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Seismic responses and energy dissipation of pure-friction and resilient‐friction base-isolated structures: A parametric study
Journal Pre-proof Seismic responses and energy dissipation of pure-friction and resilient‐friction baseisolated structures: A parametric study Sadegh Etedali, Kazem Hasankhoie, Mohammad Reza Sohrabi PII:
S2352-7102(19)32506-9
DOI:
https://doi.org/10.1016/j.jobe.2020.101194
Reference:
JOBE 101194
To appear in:
Journal of Building Engineering
Received Date: 13 November 2019 Revised Date:
13 January 2020
Accepted Date: 14 January 2020
Please cite this article as: S. Etedali, K. Hasankhoie, M.R. Sohrabi, Seismic responses and energy dissipation of pure-friction and resilient‐friction base-isolated structures: A parametric study, Journal of Building Engineering (2020), doi: https://doi.org/10.1016/j.jobe.2020.101194. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Seismic responses and energy dissipation of pure-friction and resilient‐‐friction baseisolated structures: a parametric study Sadegh Etedali*1, Kazem Hasankhoie2, Mohammad Reza Sohrabi3 1
Department of Civil Engineering, Birjand University of Technology, P.O. Box 97175-569, Birjand, Iran 2,3
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
*Correspondence to: Sadegh Etedali, Associate Professor, Department of Civil Engineering, Birjand University of Technology, Birjand, Iran Tel: +98 561 8821296 Fax: +98 561 2252098 Email: [email protected]
Seismic responses and energy dissipation of pure-friction and resilient‐‐friction baseisolated structures: a parametric study Abstract: A comprehensive parametric study is carried out on pure-friction base-isolated (PFBI) and resilient‐friction base-isolated (R-FBI) structures in this paper. For this purpose, an 8story building subjected to a band-limited white noise acceleration modeled based on a stationary process is considered. At first, the time histories of seismic response and superstructure energy for P-FBI and R-FBI structures are compared with those given for a fixed-base (F-B) structure. A vast range of values for the friction coefficient of the sliding surface, mass ratio of the base story, target period, and damping ratio of the restoring device are also considered for the parametric study. Then, the effect of changing these parameters on the maximum response of stories and superstructure energy is investigated. Considering a low friction coefficient, it is concluded that the restoring device of the R-FBI structure is able to significantly reduce displacement of the base story during earthquake excitations. It is also capable to return the base story to its original location at the end of an earthquake. Simulation results also show that the restoring device increases the maximum seismic input energy entered into the superstructure but reduces the maximum seismic damage energy of the superstructure. Results demonstrate that the amount of friction coefficient has the greatest effect on seismic responses of the studied structure. Base displacement is reduced with increasing friction coefficient, but top floor acceleration and superstructure drift are significantly increased, which results in an increment in maximum input and damage energies. Overall results indicate that an increment in damping ratio of the restoring device results in a reduction in maximum base displacement and top floor acceleration, and an increment in maximum top floor displacement and drift, while it has no effect on the residual base displacement. Moreover, base displacement and top floor drift are increased by increasing the period of the restoring device, while other seismic responses are reduced. Keywords: Pure-friction base-isolated structure, restoring device, resilient‐friction base-isolated structures, parametric study, seismic response, energy dissipation 1. Introduction Seismic isolation systems separate a part or all of a structure from the ground and reduce the seismic load applied to the main structure. They decrease the natural frequency of the structures and divert it away from the dominant frequency of seismic loads [1]. In the last few decades, several types of seismic isolators have been proposed and developed. Seismic isolators are often divided into elastomeric and friction isolators. Low damping natural rubber (LDNR) bearing, lead rubber bearing (LRB), high damping natural rubber (HDNR) bearing, pure- friction and friction pendulum system (FPS) are the well-known types of the isolators [2]. Seismic isolation is an effective method to mitigate the inter-story drift and absolute acceleration of the stories of a building [3]. The seismic performance of the base-isolated buildings with different isolation systems has been studied in the literature. Some studies have also focused on the evaluation of
the seismic performance of bridges equipped with seismic isolators. To validate the design strategy, and to provide commendations for improving the seismic performance of bridges, Luo et al. [4] studied the seismic performance of prototype quasi-isolated highway bridges. Xiang et al. [5] investigated the cost-effectiveness of using yielding steel dampers and laminated rubber bearings for highway bridges in comparison with other popular isolation systems. The performances of various isolation systems in vibration mitigation of the structures subjected to underground blast-induced ground motion are studied by Mondal et al. [6]. Pure- friction system is the simplest type of friction isolators. In this type of isolator, the rollers or sliders are provided between the foundation and the base of the structure [7]. The seismic response of an asymmetric structure equipped with the sliding bearing is studied in [8]. Jangid [9] also compared the vibration responses of an asymmetric one-story sliding isolated structure subjected to base harmonic acceleration consideration the interaction between the two lateral frictional resistances of the sliding isolation system. Fan et al. [10] conducted a comparison study on the performance of different types of isolators subjected to harmonic ground motion. Jangid [11] studied the optimal friction coefficient of the sliding surface as an effective parameter on the performance of the friction isolators. The effects of three components of an earthquake on the response of the pure-friction base-isolated structures are addressed in [12]. Krishnamoorthy [13] investigated the seismic performance of a space frame structure resting on sliding bearing equipped with the restoring device. Considering four different sliding interfaces, Nanda et al. [14] studied suitable friction sliding materials for base isolation of masonry buildings. Large displacements of the base raft in the structure equipped with a purefriction system endanger their safety during earthquake excitations [7]. In order to overcome this problem, restoring devices are supplemented to the pure- friction system. [15-17]. Fallah and Zamiri [16] utilized a multi-objective optimization based on the genetic algorithm for the optimum design of a sliding isolation system. Considering the vertical component of an earthquake, the seismic response of pure-friction sliding base-isolated structures is investigated in [17]. The numerical and theoretical studies of Sachdeva et al. [18] also showed that restoring devices can effectively reduce the maximum displacement of the base level. There are extensive studies on the seismic performance elastomeric isolation system in the literature. In addition, most studies carried out on the friction isolation system are limited to the P-FBI structures. In most researches, the seismic responses of the R-FBI structures are only taken into account to evaluate the performance of these structures, while the assessment of the efficiency of the R-FBI systems for seismic control of the building from the point of energy view is interesting. Hence, the present study aims to conduct a comprehensive parametric study on the pure-friction and resilient‐friction base-isolated structures from the points of seismic responses and energy dissipation. For this purpose, considering a vast range of values for the friction coefficient of the sliding surface, mass ratio of the base story, the target period and damping ratio of the restoring device, the performance of R-FBI system for dissipation of superstructure's energy, in the terms input, damage and damping energies, is also compared with those given for pure-friction isolation (P-FBI) system. On the other hand, numerous time history analyses to
achieve reliable results of the seismic performance of the R-FBI system are time-consuming and costly. Conventionally, a spectral density function is used rather than a collection of time history input to tackle the problem. In a stochastic analysis, an artificial acceleration of the ground motion is simulated for modeling the possible earthquakes. Therefore, the studied structures for the numerical study are subjected to a band-limited white noise acceleration modeled based on a stationary process. Time history responses of the structure in terms of base displacement, top floor displacement, acceleration and drift for two cases of PF-BI and R-FBI structures are compared with those given for the corresponding fixed-base structure. From the point of energy view, the time history of the input, damage and damping energies of the superstructure for three cases of the F-B, P-FBI, and R-FBI structures are also compared. Then, the effect of changing of the dynamic parameters of pure-friction systems and the restoring device of R-FBI structure on the maximum response of stories and superstructure energy is studied in this paper. The reminder paper is organized as follows. The mathematical models of P-FBI and R-FBI structures are presented in Sections 2. Numerical studies are carried out in Section 3. Simulation results are discussed in Section 4. The concluding remarks are drawn in Section 5. 2. Mathematical model An N-story shear-type frame equipped with a resilient friction base isolation system is schematically shown in Figure 1(a). It is notably that a restoring device can be combined with the slider in two parallel and series combinations. The restoring device includes a linear spring and viscous damper. For parallel combination, shown in Figure 1(b), the transmission force to superstructure is the sum of the restoring force of spring and friction force at the sliding interface. It is generally used in conjunction with rubber bearings, as shown in Figure 1(c). RFBI system consists of concentric layers of Teflon-coated plates in friction contact with each other and a central rubber core. 2.1. The governing equations for friction base-isolated structure with the restoring device The motion of a structure equipped with R-FBI can be stated in two phases: the non-sliding phase and the sliding phase. The governing equations in the non-sliding phase can be given by the following equation.
