13th World Conference on Earthquake Engineering
Vancouver, B.C., Canada
August 1-6, 2004
Paper No. 1362
OPTIMUM DESIGN OF RESILIENT SLIDING ISOLATION SYSTEM TO
PROTECT EQUIPMENTS
Hirokazu IEMURA1 and Touraj TAGHIKHANY 2
SUMMARY
Seismic isolation is one of the best options to protect equipments. It helps to control response acceleration
transmitted to equipment under its allowable level. Among several type of isolation system, the
combination of restoring spring and slider (resilient sliding system) is a very effective system for
protection of equipment. In design of this type of isolation system to ensure functions of equipments, there
are many suitable combinations of stiffness and friction coefficient. However at the same time it is also
necessary to control relative displacement of isolation system so as to provide safety to the connections of
equipment with other systems like power supply, main servers etc. This study deals with optimum design
of equipments with these resilient sliders that may control acceleration under allowable level and at same
time minimize the relative displacement. Optimum parameters of resilient sliding isolators are determined
analytically for different levels of allowable acceleration. The validity of analytical method used, is also
verified by shaking table tests. Results of this study show that 1) Optimum values of period are decreased
with growth of allowable acceleration and 2) The optimum friction coefficient is increased with higher
allowable acceleration.
INTRODUCTION
Traditional mitigation strategies like; bolting, cross bracing and structural stiffening may work to keep
equipment upright but actually they provide a direct path way on which damage shock and vibration can
travel. The more rigid the connection, the more likely there will be damage to fragile components like
drive heads, optical lasers, and other sensitive components.
Recently desired performance objective of “operation” or “immediate occupancy” of sensitive equipments
has made the engineers to adopt non-conventional method for protection of these systems. Seismic
isolation as a reliable and economical method can be recommended to achieve these performance
objectives.
So far almost all seismic isolation systems that were developed for equipment consist of coil springs to
provide flexibility and energy absorbing device in the form of friction slider or oil dampers [1]. There are
1
2
Professor, Dept. of Civil Engg. Systems, Kyoto University, Japan, iemura@catfish.kuciv.kyoto-u.ac.jp
Ph.D. Student, Dept. of Civil Engg. Systems, Kyoto University, ttaghikh@catfish.kuciv.kyoto-u.ac.jp
many seismic isolators like Friction Pendulum Bearing (FPS) [1, 2], Resilient Friction Base Isolation
(R_FBI) [3] and Hybrid Base Isolation [2] (Slider and Laminated Rubber bearing) which are using same
mechanism to protect equipments.
This paper focuses on dynamic behaviour and design of isolation systems that comprise of friction slider
and restoring spring. First, a numerical model of a raised floor, seismically isolated with friction slider and
spring is proposed. Then the model was validated by performing shaking table test. This model was used
to predict dynamic behaviour of seismic isolated equipments and to reach at the optimum design of
isolation system. For the purpose of this study, design of isolation system is defined as optimum if it
results in minimum displacement while maintaining the maximum acceleration below allowable level.
Two groups of earthquakes recommended by Transportation Ministry of Japan were considered in this
paper.
RESILIENT SLIDING ISOLATION (RSI) SYSTEM
Sliding bearing limits the transmission of seismic force to level that is function of friction coefficient of
sliding interface. This behaviour is interesting for protection of non-ductile and non-structural components
against earthquake when expected acceleration is more than their strength level. However there are some
negative aspects in seismic behavior of sliding bearings like lack of restoring force and transmission of
high frequencies [5,6]. Transmission of high frequency excitation causes damage in sensitive equipments.
To avoid these undesirable features, sliding bearings are typically used in combination with a restoring
spring. When spring and slider are used in series (Fig1), sliding does not occur for seismic excitation
below a certain threshold, and the isolated structure responds only in elastic part [7]. This behavior can
filter direct and indirect excitation of high frequency due to stick-slip. However in strong excitation, this
system may result in residual displacement.
When spring and slider are in parallel combination i.e. Resilient Sliding Isolation System (Fig 2)
transmission force to equipment is equal to restoring force of spring plus friction force at sliding interface.
This combination can reduce both transmission of indirect high frequency excitation and residual
displacement.
