Optimum lead–rubber isolation bearings for near-fault motions
R.S. Jangid
Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai – 400 076, India
Abstract
Analytical seismic response of multi-storey buildings isolated by lead–rubber bearings (LRB) is investigated under near-fault motions. The
superstructure is idealized as a linear shear type flexible building. The force–deformation behaviour of the LRB is modelled as bilinear with
viscous damping. The governing equations of motion of the isolated structural system are derived and the response of the system to normal
component of six recorded near-fault motions is evaluated by step-by-step numerical method. The variation of top floor absolute acceleration and
bearing displacement of the isolated building is plotted under different system parameters such as superstructure flexibility, isolation period and
bearing yield strength. The comparison of results indicated that for low bearing yield strength there is significant displacement in the bearing under
near-fault motions. In addition, there also exists a particular value of the yield strength of the LRB for which the top floor absolute acceleration
of the building attains the minimum value. Further, the optimum bearing yield strength is derived for different system parameters under near-fault
motions. The criteria selected for optimality are the minimization of both the top floor acceleration and the bearing displacement. The optimum
yield strength of the LRB is found to be in the range of 10%–15% of the total weight of the building under near-fault motions. In addition, the
response of bridge seismically isolated by the LRB is also investigated and found that there exists a particular value of the bearing yield strength
for which the pier base shear and deck acceleration attain the minimum value under near-fault motions.
Keywords: Base isolation; Earthquake; Near-fault motion; Lead–rubber bearings; Bearing yield strength; Superstructure flexibility; Optimum parameters
1. Introduction
Seismic isolation is an old design idea, proposing the
decoupling of a structure or part of it, or even of equipment
placed in the structure, from the damaging effects of ground
accelerations. One of the goals of seismic isolation is to
shift the fundamental frequency of a structure away from the
dominant frequencies of earthquake ground motion and the
fundamental frequency of the fixed base superstructure. The
other purpose of an isolation system is to provide an additional
means of energy dissipation, thereby reducing the transmitted
acceleration into the superstructure. This innovative design
approach aims mainly at the isolation of a structure from the
supporting ground, generally in the horizontal direction, in
order to reduce the transmission of the earthquake motion to
the structure. Thus, base isolation essentially decouples the
structure from the ground during earthquake excitation.
A variety of isolation devices including elastomeric bearings
(with and without lead core), frictional/sliding bearings and
roller bearings have been developed and used practically for
aseismic design of buildings during the last 20 years [1,2].
Among the various base isolation systems, the lead–rubber
bearings (LRB) had been used extensively in New Zealand,
Japan and United States. The LRB consists of alternate layers
of rubber and steel plates with one or more lead plugs that
are inserted into the holes. The lead core deforms in shear
providing the bilinear response (i.e. adds hysteretic damping
in the isolated structure) and also provides the initial rigidity
against minor earthquakes and strong winds [3]. The first
building isolated by the LRB was the William Clayton building
in Wellington, New Zealand completed in 1981 and followed
by other buildings in several countries. The buildings isolated
with LRB performed very well during the 1994 Northridge and
1995 Kobe earthquakes confirming the suitability of LRB as a
base isolator [4–6].
Several seismologists have suggested that base-isolated
buildings are vulnerable to large pulse-like ground motions
generated at near-fault locations [7,8]. The base-isolated
buildings might perform poorly because of large isolator
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(a) Flexible superstructure.
(b) Force–deformation of LRB.
Fig. 1. Model of N -story building supported on LRB and the force–deformation behaviour of LRB.
displacements due to long period pulses associated in the
near-fault motion. This led to considerable interest by the
researchers; recently several studies of the dynamic behaviour
of base-isolated buildings under near-fault motions have been
reported [9–13]. The bearing displacements under near-fault
motions are found to be significantly large which can cause
instability in the isolation system. The performance of the LRB
system with selected properties was also not reported to be very
satisfactory under near-fault motions in the above studies. Since
the LRB system is a very common isolation system equipped
with all desirable features for base isolation, it is necessary
to study the dynamic behaviour of the LRB system and its
optimum parameters under the near-fault motions.
