foundation +.+, u, - Figure 2. Free body diagram for roller

FREE ROLLING RODS

5 - v 1 0 - E

263

Peak Ground D i s = 177 cm

,--. "p 250

6 150 2 50

-50

-150

c v

3 0

- $ 4 Peak Ground Acc. = 216 crn/secz I < -250 ' J

where [MI, [C] , [ K ] are the mass, damping and stiffness matrices of the superstructure, { u } is the displacement vector of the superstructure relative to the basement, and iib is the acceleration of the basement. When the roller is fixed, the basement is also fixed, iib = U,, where U, is the acceleration of ground.

The equations of motion of the roller between the basement and the foundation of structure are

where

and M, and Jr are the summation of the masses and the moments of inertia of the whole rollers, with r representing the radius of the roller. Solving equations (2) and (3), we derive

The equation of motion of the whole superstructure is shown to be

{l}T[hf]({U} + {I}&) -k MbUb = Ff + F b = Ff + (U, - Ub)J,r-2/4 - (U, + Ub)Mr/4 (54

Ff = P M ~ sgn (4, (5b)

Ms = { I } + Mb (5c)

where Mb is the mass of the basement, and Ff and M, are defined as

and

From equation (sa), we obtain

264 T.-W. LIN AND C.-C. 'HONE

where

M, = {/}'[MI { I } + Mb + M,/4 + J , F 2 / 4 = M, + M,/4 + J,rV2/4 Substituting equation (6a) into equation (l), we get the equation of motion

(a)% 2 5 x 1 5 \ 5 0 5

, -0.5 v

V

$ - 1 5

-100 ' J (c)% 250

$ 150

6 50 -50

0

2 -150

\

v

-7

0 5 10 15 20 25 30 Time ( s e c )

Figure 4. Acceleration of roof relative to the basement

FREE ROLLING RODS 265

where

[MI = [MI - M ; [MI (11 P I T [MI (7b) By comparing equation (1) with equation (7), it can be seen that the effect of the isolation system is to diminish the mass of the superstructure and the external force in the equation of motion of the isolated structure. From equation (7a), the second term in the parentheses on the right-hand side, [ ( J , r P 2 - Mr)/4M,]iig, stands for the influence of the support excitation to the structure. We can evaluate its

0.1 p = 0.0001 TI = 2.1"'

(a) 5 A t v

,o.o 0) ._ a

-0.1 ' I

-5 ~

(d) o.ooo2 - E

0.0000 v

u! G .-

I I -0.0002 ' I

0.02 ( e ) y 0 0 1 0 v

0.00 u! G .-

-0.01

-0 02 0 2

0 1

00

(f)

L v

i? G

-0 1

0 5 10 15 20 25 30 Time (sec)

Figure 5. Displacement of roof relative to the basement

266 T.-W. LIN AND C.-C. HONE

order of magnitude to bring up a point. For a ten-storey building with an isolator of solid steel rollers with a diameter of 10 cm, the order of this term is about l oA3 ii,. This denotes that the excitation of the ground is negligible when the roller is rolling.

NUMERICAL ANALYSIS

We consider two 3-storey frames in this study. These two frames have the same mass, stiffness and height on each floor. In addition, they both have identical damping ratios (5 per cent) and isolation device (solid steel

-1.0 100

'

0 5 10 15 20 25 30

Time ( s e c )

Figure 6. Absolute acceleration of basement

FREE ROLLING RODS 267

2.5 -

1.5 - - - E

vi

(a),- 0.5 - ._ 0 -0.5 -

- -1.5-

- -2.5 25

1 5 - - -

rollers with diameters of lOcm), that is, M , = M 2 = M 3 = M , , I , = I 2 = 13, H, = H 2 = H 3 , and M , = 0.02Mb. But the periods of the frames are different. The fundamental periods of the first and second frames are 0 1 sec and 2.1 sec, respectively. The frames are analysed when they are fixed-base or when they are isolated for two coefficients of rolling friction p = 0~01,0~0001. As shown in Figures 4 and 5, the responses of acceleration and displacement of the roof relative to the basement are quite different for the isolated and the fixed-base frames. The response histories of the isolated frames are similar regardless of the values of p, and the magnitude of the responses are proportional to the values of p. The responses of the fixed-base frames are

p = 0.0001 TI = 2.lSec

p = o.o!e, - T I = 2.1

1.5 - n -

(c) ,- 0.5 - E

p = 0.0001 - T I = O.l**C

Figure 7. Absolute displacement of basement

- -2.5 2.5

- 1.5 -

n - (d); 0.5 -

-

< == orJ1oy!