Seismic Behavior of Resilient Sliding Isolation System
Since the shear force activate the slider bearing, its horizontal stiffness drops from large value to zero and
causing an unrestrained displacement. In this regards combination of slider and restoring spring provide
an additional stiffness to control displacement. Thus force-deflection relationship of the combined system
Fig.1 Slider and spring in series
Fig.2 Slider and spring in parallel
Fig.3 Comparison of dynamic Behaviour of Resilient Sliding Isolator with (i) pure slider & (ii) spring.
would be theoretically bilinear with infinite initial stiffness followed by finite stiffness [6].
In fact, response of SDOF model of Resilient Sliding Isolation during earthquake ranges between dynamic
response of a slider bearing and a spring isolator. Figure 3 shows that the response acceleration spectra of
resilient sliding isolation with friction coefficient (µ) as 0.02 is almost same as response spectra of spring
isolation. Increasing friction coefficient makes response spectra of RSI system similar to response spectra
of slider bearing. Likewise, by reducing stiffness of spring (increasing period) in this system the
acceleration spectra approaches to acceleration spectra of slider.
Response acceleration spectra of Resilient Sliding Isolation is function of input earthquake characteristics,
period and friction coefficient. But dependency of response spectra to earthquake characteristic can be
reduced by increasing the period and in such case maximum acceleration (am) limits to µ g (Fig 5).
Constantinou et al. [8] also exhibited that maximum response acceleration of resilient sliding isolation
under two different earthquakes of El Centro and Mexico City is equal when period of isolator is 4
seconds.
Fig.4 shows the steady state response of this type of isolators subjected to harmonic base motion [9]. The
µ = 0.05 , P GA=0.25g
Acc. (Cm/s^2)
300
250
K obe E-W
Pacoima
Elcentro
200
150
100
50
am= µ . g
0
1
Fig.4 Transmissibility of FPS. [9]
2
3
Period(Sec.)
4
Fig.5 Acceleration Spectra of RSI System
5
horizontal axis represents the ratio of the period of the input motion (T) and the period of spring (T0). The
vertical axis represents the ratio of the acceleration response (am) and the peak ground acceleration (ag). In
this figure response acceleration ratio (am/ag) is almost independent to variation of T/T0 for values less than
0.3. For instance, a series of isolators can be considered with period (T0 ) more than 3 sec and friction
coefficient (µ) more than 0.05. Response of these isolators under sinusoidal vibration with maximum
acceleration between 0.05g< ag <1.0g is independent to input excitation if period (T) is less than 1 sec.
Most of earthquakes, which are considered in seismic design of structure, are in this range of excitation
period and maximum acceleration.
Maximum acceleration spectra was obtained for a resilient sliding isolation system with µ=0.05 under
three earthquake with Peak Ground Acceleration of 0.25g and is shown in Fig5. This acceleration spectra
for PGA/µ=2.5 (PGA=0.25g, µ =0.10) also clearly shows that when period of isolators is more than 2
second response acceleration for three earthquakes is the same even they have different period of content.
ANALYTICAL MODELING OF RSI
In numerical model of resilient sliding isolation the essential feature that need to be modeled for behavior
of sliding bearing is the velocity dependence of the coefficient of friction and influence of bearing
pressure in the coefficient. Although, biaxial interaction and its effect can be considered as another feature
of modeling.
Here, velocity dependence of friction coefficient can be modeled by the following equation [10]:
& )
µ = µmax-∆µ exp(-α U
(1)
In which, µmax is the maximum value of the coefficient of friction, ∆µ is the difference between its
maximum and minimum value. Effect of bearing pressure on friction coefficient is accounted by factor α
& is the absolute velocity. Biaxial interaction is considered as model proposed by Park and Wen
and U
[11]. In addition to friction element, laminated rubber bearings are assumed as a linear spring and frames
is considered as elastic beam element. Mass of frame elements and blocks deemed as lumped mass
element that have degree of freedom in horizontal direction (X-Y) and rotation about vertical axis (θ).
In the present study, in addition to this numerical model, a different analytical model, termed here as
SDOF model is proposed that computes maximum values of response parameters for different sets of
friction coefficient and spring stiffness. In fact this model considers the bilinear model for forcedisplacement behavior of isolation system as shown Fig.3. The design parameters for this model are µmax
and spring stiffness. In this analytical model equipment and raised floor is modeled as rigid block.
