Journal of Building Engineering 75 (2023) 107009
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Journal of Building Engineering
journal homepage: www.elsevier.com/locate/jobe
Numerical analysis of inclined demountable precast concrete walls
with rocking-based composite columns for seismic protection of
building structures
Afshin Naserpour a, *, Mojtaba Fathi a, Rajesh P. Dhakal b
a
b
Department of Civil Engineering, Engineering Faculty, Razi University, Kermanshah, Iran
Department of Civil and Natural Resources Engineering, University of Canterbury, New Zealand
A R T I C L E I N F O
A B S T R A C T
Keywords:
Inclined demountable wall
Rocking CFST columns
Seismic resilience
Seismic demands
Energy dissipation
Initial stiffness
With the aim of simultaneously reducing all seismic demands, this paper proposes a novel
structural system comprising inclined demountable walls with rocking base composite columns
(IDWC). The proposed IDWC system combines the concepts of using inclined demountable walls
in each story and rocking-based concrete filled steel tube (CFST) columns as the wall boundary
elements. In particular, through inclined walls, the number of walls in each story is reduced,
while with the use of rocking CFST columns, damage to the boundary elements can be mitigated.
In total, 18 two-dimensional numerical models are developed and static as well as dynamic an­
alyses are conducted to evaluate the performance of conventional and demountable wall systems
of 4-, 10- and 15-stories height. For each height, 4 IDWC models, with various wall arrangements,
and a vertical demountable wall model are analyzed and compared with a conventional rein­
forcement concrete wall model. For the studied models, micro and macro numerical models are
developed and verified through experimental data. After performing cyclic and time history
nonlinear analyses, it is shown that IDWC models have lower initial stiffness and higher energy
dissipation capacity than the conventional model. According to these results, inter-story drift,
floor acceleration, and base shear in IDWC models are reduced by up to 30%, 41%, and 45%,
respectively, compared to the conventional model. Also, it is demonstrated that with the use of
rocking CFST columns, the wall boundaries remain undamaged, which ensures any residual drifts
after severe earthquakes are insignificant. Meanwhile, as the incremental dynamic analysis results
show, the collapse capacity of IDWC models is up to 53.5% higher than that of conventional
models.
1. Introduction
Reinforced concrete (RC) structural wall systems, due to their high lateral stiffness and strength, are widely used for medium to
high-rise buildings. However, in moderate-severe earthquakes, significant structural damage occurs at the base of the RC structural
walls due to the formation of plastic hinges. In most cases, the extent of damage to RC walls is so severe that repair is not feasible due to
technical/practical restrictions and prohibitive costs. In such cases, complete demolition of the building is the only option, which leads
to a significant amount of non-biodegradable landfill.
* Corresponding author.
E-mail addresses: naserpour.afshin@gmail.com, naserpour.afshin@razi.ac.ir (A. Naserpour).
https://doi.org/10.1016/j.jobe.2023.107009
Received 22 December 2022; Received in revised form 25 May 2023; Accepted 2 June 2023
Available online 3 June 2023
2352-7102/© 2023 Elsevier Ltd. All rights reserved.