A - - v n -0.5 -

- -1.5 -

- -2.5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 , 1 1 1 1 1 , 1 , 1 1

268 T.-W. LIN AND C.-C. HONE

found to be very large during the time which is close to PGA (peak ground acceleration). On the contrary, they are small during the other times. Conversely, the responses of the isolated frames are quite stable and decay slowly during the earthquake. Figures 4(d), qe), 5(d), 5(e), 6(c) and 6(d) show some bursts of high-frequency energy, which are similar to the damped free vibrations in the high-frequency structure ( T I = 0.1 sec), since the force acting on the superstructure by the rollers is the constant friction force. Since we assume that the rolling friction is constant, the responses of the structure will approach a constant level which may be positive or negative, depending upon the rolling direction of the rollers, that is, the direction of the rolling friction. Such a feature is not observed in Figure 4, for it displays the acceleration of the roof relative to the basement and not the absolute acceleration. Although the earthquake reaches its peak in the interval

Fixed Base - p = 0.1 w p = 0.01 - p = 0.001 - p = 0.0001

- 0 0 c , , A + ,:I fa-,

0 0 0 5 1 0 1 5 2 0 Period (sec)

Figure 8(a). Spectrum of absolute acceleration of roof

2 o 1 w3eec Fixed Base u p = 0 1 w p = 0 0 1 -/A = 0001 - p = 00001 -

a 0

L

0 0 Lli

0 0

0 0 0 5 1 0 1 5 20 Period ( s e c )

Figure 8(b). Spectrum of displacement of roof relative to the basement

FREE ROLLING RODS 269

- 1.5 -

- - - -

c? - a \ x 1.0 - 3

vi a

v - ._ - D - C 3

0 2 -

0 5 - c - W

.- -c - - W -

from 4 to 9 sec, Figures 4(d), 5(d) and 6(c) show that basically responses of the same magnitude are observed throughout the history. This is because of the small coefficient of rolling friction used in this case ( p = O~OOOl), and even a slight excitation of support may cause the rolling of the rollers. In fact, all the values of the responses are rather small.

The responses of the basement may be divided into three parts in Figures 6 and 7. When the excitation of the earthquake is small (0-4 sec and 20-29 sec), the basement is fixed to the foundation, and the accelerations of the basement are small and same as those of the ground. As the ground excitation increases, the rollers under the basement begin to roll. Therefore, the excitation transmitted to the superstructure is greatly reduced. In Figures 6(a) and 6(c) for p = 0.0001, the rollers roll almost all the time. This indicates that the

- p = 0.1 (we40 p = 0.01 m p = 0.001 - p = 0.0001

a - p = 0 1

- p = 00001

a M p = 0 0 1 B f f + + * p = 0001 :3

* - , I I I 1 - 1 1 - 1 1 - 1 I 1 1 - 1 I

0 0 0 5 1 0 1 5 20 Period (sec)

Figure 9(a). Spectrum of absolute acceleration of basement

270 T.-W. LIN AND C.-C. HONE

7 - - 5- 3-

- B - Q -1- v - 9

- - 0 -3-

d -5- -7

- -

basement is isolated from the ground perfectly. The accelerations of the basement are very low ( x 1 gal) and limited in magnitude for all the time. A question that should be asked is whether the displacement of the basement due to the rolling of the roller is limited? Figures 7(a)-7(d) provide the solution to this question. When p = 0.01, the basement moves with the ground; however, if p = 0*0001, the movement of the basement does not correspond to the ground motion. Besides, one can observe that the motions of the superstructure and basement are interactive as shown in Figures 4 and 6.

