Shock and Vibration
Volume 2020 (2020), Article ID 2763709, 21 pages
https://doi.org/10.1155/2020/2763709

Research Article

Seismic Performance Evaluation of Building-Damper System under Near-Fault Earthquake

Xiaoli Wu,1,2 Wei Guo,1,2 Ping Hu,³ Dan Bu,⁴ Xu Xie,⁵ and Yao Hu1,2

¹School of Civil Engineering, Central South University, Changsha 410075, China
²National Engineering Laboratory for High Speed Railway Construction, Changsha 410075, China
³School of Civil Engineering, University of South China, Hengyang 421001, China
⁴Hunan Architectural Design Institute Limited Company, Changsha 410012, China
⁵Department of Civil Engineering, University of British Columbia, Vancouver, Canada

Correspondence should be addressed to Wei Guo; guowei@csu.edu.cn

Received 22 June 2019; Revised 9 September 2019; Accepted 28 December 2019; Published 8 February 2020

Academic Editor: Ivo Caliò

Copyright © 2020 Xiaoli Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The building-damper system designed by a seismic code is usually considered to be able to withstand the attack of strong earthquakes. However, near-fault earthquakes, especially those with the forward-directivity effect, might cause early and unexpected failure of code-designed dampers and consequent severe structural damage. In this paper, by taking into account near-fault earthquakes, seismic performance of the building-damper system and damper failure’s influence are evaluated systematically. A 9-storey steel building is designed by the Chinese seismic code as the benchmark model, and five typical dampers, including buckling-restrained brace damper (BRB), friction damper (FD), self-centering damper (SCD), viscous damper (VD), and viscoelastic damper (VED), are adopted. It was found that the building-damper systems show a large response and possible damper failure under the near-fault earthquake excitations. Then, the influence of damper failure is investigated, which reveals that damper failure would significantly affect seismic performance of the building-damper system, especially for the building-SCD system. Subsequently, by introducing the artificial near-fault earthquake excitation, the influences of different pulse parameters, such as pulse velocity amplitude, pulse period, and the number of significant pulses, are studied. It shows that the pulse velocity amplitude and pulse period obviously affect the seismic performance, while the number of significant pulses presents little influence.

1. Introduction

The strong earthquakes occurred worldwide in recent decades have led to severe structural damage of buildings. The numerical and experimental analysis of structures have been fully researched [1–5], and recent research has demonstrated that seismic response of the building can be well controlled by supplementing code-designed dampers under far-fault earthquakes [6, 7]. However, near-fault earthquakes usually possess distinct effects which are different from far-fault earthquakes, such as the forward-directivity effect resulting in early and unexpected failure of code-designed dampers and severe damage of the building [8–10].

Near-fault earthquakes with the forward-directivity effect usually exhibit immense energy concentrated on narrow period bands. This energy is observed as distinct and high-velocity pulse on velocity time-history curves [11–13]. These characteristics have attracted a great deal of attention, making the forward-directivity effect an important study in the structural seismic analysis field. Vafaei and Eskandari [14] investigated the seismic performance of steel buckling-restrained braced (BRB) frames with mega configuration under near-fault earthquakes. They further studied the influence of near-fault earthquakes on steel mega brace frames equipped with shape-memory alloy braces [15]. Ghaffarzadeh et al. [16] analyzed seismic response of building frames supplemented with variable orifice dampers under near-fault earthquakes. However, the influence of the forward-directivity effect on seismic performance on building-damper systems has not been well understood because of the individual differences in each near-fault earthquake record and the scarcity of records. Moreover, the damper is usually assumed to work well without any failure under the earthquake attack.

Great effort has been made to describe the characteristics of near-fault earthquakes [17–22]; the near-fault earthquakes with the forward-directivity effect possess three main pulse parameters, such as pulse velocity amplitude, pulse period, and the number of significant pulses [19]. Khoshnoudian et al. [20–22] have conducted a series of studies on the soil-structure systems subjected to near-fault earthquakes. The results indicated that the structure-to-pulse period ratio considerably affects the high mode of the structure. In order to quantify the pulse-type effects, equivalent pulse models were adopted to artificially construct earthquake excitations [23–29]. A classical mathematical model proposed by Mavroeidis and Papageorgiou [23] could simulate near-fault earthquakes with the forward-directivity effect by clearly and physically interpreted and scaled input parameters. However, these proposed simplified mathematical models do not contain the high-frequency portion which is another important characteristic of near-fault earthquakes and obviously affects the seismic response of the high-rise building [30, 31]. Ghahari et al. [30] further developed the method by filtering with appropriate cutoff frequency to decompose original near-fault excitations (ONE) into two components: a pulse-type excitation (PTE) possessing long-period pulses and a background excitation (BGE) with a relatively high-frequency. An artificial near-fault excitation (ANE) can be generated by combining the BGE and the artificial equivalent pulse-type excitation (APTE) [32, 33].

The earthquake with forward-directivity effect generally imposes a high seismic demand on the structure, so the code-designed damper may experience early and unexpected failure under near-fault earthquakes when adopting a seismic code which mainly considers far-fault earthquakes. The damper plays an important role in resisting the earthquake attack, and experiments have demonstrated that dampers can even dissipate more than 90% of the total earthquake input energy [34]. Miyamoto et al. [35] also indicated that the failure of viscous dampers has a significant influence on the response of the structure. Therefore, it is crucial to take the damper failure into consideration when evaluating the seismic performance of the building-damper systems.

Dampers acting as fuses to protect the main structure of the building under earthquake excitation have been under development for years. The American Society of Civil Engineering Committee (ASCE) [36] has classified the passive dampers as five main typical dampers, including rate-dependent dampers, such as viscous damper (VD) and viscoelastic damper (VED), and rate-independent dampers, such as buckling-restrained brace damper (BRB), friction damper (FD), and self-centering damper (SCD). In our research group, the code-designed five typical dampers supplemented in the benchmark buildings of ASCE [37] have been utilized to analyse the progressive damage of the building subjected to the main shock-aftershocks of far-fault earthquakes [38]. The result shows that different dampers display different seismic performance from each other. But it did not evaluate the influence of the near-fault earthquake and considers the effect of the damper failure. The benchmark models established by ASCE [37] are commonly used as the platforms for the performance evaluation of the different control techniques [38, 39]. But the benchmark model established by ASCE is designed by the American code [40] which is different from the Chinese seismic code [41]. Thus, it is important to establish a benchmark model based on Chinese codes.