Figure 1. (a) An N-story R-FBI structure (b) the model of the restoring device (c) a cross-section of R-FBI system [15] ( ) + + =− (1) where , and represent the matrices of mass; stiffness and damping of the superstructure; = , ,..., refer to the displacement vector of the superstructure relative to the base story; = 1,1, . . . ,1 is the location vector of an earthquake acceleration with unit entity and is the earthquake ground acceleration. The mobilized frictional force in this phase can be written as follows: =− − − + + (2) in which is the base mass, and are the damping and stiffness coefficients of the first story of the superstructure, is the displacement of the base raft relative to the ground, and are the damping and stiffness coefficients of the restoring device, respectively which are obtained from the following equations: +!
=2
"#
+!
=
"#
"$ "$ (
2%' &
(3)
2%' ) &
(4)
In the above equations, and & refer to the damping ratio and the target period of the restoring device. Also, " is the mass of the i-th floor of the superstructure. When the mobilized frictional force crosses the boundary of the frictional force, the structure enters the sliding phase. During this phase, the equation of motion of the superstructure can be given by: +
+
=−*
+
+
,
(5)
Also, the equation of motion of the isolation system can be expressed as follows: +
- sgn(
)+
+
−
−
=−
where the frictional force can be given by:
-
=1
+! "#
"$ 2
in which 1 is the friction coefficient of the sliding surface and sgn (. ) is the sign function.
(6)
2.2. The equations of energy for friction base-isolated structure with the restoring device Evaluating the efficiency of the friction isolation systems for seismic control of the building from the point of energy view is interesting. Seismic control of a structure can be described as an energy transfer process. By integrating equation (5) with respect to during the motion, the following equation can be obtained. 5
5
3
5
4 +3
6
5
4 +3
6
4 = −3
6
6
+7
8+
,4
(7)
The first term of Equation (7) is known as the relative kinetic energy and can be expressed as follows. 5
9: = 3
4 =
6
1 2
(8)
The second term of equation (7) called the damping energy and can be rewritten as follows: 5
5
9; = 3
4 =3
6
4t
6
(9)
The third term is the recoverable strain energy: 5 1 9= = 3 4 = 2 6
(10)
Also, the right expression of equation (7) is the seismic input energy as follows: 5
9> = 3
6
+7
8+
5
,4 = 3
6
(7
8+
)4
(11)
The total seismic input energy in the base-isolated structure is dissipated by the friction isolation system and a part of this energy is entered into the superstructure. The energy transferred to the superstructure converted to both recoverable strain and relative kinetic energies. Also, a part of this energy is dissipated by the damping energy. The sum of the relative kinetic and recoverable strain energies is known as the total energy of the superstructure or the damage energy of the superstructure [19]. 3. Numerical studies
Numerical studies are carried out on an 8-story building equipped with the pure-friction isolation system. The mass of each floor is adopted as " = 360 ton. The frequencies of the first to the eighth structural mods are calculated as 1.25, 3.71, 6.04, 8.16, 10.01, 11.52, 12.63 and 13.32 Hz, respectively. The acceleration of the ground is also considered as a stationary process with the following power spectral density function [20-21]: B(C) =
4 C C C +2 C C+C
(12)
where and C represent the damping ratio and angular frequency of the ground, respectively. The artificial ground acceleration simulated by the above power spectral density function is shown in Figure 2. It can be a suitable statistical representation of different earthquakes [22-23]. First, the seismic performances of the P-FBI and R-FBI structures are compared with those given for the F-B structure. For this purpose, the time histories of the structural responses in terms of the top floor displacement, top floor acceleration, top floor drift, base displacement and the time histories of energy responses including the input, damping and damage energies are investigated. Then, a comprehensive parametric study on the seismic performance of friction base-isolated structures is conducted in this study. For this purpose, a vast range of design parameters of the friction isolators in two cases without and equipped with the restoring device is considered. These parameters are included the friction coefficient of the friction isolation system, the mass ratio of the base story, the damping ratio and the target period of the restoring device. The effect of changes of these parameters on maximum structural responses in terms of the maximum base displacement, maximum top floor displacement, maximum top floor acceleration, maximum top floor drift, maximum residual base displacement is studied. Considering two cases without and equipped with the restoring device, the effect of changes of the design parameters of the friction isolators is also investigated on the maximum energy responses in terms of maximum input, damage and damping energies.
Acceleration (cm/s2)
400 200 0 -200 -400 0
10
20
30 Time(sec)
Figure 2. Time history of the artificial earthquake acceleration
40
50
4. Results and discussions 4.1. Time history responses The seismic responses of the P-FBI and R-FBI structures are compared in this section. The damping ratio and the target period of the base isolation system is adopted as & = 2 sec and = 0.05. Also, the mass ratio of the base story and the friction coefficient of the sliding surface
is
"
Top floor absolute acceleration (m/s2)
drift
'
=1 and 1 = 0.02. The time histories of the top floor displacement, acceleration, and
5
0
-5 0
5
10
15
20
25 Time (s)
30
35
40
45
50
5
10
15
20
25 Time (s)
30
35
40
45
50
-3
Top floor drift (m)
4
x 10
2 0 -2 -4 0
Figure 3. Time histories of the top floor displacement, acceleration, and drift
Figure 4. Time histories of base displacement during the artificial earthquake excitation are shown in Figure 3. For comparison purposes, the structural responses of the F-B structure are also illustrated in the figures. As can be seen, the friction isolation system is able to reduce the top floor displacement, acceleration, and drift of the structure in comparison with those given for the fixed-base structure. In this case, it can be found that there is no significant difference between the time history responses of the base-isolated structure in terms of top floor acceleration and drift for P-FBI and R-FBI structures. However, as can be seen from Figure 3, the restoring device is able to reduce the maximum top floor displacement. The main advantage of the use of the restoring device is observed in Figure 4. As can be seen, the restoring device is able to significantly reduce displacement of the base story during the artificial earthquake excitation. Also, it is found that the residual displacement of the base story at the end of the earthquake is about 20 cm for the case without the restoring device, while the base story of the R-FBI structure has returned to its original location at the end of the earthquake. The evaluation of the seismic performance of a structure can be attractive from the point of energy transfer. Seismic input energy (9> ) entering the superstructure is converted to both recoverable strain (9- ) and relative kinetic (9F ) energies. Also, some amount of the input energy is dissipated by the damping energy (9; ). The sum of the relative kinetic and recoverable strain energies is the total energy of the system or the damage energy. Figure 5 illustrates the time histories of the input, damage and damping energies of the superstructure for three cases of the F-B, P-FBI and R-FBI structures. It is found that a significant portion of the seismic input energy is wasted by the isolation system and a small amount of the input energy is entered into the superstructure. Hence, the maximum values of the seismic input energy of the superstructure for the base-isolated structures are smaller than those given for the fixed-base structure. It is also found that the use of the restoring device reduces the maximum seismic input energy entered into the superstructure. Also, it reduces the maximum seismic damage energy of the superstructure. A significant portion of the energy entered into the base-isolated structure is dissipated by the
isolation system and the restoring device and a small amount of it is wasted by the damping of the superstructure.