Here, the response of multi-storey buildings and bridges
isolated by the LRB is investigated under near-fault motions.
The specific objectives of the study are (i) to study the
performance of structures isolated by LRB under near-fault
motions, (ii) to investigate the optimum parameters of the
LRB for minimum earthquake response of the isolated system
under near-fault motions, (iii) to study the variation of optimum
parameters of the LRB under different system parameters of
superstructure and isolation systems, and (iv) to investigate the
seismic response of bridge with LRB under near-fault motions.
2. Modelling of base-isolated building with LRB
Fig. 1 shows the structural system under consideration
which is an idealized N -story shear type building mounted
on the LRB system. The lead-core of the LRB provides an
additional hysteretic damping through its yielding to dissipate
the seismic energy and reduction in the bearing displacement.
Various assumptions made for the structural system under
consideration are: (i) floors of each story of the superstructure
are assumed as rigid, (ii) force–deformation behaviour of the
superstructure is considered to be linear with viscous damping,
(iii) the force–deformation behaviour of the LRB is considered
as bilinear defined by the three parameters Fy , kb and q which
denote to the yield strength, post-yield stiffness and yield
displacement, respectively, and (iv) the structure is excited by
a single horizontal component of near-fault earthquake ground
motion and the effects of vertical component of the earthquake
acceleration are neglected.
At each floor and base mass one lateral dynamic
degree-of-freedom is considered. Therefore, for the N -storey
superstructure the dynamic degrees-of-freedom are N + 1.
The governing equations of motion for fixed-base N -story
superstructure model is expressed in matrix form as:
[M]{ẍ} + [C]{ẋ} + [K ]{x} = −[M]{1} (ẍ g + ẍb )
(1)
where [M], [K ] and [C] are the mass, stiffness and damping
matrices of the fixed base structure of the order N × N ;
{x} = {x1 , x2 , . . . , x N }T is the displacement vector of the
superstructure; x j ( j = 1, 2, . . . , N ) is the lateral displacement
of the jth floor relative to the base mass; {1} = {1, 1, 1, . . . , 1}T
is the influence coefficient vector; ẍb is the acceleration of
base mass relative to ground; and ẍ g is the acceleration of
earthquake ground motion. Note that the damping matrix of the
superstructure, [C] is not known explicitly. It is constructed by
assuming the modal damping ratio which is kept constant in
each mode of vibration.
The governing equation of motion of the base mass is
expressed by:
m b ẍb + cb ẋb + Fb − c1 ẋ1 − k1 x1 = −m b ẍ g
(2)
where m b is the mass of base raft; Fb is the restoring force
mobilized in the LRB (i.e. represents the bilinear behaviour as
shown in Fig. 1(b)); cb is the viscous damping due to rubber
of the LRB or additional viscous dampers; and k1 and c1 is the
stiffness and damping of the first storey of the superstructure.
The governing equations of motion of the isolated structure
cannot be solved using the classical modal superposition
technique due to non-linear force–deformation behaviour of
the LRB. As a result, the governing equations of motion are
solved in the incremental form using Newmark’s step-by-step
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Table 1
Peak acceleration of normal component of six near-fault motions
Near-fault earthquake motions
Peak acceleration (g)
Peak velocity (m/s)
October 15, 1979 Imperial Valley, California (Array # 5)
October 15, 1979 Imperial Valley, California (Array # 7)
January 17, 1994 Northridge, California (Newhall station)
June 28, 1992 Landers, California (Lucerene Valley station)
January 17, 1994 Northridge, California (Rinaldi station)
January 17, 1994 Northridge, California (Sylmar station)
Average
0.36
0.45
0.70
0.71
0.87
0.72
0.64
0.746
1.132
1.188
0.625
1.745
1.222
1.110
method assuming linear variation of acceleration over small
time interval, 1t. The maximum time interval selected for
solving the equations of motion is 10−3 s.