In this paper, firstly a 9-storey steel building was designed by the Chinese seismic code [41] and adopted as the benchmark model. These five typical dampers were designed by the Chinese code [42]. Then, the limit values of the dampers are provided by 30 far-fault earthquake records corresponding to the code design response spectra. Next, 20 near-fault earthquake records with the forward-directivity effect and ordinary ones are selected, and the ANEs are created by combining the BGE and APTE. Finally, the performance of the building-damper system under near-fault earthquakes and the damper failure’s influence are systematically investigated.

2. Building-Damper Systems

2.1. Building Benchmark Model

A 9-storey steel building adopted as the benchmark model here is designed by the Chinese seismic code [41] and PKPM software. The model configuration, component, and quality detail information are displayed in Figure 1. The material of columns is Q345 steel with the nominal yield strength of 345 MPa, while that of beams is Q235 steel with the nominal yield strength of 235 MPa. The simulation material of steel is steel01 material [43] in OpenSees, and its constitutive model object with kinematic hardening and isotropic hardening is also given in Figure 1. The finite element model was constructed in OpenSees, and all the beam and column components were modeled by the dispBeamColumn element with the fiber section [43]. The rigid floor is established by setting a master node and slave nodes so as to make uniform vibration, and the columns were fixed at base. The mass was applied and distributed proportionally to the beam nodes. In the time-history analyses, Rayleigh damping of this building is used to obtain a damping ratio of 2% at the first period T₁ and fifth period T₅ [44] in order to have a suitable damping of the structure.

Figure 1: The 9-storey steel building benchmark model.

Table 1 compares the first three periods between the finite element model in OpenSees and the building model in PKPM, including the first period T₁, the second period T2, and the third period T₃. It shows that the finite element model corresponds well to the building model in PKPM.

Table 1: Periods of building benchmark model (unit: seconds).

Models
Periods

First period T₁
Second period T₂
Third period T₃

Building model in PKPM
2.4135
0.8274
0.4538

Finite element model in OpenSees
2.4926
0.8807
0.4858

2.2. Five Typical Dampers

Five typical dampers, including the buckling-restrained brace damper (BRB), the friction damper (FD), the self-centering damper (SCD), the viscous damper (VD), and the viscoelastic damper (VED), are studied here. The dampers were installed on each storey of the 9-storey building as shown in Figure 1 and modeled by the two-node-link element in OpenSees. Especially, the damper failure is a major consideration in this paper and was simulated by the “Removal” command in OpenSees in the latter chapter. The characteristics of dampers have been studied by many researchers and could be expressed by corresponding mathematical models. The hysteretic characteristics of the rate-independent dampers, such as BRB and FD, are described by the Bouc–Wen material [45, 46] as follows:

where A, γ, β are the parameters that control the shape of the hysteretic loop, α is the stiffness ratio after yielding, z is a nonobservable hysteretic parameter, Fd is the force, ud is the displacement, is the velocity, and Kd is the stiffness. The Maxwell material [47] is used to simulate the hysteretic characteristics of VED:

where Fc and uc are the force and displacement of the damping component and Fk and uk are the force and displacement of the spring, respectively. The linear viscous material is utilized to represent the hysteretic characteristics of VD by

where the parameters are identical to those of equation (1). Self-centering material [48] in OpenSees with the constitutive model shown in Figure 2 is utilized to model the hysteretic characteristics of SCD. The parameters, such as the initial stiffness K₁, the postactivation stiffness K2, and ratio of forward to reverse force δ, determine the hysteretic shape of SCD, where F₀ is the forward activation force, and more detail is given in Ref. [48].

Figure 2: Constitutive model of self-centering material in Ref. [48].

The basic design principle is as the code [42] proposed that the dampers can be seen to provide the building with the effective stiffness Keff and effective damping ratio ξd which can be calculated by Equations (4) and (5):

where Wcj is the seismic energy absorbed by the jth damper; Aj is the hysteretic loop area of the jth damper; Ws is the total energy dissipation under excitations; Fi is the horizontal shear force of building at ith floor; x is the horizontal displacement of dampers; F is the horizontal damping force of dampers (+ and ‒ are the positive and negative direction, respectively).

Five dampers were designed by the Chinese code [42] with the objective of reducing the maximum interstorey drift to 75% of the original value, in other words, the vibration reduction ratio is 25%. The damper design is based on the code [42], and the detail design flow can be obtained from ref. [38]. Table 2 shows the model parameters of the designed dampers, and the corresponding theoretical hysteresis curves of these five dampers are shown in Figure 3.

Table 2: The designed model parameters of five typical dampers.

Dampers
Mathematical model
Designed model parameters
Equivalent parameters in code

BRB
Bouc–Wen material in Equation (1)
, , , , ,
, ,

FD
Bouc–Wen material in Equation (1)
, , , , ,
, ,

SCD
Self-centering material in Figure 2
, ,
, ,

VD
Linear viscous material in Equation (3)

,

VED
Maxwell material in Equation (2)
,
, ,

(a)

(b)

(c)

(d)

(e)

Figure 3: Hysteresis curves of five typical dampers: (a) BRB; (b) FD; (c) SCD; (d) VD; (e) VED.

2.3. Limit Values of Dampers

In this paper, the limit values of designed dampers are given by 30 far-fault earthquake records corresponding to the target design response spectrum, and the frequent earthquake (FE) density of the benchmark building is of 0.2 g ground peak acceleration (PGA). These records were selected from the database of the Pacific Earthquake Engineering Center (PEER), and the general information is listed in Table 3. Figure 4 shows the acceleration spectra, and it indicated that the mean spectrum of records matches well with the target design response spectrum.

Table 3: Information of selected 30 far-fault earthquake records.