Journal of Building Engineering 75 (2023) 107009
A. Naserpour et al.
To improve the seismic performance of RC wall buildings, researchers have conducted various investigations in recent decades. In
addition to studies aiming to improve the seismic design and performance of RC walls to avoid different failure mechanisms [1–4],
significant efforts are being invested to develop novel wall systems that naturally minimize/avoid damage during earthquakes. Most of
these studies have led to the development of post-tensioned precast concrete rocking wall systems. In this system, instead of forming a
plastic hinge, a rocking mechanism is introduced at the wall base to govern the nonlinear behavior. The connection between the wall
and the foundation consists of post-tensioned tendons, which provide self-centering ability while increasing the lateral resistance of the
system. Also, supplemental dampers are used to increase the energy dissipation capacity of the post-tensioned rocking wall system. The
first post-tensioned rocking wall system was developed in the PRESSS project [5]. In this system, two post-tensioned wall panels were
used side by side, which was known as the jointed rocking wall system. To increase the energy dissipation capacity of the system,
U-shaped steel connectors were attached to the vertical joint between the wall panels. The pseudo dynamic testing results showed that
the proposed jointed rocking wall system remained almost undamaged even after experiencing very high intensity earthquakes. The
results of the PRESSS project encouraged other researchers to further explore the scope and limitations of post-tensioned rocking wall
systems. In this regard, Kurama et al. [6–8] proposed the use of a large post-tensioned precast wall with internal steel bars, which is
known as hybrid wall system. In the last two decades, relatively extensive numerical and experimental studies have been devoted to
the performance evaluation of the hybrid wall system [9–12]. In order to improve the seismic performance of the hybrid wall system,
instead of using internal steel bars, external dampers including yielding-based mild steel, viscous and friction dampers have been
applied [13–18]. In these cases, externally used dampers play the role of seismic fuses that can be easily replaced after a severe
earthquake. In addition to studies investigating the hybrid wall system in isolation, several building models with this system have also
been subjected to shaking table tests by researchers [19–21]. In general, all shaking table test results show that buildings with the
hybrid wall system remain almost undamaged in severe earthquakes and the damage is concentrated only in the supplemental
dampers. In addition to precast concrete buildings, analysis and design of pre-stressed concrete technology has been investigated for
sheet pile walls, too [22].
Although the above studies confirm that post-tensioned rocking wall systems have very favorable seismic performance, their
practical application has been very limited. One of the significant challenges regarding rocking wall systems is the effect of higher
modes on the increase in shear and moment of stories. This adverse effect causes damage to non-structural elements when using posttensioned rocking wall systems [23]. To reduce the effect of higher modes, the application of multiple rocking wall systems has been
suggested by researchers [24–28]. However, numerical studies show that the use of multiple rocking walls increases the inter-story
drifts in upper stories compared to conventional RC shear walls [29].
Besides the post-tensioned rocking wall system, other approaches have also been explored to improve the post-earthquake per­
formance of buildings. RC frame buildings consisting of precast frame members connected using post-tensioned tendons with external
and internal energy dissipaters to accommodate the drift demand by rocking mechanisms without undergoing much damage has also
been extensively investigated and advocated for improved seismic performance [30–34]. Nevertheless, despite reducing structural
damage, such rocking precast frame buildings are not able to reduce damage to non-structural components; and consequently their
ability to reduce seismic losses for most buildings has been questioned [35].
A demountable precast concrete system is one such system, which has been shown to improve the post-earthquake performance of
buildings. In this system, prefabricated concrete components are connected to each other by bolted steel connections. There are two
approaches regarding the steel connections of demountable systems. In the first approach, dry rigid connections are used while
nonlinear behavior is assigned to precast concrete members. The first study on the use of rigid steel connections for demountable
precast concrete frames was conducted by Aninthaneni and Dhakal [36]. After that, Aninthaneni et al. [37–39] carried out several
experimental studies to compare different types of dry strong steel connections for precast beam-to-column joints, and showed that the
dry end plate connection provided the best nonlinear cyclic behavior. Meanwhile, other efforts have been made in recent years to use
strong dry steel connections for demountable precast concrete frames [40–43]. In these studies, mainly, the cyclic nonlinear behavior
of the beam-to-column connection has been evaluated. In general, it was shown that if strong dry steel connections are used for
beam-column joints, a plastic hinge is formed at the end of precast concrete beam elements. In this case, due to the use of bolted steel
connections, the damaged beams can be replaced with new ones after a damaging earthquake.
In addition to strong steel connections, in recent years, special attention has been paid to the use of ductile joints for precast
concrete frames. In such connections, a series of yielding-based steel or friction dampers are used to connect precast concrete beams to
columns. Witzany et al. [44–46] conducted several studies on the application of controllable ductile joints for precast concrete frame
buildings. Hu et al. [47] numerically evaluated the mechanical behavior of a replaceable yielding-based steel damper for precast
concrete beam-column connections. Li et al. [48] proposed the use of low-yield-point steel dampers for precast concrete beam-column
connections. These steel dampers were attached to prefabricated concrete elements by means of bolts so that they could be replaced in
case of damage. Huang et al. [49] proposed a multiple-slit steel damper to improve the seismic performance of precast concrete
beam-column connections. More recently, the nonlinear cyclic performance of various yielding-based steel dampers has been eval­
uated for demountable precast concrete frame connections [50–54]. In general, the above studies reveal that in the ductile joints of
precast concrete frame buildings, damage is concentrated in the replaceable steel dampers while the precast concrete elements remain
almost undamaged.