3. Bilinear modelling of lead–rubber bearings
The bilinear force–deformation behaviour of the LRB
requires the specification of three parameters namely Fy , kb and
q as shown in Fig. 1(b). The post-yield stiffness, kb of the LRB
is designed in such a way as to provide the specific value of the
isolation period, Tb expressed as:
s
M
Tb = 2π
(3)
kb
P
where M = m b + Nj=1 m j is the total mass of the isolated
building; and m j is the mass of the jth floor.
The yield strength of the bearing is normalized with respect
to the total weight of the isolated building and expressed by the
parameter, F0 defined as:
F0 =
Fy
W
(4)
where W = Mg is the total weight of the isolated building; and
g is the acceleration due to gravity.
The viscous damping, cb in the bearing due to rubber is
evaluated by the damping ratio, ξb expressed as:
ξb =
cb
2Mωb
(5)
where ωb = 2π/Tb is the base isolation frequency.
Thus, the modelling of LRB requires the specification of
four parameters namely the isolation period (Tb ), damping ratio
(ξb ), normalized yield strength (F0 ) and yield displacement
(q).
4. Numerical study
For the present study, the mass matrix of the superstructure,
[M] is diagonal and characterised by the mass of each floor
which is kept constant (i.e. m i = m for i = 1, 2, . . . , N ).
Also, for simplicity the stiffness of all the floors is taken
as constant expressed by the parameter k. The value of k
is selected such as to provide the required fundamental time
period of superstructure as a fixed base. The damping matrix of
the superstructure, [C] is not known explicitly. It is constructed
Fig. 2. Time variation of top floor absolute acceleration and bearing
displacement of a five-storey base-isolated structure under Imperial Valley,
1979 (Array # 5) earthquake ground motion (Ts = 0.5 s, Tb = 2.5 s, ξb = 0.05
and q = 5 cm).
by assuming the modal damping ratio which is kept constant
in each mode of vibration. Thus, the superstructure and the
base mass of the isolated structural system under consideration
can be completely characterized by the parameters namely,
the fundamental time period of the superstructure (Ts ),
damping ratio of the superstructure (ξs ), number of stories
in the superstructure (N ), and the ratio of base mass to the
superstructure floor mass (m b /m). For the present study, the
parameters ξs and m b /m are held constant with ξs = 0.02 and
m b /m = 1.
The seismic response of the base-isolated structure is
obtained under the normal component of six near-fault
earthquake ground motions. The peak ground acceleration
and velocity of the selected earthquake motions is given in
Table 1. For the base-isolated building, the response quantities
of interest are the top floor absolute acceleration (i.e. ẍa =
ẍ N + ẍb + ẍ g ) and the relative bearing displacement (xb ).
The absolute acceleration is directly proportional to the forces
exerted in the superstructure due to earthquake ground motion.
On the other hand, the relative base displacement is crucial from
the design point of view of the isolation system.
Fig. 2 shows the time variation of the top floor absolute
acceleration and bearing displacement of structure isolated
by the LRB system under Imperial Valley, 1979 earthquake
motion. The response is shown for two values of the bearing
yield strength i.e. F0 = 0.075 and 0.15 with Tb = 2.5 s,
ξb = 0.05 and q = 5 cm. The superstructure considered
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Fig. 3. Time variation of top floor absolute acceleration and bearing
displacement of a five-storey base-isolated structure under Northridge, 1994
(Sylmar station) earthquake ground motion (Ts = 0.5 s, Tb = 2.5 s, ξb = 0.05
and q = 5 cm).
is of five-storey with fundamental time period, Ts = 0.5 s.
The figure indicates that there is same reduction in the
top floor acceleration of the building for both values of
the yield strengths of LRB. The reduction in the top floor
acceleration is of the order of about 80% implying that the
LRB is quite effective for buildings under near-fault motions.
However, there is significant difference in the peak values
of the bearing displacement. The peak bearing displacements
are 42.95 cm and 17.88 cm for F0 = 0.075 and 0.15,
respectively. This implies that under the near-fault motions
the increase in the bearing yield strength can reduce the peak
bearing displacement significantly without much altering to the
superstructure accelerations. Similar differences in the response
of isolated structure for two values of the bearing yield strengths
are also depicted in Fig. 3 under 1994 Northridge earthquake
motion (recorded at Sylmar station). Thus, it is possible to
reduce the peak displacement in the LRB by increasing its yield
strength without sacrificing the benefits of base isolation in
the reduction of superstructure accelerations under near-fault
motions.