500 Input energy (J)
400 300 200 100 0
Damage energy (J)
-100 0
5
10
15
20
25 Time (s)
30
35
40
45
50
5
10
15
20
25 Time (s)
30
35
40
45
50
5
10
15
20
25 Time (s)
30
35
40
45
50
100
50
0 0
Damping energy (J)
500 400 300 200 100 0 0
Figure 5. Time histories of the input, damage and damping energies of the superstructure
As an overall result, it is concluded that the large base displacement and residual deformation after earthquakes may result in a pure-friction isolation system without the restoring device experience. However, At the cost of increasing some seismic responses, advantages in terms of dramatical reduction of the base displacements during an earthquake excitation and eliminate their residual displacements at the end of an earthquake may be achieved due to the use of the restoring device. 4.2. Parametric studies In order to perform a parametric study on the dynamic parameters of the friction isolation system, a vast range of values for the friction coefficient of the sliding surface of the isolation system and mass ratio of the base story is considered. Parametric studies are also carried out on a vast range of the target period and damping ratio of the restoring device. In this study, the ranges of these parameters are considered as 0.01 ≤ 1 ≤ 0.2, 0.5 ≤ and 0.01 ≤
≤ 0.4.
'
"
≤ 1.5, 1 ≤ & ≤ 4
4.2.1. The effect of the friction coefficient Considering the material used for the surface of the pure- friction isolator, a wide range of values for the friction coefficients as 0.01 ≤ 1 ≤ 0.2 is adopted in this study. Figure 6 shows the effect of the friction coefficients on the structural responses in terms of the maximum base and top floor displacements; maximum top floor acceleration and drift, maximum input, damage and damping energies, and maximum residual base displacement. It can be seen that the maximum base displacement is significantly decreased by increasing the friction coefficient in the range of 0.01 ≤ 1 ≤ 0.1 for the P-FBI structure, while the maximum base displacement is often constant for the R-FBI structure. For the large friction coefficient, there is no change in the maximum base displacement for both cases. An increase is observed in the maximum top floor displacement by increasing the friction coefficient. Moreover, the top floor acceleration and drift are often increased by increasing the friction coefficient for both cases. For a low friction coefficient, the P-FBI structure experiences large displacements. Also, a large residual displacement is observed in the base story at the end of the earthquake in this case, while the base story of the R-FBI structure has returned to its original location at the end of the earthquake. It is also found that the maximum input, damage and damping energies for both cases are increased by increasing the friction coefficient. In fact, by increasing the friction coefficient and preventing the free movement of the isolation at the base level, the isolation system gets away from its ideal behavior. Hence, the maximum input and damage energy entering the superstructure increase by increasing the friction coefficient. 4.2.2. The effect of the mass ratio of the base story Considering the P-FBI and R-FBI structures, the effect of the base story mass ratio on the maximum base and top floor displacements; top floor acceleration and drift is shown in Figure 7.
Maximum top floor displacement (cm)
5
4
3
2
1 0.05 0.1 µ 0.15 0.2
8 6 4 2 0 0
0.05
0.1 µ
0.15
400 300 200 100 0.05
0.1 µ
0.15
0.2 0.1 0
200
0.05
0.1 µ
0.15
0.1 µ
0.15
0.2
0.05
0.1 µ
0.15
0.2
0.15
0.2
100
Residual base displacement (m)
400
0.05
120
0.2
600
0 0
0.3
-0.1 0
0.2
500
0 0 Maximum damping energy (J)
Maximum top floor drift (cm)
10
Maximum damage energy (J)
Maximum top floor acceleration (m/s2) Maximum input energy (J)
0.4
0.2
80 60 40 20 0 0 0.2 0.15 0.1 0.05 0 -0.05
0.05
0.1
µ
Maximum top floor displacement (cm)
Figure 6. The effect of friction coefficient on seismic responses of the P-FBI and R-FBI structures
4 3.8 3.6 3.4 3.2 0.5
1 m /m b
1.5
Maximum top floor drift (cm)
Maximum top floor acceleration (m/s2)
0.25
10 9 8 7 6 5 4 0.5
1 m /m
0.2
0.15
0.1 0.5
1.5
b
Maximum damage energy (J)
Maximum input energy (J)
460 450 440 430 420 410 1 m /m
1.5
1 m /m
1.5
b
470
400 0.5
1 m /m
85
80
75
70 0.5
1.5
b
-3
280 275 270 265 260 255 250 245 0.5
1 m /m b
1.5
Residual base displacement (m)
Maximum damping energy (J)
b
x 10 5
0
-5 0.5
1 m /m
1.5
b
Figure 7. The effect of the mass ratio of the base story on seismic responses of the P-FBI and R-FBI structures The effect of the mass ratio of the base story on the maximum input, damage and damping energies of the superstructure is also illustrated in this figure. By increasing the mass ratio, the overall trend shows a decrease in the maximum base displacement and an increase in the maximum top floor displacement and drift of the structure. It is also found that the response level of the R-FBI structure in terms of maximum base displacement and drift is lower than the P-FBI structure. However, the maximum top floor displacement and acceleration are increased as a result of using the restoring device. The superstructure energy responses show a decreasing trend in the maximum input energy responses and an incremental trend in the maximum damping and damage energy responses.