As mentioned above, a relatively large number of studies have been conducted on the cyclic behavior of demountable precast
concrete frame buildings. However, studies on demountable precast concrete walls have been limited. In this case, Han et al. [55]
investigated the dry steel connections for the precast concrete wall system. In this study, a precast concrete wall was connected to the
adjacent beam and foundation by bolted steel connections. The design philosophy was such that the nonlinear behavior was
concentrated in the precast concrete wall and the steel connections remained in an elastic state. Nonlinear cyclic results showed that
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A. Naserpour et al.
the hysteresis behavior of the proposed system was almost similar to that of conventional RC wall systems. Li et al. [56] proposed a
bolt-plate steel connection for a precast concrete wall system. In this system, a precast concrete wall was connected to the foundation
by bolt-plate connections. The experimental results showed that the precast concrete wall with the proposed bolt-plate connection has
the same damage pattern as the conventional concrete wall. However, in these experimental studies, precast concrete walls with
relatively short lengths were tested. Meanwhile, according to the proposed details, it is necessary to use large precast concrete walls in
real buildings. In this case, due to the significant increase in the length of the precast concrete wall, providing a strong steel connection
would be a very complicated and challenging task. To overcome this drawback, Naserpour and Fathi [57] used several small walls,
instead of a large wall panel, for demountable precast concrete systems. These small precast concrete walls were attached to the
adjacent beams by strong bolted steel connections. Numerical results showed that by using small precast concrete walls, in addition to
reducing damage to wall elements, a more uniform inter-story drift profile developed across the height of the building. Recently,
Naserpour et al. [58] proposed demountable small walls with rocking boundary columns. The most important goal of this study was to
keep the boundary columns in an elastic state while forcing any damage to concentrate on the demountable small walls. However, due
to the use of a large number of small demountable walls, installing the wall panels in each story becomes very cumbersome.
In recent years, friction dampers have been used to connect wall panels to other structural members. Nabid et al. [59,60] proposed a
precast concrete wall system with friction joints, as dissipative devises, to increase the energy dissipation capacity of RC frame
buildings. This system consists of a precast concrete panel that is connected to adjacent beams by means of friction dampers. For the
height-wise distribution of the slip loads of these dampers, a practical optimization method, named the uniform damage distribution
Fig. 1. The configuration of the IDWC system.
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method, was applied. This design method ensures that the damage parameters such as inter-story drift ratio and energy dissipation
capacity are uniformly distributed along the height of the building. Hashemi et al. [61] used the Resilient Slip Friction Joint (RSFJ) for
the panelized timber structures. These joints can simultaneously provide enough energy dissipation capacity and self-centering ability
for the panelized structures. In fact, a large amount of seismic energy is dissipated by sliding the friction plates of RSFJs. Also, the
grooved-shape of the friction plates allows them to return to their original state after sliding by the semi-compressed disc springs, and
thus the self-centering is provided for the joints. Due to these features, RSFJs can be a good alternative to the traditional steel con­
nections in building structures. Another study on the use of friction-based dissipative devices in the wall panels was conducted by Du
et al. [62]. In this study, dry slip-friction connectors were attached at the bottom two corners of a self-centering precast concrete wall
panel. These connectors are activated by tensile and compressive axial forces on the wall corner, thereby dissipating seismic energy.
With the purpose of improving the seismic resilience of RC frames, Wang et al. [63] proposed the use of friction-damped self-­
centering tension braces. These self-centering braces include two main parts: pre-compressed disc springs and friction dampers. The
disc springs increase the self-centering ability while friction dampers absorb seismic energy. Numerical results demonstrated that by
using self-centering tension braces, inter-story drifts and residual displacements were simultaneously reduced for RC frames. More
recently, Zhang et al. [64] evaluated the cyclic performance of conventional reinforced concrete walls with tension-compression disc
spring devises. The main purpose of this study was to increase the self-centering ability and reduce the strength degradation for RC
walls.