In order to distinguish the difference in the response of the
isolated building for two values of the bearing yield strengths,
the corresponding force–deformation loops are plotted for
comparison in Fig. 4. It is observed that for F0 = 0.075
the bearing displacement and ductility is quite excessive as
compared with F0 = 0.15. The figure indicates that the
relatively better performance of the LRB at higher yield
strength is not due to hysteretic damping of the LRB (as there
are not many force reversal cycles). The better performance can
be attributed due to stiffening of the isolator produced by the
higher yield strength under near-fault motions. This stiffening
effect results in a period of the isolated structure away from the
typical pulse periods (i.e. in the range of 2–3 s). For relatively
low values of the bearing yield strength, the effective period of
the isolated structure is about 2.5 s which is quite close to the
pulse duration resulting in large bearing displacements. Thus,
the yield strength of the LRB should be such that it provides
the enough initial rigidity as well as isolation when there is no
yielding in the lead-core.
Fig. 5 shows the variation of the peak top floor
absolute acceleration and the bearing displacement against the
normalized bearing yield strength, F0 under different near-fault
motions. The responses are shown for a five-storey building
with Ts = 0.5 s, Tb = 2.5 s, ξb = 0.05 and for two
values of bearing yield displacements (i.e. q = 2.5 cm and
5 cm). It is observed from the Fig. 5 that as the bearing
yield strength increases the top floor absolute acceleration first
decreases attaining a minimum value and then increases with
the increase of yield strength. This indicates that there exists
a particular value of the yield strength of the LRB for which
the top floor superstructure acceleration of a given structural
system attains the minimum value under the near-fault motions.
In Fig. 5, the variation of the average top floor acceleration
and bearing displacement is also plotted for comparison. The
average of peak top floor acceleration attains the minimum
value at F0 = 0.04 and 0.07 for q = 2.5 cm and 5 cm,
respectively. Further, the top floor acceleration is not much
influenced by the variation of the bearing yield strength up to a
certain value (i.e. up to 0.15). On the other hand, the bearing
displacement continues to decrease with the increase in the
bearing yield strength. The above observations imply that by
designing an optimum LRB, it is possible to reduce the bearing
displacements significantly without much increasing the top
floor accelerations under near-fault motions.
Fig. 6 shows the variation of average peak top floor
absolute acceleration and the bearing displacement against
the normalized bearing yield strength, F0 for four values of
damping ratio of the LRB (i.e. ξb = 0.025, 0.05, 0.075 and
0.1). As observed earlier, there exists a particular value of
the bearing yield strength for minimum top floor acceleration
for all values of the bearing damping. In general, the viscous
damping of the bearing does not have very significant influence
on the peak response of the isolated structure except for the
lower bearing yield strengths. Thus, the viscous damping of
the LRB does not significantly influence the peak response of
base-isolated building under near-fault motions. Further, the
comparison of the response of the LRB for two values of
the yield displacements indicates that the bearing with higher
yield displacement appears to perform better under near-fault
motions. The corresponding minimum top floor acceleration for
the higher yield displacement of the LRB occurs at a higher
value of the bearing yield strength where the peak bearing
displacement is significantly less. Thus, the LRB with relatively
higher yield displacement performs better than the bearing with
low yield displacement under near-fault motions.
The Figs. 5 and 6 had indicated that due to increase in the
yield strength of the LRB there is a decrease in the bearing
displacement without much increase in the superstructure
accelerations under near-fault motions. Infact, there exists a
particular value of the yield strength for which the top floor
acceleration is minimum. Further, it is also observed that
in the vicinity of the particular yield strength, the top floor
acceleration is not much influenced with the variation of the
bearing yield strength. One can take the advantage of the above
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Fig. 4. Force–displacement behaviour of the LRB isolating the five-storey building for two different levels of yield strength (Ts = 0.5 s, Tb = 2.5 s, ξb = 0.05 and
q = 5 cm).