No
Earthquake
Year
Station
Fault distance (km)
Richter magnitude

1
Imperial Valley-06
1979
Niland fire station
36.92
6.53

2
Imperial Valley-06
1979
Victoria
31.92
6.53

3
Loma Prieta
1989
Palo Alto—1900 embarc
30.81
6.93

4
Kocaeli, Turkey
1999
Ambarli
69.62
7.51

5
Chi-Chi, Taiwan
1999
CHY093
49.82
7.62

6
Chi-Chi, Taiwan
1999
CHY107
50.61
7.62

7
Manjil, Iran
1990
Rudsar
64.47
7.37

8
Chi-Chi, Taiwan-03
1999
CHY090
80.34
6.2

9
Chi-Chi, Taiwan-04
1999
TCU145
56.37
6.2

10
Chi-Chi, Taiwan-05
1999
CHY015
81.71
6.2

11
Chi-Chi, Taiwan-05
1999
CHY054
92.28
6.2

12
Chi-Chi, Taiwan-05
1999
CHY107
94.45
6.2

13
Chi-Chi, Taiwan-06
1999
CHY094
59.65
6.3

14
Chi-Chi, Taiwan-06
1999
TCU112
51.72
6.3

15
Chi-Chi_Taiwan-06
1999
TCU118
51.27
6.3

16
Chi-Chi, Taiwan-06
1999
TCU140
57.26
6.3

17
Tottori, Japan
2000
SMN005
45.73
6.61

18
Niigata, Japan
2004
NIG010
57.69
6.63

19
Niigata, Japan
2004
NIG013
40.59
6.63

20
Chuetsu-oki, Japan
2007
NIG003
47.45
6.8

21
Iwate, Japan
2008
AKT016
48.36
6.9

22
Iwate, Japan
2008
Takanashi, Daisen
46.41
6.9

23
El Mayor-Cucapah, Mexico
2010
Niland fire station
66.91
7.2

24
El Mayor-Cucapah, Mexico
2010
Westmorland fire Station
42.61
7.2

25
El Mayor-Cucapah, Mexico
2010
Bonds corner
32.85
7.2

26
El Mayor-Cucapah, Mexico
2010
Brawley Airport
41.48
7.2

27
El Mayor-Cucapah, Mexico
2010
Meloland, E Holton
30.63
7.2

28
El Mayor-Cucapah, Mexico
2010
Holtville Post Office
36.52
7.2

29
Darfield, New Zealand
2010
ADCS
31.41
7

30
El Mayor-Cucapah, Mexico
2010
El Centro array #4
35.46
7.2

Figure 4: Acceleration spectra of far-fault earthquake records, mean spectrum, and target response spectrum.

The axial displacement and force of dampers were gained by scaling these records to 0.4 g PGA which corresponds to the rare earthquake intensity in the Chinese seismic code [41]. The 1.2 times of the envelope values of corresponding displacement and force responses were assumed to be the limit values, which is given in Table 4. The limit index of each damper is selected based on the damper mechanism. The limit values of BRB, FD, and SCD are described by the displacement. The limit value of VD is related to the velocity-based damping force, and the limit value of VED is given by the maximum value of the displacement and the force.

Table 4: Limit values of displacement and force of five dampers.

Damper
Location

Storey 1
Storey 2
Storey 3
Storey 4
Storey 5
Storey 6
Storey 7
Storey 8
Storey 9

BRB
Displacement (m)
0.0611
0.1073
0.1124
0.0912
0.0703
0.0807
0.0745
0.0515
0.0303

FD
Displacement (m)
0.0743
0.1324
0.1443
0.1233
0.0897
0.0812
0.0810
0.0571
0.0340

SCD
Displacement (m)
0.0582
0.0964
0.0983
0.0857
0.0680
0.0801
0.0742
0.0599
0.0338

VD
Force (N)
202151
293156
282007
242398
233743
268882
293864
287855
198631

VED
Displacement (m)
0.0578
0.1095
0.1207
0.1024
0.0748
0.0664
0.0583
0.0406
0.0234

Force (N)
165306
247043
246505
209566
217900
271423
267853
276776
215094

3. Near-Fault Earthquake Excitations

3.1. Earthquake Records

In this section, 10 near-fault earthquake records with obvious forward-directivity effect and other 10 ordinary records with no obvious characteristic effects were selected from the database of the PEER center. These records belong to two famous earthquake events located at the Imperial Valley of America and Chi-Chi of the Taiwan region. The detailed information is listed in Table 5, and the site type refers to the NEHRP classification [49]. Figure 5 shows the velocity time-history curves, and it indicates that the obvious difference between the forward-directivity and ordinary near-fault earthquakes is the distinct velocity pulse and high peak ground velocity (PGV). The velocity pulse of the forward-directivity near-fault earthquake can be parameterized by the velocity amplitude of pulse, the pulse period, and the number of significant pulses.

Table 5: Selected near-fault earthquake records form the database of the PEER center.

Earthquake
Station (component)
Rupture distance (km)
Site type
PGA(g)
PGV(cm/s)
Pulse period (s)

(a) Forward-directivity records

Imperial Valley
EC County Center FF (002)
7.31
D
0.21
52.40
4.417

El Centro Array #6 (230)
0
D
0.45
87.80
3.773

El Centro Array #7 (230)
0.56
D
0.47
82.70
4.375

El Centro Differential Array (360)
5.09
D
0.48
57.80
6.265

Chi-Chi
TCU029 (EW)
28.04
C
0.16
47.00
5.285

TCU039 (EW)
19.89
C
0.20
61.60
7.850

TCU042 (EW)
26.31
C
0.25
37.70
2.57

TCU045 (EW)
26
C
0.47
46.00
9.338

TCU046 (EW)
16.74
C
0.14
28.40
8.043

TCU128 (EW)
13.13
C
0.14
63.75
9.023

(b) Ordinary records

Imperial Valley
Cerro Prieto (237)
15.19
C
0.16
19.28
—

Chihuahua (012)
7.29
D
0.27
28.70
—

Compuertas (015)
13.52
D
0.19
10.60
—

Delta (262)
22.03
D
0.24
27.00
—

Chi-Chi
CHY006 (EW)
9.76
C
0.36
60.25
—

CHY010 (EW)
19.93
C
0.22
18.52
—

CHY029 (EW)
10.96
C
0.29
36.10
—

CHY034 (EW)
14.82
C
0.25
34.95
—

CHY035 (EW)
12.6
C
0.25
43.65
—

CHY041 (EW)
19.37
C
0.50
30.30
—

(a)

(b)

Figure 5: Velocity time-history curves of the near-fault earthquake records. (a) Forward-directivity near-fault earthquake. (b) Ordinary near-fault earthquake.

3.2. Artificial Earthquake Excitations

The scarcity of near-fault earthquake records promotes the development of artificial earthquake excitations to facilitate the study of the influence of pulse parameters, such as velocity amplitude, the pulse period, and the number of significant pulses, on seismic response of the building-damper system. It is critical for the artificial pulse-type excitation (APTE) to capture the important characteristics of the natural near-fault earthquake records. Firstly, the original near-fault earthquake excitation (ONE) was decomposed into two components: the pulse-type excitation (PTE) possessing long-period pulses and the background excitation (BGE) with a relatively high-frequency component. Next, the APTE was set up by a mathematical model to replace the PTE. Therefore, an artificial near-fault excitation (ANE) can be generated by combining the BGE and the APTE. A mathematical model with physical interpretation was proposed by Mavroeidis and Papageorgiou [23] to simulate the pulse-type excitation, which is given as follows:

where A and fp are the amplitude and excitation frequency, respectively; t₀ specifies the epoch of the envelope’s peak; φ is the phase of the amplitude-modulated harmonic; and γ is the parameter that defines the oscillatory characteristics of excitation. The parameters A, fp, and t₀ are preliminarily determined according to the original excitation, while the parameters γ and φ need to be adjusted several times so that the relative error between the velocity of APTE and PTE is less than 5%.