4.2.3. The effect of the damping ratio of the restoring device Figure 8 shows the effect of the damping ratio of the restoring device on the maximum structural responses for the base-isolated structure. As can be seen, increments in the damping ratio of the restoring device result in a reduction in maximum base displacement and top floor acceleration, and an increment in maximum top floor displacement and drift, while it has no effect on the residual base displacement. There is no clear trend in the variation of energy responses against the increase in the damping ratio of the restoring device. 4.2.4. The effect of the period of the restoring device The effect of the period of the restoring device on the maximum structural responses is illustrated in Figure 9. It can be seen that increasing the period of the restoring device increases the maximum base displacement and top story drift. Also, it results in a slight reduction in maximum top floor displacement. For an increase in the target period of the restoring device, small changes with a variable trend are observed in the energy responses of the superstructure. For different ranges of the period of the restoring device, the residual base displacement has not changed and the base story has returned to its original location at the end of the earthquake. 5. Conclusions
1.8 1.6 1.4 1.2 1 0
0.1
0.2 ζb
0.3
0.4
Maximum top floor displacement (cm)
Maximum base displacement (cm)
The present paper aimed to carry out a comprehensive parametric study on the seismic performance of the P-FBI and R-FBI structures from the points of seismic responses and energy dissipation. Based on a stationary process, a band-limited white noise acceleration was utilized for the simulation of artificial earthquake excitation. An 8-story building subjected to the artificial earthquake excitation, in three cases of F-B, P-FBI, and R-FBI, was considered. For the parametric study, a vast range of values for the friction coefficient of the sliding surface, mass ratio of the base story, target period and damping ratio of the restoring device was taken into account and the effect of changing these parameters on the maximum responses of stories and superstructure’s energy was studied. The conclusions remarks are as follows:
4 3.9 3.8 3.7 3.6 3.5 0
0.1
0.2 ζ b
0.3
0.4
2.5 2 1.5 1 1
1.5
2
2.5 Tb
3
3.5
4
Maximum top floor drift (cm)
8
7.5
7
6.5 0
Maximum top floor displacement(cm)
Maximum base displacement (cm)
Maximum top floor acceleration (m/s2)
3
0.1
0.2 ζ
0.3
4.2 4 3.8 3.6 3.4 1
1.5
2
0.18 0.16 0
0.1
0.2 ζb
0.3
0.4
80 0
0.1
0.2 ζ
0.3
0.4
0.2 ζb
0.3
0.4
0.4
92 Maximum damage energy (J)
Maximum input energy (J)
4
0.2
450 445 440 435 430 425 0.1
0.2 ζ
0.3
0.4
90 88 86 84 82
b
b
290
-3
Residual base displacement (m)
Maximum damping energy (J)
3.5
0.22
b
285 280 275 270 265 260 0
3
0.24
455
420 0
2.5 Tb
0.1
0.2 ζ b
0.3
0.4
4
x 10
2 0 -2 -4 0
0.1
Figure 8. The effect of the damping ratio of the restoring device on seismic responses of the R-FBI structure
Maximum top floor drift (cm)
Maximum top floor acceleration (m/s2)
0.24
10 9.5 9 8.5 8 7.5 7 1
1.5
2
2.5 T
3
3.5
0.22 0.2 0.18 0.16 0.14 0.12 1
4
1.5
2
2.5 Tb
3
3.5
4
1.5
2
2.5 T
3
3.5
4
2.5 Tb
3
3.5
4
Maximum damage energy (J)
Maximum input energy (J)
b
460 450 440 430 420 1
1.5
2
2.5 T
3
3.5
85
80
75 1
4
b
Residual base displacement (m)
Maximum damping energy (J)
b
270 265 260 255 1
1.5
2
2.5 T b
3
3.5
4
0.03 0.02 0.01 0 -0.01 1
1.5
2
Figure 9. The effect of the period of the restoring device on seismic responses of the R-FBI structure
•
•
The time histories of the P-FBI and R-FBI structure for a low friction coefficient of the pure-friction showed that the restoring device was able to significantly reduce displacement of the base story without a significant effect on the time responses of the top floor acceleration and drift. The restoring device was also capable to return the base story to its original location at the end of an earthquake.
•
•
•
•
•
The use of the restoring device resulted in an increase in the maximum seismic input energy entered into the superstructure, but it reduced the maximum seismic damage energy of the superstructure. The parametric study indicated that the seismic responses of the studied structures were significantly affected by the amount of the friction coefficient of the pure-friction system so that the base displacement was reduced by increasing the friction coefficient, but top floor acceleration and superstructure drift were significant increases. By increasing the friction coefficient, a significant increment was given for the maximum input and damage energies of the superstructure. The maximum top floor acceleration has not changed by increasing the mass ratio. Furthermore, the maximum top floor drift changed within a permitted range. However, increasing the mass ratio resulted in an increment in the maximum damage energy and a reduction in input energy entering the superstructure. An increase in the period of the restoring device resulted in an increment in the maximum base displacement and top floor drift, while it often reduced the other seismic and energy responses. By increasing the damping ratio of the restoring device, the maximum base displacement and top floor acceleration were reduced and the maximum top floor displacement and drift, as well as maximum damage and damping energies, were often increased, while it has no effect on the residual base displacement.
References 1. Etedali, S., Sohrabi, M. R., and Tavakoli, S. (2013). Optimal PD/PID control of smart base isolated buildings equipped with piezoelectric friction dampers. Earthquake Engineering and Engineering Vibration, 12(1), 39-54. 2. Tolani, S., and Sharma, A. (2016). Effectiveness of base isolation technique and influence of isolator characteristics on response of a Base isolated building. American Journal of Engineering Research, 5(5), 198-209. 3. Etedali, S., and Sohrabi, M. R. (2016). A proposed approach to mitigate the torsional amplifications of asymmetric base-isolated buildings during earthquakes. KSCE Journal of Civil Engineering, 20(2), 768-776. 4. Luo, J., Fahnestock, L. A., and LaFave, J. M. (2020). Seismic performance assessment of quasi-isolated highway bridges with seat-type abutments. Journal of Earthquake Engineering, Article in Press. DOI: 10.1080/13632469.2019.1628125. 5. Xiang, N., Alam, M. S., and Li, J. (2019). Yielding steel dampers as restraining devices to control seismic sliding of laminated rubber bearings for highway bridges: analytical and experimental study. ASCE Journal of Bridge Engineering, 24(11), Article # 04019103. 6. Mondal, P. D., Ghosh, A. D., and Chakraborty, S. (2017). Performances of various base isolation systems in mitigation of structural vibration due to underground blast induced
ground motion. International Journal of Structural Stability and Dynamics, 17(04), 1750043. 7. Mayes, R. L., and Naeim, F. (2001). Design of structures with seismic isolation. In: The seismic design handbook (pp. 723-755). Springer, Boston, MA. 8. Jangid, R. S. (1996). Seismic response of an asymmetric base isolated structure. Computers and structures, 60(2), 261-267. 9. Jangid, R. S. (1997). Response of pure-friction sliding structures to bi-directional harmonic ground motion. Engineering Structures, 19(2), 97-104. 10. Fan, F. G., Ahmadi, G., and Tadjbakhsh, I. G. (1988). Base Isolation of a Multi-story Building Under a Harmonic Ground Motion: A Comparison of Performances of Various Systems. National Center for Earthquake Engineering Research. 11. Jangid, R. S. (2000). Optimum frictional elements in sliding isolation systems. Computers and Structures, 76(5), 651-661. 12. Shakib, H., and Fuladgar, A. (2003). Response of pure-friction sliding structures to three components of earthquake excitation. Computers and Structures, 81(4), 189-196. 13. Krishnamoorthy, A. (2008). Response of sliding structure with restoring force device to earthquake support motion. Journal of Seismology and Earthquake Engineering, 10(1), 2539. 14. Nanda, R. P., Agarwal, P., and Shrikhande, M. (2012). Suitable friction sliding materials for base isolation of masonry buildings. Shock and Vibration, 19(6), 1327-1339. 15. Mostaghel, N., and Khodaverdian, M. (1987). Dynamics of resilient‐friction base isolator (R‐FBI). Earthquake engineering and structural dynamics, 15(3), 379-390. 16. Fallah, N., and Zamiri, G. (2013). Multi-objective optimal design of sliding base isolation using genetic algorithm. Scientia Iranica, 20(1), 87-96. 17. Gu, W., Wang, S., and Cai W. (2015). Seismic response of pure-friction sliding baseisolated structures. Electronic Journal of Geotechnical Engineering 20(14):5979-5980. 18. Sachdeva, G., Chakraborty, S., and Ray-Chaudhuri, S. (2018). Seismic response control of a structure isolated by flat sliding bearing and nonlinear restoring spring: experimental study for performance evaluation. Engineering Structures, 159, 1-13. 19. Etedali, S., Tavakoli, S., and Sohrabi, M. R. (2016). Design of a decoupled PID controller via MOCS for seismic control of smart structures. Earthquakes and Structures, 10(5), 1067-1087. 20. Zamani, A. A., Tavakoli, S., Etedali, S., and Sadeghi, J. (2018). Adaptive fractional order fuzzy proportional–integral–derivative control of smart base-isolated structures equipped with magnetorheological dampers. Journal of Intelligent Material Systems and Structures, 29(5), 830-844. 21. Shourestani, S., Soltani, F., Ghasemi, M., and Etedali, S. (2018). SSI effects on seismic behavior of smart base-isolated structures. Geomechanics and Engineering, 14(2), 161-174.