Fig. 5. Variation of peak top floor absolute acceleration and bearing displacement of a five-storey base-isolated building against normalized yield strength of LRB,
F0 = Fy /W (Ts = 0.5 s, Tb = 2.5 s and ξb = 0.05).
behaviour of the isolated structure in designing the optimum
LRB in which the yield strength can be kept to a value slightly
higher than the corresponding particular value of minimum
acceleration to achieve maximum isolation with lesser bearing
displacement. Thus, the optimum yield strength of the LRB
can be obtained by minimization of a force quantity which is
2508
Fig. 6. Variation of average peak top floor absolute acceleration and bearing displacement of a five-storey base-isolated structure against normalized yield strength
of LRB, F0 = Fy /W (Ts = 0.5 s and Tb = 2.5 s).
function of both the peak top floor absolute acceleration as well
as bearing displacement defined as
f (ẍa , xb ) = Q + 2kb xb + M ẍa
(6)
where f (ẍa , xb ) is the force function selected for optimum
yield strength of the LRB; Q is the characteristic strength
of the LRB or the yield strength of the lead-core (refer
Fig. 1(b)). The term M ẍa indicates the maximum force exerted
in the superstructure due to earthquake motion (under rigid
superstructure condition). The factor 2 used in the Eq. (6)
implies that relatively more weightage is given for reduction in
the bearing displacement in comparison to the reduction in the
top floor absolute acceleration. This is due to the fact that the
Q+kb xb ≈ M ẍa (i.e. the maximum bearing force is equal to the
maximum earthquake force on the superstructure). If the factor
2 is not used in Eq. (6) then the forcing function, f (ẍa , xb )
will be minimum when the top floor acceleration is minimum.
The factor 2 is selected by trial and error with the criterion that
the superstructure acceleration does not increase significantly
with the decrease in the bearing displacement. It is to be noted
that the proposed study for the optimum parameter of the LRB
is quite different than that reported in the past [14–17]. In
these studies the optimum parameters especially the damping
were obtained for the minimum superstructure accelerations
using the probabilistic approach. The optimum damping exists
because of the fact that the higher damping in the isolation
system transmits more acceleration for the high frequency
components of excitation. The present optimization study is
quite different than earlier studies and it is for low frequency
pulses associated in the typical of near-fault earthquake motion
records for the minimum isolator displacement.
Fig. 7 shows the variation of different terms of the Eq. (6)
against the normalized yield strength of the LRB, F0 for
one and five-storey building with two values of bearing yield
displacement (i.e. q = 2.5 and 5 cm). The f (ẍa , xb ) attains
the minimum value for a certain value F0 for all cases which
is referred as the optimum normalized yield strength of the
LRB. The optimum value of F0 for one-storey building is
found to be 0.1 for q = 2.5 cm which is slightly higher
than the corresponding value of yield strength when the top
floor superstructure acceleration attains the minimum values
(i.e. F0 = 0.08). The top floor acceleration is found to be
0.35g and 0.36g and bearing displacement are 38.35 cm and
33.24 cm for F0 = 0.08 and 0.1. This justifies the use
of Eq. (6) for evaluation of the optimum yield strength of
the LRB where the top floor acceleration of the structure
remains close to the minimum value but with lesser bearing
displacement. The optimum F0 for one-story building with
q = 5 cm is 0.12 implying that the optimum bearing yield
strength increases marginally with the increase of the yield
displacement. The corresponding optimum values of F0 for the
five-storey building are 0.1 and 0.11 for q = 2.5 and 5 cm.
Figs. 8 and 9 shows the variation of optimum F0 of the
LRB along with the corresponding peak top floor acceleration
and relative bearing displacement against the fundamental
time period of the superstructure, Ts for a one and five-story
superstructure. The optimum parameters are obtained for three
periods of isolation (i.e. Tb = 2, 2.5 and 3 s) and two values
of yield displacement (i.e. q = 2.5 and 5 cm). The optimum
F0 of the LRB for different system parameters is found to
be in the range of 0.1–0.15. It is also observed from these
figures that as the time period of the superstructure increases
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Fig. 7. Variation of the function f (ẍa , xb ) and its different terms against normalized yield strength of LRB, F0 = Fy /W (Ts = 0.5 s, Tb = 2.5 s and ξb = 0.05).