In this section, the near-fault earthquake record TCU039 is adopted as the ONE, and the corresponding parameters of APTE are listed in Table 6. The ANE can be synthesized by combing the BGE and the APTE, which is expressed by the following equation:

Table 6: Model parameters of APTE.

Original excitation
Parameters

A (cm/s)
fp (rad/s)
γ
t₀
φ (°)

TCU039-EW
38.16
0.102
5.8
51.25
97.4

Figure 6 compares the velocity time-history curves between the ANE and ONE, and their response spectra are shown in Figure 7. It indicates that the ANE coincides well with the ONE, and it can be seen as an effective artificial excitation representing near-fault earthquake.

Figure 6: Velocity time-history curves of the ANE record and the ONE record.

(a)

(b)

Figure 7: Response spectra of the ANE record and the ONE record: (a) velocity spectra; (b) acceleration spectra.

4. Influence of the Forward-Directivity Effect

Figure 8 shows maximum interstorey drifts and maximum response standard deviation of the building subjected to near-fault earthquake records. It is observed that the mean value of drift responses of the building under the forward-directivity effect records is obviously higher than those under the ordinary records. While the ordinary records and the forward-directivity records adopt the same PGA, the PGVs are distinctly different due to the velocity pulse. The high-speed velocity pulse of the forward-directivity record produces higher response demands and larger nonlinear deformation of the building. Moreover, the dispersion of the seismic response is larger for the forward-directivity records, which is evidenced by the maximum response standard deviation of the interstorey drift, that is, 0.0137 for the forward-directivity records and 0.0047 for the ordinary records, respectively. The low-frequency velocity pulse in the forward-directivity records generally excites the vibration of low-order modes of the building, while the ordinary records lead to vibration response of the high-order modes. This conclusion was also given by Vafaei and Eskandari [14, 15].

(a)

(b)

(c)

Figure 8: Seismic responses of the building under near-fault earthquakes. (a) Forward-directivity records. (b) Ordinary records. (c) TCU039 and CHY010 excitation.

The TCU039 record presents obvious forward-directivity effect, and the CHY010 record has no obvious characteristic effects which can be considered to be the ordinary record. The two records are obtained from stations with the same site type, and the stations are in close distances of 19.89 km and 19.93 km from the fault. Thus, the significant difference between the TCU039 and the CHY010 is the forward-directivity effect. Figure 8(c) gives the maximum interstorey drift of the building under TCU039 and CHY010 excitations. The same conclusion is given as discussed above. It can be explained by the acceleration spectra shown in Figure 9. For TCU039 excitation, the value of the spectra acceleration of the first period of building is larger than that of the higher period, such as the second period T₂ and the third period T₃, while CHY010 excitation exhibits contrasting results.

Figure 9: Spectra acceleration responses of TCU039 and CHY010 excitation.

5. Seismic Performance of Building-Damper System

5.1. Assumption of No Damper Failure

In this section, seismic analysis of the building is conducted based on the assumption of no damper failure under earthquake, and five building-damper systems are subjected to the forward-directivity near-fault earthquake and ordinary one, such as the TCU039 record and the CHY010 record. Figure 10 presents the maximum interstorey drift of the building-damper system under the frequent earthquake (FE), the occasional earthquake (OE), and the rare earthquakes (RE). The vibration control performance is described by the vibration reduction ratio given by

where λ is the vibration reduction ratio, r₀ is the maximum interstorey drift of the building, and rd corresponds to the maximum drift response of the building-damper system. According to the response magnitude of the interstorey drift of the building, earthquake excitations are ordered as follows: the FE of CHY010, the OE of CHY010, the FE of TCU039, the RE of CHY010, the OE of TCU039, and the RE of TCU039. Figure 11 presents the curves of the vibration reduction ratio of the building-damper systems. It can be seen that the vibration reduction ratios of FD, VD, and VED decrease with the increase of the interstorey drift response of the building. While the vibration reduction ratios of SCD are nearly identical, the vibration reduction ratios of BRB are small at the high and low interstorey drift responses of the building but large at the moderate drift.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 10: Maximum interstorey drift of building-damper systems under the frequent, occasional, and rare earthquakes of TCU039 and CHY010. (a) The FE of CHY010. (b) The OE of CHY010. (c) The RE of CHY010. (d) The FE of TCU039. (e) The OE of TCU039. (f) The RE of TCU039.

Figure 11: Curves for the vibration reduction ratios of building-damper systems with five types of dampers.

Figure 11 compares the vibration reduction ratios of building-damper systems with five types of dampers. Rate-dependent dampers, such as VD and VED, can provide stable and similar vibration reduction effects. The performances of rate-independent dampers, such as BRB, FD, and SCD, are generally related to the relative displacement response, and the plastic cumulative displacement occurs and accumulates under near-fault earthquake excitations. The FD dissipates energy through a friction mechanism between the plates, and it performs well under small excitations, while under great excitations, the performance deteriorates greatly. The BRB generates sufficient axial force while a large displacement occurs and then dissipates seismic energy. Its vibration reduction performance could not be fully utilized in the FE of CHY010 and is optimal among the five typical dampers for the OE of CHY010. The SCD can automatically reset, so no permanent displacement accumulates, and the vibration reduction ratios of SCD under different earthquake intensities are stable.

It is well known that the dampers control the vibration performance of the building through the energy dissipation. In order to further study the energy dissipation of the dampers, Figure 12 shows the dissipated energy by dampers on each floor when subjected to the OE of CHY010 and TCU039. The dissipated energy of the dampers is larger when they are under the TCU039 (with forward-directivity effect) than that of the CHY010 (with no obvious characteristic effects). But the energy dissipated by different dampers increases at different rates. And it can also be seen from the previous discussion that the vibration reduction ratios of SCD remain the same due to its self-reset characteristics, while other dampers are reduced. Furthermore, it is consistent that the damper dissipated more energy as shown in Figure 12 and has a higher vibration reduction ratio shown in Figure 11 when under the same earthquake records.

(a)

(b)

Figure 12: Dissipated energy by dampers on each floor. (a) The OE of CHY010. (b) The OE of TCU039.