The present study proposes a seismically resilient structural system comprising inclined demountable precast concrete walls with
rocking-based concrete filled steel tube (CFST) columns. The main reasons for using rocking based CFST columns for boundary ele­
ments are to increase the flexural stiffness of the columns, reduce structural damage and provide easy access for steel connections. Past
studies have shown that CFST columns, in addition to improving concrete confinement conditions, prevent local buckling of columns
and increase fire resistance [65–67]. Also, the most important purpose of using inclined demountable walls is to reduce the number of
walls on each floor and decrease the initial construction cost. To the best of the authors’ knowledge, this is the first study to investigate
inclined precast concrete walls for demountable systems in high seismic regions. In general, by combining the concepts of
rocking-based CFST columns and inclined demountable walls, the present study aims to propose a structural system that simulta­
neously reduces inter-story drifts, floor acceleration and residual inter-story drifts as compared to conventional RC wall systems.
The research questions that this study seeks to answer are as follows:
1. Is it possible to mitigate seismic demands for reducing structural and non-structural damage in precast concrete wall systems by
applying CFST columns?
2. Can inclined demountable walls be designed to have good seismic performance while reducing the number of strong steel joints and
wall panels?
3. Can the system ensure that the structural damage is concentrated only on the demountable walls while the boundary columns
remain stable?
2. The configuration of the proposed system
Fig. 1 shows the details of the Inclined Demountable Wall with composite boundary Columns (IDWC). As can be seen, in the IDWC
system, several inclined walls are connected to adjacent beams and foundations by means of bolted steel connections. In particular, the
volume of concrete and the number of steel connections are significantly reduced by using inclined demountable walls instead of one
large wall in each story. In this situation, due to the bolted steel connections, the inclined walls act as a seismic fuse, thus enhancing the
sustainability and resilience of the system. Also, concrete filled steel tube (CFST) columns are used as boundary elements. The most
important features that CFST columns provide are high flexural stiffness, high strength and easy conditions for connecting columns to
the prefabricated elements. Hence, the CFST columns provide a reliable structural frame for the demountable precast walls and help
the system maintain stable performance after a severe earthquake. It is worth mentioning that a rocking mechanism is introduced at
the column to foundation connections. The rocking mechanism at the base of the columns, while mitigating the structural damage to
the column members, decreases permanent residual displacements. To provide enough shear resistance for preventing the slipping of
the column bases, shear keys with vertical slots are utilized (see Fig. 1b). Due to their configuration, shear keys allow the column bases
to rock while providing enough restraint in the horizontal direction. The columns are connected to the shear keys by means of highstrength bolts. Also, to enhance the energy dissipation capacity of the system, replaceable slit steel connectors are attached to the shear
keys and columns. In order for the slit steel connectors to undergo nonlinear behavior before the columns, their yield strength should
be less than that of the columns. To this end, the following equation is used to determine the yield strength of each damper (Fd ).
′
Fd <
As fy + Ac fc
nd
(1)
Where As , Ac , fy and fc are steel area, concrete area, yield strength of steel and confined compressive strength of concrete in CFST
columns, respectively. Also, nd represents the number of slit sleet connectors in each column.
It is worth noting that the weak wall-strong connection design philosophy is taken into account for the IDWC system. In this case,
the demountable walls are expected to behave nonlinearly before the joints. For this purpose, any possible slippage between the steel
connectors should be avoided by providing a sufficient number of post-tensioned bolts.