For finding more characteristics of this isolator, a single-degree-of-freedom frame subjected to the above earthquake is analysed, which has a damping ratio of 5 per cent, with different periods T = 0.05,01, . . . , 2.0 sec, either fixed in base or isolated with p = 0~1,0~01,0~001 and O.OOO1 and M , = 0.02,004 and 0.08Mb. The results show that the responses are almost identical for different M,. Thus we only plot the responses of the system whose M , = 0'02Mb. Figures 8(a) and 8(b) display the spectra of the absolute acceleration ii and

1 - m

V Peak Ground Dis = 6.61 cm

1 1 1 1 , 1 1 1 1 , 1 1 1 ( 1 1 1 1 , , 1 1 1 , ( 1 ~ , ~ 1 , 1 1 1 ~ ( 1 1 1 1

- p = 0.1 w /A = 0.01 %t++++ /A = 0.001 - 1'5 i m u . = 0.0001

D

O D

Period ( s e c )

Figure 10. Spectrum of residual displacement of basement

FREE ROLLING RODS 27 1

the relative-to-basement displacement u, of the roof which are normalized to PGA (216 cm/sec2) and PGD (peak ground displacement, 1.77 cm), respectively. For p < 0.01, the effect of the isolator is independent of the periods of the structures. It should be noted that the structure is almost detached from the ground for p = O.OOO1, which is our intention. Figure 9(a) presents the spectrum of the absolute acceleration of the basement iib normalized to PGA. It represents the actual excitation transmitted to the superstructure from the earthquake through rollers, whose responses are similar to the absolute acceleration of the roof (Figure 8(a)) for the interaction of the basement and the superstructure.

Relative-to-ground displacement of the basement ubg normalized to PGD is given in Figure 9(b). The conclusion may be drawn that Ubg is limited to a range of 1.5 times PGD. That is an important criteria in the design of the foundation. At the time an earthquake stops and the basement is fixed to the foundation again,

08880 Fixed Base - p = 0.1 w p = 0.01

-001

0 0 I * z l - , 2 I 1 1 - 1 1 T 1 1 *

0 0 0 5 1 0 1 5 2 0 Period (sec)

Figure 12(a). Spectrum of absolute acceleration of roof

c*BBBo Fixed Base - p = 0.1 M p = 0.01 - I ( = 0.001 - f i = 0.0001

h

9

2 1.0 L

0

(1:

c

ui .- 0

0.0 0.0 0.5 1 .o 1.5 2.0

/- 0.0 -

0.0 0.5 1 .o 1.5 2.0 Period (sec)

Figure 12(b). Spectrum of displacement of roof relative to the basement

272 T.-W. LIN AND C.-C. HONE

the displacement of the basement is called the residual displacement urb, the distance by which the structure should be recentered. Figure 10 shows the response of tdrb normalized to PGD, the maximum value of tdrb being of the order of 1.2 times PGD. Remarkably, it is reasonable and acceptable for the design of re-centring instrument. A long-period earthquake of the SMART-I array in Taiwan (Figure 11, PGA = 239 cm/secz and PGD = 6.61 cm) is also calculated for the spectra. Comparing its results (Figures 12-14) with those of the short-period earthquake (Figures 8-10), one finds that their responses are similar. The values of p dominated the responses of the roof and the basement. The relative-to-ground displacement of the basement ubg normalized to PGD (Figure 13(b)) is limited to a range of 1.5 times PGD. It shows that the responses of the isolator are insensitive to the periods of the support excitations.

- p = 0.1 M p = 0.01 - w = 0.001

~ - p = 0.0001

Figure 13(a). Spectrum of absolute acceleration of basement

,-. d

2 3 1 0 \

v

v C 3

2 a 0.5 0 4-

0.0 l l I l , I 1 I 1 1 I I I I I I 1 1 - 1 I 0 0 0 5 1 0 1 5 2 0

Period ( se t )

Figure 13(b). Spectrum of relative-to-ground displacement of basement

FREE ROLLING RODS

- p = 0 1 - p = 0 0 1 -9 = 0001 - p = 00001

2 . 51 273

0 0

Period (sec)

Figure 14. Spectrum of residual displacement of basement

CONCLUSIONS

Through the study of the isolator whose mechanism is rolling friction, it is exhibited that the device can be quite effective in controlling the acceleration of the superstructure, with no regard to the dominant periods of the support excitation and the superstructure for p < 0.01. This indicates that the device can be effectively used on any site. The responses of the superstructure will be reduced if we decrease the coefficient of the rolling friction. It is possible to have the order of p as low as Since the maximum relative-to-ground displacement and the residual displacement of the basement is only 1.5 times PGD, it is concluded that the rolling rods under the basement are a practical isolation scheme. Furthermore, a possible application of active structural control can be achieved by adding a control force in the basement. The best control is to keep the absolute displacement of the basement equal to zero. In this case, the necessary maximum control force is equal to the rolling friction, and the superstructure will not be subjected to any lateral force.

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