VERIFICATION OF ANALYTICAL MODEL
Provisions and codes provided procedures to verify acceptable performance of equipment for expected
ground motions [12]. For example IEEE 693 [13] recommends procedures, which comprise analytical
studies (Static analysis, response spectrum analysis) and experimental methods (response history testing,
shaking table test). The economical impact of failure of equipment in earthquake generally makes it
necessary, any seismic design method or protection strategy to be verified for its accuracy with precise
numerical analysis or with experimental test.
Experimental Test
In order to establish the reliability of numerical model for the isolation system used in the study a series of
shaking table were performed at Disaster Prevention Research Institute of Kyoto University. This shaking
Fig.7 Details of Test Setup
Fig.6 Experimental Setup
table system can reproduce acceleration of 1.0g in three direction with maximum stroke of 0.3m in
horizontal and 0.2m in vertical direction.
In this experiment a 4.15 m x 2.65 m raised steel floor, supported on four frictional sliders at the corner
and two laminated-rubber bearings was considered (Fig 6 and 7). The total weight of this raised floor was
100 KN. Rubber bearings have a square plan of 250 mm x 250 mm with three different thicknesses.
Modulus of elasticity of rubber is 1.2 KN/mm2. The bearings were designed for periods of 1.1, 1.75 and
3.0 seconds respectively. Sinusoidal tests on sliding bearings before shaking table test showed that the
minimum and maximum values of friction coefficient are 0.05 and 0.15 respectively.
The system was tested using two groups of earthquakes, recommended by Transportation Ministry of
Japan. These groups are T1 (offshore) and T2 (inland) and each one contain 9 records. Each group, based
on soil condition of recording station further divided into three categories, records on stiff soil (soil typeI),
medium soil (soil type II) and soft soil (soil type III). Almost 70 runs were made with different isolators
and earthquakes. Displacement, acceleration, vertical pressure on bearing and lateral force of System were
Shear Force Time History
Relative Displacement Time History
K ob e-S oil Type I , Period=1.1 S ec
K obe-S oil Type II , P eriod=1.75 Sec
150.00
4 .00
Disp lace me n t (Cm.)
50.00
0.00
-50.00
Numerical Model
-100.00
Experiment Model
-150.00
0.00
2.00
4.00
6.00
8.00
10.00
2 .00
0 .00
-2 .00
Numerical Model
-4 .00
Expe rimental Model
-6 .00
0.00
2.00
4 .00
Time (se c.)
6.00
8.00
1 0.00
12.0 0
14.00
Time (s e c .)
(a)
(b)
Fig.8 Comparison of Response of Experimental and Numerical Model
Maximum Relativ e Displacement
M aximum Shear Force
0.2
0 .2
0.1
0 .1
0
R e l. D iffe re nce
R e l. D iffe re nce
F orce (KN)
100.00
S oil I
S oil II
S oil III
-0.1
-0.2
0
S oil I
S oil II
S oil III
-0 .1
-0 .2
0
0.5
1
1.5
2
Period (Se c.)
2.5
3
3.5
0
0.5
1
1 .5
2
2.5
3
3 .5
Pe riod (Se c.)
Fig.9 Relative Difference Between Maximum Responses of Experimental and of Numerical Model
measured during these tests.
The response of system recorded in experiment and computed by numerical model, which was compared
for different design parameters of earthquake motions. Shear force of system under earthquake recorded
on soil type I is shown in Fig.8a when period of spring is 1.1 second. In Fig.8b lateral relative
displacement of raised floor recorded at soil type II is illustrated when period of spring is 1.75 second.
These figures shows relation of results obtained from numerical model for different conditions.
Fig.9 depicts relative difference of maximum response of experimental and numerical model under three
earthquakes for three different periods. This figure confirms that the relative difference between maximum
recorded shear force and displacement in experiment and numerical analysis is less than 20%.
One of the main sources of this difference is possibly change in vertical pressure on sliders due to rocking
motion. This level of accuracy for numerical model can be accepted depending on sensitivity of equipment
and allowable margin of error for protecting equipment.