5.2. Influence of Damper Failure

As discussed above, five typical dampers possess different vibration control performance under near-fault earthquake records. However, an important assumption of no damper failure is adopted in the above analysis. Actually, dampers are possible to undergo unexpected failure under strong near-fault earthquake attack. Thus, the influence of damper failure on seismic response of building-damper systems should be considered. In the software OpenSees, the “removal” command is used when the dampers reach the limit values. The analysis indicates that five building-damper systems still work under the RE of ordinary earthquakes, but would experience damper failure under most of the forward-directivity near-fault earthquakes in the RE intensity which are shown in Table 7. It also proves that the near-fault earthquake records with forward-directivity effect cause more severe damage to the building than the ordinary ones. Because of the space limitations, one typical earthquake TCU039 under which the whole five dampers have failed is selected to conduct the in-depth analysis of damper failure and their influence on the building-damper systems.

Table 7: Damper failure conditions under the RE of forward-directivity near-fault earthquakes.

Earthquake events
Forward-directivity near-fault earthquake records
Damper failure location

BRB
FD
SCD
VD
VED

Imperial Valley
EC County Center FF (002)
2–6 storey

2–4 storey
—
1–3 storey

El Centro Array #6 (230)
1–5 storey
1–4 storey
2-3 storey
2–5 storey
1–7 storey

El Centro Array #7 (230)
2–4 storey
2 storey
—
—
2–6 storey

El Centro Differential Array (360)
—
—
—
—
—

Chi-Chi
TCU029 (EW)
4 storey
2-3 storey
—
—
1–4 storey

TCU039 (EW)
2–7 storey
1–7 storey
1–6 storey
3–6 storey
1–8 storey

TCU042 (EW)
—
—
2 storey
—
—

TCU045 (EW)
1–3 storey
2-3 storey
3–6 storey
2 storey
1–3 storey

TCU046 (EW)
2–4 storey

2-3 storey
2 storey
1–4 storey

TCU128 (EW)
1–7 storey
1–9 storey
1–6 storey
1–6 storey
1–9 storey

Figure 13 presents the displacement responses of the top storey of building-damper systems subjected to the TCU039’s RE excitation, and the damper failure information is marked. It can be seen that five dampers of different storeys have experienced failure at different time. The seismic response of dampers excited by the TCU039 record exceeds the corresponding limit values, and the influence of pulse parameters of near-fault earthquake would be discussed in Section 6. Figure 13 also indicates that the early and unexpected damper failure has obvious effect on the seismic response of building-damper systems and with the accumulation of seismic energy, more and more dampers fail and the influence of damper failure increases and the displacement response of the building becomes large.

(a)

(b)

(c)

(d)

(e)

Figure 13: Displacement responses of the top storey of building-damper systems. (a) Building-BRB system. (b) Building-FD system.(c) Building-SCD system. (d) Building-VD system. (e) Building-VED system.

Figure 14 gives the interstorey drift response of building-damper systems under the TCU039’ RE excitation. The result shows that the damper failure distinctly affects the vibration reduction performance. The vibration reduction of the SCD is most sensitive to damper failure, and it leads to more than doubled interstorey drift increase when the damper fails.

(a)

(b)

(c)

(d)

(e)

Figure 14: Maximum interstorey drift response of building-damper systems with and without damper failure. (a) Building-BRB system.(b) Building-FD system. (c) Building-SCD system. (d) Building-VD system. (e) Building-VED system.

The dampers supplemented on the building actually provide the additional stiffness and damping to reduce the seismic response. Sehhati et al. [13] discovered that the additional damping usually does not play a key role in the vibration control of building-damper systems under the pulse-type ground motion and additional stiffness is important. As shown in Table 2, the VD merely provides additional damping to the building and other four dampers can produce additional stiffness. The SCD adds distinct stiffness to the building, the BRB and VED followed, and the FD produces limited stiffness. When the VDs in several storeys fail in earthquake, the interstorey drift increase of the building-damper system is relatively small. Conversely, the maximum interstorey drift increases more than twice of the building-SCD system if the SCD fails. It can be concluded that the influence of damper failure on seismic response of the building-damper system under near-fault earthquake is obvious if dampers could provide great additional stiffness. The interstorey drift of the building-FD system decreases when the FD fails, but the influence is not obvious as the FD only provided limited stiffness.

6. Influence of Pulse Parameters

TCU039 of Chi-Chi earthquake is adopted here as the original near-fault earthquake excitation (ONE) with forward-directivity effect. As shown in Table 5, the peak ground acceleration (PGA) of the TCU039 record is 0.2 g. The artificial near-fault earthquake excitation (ANE) which could catch the main characteristics of the ONE is generated by combing the background excitation (BGE) and the artificial pulse-type excitation (APTE). The pulse parameters could be expressed by the adjustable parameters in the mathematical model of APTE. Then, the influence of pulse parameters on damper failure and seismic performance of building-damper systems is systematically analyzed.

6.1. Pulse Velocity Amplitude

The ANE is synthesized by setting different pulse velocity amplitudes (PVA) which is different from the peak ground velocity (PGV). The amplitude of the APTE, that is, the parameter A in the mathematical model in equation (7), varies in the range of 30∼160 cm/s. The other parameters are consistent with the ONE, as shown in Table 6. Table 8 lists the storeys where five dampers fail under ANEs with different PVAs. The BRB, FD, SCD, and VED all undergo failure when the PVAs are greater than 80 cm/s while VD does not fail and always works well. This is because the PVA mainly influenced the displacement response rather than the velocity response and the VD’s failure concerns about the velocity. Figure 15 shows seismic response of the top storey of the building-VD system. It is seen that the displacement response increases as the PVA increases, while the velocity response value is almost the same. Therefore, for the displacement-dependent damper, such as BRB, FD, SCD, and VED, more dampers of different storeys would fail as the PVA increases.

Table 8: Storeys where the five dampers fail under the ANE with different PVAs.