In general, it can be said that the IDWC system, with a holistic approach, combines several concepts. The first concept is to use
inclined demountable walls as seismic fuses. In this case, the number of walls is reduced as compared to other systems. Moreover, after
′
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a severe earthquake, the damaged wall panels can be easily removed and replaced with new members, which makes the system more
sustainable and flexible. Another new concept is to use the CFST columns as boundary conditions for the demountable precast concrete
walls. It is obvious that the use of CFST boundary columns increases the flexural stiffness and ductility of the boundary elements. By
increasing the flexural stiffness of the boundary columns, it is expected that the lateral drifts will decrease. Also, CFST columns are
easily connected to other prefabricated members, thus easing the erection and construction processes. The last concept used in the
IDWC system is the introduction of a rocking mechanism at the column bases. The main purpose of using the rocking mechanism is to
prevent damage to the boundary columns, because it is almost impossible to replace damaged columns with new ones after a strong
earthquake. It is worth mentioning that the details of the proposed IDWC system are such that it can be used for seismic retrofitting.
It is worth mentioning that for beam-column joints, a simple shear connection that has only shear and axial resistance is used. In
this situation, due to the CFST columns, all kinds of common shear steel connections can be applied. Also, for medium and high rise
buildings, column to column connection is required. For this purpose, an end plate steel connection can be accommodated at the mid
height of a story.
The above mention details ensure that the inclined wall segments act as seismic fuses and can be replaced with new members in
case of damage. In other words, for the proposed IDWC system, the lateral stability is provided by the surrounding frame and the
inclined demountable walls play the role of seismic energy dissipaters. This means that the surrounding frame members such as
columns and beams should remain undamaged while the replaceable wall members suffer extensive damage in order to dissipate the
seismic energy.
3. Studied models
To evaluate the seismic performance of the IDWC system, buildings with heights of 4, 10 and 15-stories are considered. Assuming
that the building plan is regular, two-dimensional models are developed for the studied buildings. For each building height, four
models of the IDWC system are compared with one model of the conventional RC wall system. Also, in order to better demonstrate the
seismic performance of inclined demountable wall elements, a model with vertical demountable wall elements, named VDi, is also
Fig. 2. The studied models.
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A. Naserpour et al.
Table 1
Design characteristics of different structural elements.
Model
6
4-story
models
10-story
models
15-story
models
Wall
boundary condition of conventional wall
CFST Column
Beam
Vertical reinforcement
ratio (%)
Horizontal reinforcement
ratio (%)
Vertical reinforcement
ratio (%)
Horizontal reinforcement
ratio (%)
Size (mm ×
mm)
B
t
α (%)
Size (mm ×
mm)
Top and bottom reinforcement
ratio (%)
0.45
0.35
1.5
0.35
500 × 400
60
7.1
500 × 400
0.75
0.45
0.35
1.5
0.35
600 × 400
60
8.9
600 × 400
0.75
0.45
0.35
1.5
0.35
700 × 400
60
10.2
700 × 400
0.75
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included for each building height. The details of the studied models are depicted in Fig. 2 for i-story building. As can be seen, four
different arrangements of inclined demountable walls are evaluated for the IDWC system. The purpose of this work is to find the best
and most optimal arrangement of inclined demountable walls for the IDWC system. It is worth mentioning that the present study only
evaluates the different arrangements of the wall panels while other parameters, such as the number and angle of inclined walls related
to horizontal axis, are constant for all models.
It is assumed that the buildings are located in Los Angeles, California on soil type D [68]. Also, the dead and live uniform loads
imposed on the beams are equal to 20 kN/m and 5 kN/m, respectively, and lumped mass of each story is 80 t. It should be noted that
these values were chosen due to an arbitrary area of the building plan. To design the studied models, first, the structural members of
conventional RC wall models are designed according to ASCE standard [68] and ACI code [69]. The amount of steel reinforcement
used in the RC members is considered to satisfy the minimum requirements of the ACI Code. Then, to design the structural members of
the IDWC models the following steps are taken into account.
- For a fair comparison between the IDWC and the conventional models, the CFST column dimensions are decided using the
specifications obtained for conventional wall boundary columns. Then, according to the following equations [70], the thickness of
the steel tube is determined.
√̅̅̅̅̅
B
Es
(2a)
≤5
t
fy
(3a)
α ≥ 1%
Where, B is width of rectangular column, t is thickness of steel tube, Es is elastic modulus of steel, fy is yield strength of steel and α is
steel ratio of CFST column.