Validation of SDOF Model
The validated numerical model was then used to test reliability of proposed SDOF model. Maximum
response of system is computed by using precise numerical model for different stiffness of laminated
rubber bearings and friction coefficient of sliders. In other words, response spectra of this system is
computed for different values friction coefficient. By comparing this spectra with response acceleration
spectra of Resilient Sliding Isolation of SDOF model (Fig.3), the accuracy of SDOF model can be
established for different periods and friction coefficients. In Fig 10 for maximum friction coefficient (µmax)
0.10, maximum acceleration spectra of model has been plotted for ∆µ=0.05. This figure show that
maximum accelerations obtained by SDOF model in long periods is very close to numerical model. In
Fig.11 relative difference of maximum acceleration obtained by numerical model and SDOF model has
been shown for different values of friction coefficient under El Centro earthquake. This figure confirms
that increase in the period reduces difference of maximum acceleration between two models. In this graph
relative difference between acceleration of SDOF model and numerical model, for friction coefficient
more than 0.08 is less than 20 percent when the period is longer than 2 seconds.
DESIGN METHODOLOGY
Dynamic characteristics of equipments like stiffness or damping may effect on any decision about
modeling and design methodology of their isolation systems. In this regard, Almazan et al. [14] compared
response parameters of a rigid block and flexible superstructure (period 0.5 sec.) were isolated by FPS
isolator. Their result show that difference between the isolator deformation computed from both models is
very small; however slightly larger discrepancies (about 10 percent) was observed in shear force. Though
µ m=0.10, ∆ µ =0.05
2
0.4
µ = 0.0 6
0.3
1.5
1.25
R el. Diffe re nce
N ormalize d Acc.
1.75
SDOF Model
1
Numerical Model
0.75
µ = 0.0 7
∆ µ =0 .0 5
µ = 0.08
µ = 0.1 0
0.2
0.1
0.5
0.25
0
1.5
0
0
2
4
6
8
10
Period(Sec.)
Fig.10 Sliding Isolation Acceleration Spectra
of El Centro Earthquake
3
4.5
6
7.5
9
10.5
12
Period (Sec.)
Fig.11 Relative Difference Between Maximum
Acceleration of SDOF and Numerical Model
under El Centro earthquake
most of equipments have solid components, flexibility of equipment if there, do not have considerable
effects on response of their isolation system. Thus in isolated equipment, response of seismic isolation
system can be obtained with acceptable accuracy by assuming “equipments + raised floor” as a rigid mass.
This SDOF model of sliding isolation system has been shown in Fig3. Determination of stiffness and
friction coefficient of SDOF model based on seismic performance objective of equipments is purpose of
design methodology in this part.
Since seismic performance objective of equipments is qualitative term (operation during or immediately
after earthquake) it should be quantified by limiting values of measurable response parameters for
practical design. For example in structures, this measurable response parameter is “story drift” and it is
limited to 2%~3% when level of performance is Life Safety [4]. In equipments and nonstructural
elements, because of their rigid behaviour, performance objective is defined by “limiting response
acceleration” or “lateral force”. For nonstructural components above the isolation interface, provisions and
codes of seismic isolated structures [15] recommends that they shall “resist the total lateral seismic force
equal to the maximum dynamic response of element or component”. In other words, if due to any reason
nonstructural components cannot resist more than specific level of lateral seismic force, isolation system
should design to control maximum lateral seismic force to less than or equal to level of resistance of
equipment.
Table 2 indicates suggested peak accelerations by manufacturer for some models of disk drives in
computer systems. The response acceleration if exceeds this value may cause permanent damage and loss
of readable data [16]. In this table, for operating and non-operating condition of different disk drives
maximum seismic bearable acceleration varies between 0.2g-1.0g. These values in practice are reduced by
safety factors to Maximum Allowable Acceleration. For protecting these systems during earthquakes,
stiffness of spring and friction coefficient of slider should be selected to limit horizontal input acceleration
under their allowable values.