22. Zamani, A. A., Tavakoli, S., Etedali, S., and Sadeghi, J. (2018). Online tuning of fractional order fuzzy PID controller in smart seismic isolated structures. Bulletin of Earthquake Engineering, 16(7), 3153-3170. 23. Etedali, S. (2019). Sensitivity analysis on optimal PID controller for nonlinear smart baseisolated structures. International Journal of Structural Stability and Dynamics, 19(7), 1950080.
Highlights: • • • • •
A comprehensive parametric study on pure-friction and resilient friction base-isolated structures is carried out. A vast range of values for the friction coefficient of the sliding surface, the mass ratio of the base story, target period and damping ratio of the restoring device is considered. The restoring device with a small friction coefficient is able to significantly reduce base displacement during earthquake excitations. The amount of friction coefficient has the greatest effect on the seismic responses of the studied structure. Base displacement is reduced by increasing the friction coefficient, but top floor acceleration and superstructure drift, input and damage energies are significantly increased.
Conflict of Interest: The authors declare that they have no conflict of interest.
Author Statement: Sadegh Etedali and Kazem Hasankhoie conceived the presented idea. Kazem Hasankhoie carried out the simulations and performed the numerical simulations. Sadegh Etedali and Mohammad Reza Sohrabi supervised the project and investigated the findings of this work. Sadegh Etedali wrote the manuscript with input from all authors. All authors discussed the results and contributed to the final manuscript.
S2352-7102(19)32506-9
DOI:
https://doi.org/10.1016/j.jobe.2020.101194
Reference:
JOBE 101194
To appear in:
Journal of Building Engineering
Received Date: 13 November 2019 Revised Date:
13 January 2020
Accepted Date: 14 January 2020
Please cite this article as: S. Etedali, K. Hasankhoie, M.R. Sohrabi, Seismic responses and energy dissipation of pure-friction and resilient‐friction base-isolated structures: A parametric study, Journal of Building Engineering (2020), doi: https://doi.org/10.1016/j.jobe.2020.101194. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.
Seismic responses and energy dissipation of pure-friction and resilient‐‐friction baseisolated structures: a parametric study Sadegh Etedali*1, Kazem Hasankhoie2, Mohammad Reza Sohrabi3 1
Department of Civil Engineering, Birjand University of Technology, P.O. Box 97175-569, Birjand, Iran 2,3
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
*Correspondence to: Sadegh Etedali, Associate Professor, Department of Civil Engineering, Birjand University of Technology, Birjand, Iran Tel: +98 561 8821296 Fax: +98 561 2252098 Email: [email protected]
Seismic responses and energy dissipation of pure-friction and resilient‐‐friction baseisolated structures: a parametric study Abstract: A comprehensive parametric study is carried out on pure-friction base-isolated (PFBI) and resilient‐friction base-isolated (R-FBI) structures in this paper. For this purpose, an 8story building subjected to a band-limited white noise acceleration modeled based on a stationary process is considered. At first, the time histories of seismic response and superstructure energy for P-FBI and R-FBI structures are compared with those given for a fixed-base (F-B) structure. A vast range of values for the friction coefficient of the sliding surface, mass ratio of the base story, target period, and damping ratio of the restoring device are also considered for the parametric study. Then, the effect of changing these parameters on the maximum response of stories and superstructure energy is investigated. Considering a low friction coefficient, it is concluded that the restoring device of the R-FBI structure is able to significantly reduce displacement of the base story during earthquake excitations. It is also capable to return the base story to its original location at the end of an earthquake. Simulation results also show that the restoring device increases the maximum seismic input energy entered into the superstructure but reduces the maximum seismic damage energy of the superstructure. Results demonstrate that the amount of friction coefficient has the greatest effect on seismic responses of the studied structure. Base displacement is reduced with increasing friction coefficient, but top floor acceleration and superstructure drift are significantly increased, which results in an increment in maximum input and damage energies. Overall results indicate that an increment in damping ratio of the restoring device results in a reduction in maximum base displacement and top floor acceleration, and an increment in maximum top floor displacement and drift, while it has no effect on the residual base displacement. Moreover, base displacement and top floor drift are increased by increasing the period of the restoring device, while other seismic responses are reduced. Keywords: Pure-friction base-isolated structure, restoring device, resilient‐friction base-isolated structures, parametric study, seismic response, energy dissipation 1. Introduction Seismic isolation systems separate a part or all of a structure from the ground and reduce the seismic load applied to the main structure. They decrease the natural frequency of the structures and divert it away from the dominant frequency of seismic loads [1]. In the last few decades, several types of seismic isolators have been proposed and developed. Seismic isolators are often divided into elastomeric and friction isolators. Low damping natural rubber (LDNR) bearing, lead rubber bearing (LRB), high damping natural rubber (HDNR) bearing, pure- friction and friction pendulum system (FPS) are the well-known types of the isolators [2]. Seismic isolation is an effective method to mitigate the inter-story drift and absolute acceleration of the stories of a building [3]. The seismic performance of the base-isolated buildings with different isolation systems has been studied in the literature. Some studies have also focused on the evaluation of
the seismic performance of bridges equipped with seismic isolators. To validate the design strategy, and to provide commendations for improving the seismic performance of bridges, Luo et al. [4] studied the seismic performance of prototype quasi-isolated highway bridges. Xiang et al. [5] investigated the cost-effectiveness of using yielding steel dampers and laminated rubber bearings for highway bridges in comparison with other popular isolation systems. The performances of various isolation systems in vibration mitigation of the structures subjected to underground blast-induced ground motion are studied by Mondal et al. [6]. Pure- friction system is the simplest type of friction isolators. In this type of isolator, the rollers or sliders are provided between the foundation and the base of the structure [7]. The seismic response of an asymmetric structure equipped with the sliding bearing is studied in [8]. Jangid [9] also compared the vibration responses of an asymmetric one-story sliding isolated structure subjected to base harmonic acceleration consideration the interaction between the two lateral frictional resistances of the sliding isolation system. Fan et al. [10] conducted a comparison study on the performance of different types of isolators subjected to harmonic ground motion. Jangid [11] studied the optimal friction coefficient of the sliding surface as an effective parameter on the performance of the friction isolators. The effects of three components of an earthquake on the response of the pure-friction base-isolated structures are addressed in [12]. Krishnamoorthy [13] investigated the seismic performance of a space frame structure resting on sliding bearing equipped with the restoring device. Considering four different sliding interfaces, Nanda et al. [14] studied suitable friction sliding materials for base isolation of masonry buildings. Large displacements of the base raft in the structure equipped with a purefriction system endanger their safety during earthquake excitations [7]. In order to overcome this problem, restoring devices are supplemented to the pure- friction system. [15-17]. Fallah and Zamiri [16] utilized a multi-objective optimization based on the genetic algorithm for the optimum design of a sliding isolation system. Considering the vertical component of an earthquake, the seismic response of pure-friction sliding base-isolated structures is investigated in [17]. The numerical and theoretical studies of Sachdeva et al. [18] also showed that restoring devices can effectively reduce the maximum displacement of the base level. There are extensive studies on the seismic performance elastomeric isolation system in the literature. In addition, most studies carried out on the friction isolation system are limited to the P-FBI structures. In most researches, the seismic responses of the R-FBI structures are only taken into account to evaluate the performance of these structures, while the assessment of the efficiency of the R-FBI systems for seismic control of the building from the point of energy view is interesting. Hence, the present study aims to conduct a comprehensive parametric study on the pure-friction and resilient‐friction base-isolated structures from the points of seismic responses and energy dissipation. For this purpose, considering a vast range of values for the friction coefficient of the sliding surface, mass ratio of the base story, the target period and damping ratio of the restoring device, the performance of R-FBI system for dissipation of superstructure's energy, in the terms input, damage and damping energies, is also compared with those given for pure-friction isolation (P-FBI) system. On the other hand, numerous time history analyses to