Dampers
PVA (cm/s)

30
50
80
100
130
150
160

BRB
—
—
Storey 5, 4, 3, 2, 1
Storey 5, 4, 3, 2, 1
Storey 5, 4, 3, 2, 1, 6
Storey 5, 4, 3, 2, 1, 6
Storey 5, 4, 3, 2, 1, 6

FD
—
—
Storey 2, 1, 3, 4, 5
Storey 1, 2, 3, 4, 5
Storey 1, 2, 3, 4, 5, 6
Storey 1, 2, 3, 4, 5, 6
Storey 1, 2, 3, 4, 5, 6

SCD
—
—
Storey 5, 4, 3, 2, 1
Storey 5, 4, 3, 2, 1
Storey 3, 4, 2, 5, 6, 1, 7, 8
Storey 3, 2, 4, 5, 6, 1, 7, 8
Storey 3, 2, 4, 5, 6, 1, 7, 8

VD
—
—
—
—
—
—
—

VED
—
—
Storey 1, 2, 3, 4, 5
Storey 1, 2, 3, 4, 5
Storey 5, 1, 4, 2, 3, 6
Storey 5, 1, 4, 2, 3, 6
Storey 5, 1, 4, 2, 3, 6

(a)

(b)

Figure 15: Seismic response of the top storey of the building-VD system subjected to ANEs with different PVAs. (a) Displacement response. (b) Velocity response.

Figure 16 gives the interstorey drift responses of building-damper systems under the ANEs with different PVAs of 30, 50, 80, 100, 130, 150, and 160 cm/s. It shows that the maximum interstorey drift of the building-BRB, building-FD, building-SCD, and building-VED systems increases with the increasing of PVAs. For the building-VD system, the influence of the PVA does not give an obvious regular pattern as the VD is a rate-dependent damper whose damping force is related to the interstorey velocity and the building velocity response almost maintains the small value corresponding to different PVAs. The PVAs of 50, 130, and 160 cm/s were selected as examples to compare the vibration reduction performance of five building-damper systems, which is shown in Figure 17. It is clearly observed that the VD had an excellent energy reduction performance at a large PVA that far exceeded other four dampers, but relatively poor performance when the PVA is small, such as at 50 cm/s. As for the other four dampers, when the PVA is small, they have nearly identical vibration control performance. With the increase of PVA, there exists a little difference of vibration reduction performance.

(a)

(b)

(c)

(d)

(e)

Figure 16: Interstorey drift of building-damper systems subjected to ANEs with different PVAs. (a) BRB. (b) FD. (c) SCD. (d) VD. (e) VED.

(a)

(b)

(c)

Figure 17: Vibration reduction performance of five typical dampers under different PVAs. (a) PVA = 50 cm/s. (b) PVA = 130 cm/s.(c) PVA = 160 cm/s.

6.2. Pulse Period

In this case, the PVA of APTE is extracted from the ONE, that is, 38.16 cm/s, and other parameters of ANE except for the pulse period are consistent with the ONE. The influence of pulse periods on damper failure and seismic response of building-damper systems are investigated, and the ratio Tp/T of the ANE’s period to the first period of building ranges from 0.3 to 2.0. Table 9 lists the storeys where the five dampers fail under ANEs with different pulse periods. It is found that the pulse period generally affects the damper failure. Five typical dampers in different storeys all have failed in this range of pulse periods, and the failure condition is severer when the Tp/T is around 1.0. Figure 18 shows the seismic response of the top storey of the building-BRB system as an example. It shows that both displacement and velocity responses are affected by the pulse periods, and their peak values are larger as the period ratio Tp/T is closer to 1.0. Therefore, the damper failure is prone to happen when the building-damper system is subjected to ANE with Tp/T around 1.0. To be more precise and meticulous, the maximum value of the peak displacement response happens when the Tp/T is equal to 1.2, while the maximum value of the peak velocity response occurs when the Tp/T is equal to 1.0. This can exactly explain the phenomenon shown in Table 9 that the VD failed when the Tp/T is equal to 1.0, while the FD failed when Tp/T is equal to 1.2.

Table 9: Storeys where the five dampers fail under ANEs with different pulse periods.

Dampers
Tp/T

0.3
0.5
0.8
1.0
1.2
1.5
2

BRB
—
Storey 5, 6
Storey 6
Storey 5
Storey 4, 3, 5, 2
Storey 4, 3
—

VED
—
Storey 6
Storey 4
Storey 3, 4
Storey 5, 4, 3
—
—

FD
—
—
—
—
Storey 5
—
—

VD
—
—
—
Storey 4
—
—
—

SCD
—
Storey 5, 6
Storey 5
Storey 5, 4
Storey 3, 4, 2, 5
Storey 3, 2, 4
Storey 3, 4, 2

(a)

(b)

Figure 18: Seismic response of the top storey of the building-BRB system. (a) Displacement response. (b) Velocity response.

Figure 19 gives the maximum interstorey drifts of building-damper systems subjected to ANEs at the period ratios from 0.3 to 2.0. The peak interstorey drifts of all five building-damper systems all reach their maximum values when Tp/T is 1.2, and the effects of the pulse periods are constant when Tp/T exceeds 1.2. This is because the building-damper systems mainly respond at the fundamental mode when Tp/T reaches 1.2. The fundamental mode of five building-damper systems in the grey line is marked in Figure 19, and it can be seen that the response shape when Tp/T reaches 1.2 is more similar to that of the fundamental mode. It can also be seen that when the pulse-to-building period ratio is small, the higher mode of the building-damper systems is activated and accounts for larger number of components. While the pulse period elongates, the components of the higher mode decrease, and the building-damper systems mainly respond at the fundamental mode. This phenomenon is similar to the work of Khoshnoudian et al. [20–22].

(a)

(b)

(c)

(d)

(e)

Figure 19: The interstorey drift of building-damper systems subjected to ANEs with different pulse periods. (a) BRB. (b) FD. (c) SCD.(d) VD. (e) VED.

As for the BRB, FD, and SCD dampers, the interstorey drift when Tp/T equals to 0.8 is larger than that when Tp/T is 1.0. This can be explained by the acceleration spectra, shown in Figure 20. The acceleration spectra value of the first period of these three building-damper systems is large when the Tp/T is 0.8 then that when the Tp/T is 1.0.

Figure 20: Acceleration spectra of ANEs with different pulse periods.

6.3. Number of Significant Pulses

In this case, the PVA and pulse period of APTE are extracted from the ONE (TCU039 record), that is, 38.16 cm/s and 7.8 s (Tp/T = 3.1), respectively. Other parameters of ANE except for the number of significant pulses are consistent with the ONE, such as the peak ground acceleration (PGA) which is 0.2 g. Artificial pulse-type excitation (APTE) with different numbers of significant pulses, such as 2, 3, 4, and 5, were simulated by adjusting the parameters γ and φ in the above mathematical model, and it is shown in Figure 21. In this paper, a wave with the amplitude of not less than 50% of the PVA is seen as a significant pulse. The influence of the number of significant pulses on damper failure and seismic response of building-damper systems is studied. The result shows that five typical dampers remained working, and no damper failure occurred. It is identical to the results of the building-damper systems subjected to the ONE of 0.2 g. Figure 22 depicts the interstorey drift of the building-damper systems subjected to ANEs with different numbers of significant pulses. It shows that the increase in the number of significant pulses only slightly affects seismic responses of the building-damper systems. It can be concluded that the number of significant pulses presents little influence on the seismic response of building-damper systems.