Optimum Design Procedure
Any combination of stiffness and friction coefficient of resilient sliding isolation, which control response
acceleration under allowable level of acceleration, can be accepted as eligible design parameters for
protecting equipment in earthquake. But most of equipments have connections with other systems like
power, water supply or main server and safety of connections to these systems is essential to ensure the
functioning of equipment during earthquake. Therefore beside safety of equipments, designer should
control displacement of isolated equipments in earthquake to minimum value. In this regard,
determination of stiffness and friction coefficient of isolators to control input acceleration under allowable
level and to minimize lateral displacement is the optimum design of resilient sliding isolation.Fig.12
clearly depicts procedure of optimum parameter recognition for specific allowable acceleration. Maximum
response acceleration and displacement spectra of SDOF model of isolated equipment under El Centro
earthquake is shown in Fig12-a for isolation system with friction coefficient of 0.03. In this figure
allowable acceleration of equipment is assumed as 0.08g. Safety of equipment can system
Table 2 Maximum seismic resistant acceleration on disk drives [16]
Max. g / Operating
Max. g /
Non-Operating
DEC - Alpha Server - #8200
0.5 g
0.5 g – 1.0 g
SUN - Class III Drive
0.25 g
1.0 g
DEC - RZ 28 Drive Unit
0.5 g
0.5 g
HP - Model 20 Drive Unit
0.25g
N/A
HP - Enterprise 9000
0.2g-0.5 g
0.5 g – 1.0 g
Manufacturer's Model #
800
µ =0 .03
600
Allowable
Σ ε ριε σ1
Level=0.0 8
400
200
0.08*g
0
0
5
10
Acce leration (Cm/Se c^2)
Accelertation Spectra
Acce leration (Cm/Se c^2)
Accelertation Spectra
1000
1000
800
µ =0.03
600
µ =0.07
400
200
0.08* g
0
15
0
5
Min. Allow able Disp.
µ =0.03
12
10
8
6
4
2
0
0
5
Period(Se c.)
10
15
Pe riod(Se c.)
Displacment Spectra
D is placme nt(Cm)
Displacment Spectra
Pe riod(Sec.)
14
µ= 0.05
Allowable
Σ ε ριε σ1
Level=0 .0 8g
10
14
12
10
8
6
4
2
0
Min. Allow able Disp.
µ =0.03
Min. Allow able Disp.
µ =0.05
0
15
Min. Allow able Disp.
µ =0.07
5
10
15
Pe riod(Se c.)
(a)
(b)
Fig.12 Procedure of Optimum Parameter Recognition for El Centro Earthquake
be guaranteed when maximum acceleration of its isolated model is equal or less than this level of
acceleration. Safety region begins from crossing point of dashed-line with response spectra. Isolation
systems with period longer than this point are eligible to ensure operation of equipment during or
immediately after El Centro earthquake. Among these eligible periods just one of them has minimum
displacement that is shown in displacement spectra with star symbol.
This procedure is repeated for different values of friction coefficient in Fig12-b. Crossing point of dashed
lines with each spectra show start point of their eligible range for allowable acceleration 0.08g. Period at
these points for three coefficient friction µ=0.03,0.05,0.07 are Ti=2.9,3.0,4.6 seconds. For periods more
than Ti , minimum displacement of each friction coefficient has been highlighted with star symbol. Among
three highlighted points, displacement of one of them with friction coefficient 0.07 and period 4.6 seconds
has minimum value. Between three friction coefficients for allowable acceleration 0.08g this point
introduce property of an isolator that can protect equipment under El Centro earthquake with minimum
displacement. By using this procedure for range of friction coefficients, optimum parameters of resilient
sliding isolator can be determined for allowable acceleration 0.08g or other values of allowable
acceleration.
In Fig.13 optimum parameters of resilient sliding isolator for different allowable accelerations of this
isolator were computed for feasible range of friction coefficient between (0.03~0.10) and periods between
(0~15sec.). These parameters were computed by using cited procedure for any allowable level of
Optimum Friction Coeff.
Optimum Period
15
12.5
0.1
Pe riod (Sec.)
Friction Coe f. (µ )
0.125
PGA =g
0.075
PGA =0.75g
PGA =0.5g
0.05
PGA =0.25g
0.025
10
PGA =g
7.5
PGA =0.75g
PGA =0.5g
5
PGA =0.25g
2.5
0
0
0
0.02
0.04
0.06
0.08
Allowable Acce le ration/g
0.1
0.12
0
0.02
0.04
0.06
0.08
0.1
Allowable Acceleration/g
(a)
(b)
Fig.13 Optimum Parameter of Resilient Sliding Isolation for El Centro Earthquake
0.12
acceleration between (0.04g-0.11g). Input earthquake was scaled to 0.25g, 0.5g, 0.75g and 1.0g to
evaluate the effect of Peak Ground Acceleration (PGA) on optimum parameters. Fig.13-a illustrates,
optimum friction coefficient has ascending trend with increasing of allowable level of acceleration but
different values of peak ground acceleration have not clear effect on optimum value of this parameter.