- After designing the CFST columns, the design force for the steel connectors at the column bases is calculated using Eq. (1).
- The width of each demountable wall panel is considered equal to one-eighth of the frame span. Hence, the width of each
demountable wall is equal to 50 cm. For a fair comparison, the number of reinforcing bars in inclined demountable walls is assumed
to be equal to that in the web of a conventional wall.
- To protect the wall-beam steel joints, the yield strength of the steel connectors should be at least 125% higher than that of the
adjacent inclined demountable wall [55]. In this case, the number of post-tensioned bolts should be determined in such a way that a
rigid connection is provided for steel joints. For this purpose, the shear capacity of each post-tensioned bolt (Nb ) should be
determined from the following equation [55].
(4a)
Nb = k1 k2 nf μf P
Where k1 = 0.9, k2 = 1, nf is number of frictional surfaces, μf is frictional coefficient which is equal to 0.5, and P is pre-stressing of
each bolt [55].
In Tables 1 and 2, the design specifications of structural members and dampers are reported, respectively. Also, the details of the
wall-frame steel connection are shown in Fig. 2b.
4. Analyses
Seismic performance of the studied models is evaluated by nonlinear cyclic and time history analyses. To perform nonlinear cyclic
analysis, the studied models are subjected to a lateral load profile of an inverted triangular shape. It is worth mentioning that the lateral
loading is displacement controlled; the applied inter-story drift history is shown in Fig. 3.
To perform time history analysis, seven earthquake records were selected and scaled to the design spectrum for soil type D of ASCE
standard [68]. While the choice of ground motion selection and scaling methods has been shown to influence the response predicted by
time-history modeling [71], choosing one of the common GM selection and scaling methods should be acceptable for this study as the
purpose of time history analyses in this study is to compare between different structural models (rather than predicting the absolute
response of one model). These earthquake records were scaled for two intensities, design-basis earthquake (DBE) and maximum
credible earthquake (MCE). It should be noted that DBE and MCE define the earthquake records with 10% and 2% probability of
exceedance in 50 years, respectively.
The scale factor of the earthquake records was considered in such a way that the average acceleration response spectrum of the
earthquake records matches the target spectra in the period range of interest. For defining the period range of interest, a modal analysis
was carried out for each model. The fundamental periods of the studied models are reported in Table 3. As can be seen, the minimum
Table 2
Design specification of slit steel connectors at the column bases.
Design specifications
Yield strength (kN)
Initial stiffness (kN/mm)
Models
4-story IDWC models
10-story IDWC models
15-story IDWC models
800
400
1100
550
1500
750
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Fig. 3. Time history of cyclic loading [58].
and maximum periods are 0.25 and 2.58 s, respectively. Therefore, the period range of interest is considered to be between these two
values. It is worth mentioning that as the studied models are two-dimensional, only one component of the earthquake records is used in
the time history analysis. In Table 4, the details of the scaled records are presented. Also, Fig. 4 demonstrates the response spectra of
the scaled earthquake records and the target spectra. The inherent damping value of 5% is taken into account for the first three modes
of the models.
5. Numerical modeling and verifications
5.1. Development of numerical models
In this study, micro and macro modeling are used for numerical simulations. By using micro modeling, i.e. solid finite element
modeling, more details of the seismic behavior and crack propagations can be simulated in the studied models. For micro modeling,
Abaqus software [72] is used herein with assumptions explained below.
All concrete structural members were modeled using the 8-node three-dimensional solid element with reduced integration (C3D8R)
available in Abaqus. Also, the same solid element was used to model all steel connectors. For modeling the steel tube in the CFST
columns, the 4-node doubly curved shell element with reduced integration (S4R) was considered. The reinforcing bars were simulated
using the three dimensional truss (T3D2) element.
For finite element modelling, proper consideration of the nonlinear behavior of materials is an important and necessary condition.
For this purpose, the damaged plasticity concrete material available in the Abaqus library was used to define the behavior of concrete.