achieve reliable results of the seismic performance of the R-FBI system are time-consuming and costly. Conventionally, a spectral density function is used rather than a collection of time history input to tackle the problem. In a stochastic analysis, an artificial acceleration of the ground motion is simulated for modeling the possible earthquakes. Therefore, the studied structures for the numerical study are subjected to a band-limited white noise acceleration modeled based on a stationary process. Time history responses of the structure in terms of base displacement, top floor displacement, acceleration and drift for two cases of PF-BI and R-FBI structures are compared with those given for the corresponding fixed-base structure. From the point of energy view, the time history of the input, damage and damping energies of the superstructure for three cases of the F-B, P-FBI, and R-FBI structures are also compared. Then, the effect of changing of the dynamic parameters of pure-friction systems and the restoring device of R-FBI structure on the maximum response of stories and superstructure energy is studied in this paper. The reminder paper is organized as follows. The mathematical models of P-FBI and R-FBI structures are presented in Sections 2. Numerical studies are carried out in Section 3. Simulation results are discussed in Section 4. The concluding remarks are drawn in Section 5. 2. Mathematical model An N-story shear-type frame equipped with a resilient friction base isolation system is schematically shown in Figure 1(a). It is notably that a restoring device can be combined with the slider in two parallel and series combinations. The restoring device includes a linear spring and viscous damper. For parallel combination, shown in Figure 1(b), the transmission force to superstructure is the sum of the restoring force of spring and friction force at the sliding interface. It is generally used in conjunction with rubber bearings, as shown in Figure 1(c). RFBI system consists of concentric layers of Teflon-coated plates in friction contact with each other and a central rubber core. 2.1. The governing equations for friction base-isolated structure with the restoring device The motion of a structure equipped with R-FBI can be stated in two phases: the non-sliding phase and the sliding phase. The governing equations in the non-sliding phase can be given by the following equation.
Figure 1. (a) An N-story R-FBI structure (b) the model of the restoring device (c) a cross-section of R-FBI system [15] ( ) + + =− (1) where , and represent the matrices of mass; stiffness and damping of the superstructure; = , ,..., refer to the displacement vector of the superstructure relative to the base story; = 1,1, . . . ,1 is the location vector of an earthquake acceleration with unit entity and is the earthquake ground acceleration. The mobilized frictional force in this phase can be written as follows: =− − − + + (2) in which is the base mass, and are the damping and stiffness coefficients of the first story of the superstructure, is the displacement of the base raft relative to the ground, and are the damping and stiffness coefficients of the restoring device, respectively which are obtained from the following equations: +!
=2
"#
+!
=
"#
"$ "$ (
2%' &
(3)
2%' ) &
(4)
In the above equations, and & refer to the damping ratio and the target period of the restoring device. Also, " is the mass of the i-th floor of the superstructure. When the mobilized frictional force crosses the boundary of the frictional force, the structure enters the sliding phase. During this phase, the equation of motion of the superstructure can be given by: +
+
=−*
+
+
,
(5)
Also, the equation of motion of the isolation system can be expressed as follows: +
- sgn(
)+
+
−
−
=−
where the frictional force can be given by:
-
=1
+! "#
"$ 2
in which 1 is the friction coefficient of the sliding surface and sgn (. ) is the sign function.
(6)
2.2. The equations of energy for friction base-isolated structure with the restoring device Evaluating the efficiency of the friction isolation systems for seismic control of the building from the point of energy view is interesting. Seismic control of a structure can be described as an energy transfer process. By integrating equation (5) with respect to during the motion, the following equation can be obtained. 5
5
3
5
4 +3
6
5
4 +3
6
4 = −3
6
6
+7
8+
,4
(7)
The first term of Equation (7) is known as the relative kinetic energy and can be expressed as follows. 5
9: = 3
4 =
6
1 2
(8)
The second term of equation (7) called the damping energy and can be rewritten as follows: 5
5
9; = 3
4 =3
6
4t
6
(9)
The third term is the recoverable strain energy: 5 1 9= = 3 4 = 2 6
(10)
Also, the right expression of equation (7) is the seismic input energy as follows: 5
9> = 3
6
+7
8+
5
,4 = 3
6
(7
8+
)4
(11)
The total seismic input energy in the base-isolated structure is dissipated by the friction isolation system and a part of this energy is entered into the superstructure. The energy transferred to the superstructure converted to both recoverable strain and relative kinetic energies. Also, a part of this energy is dissipated by the damping energy. The sum of the relative kinetic and recoverable strain energies is known as the total energy of the superstructure or the damage energy of the superstructure [19]. 3. Numerical studies
Numerical studies are carried out on an 8-story building equipped with the pure-friction isolation system. The mass of each floor is adopted as " = 360 ton. The frequencies of the first to the eighth structural mods are calculated as 1.25, 3.71, 6.04, 8.16, 10.01, 11.52, 12.63 and 13.32 Hz, respectively. The acceleration of the ground is also considered as a stationary process with the following power spectral density function [20-21]: B(C) =
4 C C C +2 C C+C
(12)
where and C represent the damping ratio and angular frequency of the ground, respectively. The artificial ground acceleration simulated by the above power spectral density function is shown in Figure 2. It can be a suitable statistical representation of different earthquakes [22-23]. First, the seismic performances of the P-FBI and R-FBI structures are compared with those given for the F-B structure. For this purpose, the time histories of the structural responses in terms of the top floor displacement, top floor acceleration, top floor drift, base displacement and the time histories of energy responses including the input, damping and damage energies are investigated. Then, a comprehensive parametric study on the seismic performance of friction base-isolated structures is conducted in this study. For this purpose, a vast range of design parameters of the friction isolators in two cases without and equipped with the restoring device is considered. These parameters are included the friction coefficient of the friction isolation system, the mass ratio of the base story, the damping ratio and the target period of the restoring device. The effect of changes of these parameters on maximum structural responses in terms of the maximum base displacement, maximum top floor displacement, maximum top floor acceleration, maximum top floor drift, maximum residual base displacement is studied. Considering two cases without and equipped with the restoring device, the effect of changes of the design parameters of the friction isolators is also investigated on the maximum energy responses in terms of maximum input, damage and damping energies.