Optimum period in Fig.13-b has descending variation with increase of allowable acceleration. In this
figure optimum period of isolation system under higher level of peak ground acceleration of earthquake is
longer.
EVALUATION OF OPTIMUM PARAMETERS
To determine variation of optimum parameters of resilient sliding isolators under several earthquakes
gives an evaluation about optimum design of these isolators based on seismic performance objective of
equipments. In this part, optimum parameters of resilient sliding isolators are obtained analytically for T1
(offshore) and T2 (in land) groups of motions. In order to have proper comparison all earthquakes are
scaled to site specific Peak Ground Acceleration (PGA) equal 0.25g (Moderate seismic zone) and 0.5g
(High seismic zone)[17].
Fig.14 shows optimum parameters of resilient sliding isolators under records of T1 that were scaled to
0.25g. In this figure earthquakes recorded on stiff, medium and soft soil are scripted with T1-I, T1-II and
T1-III. Variation of optimum period and friction coefficient with allowable level of acceleration has same
trend with variation of these parameters in El Centro earthquake. For design purposes Mean and,
“Mean ± Standard deviation” of optimum values for all earthquakes show that optimum frictions are
almost in the same line for all earthquakes in T1 while optimum period can be selected from a band of
period for any allowable acceleration of equipments.
In Fig 15 optimum parameters are computed for T2 motions that were also scaled for same peak ground
acceleration of 0.25g. These earthquakes depending on soil type of recording station were divided in three
Optimum Friction
Optimum Period
Earthquakes Type 1 (PGA=0.25g )
18
T1-I-1
T1-I-2
T1-I-3
T1-II-1
T1-II-2
T1-II-3
T1-III-1
T1-III-2
T1-III-3
mean
mean+st
mean-st
0.1
0.08
0.06
0.04
0.02
T1- I-1
T1- I-2
T1- I-3
T1- II- 1
T1- II- 2
T1- II- 3
T1- III-1
T1- III-2
T1- III-3
mean
mean+st
mean-st
15
Pe riod (Se c.)
Friction Coe ff. (µ )
0.12
Earthquakes Type 1 (P GA=0.25g)
12
9
6
3
0
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.02
Allowable Acceleration/g
0.04
0.06
0.08
0.1
0.12
Allowable Acce le ration/g
Fig.14 Optimum Friction and Period of Resilient Sliding Isolation System under records of T1
Optimum Friction
Optimum Period
Earthquake Type 2 (PGA=0.25g)
Earthquake Type 2 (PGA=0.25g)
18
T2-I-1
T2-I-2
T2-II-1
T2-II-2
T2-II-3
T2-III-1
T2-III-2
T2-III-3
mean
mean+st
mean-st
0.1
0.08
0.06
0.04
0.02
0
T2-I-1
T2-I-2
T2-II-1
T2-II-2
T2-II-3
T2-III-1
T2-III-2
T2-III-3
mean
mean+st
mean-st
15
Pe riod (Sec.)
Friction Coe ff. (µ )
0.12
12
9
6
3
0
0
0.02
0.04
0.06
0.08
0.1
Allowable Acce le ration/g
0.12
0.14
0
0.02
0.04
0.06
0.08
0.1
0.12
Allowable Acce le ration/g
Fig.15 Optimum Friction and Period of Resilient Sliding Isolation System under records of T2
0.14
O ptimum Friction
O ptimum Period
Earthquakes Type1 & 2 (PG A=0.25g )
Earthquakes Type1 & 2 (PG A=0.25g)
0.12
18
0.1
15
0.08
Pe riod (Se c.)
Coe f. Friction (µ )
categories T2-I, T2-II and T2-III. Even the variation of optimum parameters is the same as earthquakes in
T1 but Standard deviation of optimum values is further. Comparison between mean values of optimum
parameters under records of T1 and T2 and their Standard deviation is shown in Fig 16. In this figure
mean values of optimum friction coefficient for two types of earthquakes are nearly same and have linear
variation with increasing of allowable level of acceleration. But it can be seen that the difference between
mean values of optimum period in two types of earthquakes is around 2 seconds and both have
descending variation by increasing allowable level of acceleration. For these earthquakes that scaled to
PGA=0.25g, optimum parameter selected among range of friction coefficient between (0.03~0.10) and
period between (0~15sec.) and computed for equipments that their allowable level of acceleration varies
between (0.04g-0.11g).