Figure 21: Velocity time-history curves of APTE with different numbers of significant pulses.

(a)

(b)

(c)

(d)

(e)

Figure 22: The interstorey drift of building-damper systems subjected to ANEs with different pulse numbers. (a) BRB. (b) FD. (c) SCD.(d) VD. (e) VED.

7. Conclusions

In this paper, seismic performance of building-damper systems subjected to near-fault excitations with forward-directivity effect was analyzed and damper failure’s influence was discussed. The following conclusions are obtained:

(1)The near-fault earthquake with forward-directivity effect causes larger seismic response of the building than ordinary ones. Code-designed dampers probably undergo unexpected failure when subjected to the forward-directivity near-fault earthquakes in the rare earthquake intensity. The damper failure significantly affects the vibration reduction performance, especially for SCD whose failure leads to more than doubled interstorey drift increase.(2)Pulse velocity amplitude (PVA) of the forward-directivity near-fault excitation greatly affects the displacement response of the building-damper systems; however, the velocity response remains almost the same. Therefore, the VD which is velocity-dependent can work well even under high PVA and the other four dampers would fail when the PVA is higher than 80 cm/s. The peak interstorey drifts of all five building-damper systems all reach their maximum values when Tp/T is 1.2, and the effects of the pulse periods is constant when Tp/T exceeds 1.2. The number of significant pulses presents little influence.

Data Availability

Some or all data, models, or code generated or used during the study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors are grateful for the financial support from the National Natural Science Foundation (no. 51878674) and the Project of Yuying Plan in Central South University.

References

W. Guo, Z. Zhai, Y. Cui, Z. Yu, and X. Wu, “Seismic performance assessment of low-rise precast wall panel structure with bolt connections,” Engineering Structures, vol. 181, pp. 562–578, 2019.

W. Guo, Y. Hu, H. Liu, and D. Bu, “Seismic performance evaluation of typical piers of China’s high-speed railway bridge line using pushover analysis,” Mathematical Problems in Engineering, vol. 2019, Article ID 9514769, 17 pages, 2019.

W. Guo, Z. Zhai, Z. Yu, and Y. Long, “Facility performance indexes and rapid test feasibility evaluation method of shaking tables,” KSCE Journal of Civil Engineering, vol. 23, no. 7, pp. 3097–3112, 2019.

W. Guo, Z. P. Zhai, Z. W. Yu, F. Chen, Y. Gong, and T. Tan, “Experimental and numerical analysis of the bolt connections in a low-rise precast wall panel structure system,” Advances in Civil Engineering, vol. 2019, Article ID 7594132, 22 pages, 2019.

W. Guo, Z. P. Zhai, H. Wang et al., “Shaking table test and numerical analysis of an asymmetrical twin-tower super high-rise building connected with long-span steel truss,” The Structural Design of Tall and Special Buildings, vol. 28, no. 13, p. e1630, 2019.

W. Guo, J. Wu, Y. Hu, Y. Li, and T. Y. Yang, “Seismic performance evaluation of typical dampers designed by Chinese building code,” Earthquake Engineering and Engineering Vibration, vol. 18, no. 2, pp. 433–446, 2019.

Y.-F. Liu, T.-K. Lin, and K.-C. Chang, “Analytical and experimental studies on building mass damper system with semi-active control device,” Structural Control and Health Monitoring, vol. 25, no. 6, p. e2154, 2018.

B. Alavi and H. Krawinkler, “Behavior of moment-resisting frame structures subjected to near-fault ground motions,” Earthquake Engineering & Structural Dynamics, vol. 33, no. 6, pp. 687–706, 2004.

E. Kalkan and S. K. Kunnath, “Effects of fling step and forward directivity on seismic response of buildings,” Earthquake Spectra, vol. 22, no. 2, pp. 367–390, 2006.

H. Beiraghi, A. Kheyroddin, and M. A. Kafi, “Forward directivity near-fault and far-fault ground motion effects on the behavior of reinforced concrete wall tall buildings with one and more plastic hinges,” The Structural Design of Tall and Special Buildings, vol. 25, no. 11, pp. 519–539, 2016.

P. G. Somerville, N. F. Smith, R. W. Graves, and N. A. Abrahamson, “Modification of empirical strong ground motion attenuation relations to include the amplitude and duration effects of rupture directivity,” Seismological Research Letters, vol. 68, no. 1, pp. 199–222, 1997.

R. Rupakhety, S. U. Sigurdsson, A. S. Papageorgiou, and R. Sigbjörnsson, “Quantification of ground-motion parameters and response spectra in the near-fault region,” Bulletin of Earthquake Engineering, vol. 9, no. 4, pp. 893–930, 2011.

R. Sehhati, A. Rodriguez-Marek, M. ElGawady, and W. F. Cofer, “Effects of near-fault ground motions and equivalent pulses on multi-story structures,” Engineering Structures, vol. 33, no. 3, pp. 767–779, 2011.

D. Vafaei and R. Eskandari, “Seismic response of mega buckling-restrained braces subjected to fling-step and forward-directivity near-fault ground motions,” The Structural Design of Tall and Special Buildings, vol. 24, no. 9, pp. 672–686, 2014.

D. Vafaei and R. Eskandari, “Seismic performance of steel mega braced frames equipped with shape-memory alloy braces under near-fault earthquakes,” The Structural Design of Tall and Special Buildings, vol. 25, no. 1, pp. 3–21, 2016.

H. Ghaffarzadeh, E. A. Dehrod, and N. Talebian, “Semi-active fuzzy control for seismic response reduction of building frames using variable orifice dampers subjected to near-fault earthquakes,” Journal of Vibration and Control, vol. 19, no. 13, pp. 1980–1998, 2016.

J. D. Bray and A. Rodriguez-Marek, “Characterization of forward-directivity ground motions in the near-fault region,” Soil Dynamics and Earthquake Engineering, vol. 24, no. 11, pp. 815–828, 2004.

I. Iervolino, E. Chioccarelli, and G. Baltzopoulos, “Inelastic displacement ratio of near-source pulse-like ground motions,” Earthquake Engineering & Structural Dynamics, vol. 41, no. 15, pp. 2351–2357, 2012.