Acceleration (cm/s2)
400 200 0 -200 -400 0
10
20
30 Time(sec)
Figure 2. Time history of the artificial earthquake acceleration
40
50
4. Results and discussions 4.1. Time history responses The seismic responses of the P-FBI and R-FBI structures are compared in this section. The damping ratio and the target period of the base isolation system is adopted as & = 2 sec and = 0.05. Also, the mass ratio of the base story and the friction coefficient of the sliding surface
is
"
Top floor absolute acceleration (m/s2)
drift
'
=1 and 1 = 0.02. The time histories of the top floor displacement, acceleration, and
5
0
-5 0
5
10
15
20
25 Time (s)
30
35
40
45
50
5
10
15
20
25 Time (s)
30
35
40
45
50
-3
Top floor drift (m)
4
x 10
2 0 -2 -4 0
Figure 3. Time histories of the top floor displacement, acceleration, and drift
Figure 4. Time histories of base displacement during the artificial earthquake excitation are shown in Figure 3. For comparison purposes, the structural responses of the F-B structure are also illustrated in the figures. As can be seen, the friction isolation system is able to reduce the top floor displacement, acceleration, and drift of the structure in comparison with those given for the fixed-base structure. In this case, it can be found that there is no significant difference between the time history responses of the base-isolated structure in terms of top floor acceleration and drift for P-FBI and R-FBI structures. However, as can be seen from Figure 3, the restoring device is able to reduce the maximum top floor displacement. The main advantage of the use of the restoring device is observed in Figure 4. As can be seen, the restoring device is able to significantly reduce displacement of the base story during the artificial earthquake excitation. Also, it is found that the residual displacement of the base story at the end of the earthquake is about 20 cm for the case without the restoring device, while the base story of the R-FBI structure has returned to its original location at the end of the earthquake. The evaluation of the seismic performance of a structure can be attractive from the point of energy transfer. Seismic input energy (9> ) entering the superstructure is converted to both recoverable strain (9- ) and relative kinetic (9F ) energies. Also, some amount of the input energy is dissipated by the damping energy (9; ). The sum of the relative kinetic and recoverable strain energies is the total energy of the system or the damage energy. Figure 5 illustrates the time histories of the input, damage and damping energies of the superstructure for three cases of the F-B, P-FBI and R-FBI structures. It is found that a significant portion of the seismic input energy is wasted by the isolation system and a small amount of the input energy is entered into the superstructure. Hence, the maximum values of the seismic input energy of the superstructure for the base-isolated structures are smaller than those given for the fixed-base structure. It is also found that the use of the restoring device reduces the maximum seismic input energy entered into the superstructure. Also, it reduces the maximum seismic damage energy of the superstructure. A significant portion of the energy entered into the base-isolated structure is dissipated by the
isolation system and the restoring device and a small amount of it is wasted by the damping of the superstructure.
500 Input energy (J)
400 300 200 100 0
Damage energy (J)
-100 0
5
10
15
20
25 Time (s)
30
35
40
45
50
5
10
15
20
25 Time (s)
30
35
40
45
50
5
10
15
20
25 Time (s)
30
35
40
45
50
100
50
0 0
Damping energy (J)
500 400 300 200 100 0 0
Figure 5. Time histories of the input, damage and damping energies of the superstructure
As an overall result, it is concluded that the large base displacement and residual deformation after earthquakes may result in a pure-friction isolation system without the restoring device experience. However, At the cost of increasing some seismic responses, advantages in terms of dramatical reduction of the base displacements during an earthquake excitation and eliminate their residual displacements at the end of an earthquake may be achieved due to the use of the restoring device. 4.2. Parametric studies In order to perform a parametric study on the dynamic parameters of the friction isolation system, a vast range of values for the friction coefficient of the sliding surface of the isolation system and mass ratio of the base story is considered. Parametric studies are also carried out on a vast range of the target period and damping ratio of the restoring device. In this study, the ranges of these parameters are considered as 0.01 ≤ 1 ≤ 0.2, 0.5 ≤ and 0.01 ≤
≤ 0.4.
'
"
≤ 1.5, 1 ≤ & ≤ 4
4.2.1. The effect of the friction coefficient Considering the material used for the surface of the pure- friction isolator, a wide range of values for the friction coefficients as 0.01 ≤ 1 ≤ 0.2 is adopted in this study. Figure 6 shows the effect of the friction coefficients on the structural responses in terms of the maximum base and top floor displacements; maximum top floor acceleration and drift, maximum input, damage and damping energies, and maximum residual base displacement. It can be seen that the maximum base displacement is significantly decreased by increasing the friction coefficient in the range of 0.01 ≤ 1 ≤ 0.1 for the P-FBI structure, while the maximum base displacement is often constant for the R-FBI structure. For the large friction coefficient, there is no change in the maximum base displacement for both cases. An increase is observed in the maximum top floor displacement by increasing the friction coefficient. Moreover, the top floor acceleration and drift are often increased by increasing the friction coefficient for both cases. For a low friction coefficient, the P-FBI structure experiences large displacements. Also, a large residual displacement is observed in the base story at the end of the earthquake in this case, while the base story of the R-FBI structure has returned to its original location at the end of the earthquake. It is also found that the maximum input, damage and damping energies for both cases are increased by increasing the friction coefficient. In fact, by increasing the friction coefficient and preventing the free movement of the isolation at the base level, the isolation system gets away from its ideal behavior. Hence, the maximum input and damage energy entering the superstructure increase by increasing the friction coefficient. 4.2.2. The effect of the mass ratio of the base story Considering the P-FBI and R-FBI structures, the effect of the base story mass ratio on the maximum base and top floor displacements; top floor acceleration and drift is shown in Figure 7.
Maximum top floor displacement (cm)
5
4
3
2
1 0.05 0.1 µ 0.15 0.2
8 6 4 2 0 0
0.05
0.1 µ
0.15
400 300 200 100 0.05
0.1 µ
0.15
0.2 0.1 0
200
0.05
0.1 µ
0.15
0.1 µ
0.15
0.2
0.05
0.1 µ
0.15
0.2
0.15
0.2
100
Residual base displacement (m)
400
0.05
120
0.2
600
0 0
0.3
-0.1 0
0.2
500
0 0 Maximum damping energy (J)
Maximum top floor drift (cm)
10
Maximum damage energy (J)
Maximum top floor acceleration (m/s2) Maximum input energy (J)
0.4
0.2
80 60 40 20 0 0 0.2 0.15 0.1 0.05 0 -0.05
0.05
0.1
µ
Maximum top floor displacement (cm)
Figure 6. The effect of friction coefficient on seismic responses of the P-FBI and R-FBI structures
4 3.8 3.6 3.4 3.2 0.5
1 m /m b
1.5
Maximum top floor drift (cm)
Maximum top floor acceleration (m/s2)
0.25
10 9 8 7 6 5 4 0.5
1 m /m
0.2
0.15
0.1 0.5
1.5
b
Maximum damage energy (J)
Maximum input energy (J)
460 450 440 430 420 410 1 m /m
1.5
1 m /m
1.5
b
470
400 0.5
1 m /m
85
80
75
70 0.5
1.5
b
-3
280 275 270 265 260 255 250 245 0.5
1 m /m b
1.5
Residual base displacement (m)
Maximum damping energy (J)
b
x 10 5
0
-5 0.5
1 m /m
1.5
b
Figure 7. The effect of the mass ratio of the base story on seismic responses of the P-FBI and R-FBI structures The effect of the mass ratio of the base story on the maximum input, damage and damping energies of the superstructure is also illustrated in this figure. By increasing the mass ratio, the overall trend shows a decrease in the maximum base displacement and an increase in the maximum top floor displacement and drift of the structure. It is also found that the response level of the R-FBI structure in terms of maximum base displacement and drift is lower than the P-FBI structure. However, the maximum top floor displacement and acceleration are increased as a result of using the restoring device. The superstructure energy responses show a decreasing trend in the maximum input energy responses and an incremental trend in the maximum damping and damage energy responses.