Fig17 shows optimum parameters of resilient sliding isolators under records T2 with PGA 0.5g. In this
figure optimum parameters were selected among range of friction coefficient between (0.07~0.14) and
allowable level of acceleration between (0.08g-0.15g). Standard deviation of optimum parameters for
PGA=0.5g is observed to be more than this variable in Fig.15. Also, such as variation of optimum
parameters of isolation system under El Centro earthquake, mean values of optimum periods for higher
level of PGA is more than lower levels. Increasing of standard deviation of optimum parameters for higher
value of PGA can be explained with behaviour of resilient sliding isolators (FPS isolation) under
harmonic loading. It was shown for range of relative periods (T/T0) and maximum acceleration ratios
(ag/µ), maximum response acceleration is constant and independent to frequency of input motion. For an
isolator with period T0 and friction coefficient µ, Fig.4 shows for lower values of ag/µ, range of constant
response of isolator is longer than that for higher values. In other words when maximum acceleration ratio
Type2
0.06
Type2+st
0.04
Type1
Type1-st
0.02
12
Type 2
9
Type2+st
6
Type1
3
Type1-st
0
0
0
0.02
0.04
0.06
0.08
0.1
0
0.12
0.02
0.04
Allowable Acce le ration/g
0.06
0.08
0.1
0.12
Allowable Acce le ration/g
Fig.16 Optimum Friction and Period of Resilient Sliding Isolation under records of T2
Optimum Period
Optimum Friction C oef.
Earthquake Type 2 (PG A=0.5g)
Earthquake Type2 (P GA=0.5g)
18
T2-I-1
T2-I-2
T2-I-3
T2-II-1
T2-II-2
T2-II-3
T2-III-1
T2-III-2
T2-III-3
Mean
Mean+s
Mean-s
0.125
0.1
0.075
0.05
0.025
T2-I-1
T2-I-2
T2-I-3
T2-II-1
T2-II-2
T2-II-3
T2-III-1
T2-III-2
T2-III-3
Mean
Mean+s
Mean-s
15
Pe riod (Se c.)
Friction Coe ff. ( µ )
0.15
12
9
6
3
0
0
0.02
0.04
0.06
0.08
0.1
0.12
Allowable Acce le ration/g
0.14
0.16
0.02
0.04
0.06
0.08
0.1
Allowable Acce le ration/g
0.12
0.14
Fig.17 Optimum Friction and Period of Resilient Sliding Isolation under records of T2
0.16
of input motion (ag/µ) reduces, response of isolator below certain value of excitation period (T) will be
constant. Though earthquake is comprised several harmonic excitation with different period but its
maximum response acceleration is dominated by two or three harmonic excitation. Therefore for higher
value of PGA, optimum design parameter also depends on frequency content of input motion and thereby
increases the Standard deviation.
CONCLUSIONS
The paper discusses the evaluation of design parameters of the Resilient Sliding Isolation system to
achieve performance objective of equipments. Analytical method based on single degree of freedom is
proposed to obtain these parameters. In addition the design parameters obtained by this method also lead
minimum relative displacement. The accuracy of the method is validated by shaking table test of raised
floor isolated by resilient sliders. Optimum design parameters of these resilient sliding systems subjected
to two type of Japan standard earthquakes are obtained for different values of allowable level of
acceleration for the equipments. Results of analysis show:
1. For higher values of peak ground acceleration of earthquake, optimum period of resilient sliding
isolation is longer.
2. Optimum friction coefficient of isolation system under earthquakes T1 and T2 in moderate
seismic zone has almost linear relation with increasing level of allowable acceleration.
3. Optimum period of isolation system under earthquakes T1 and T2 in moderate seismic zone
becomes shorter when allowable level of acceleration increases.
4. In high seismic zone, standard deviation of optimum parameters is larger than moderate seismic
zone. Mean of optimum parameters in high seismic zone has same trend of variation with
moderate seismic zones.
ACKNOWLEDGEMENT
Authors acknowledge the constructive comments given by Dr. Sarvesh K. Jain that helped in
improvement of the manuscript.
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