Y. J. Ni, X. Zhu, S. M. Huang et al., “The characteristic parameters of velocity pulse and simulation,” in Proceedings of the 3rd International Conference on Earthquake Engineering, vol. 19-20, Nanjing, China, October 2004.

F. Khoshnoudian and E. Ahmadi, “Effects of pulse period of near-field ground motions on the seismic demands of soil-MDOF structure systems using mathematical pulse models,” Earthquake Engineering & Structural Dynamics, vol. 42, no. 11, pp. 1565–1582, 2013.

F. Khoshnoudian, E. Ahmadi, S. Sohrabi, and M. Kiani, “Higher-mode effects for soil-structure systems under different components of near-fault ground motions,” Earthquakes and Structures, vol. 7, no. 1, pp. 83–99, 2014.

F. Khoshnoudian, E. Ahmadi, and S. Sohrabi, “Response of nonlinear soil-MDOF structure systems subjected to distinct frequency-content components of near-fault ground motions,” Earthquake Engineering & Structural Dynamics, vol. 43, no. 5, pp. 701–716, 2014.

G. P. Mavroeidis and A. S. Papageorgiou, “A mathematical representation of near-fault ground motions,” Bulletin of the Seismological Society of America, vol. 93, no. 3, pp. 1099–1131, 2003.

G. P. Mavroeidis, G. Dong, and A. S. Papageorgiou, “Near-fault ground motions, and the response of elastic and inelastic single-degree-of-freedom (SDOF) systems,” Earthquake Engineering & Structural Dynamics, vol. 33, no. 9, pp. 1023–1049, 2004.

W. He and A. Agrawal, “Analytical model of ground motion pulses for the design and assessment of seismic protective systems,” Journal of Structural Engineering, vol. 134, no. 7, pp. 1177–1188, 2008.

D. Yang and J. Zhou, “A stochastic model and synthesis for near-fault impulsive ground motions,” Earthquake Engineering & Structural Dynamics, vol. 44, no. 2, pp. 243–264, 2015.

M. Dabaghi and A. Der Kiureghian, “Stochastic model for simulation of near-fault ground motions,” Earthquake Engineering & Structural Dynamics, vol. 46, no. 6, pp. 963–984, 2017.

A. A. Rodriguez and E. Miranda, “Assessment of building behavior under near-fault pulse-like ground motions through simplified models,” Soil Dynamics and Earthquake Engineering, vol. 79, pp. 47–58, 2015.

H. Tajammolian, F. Khoshnoudian, and V. Bokaeian, “Seismic responses of asymmetric steel structures isolated with the TCFP subjected to mathematical near-fault pulse models,” Smart Structures and Systems, vol. 18, no. 5, pp. 931–953, 2016.

S. F. Ghahari, H. Jahankhah, and M. A. Ghannad, “Study on elastic response of structures to near-fault ground motions through record decomposition,” Soil Dynamics and Earthquake Engineering, vol. 30, no. 7, pp. 536–546, 2010.

J. W. Baker, “Quantitative classification of near-fault ground motions using wavelet analysis,” Bulletin of the Seismological Society of America, vol. 97, no. 5, pp. 1486–1501, 2007.

G. Yan and F. Chen, “Seismic performance of midstory isolated structures under near-field pulse-like ground motion and limiting deformation of isolation layers,” Shock and Vibration, vol. 2015, Article ID 730612, 17 pages, 2015.

S. Li, F. Zhang, J. Q. Wang et al., “Effects of near-fault motions and artificial pulse-type ground motions on super-span cable-stayed bridge systems,” Journal of Bridge Engineering, vol. 22, no. 3, Article ID 04016128, 2017.

T. T. Song and G. F. Dargush, “Passive energy dissipation and active control,” in Structural Engineering Handbook, CRC Press LLC, Boca Raton, FL, USA, 1999.

H. K. Miyamoto, A. S. J. Gilani, A. Wada, and C. Ariyaratana, “Limit states and failure mechanisms of viscous dampers and the implications for large earthquakes,” Earthquake Engineering & Structural Dynamics, vol. 39, no. 11, pp. 1279–1297, 2010.

M. D. Symans, F. A. Charney, A. S. Whittaker et al., “Energy dissipation systems for seismic applications: current practice and recent developments,” Journal of Structural Engineering, vol. 134, no. 1, pp. 3–21, 2008.

Y. Ohtori, R. E. Christenson, B. F. Spencer, and S. J. Dyke, “Benchmark control problems for seismically excited nonlinear buildings,” Journal of Engineering Mechanics, vol. 130, no. 4, pp. 366–385, 2004.

W. Guo, Y. Hu, Y. Li, Z. Zhai, and P. Shao, “Seismic performance evaluation of typical dampers designed by Chinese code subjected to the main shock-aftershocks,” Soil Dynamics and Earthquake Engineering, vol. 126, Article ID 105829, 2019.

O. A. S. Al-Fahdawi, L. R. Barroso, and R. W. Soares, “Simple adaptive control method for mitigating the seismic responses of coupled adjacent buildings considering parameter variations,” Engineering Structures, vol. 186, pp. 369–381, 2019.

ASCE-7-10, Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineering, Reston, VA, USA, 2013.

GB 50011-2010, Code for Seismic Design of Buildings, China Architecture Building Press, Beijing, China, 2016.

JGJ297-2013, Building Energy Dissipation Technology Regulation, China Architecture Building Press, Beijing, China, 2013.

Opensees, Command Manual, 2010, http://opensees.berkeley.edu/wiki/index.php/Command_Manual.

A. P. Jeary, “Damping in tall buildings-a mechanism and a predictor,” Earthquake Engineering & Structural Dynamics, vol. 14, no. 5, pp. 733–750, 1986.

R. Bouc, Mathematical Model for Hysteresis, Report to the Centre de Recherches Physiques, Marseille, France, 1971.

Y. K. Wen, “Method for random vibration of hysteretic systems,” Journal of Engineering Mechanics Division, vol. 102, no. 2, pp. 249–263, 1976.

M. D. Mosia, “A simplified nonlinear generalized maxwell model for predicting the time dependent behavior of viscoelastic materials,” Word Journal of Mechanics, vol. 1, no. 3, pp. 158–167, 2011.

C. Christopoulos, R. Tremblay, H.-J. Kim, and M. Lacerte, “Self-centering energy dissipative bracing system for the seismic resistance of structures: development and validation,” Journal of Structural Engineering, vol. 134, no. 1, pp. 96–107, 2008.

FEMA-273, NEHRP Guidelines for the Seismic Rehabilitation of Buildings, Federal Emergency 634 Management Agency, Washington, DC, USA, 1997.