Fig. 8. Variations of optimum bearing yield strength and corresponding average peak top floor absolute acceleration and bearing displacement of a one-storey
base-isolated building against fundamental time period of superstructure (ξb = 0.05).
the optimum F0 decreases. The optimum F0 also decreases with
the increase of the isolation period of the structure based on
the post-yield stiffness of the LRB. The decrease of optimum
F0 with the increase of isolation period (i.e. lower value of
the post-yield stiffness, kb ) is expected from the selected form
of objective function expressed by Eq. (6) where the weighing
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Fig. 9. Variation of optimum bearing yield strength and corresponding average peak top floor absolute acceleration and bearing displacement of a five-storey
base-isolated building against fundamental time period of superstructure (ξb = 0.05).
factor to displacement is reduced which favours the acceleration
control of structure resulting in the lower optimal bearing yield
strength. Further, the optimum F0 are relatively higher for
bearing with q = 2.5 as compared to that of q = 5 cm. On
the other hand, the peak bearing displacement corresponding to
the optimum F0 increases with the increase of the time period
of superstructure and isolation system. The corresponding top
floor absolute acceleration increases mildly with the increase of
the flexibility of the structure and decreases with the increase
of the flexibility of the LRB. Thus, the optimum yield strength
of the LRB under near-fault motions is found to be in the
range of the 10%–15% of the weight of the isolated structure
and it increases with stiffness of both superstructure as well
as LRB. The desired value of the yield strength of the bearing
can be achieved by suitably selecting the size of the lead-core
of the LRB. In Fig. 10, the variation of the optimum F0 of
the LRB and corresponding top floor acceleration and bearing
displacement are plotted against the number of stories in the
superstructure, N . The period of the superstructure, Ts is fixed
as 0.1N s. For a given value of N , the inter-story stiffness of
the superstructure is adjusted such that the fundamental time
period obtained from the eigenvalues analysis of the mass and
stiffness matrix provides the desired value of Ts . It is observed
from the Fig. 10 that the effects of the superstructure and
isolator flexibility on the optimum parameters of the LRB and
corresponding peak responses are similar to that observed in
Figs. 8 and 9.
5. Response bridges with LRB
Bridges are lifeline structures and act as an important link
in surface transportation network. Failure of bridges during a
seismic event will seriously hamper the relief and rehabilitation
work. There has been considerable interest in earthquakeresistant design of bridges by seismic isolation in which the
isolation bearings are used which replace the conventional
bridge bearings to decouple the bridge deck from bridge
substructure during earthquakes [17–21]. There are several
bridges constructed and retrofitted using the seismic isolation
devices including the LRB. In order to study the performance
of LRB for bridges under near-fault motions, consider a threespan span continuous deck bridge as shown in Fig. 11(a). The
LRB are provided both at abutment as well as at pier level.
The bridge is mathematically modelled for studying the seismic
response as shown in Fig. 11(b) assuming the rigid deck17 . The
same numbers of LRB with identical properties are provided
at piers and abutments level. The entire LRB are designed to
provide the specific values of three parameters namely, Tb , ξb
and F0 based on the parameter M equal to the deck mass (refer
Eqs. (4)–(6)). The properties of the three-span bridge taken
from Ref. [18] are: deck mass = 771.12 × 103 kg; mass of each
pier = 39.26 × 103 kg; moment of inertia of piers = 0.64 m4 ;
Young’s modules of elasticity = 20.67 × 109 (N/m2 ); pier
height = 8 m; and total length of bridge = 90 m.