4.2.3. The effect of the damping ratio of the restoring device Figure 8 shows the effect of the damping ratio of the restoring device on the maximum structural responses for the base-isolated structure. As can be seen, increments in the damping ratio of the restoring device result in a reduction in maximum base displacement and top floor acceleration, and an increment in maximum top floor displacement and drift, while it has no effect on the residual base displacement. There is no clear trend in the variation of energy responses against the increase in the damping ratio of the restoring device. 4.2.4. The effect of the period of the restoring device The effect of the period of the restoring device on the maximum structural responses is illustrated in Figure 9. It can be seen that increasing the period of the restoring device increases the maximum base displacement and top story drift. Also, it results in a slight reduction in maximum top floor displacement. For an increase in the target period of the restoring device, small changes with a variable trend are observed in the energy responses of the superstructure. For different ranges of the period of the restoring device, the residual base displacement has not changed and the base story has returned to its original location at the end of the earthquake. 5. Conclusions
1.8 1.6 1.4 1.2 1 0
0.1
0.2 ζb
0.3
0.4
Maximum top floor displacement (cm)
Maximum base displacement (cm)
The present paper aimed to carry out a comprehensive parametric study on the seismic performance of the P-FBI and R-FBI structures from the points of seismic responses and energy dissipation. Based on a stationary process, a band-limited white noise acceleration was utilized for the simulation of artificial earthquake excitation. An 8-story building subjected to the artificial earthquake excitation, in three cases of F-B, P-FBI, and R-FBI, was considered. For the parametric study, a vast range of values for the friction coefficient of the sliding surface, mass ratio of the base story, target period and damping ratio of the restoring device was taken into account and the effect of changing these parameters on the maximum responses of stories and superstructure’s energy was studied. The conclusions remarks are as follows:
4 3.9 3.8 3.7 3.6 3.5 0
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0.2 ζ b
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Maximum top floor drift (cm)
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Maximum top floor displacement(cm)
Maximum base displacement (cm)
Maximum top floor acceleration (m/s2)
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92 Maximum damage energy (J)
Maximum input energy (J)
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450 445 440 435 430 425 0.1
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Residual base displacement (m)
Maximum damping energy (J)
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420 0
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x 10
2 0 -2 -4 0
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Figure 8. The effect of the damping ratio of the restoring device on seismic responses of the R-FBI structure
Maximum top floor drift (cm)
Maximum top floor acceleration (m/s2)
0.24
10 9.5 9 8.5 8 7.5 7 1
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Maximum input energy (J)
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Residual base displacement (m)
Maximum damping energy (J)
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0.03 0.02 0.01 0 -0.01 1
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Figure 9. The effect of the period of the restoring device on seismic responses of the R-FBI structure
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The time histories of the P-FBI and R-FBI structure for a low friction coefficient of the pure-friction showed that the restoring device was able to significantly reduce displacement of the base story without a significant effect on the time responses of the top floor acceleration and drift. The restoring device was also capable to return the base story to its original location at the end of an earthquake.
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The use of the restoring device resulted in an increase in the maximum seismic input energy entered into the superstructure, but it reduced the maximum seismic damage energy of the superstructure. The parametric study indicated that the seismic responses of the studied structures were significantly affected by the amount of the friction coefficient of the pure-friction system so that the base displacement was reduced by increasing the friction coefficient, but top floor acceleration and superstructure drift were significant increases. By increasing the friction coefficient, a significant increment was given for the maximum input and damage energies of the superstructure. The maximum top floor acceleration has not changed by increasing the mass ratio. Furthermore, the maximum top floor drift changed within a permitted range. However, increasing the mass ratio resulted in an increment in the maximum damage energy and a reduction in input energy entering the superstructure. An increase in the period of the restoring device resulted in an increment in the maximum base displacement and top floor drift, while it often reduced the other seismic and energy responses. By increasing the damping ratio of the restoring device, the maximum base displacement and top floor acceleration were reduced and the maximum top floor displacement and drift, as well as maximum damage and damping energies, were often increased, while it has no effect on the residual base displacement.
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ground motion. International Journal of Structural Stability and Dynamics, 17(04), 1750043. 7. Mayes, R. L., and Naeim, F. (2001). Design of structures with seismic isolation. In: The seismic design handbook (pp. 723-755). Springer, Boston, MA. 8. Jangid, R. S. (1996). Seismic response of an asymmetric base isolated structure. Computers and structures, 60(2), 261-267. 9. Jangid, R. S. (1997). Response of pure-friction sliding structures to bi-directional harmonic ground motion. Engineering Structures, 19(2), 97-104. 10. Fan, F. G., Ahmadi, G., and Tadjbakhsh, I. G. (1988). Base Isolation of a Multi-story Building Under a Harmonic Ground Motion: A Comparison of Performances of Various Systems. National Center for Earthquake Engineering Research. 11. Jangid, R. S. (2000). Optimum frictional elements in sliding isolation systems. Computers and Structures, 76(5), 651-661. 12. Shakib, H., and Fuladgar, A. (2003). Response of pure-friction sliding structures to three components of earthquake excitation. Computers and Structures, 81(4), 189-196. 13. Krishnamoorthy, A. (2008). Response of sliding structure with restoring force device to earthquake support motion. Journal of Seismology and Earthquake Engineering, 10(1), 2539. 14. Nanda, R. P., Agarwal, P., and Shrikhande, M. (2012). Suitable friction sliding materials for base isolation of masonry buildings. Shock and Vibration, 19(6), 1327-1339. 15. Mostaghel, N., and Khodaverdian, M. (1987). Dynamics of resilient‐friction base isolator (R‐FBI). Earthquake engineering and structural dynamics, 15(3), 379-390. 16. Fallah, N., and Zamiri, G. (2013). Multi-objective optimal design of sliding base isolation using genetic algorithm. Scientia Iranica, 20(1), 87-96. 17. Gu, W., Wang, S., and Cai W. (2015). Seismic response of pure-friction sliding baseisolated structures. Electronic Journal of Geotechnical Engineering 20(14):5979-5980. 18. Sachdeva, G., Chakraborty, S., and Ray-Chaudhuri, S. (2018). Seismic response control of a structure isolated by flat sliding bearing and nonlinear restoring spring: experimental study for performance evaluation. Engineering Structures, 159, 1-13. 19. Etedali, S., Tavakoli, S., and Sohrabi, M. R. (2016). Design of a decoupled PID controller via MOCS for seismic control of smart structures. Earthquakes and Structures, 10(5), 1067-1087. 20. Zamani, A. A., Tavakoli, S., Etedali, S., and Sadeghi, J. (2018). Adaptive fractional order fuzzy proportional–integral–derivative control of smart base-isolated structures equipped with magnetorheological dampers. Journal of Intelligent Material Systems and Structures, 29(5), 830-844. 21. Shourestani, S., Soltani, F., Ghasemi, M., and Etedali, S. (2018). SSI effects on seismic behavior of smart base-isolated structures. Geomechanics and Engineering, 14(2), 161-174.
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Highlights: • • • • •
A comprehensive parametric study on pure-friction and resilient friction base-isolated structures is carried out. A vast range of values for the friction coefficient of the sliding surface, the mass ratio of the base story, target period and damping ratio of the restoring device is considered. The restoring device with a small friction coefficient is able to significantly reduce base displacement during earthquake excitations. The amount of friction coefficient has the greatest effect on the seismic responses of the studied structure. Base displacement is reduced by increasing the friction coefficient, but top floor acceleration and superstructure drift, input and damage energies are significantly increased.
Conflict of Interest: The authors declare that they have no conflict of interest.
Author Statement: Sadegh Etedali and Kazem Hasankhoie conceived the presented idea. Kazem Hasankhoie carried out the simulations and performed the numerical simulations. Sadegh Etedali and Mohammad Reza Sohrabi supervised the project and investigated the findings of this work. Sadegh Etedali wrote the manuscript with input from all authors. All authors discussed the results and contributed to the final manuscript.