The variation of average peak base shear, deck acceleration
and bearing displacements of the isolated bridge against the
normalized yield strength of LRB is shown in Fig. 12 for six
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Fig. 10. Variation of optimum bearing yield strength and corresponding average peak top floor absolute acceleration and bearing displacement of base-isolated
building against number of stories of superstructure (Ts = N /10 s and ξb = 0.05).
Fig. 11. Model of a bridge seismically isolated by the LRB.
near-fault motions. The responses are plotted for three values
of isolation period of the bearing (i.e. Tb = 2, 2.5 and 3 s)
to study the effects of bearing flexibility. The bearing damping
ratio and yield displacements are taken as 0.05 and 5 cm. It is
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Fig. 12. Variation of average peak pier base shear, deck acceleration and bearing displacement of the isolated bridge against normalized yield strength of LRB,
F0 = Σ Fy /Wd (ξb = 0.05 and q = 5 cm).
observed from the figure that with the increase in F0 decreases
the bearing displacements. This is due to the fact that for higher
values of yield strength the isolation system becomes relative
stiff, as a result, the bearing displacements are reduced. On
the other hand, the pier base shear and deck acceleration first
decreases, attains the minimum value and than increases with
the increase of the bearing yield strength. This implies that
there exists a particular value of the bearing yield strength for
which the peak pier base shear and deck acceleration attains
the minimum value under near-fault motions. The minimum
value of the pier base shear and deck acceleration occurs for
the value of F0 in the range of 0.1–0.15 for different values of
the isolation periods. It is also observed that the pier base shear
and deck acceleration decreases with the increase in isolation
period implying that the effectiveness of LRB increases with
the increase of its flexibility. On the other hand, the relative
bearing displacements are also relatively higher for the higher
values of isolation periods especially for the lower bearing yield
strengths.
The variation of the response of isolated bridge system in
Fig. 12 indicates that the best LRB for the bridges under nearfault motions can be designed by taking the high bearing yield
strength (in the range of 0.15–0.2 times deck weight) with postyield stiffness providing the period of the isolated bridge in the
range of 2.5–3 s.
6. Conclusions
Analytical seismic response of the multi-story buildings
isolated by the lead–rubber bearings (LRB) is investigated
under near-fault motion. The normal component of six recorded
near-fault motions is used to investigate the variation of the
top floor acceleration and bearing displacement of the isolated
building. The response of the isolated building is plotted under
different system parameters such as superstructure flexibility,
isolation period and bearing yield strength. Further, the
optimum yield strength of LRB is derived for different system
parameters under near-fault motions. The criteria selected for
the optimality is to minimization of both top floor absolute
acceleration as well as the bearing displacement. In addition,
the response of bridge seismically isolated by the LRB is also
investigated under near-fault motions. From the trends of the
results of the present study, the following conclusions may be
drawn:
(1) For low values of the bearing yield strength there is
significant displacement in the LRB under near-fault
motions. The increase in the bearing yield strength can
reduce the bearing displacement significantly without much
altering to the superstructure accelerations.
(2) The LRB with appropriate properties is quite effective for
seismic isolation of structures under near-fault motions.
The LRB with higher yield displacement (i.e. soft bearings)
perform better than the bearing with low yield displacement
under near-fault motions.
(3) There exists a particular value of the yield strength of the
bearing for which the top floor absolute acceleration of the
multi-story building attains the minimum value.
(4) In the vicinity of the particular yield strength of the
bearing, the top floor absolute acceleration is not much
influenced by the variation of the bearing yield strength.
However, the bearing displacement decreases significantly
2513
with the increase of yield strength around the particular
yield strength.
(5) The optimum yield strength of the LRB based on the
criterion of minimization of both top floor absolute
acceleration and bearing displacement is found to be in the
range of 10%–15% of the total weight of the building under
near-fault motions.
(6) The optimum yield strength of LRB under near-fault
motions is found to increases with stiffness of both LRB as
well as superstructure. However, the bearing displacement
at optimum yield strength increases with the increase of the
flexibility of the bearing and the superstructure.
(7) The response of bridge seismically isolated by LRB under
near-fault motions indicated that there exists a particular
value of the bearing yield strength for which the pier base
shear and deck acceleration attain the minimum value.
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