In Fig. 5a, nonlinear behavior of the concrete model used in Abaqus is shown. To define the concrete stress-strain relationship in
compression, the Kent-Park model [73] was considered. It should be noted that the confinement effect is taken into account for
nonlinear behavior of compressive concrete. This effect is shown in Fig. 5a. To account for the effect of the rebar-concrete bond,
tension-stiffening was applied to the tensile part of the concrete stress-strain behavior. Applying tension-stiffening to the tensile part of
the concrete stress-strain model not only provides better accuracy in simulating the propagation of cracks, but also helps to reduce
problems related to convergence. To simulate the distribution of cracks, the tensile damage factor of concrete should be properly
modeled. For this purpose, the following equation proposed by Xiao et al. [74] was used.
⎧
ε
⎪
0, x = ≤ 1
⎪
⎪
εt
⎨
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
dt =
(5)
⎪
1
ε
⎪
⎪
1
−
,x = > 1
⎩
1.7
εt
αt (x − 1) + x
In Eq. (5), εt is initial cracking strain and αt is a parameter of tensile stress-strain curve of concrete which can be evaluated as in
Ref. [74].
The elasto-plastic material available in the Abaqus library was used to define the nonlinear behavior of steel components. To
determine the cyclic behavior of steel, the combination of isotropic and kinematic hardening was taken into account. To model the
stress-strain relationship of steel components, the relationship proposed by Han [75] and Wang et al. [76] was used (see Fig. 5b). It is
worth noting that to simulate steel fracture at high strains, the ductile damage model available in the Abaqus library was assigned to
the steel elements. Previous studies [57,58] show that by assigning the fracture model to the steel elements, stiffness and strength
deteriorations in their cyclic behavior can be simulated reasonably well.
After defining the materials, all members of the structure were meshed and assembled in the Abaqus software environment. For
example, in Fig. 6, details of meshing and assembly for one of the proposed IDWC models are shown. After assembling the numerical
8
A. Naserpour et al.
Table 3
The fundamental periods of the studied models.
Period (sec)
9
4-story models
CW4
0.25
VD4
0.56
ID14
0.44
10-story models
ID24
0.53
ID34
0.45
ID44
0.47
CW10
1.12
VD10
1.48
15-story models
ID110
1.32
ID210
1.44
ID310
1.34
ID410
1.35
CW15
2.14
VD15
2.58
ID115
2.33
ID215
2.56
ID315
2.35
ID415
2.37
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Table 4
Ground motion records and scaling.
ID No.
Earthquake name
Station name
Comp.
PGAmax(g)
Year
1
2
3
4
5
6
7
Imperial Valley-06
Loma Prieta
Northridge-01
Kobe, Japan
Chi-Chi, Taiwan
Gazli USSR
Superstition Hills-02
Aeropuerto Mexicali
Gilroy-Historic Bldg
Canyon Country
Shin-Osaka
CHY036
Karakyr
El Centro Imp.
45
160
00
00
EW
00
00
0.307
0.285
0.403
0.225
0.272
0.701
0.357
1979
1989
1994
1995
1999
1976
1987
Scale factor
DBE
MCE
1.63
1.75
1.24
1.83
1.79
0.71
1.39
2.45
2.63
1.86
2.75
2.69
1.07
2.09
Fig. 4. Pseudo Acceleration spectra of scaled records and target spectra.
Fig. 5. Nonlinear behavior of materials in Abaqus.
models, the interaction between the different members was defined. To consider the post-tensioning force in steel connection bolts, the
initial bolt load feature available in the Abaqus library was applied. To simulate the rocking behavior at the column bases, a standard
surface-to-surface interaction was defined that included a hard contact in the normal direction and a frictional behavior with a
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Fig. 6. Abaqus finite element mesh discretization for ID44 model.
coefficient of 0.4 in the tangential direction [27]. It should be noted that this value was determined based on trial and error and its
accuracy was verified by experimental data, which will be shown in the next section. Also, to account for the interactions of the steel
tube with the CFST column and reinforcing bars with concrete, the “embedded region constraint” was applied.
As analyses using solid finite element models for large structures are computationally demanding and time-consuming, in this study
the micro solid finite element models are used only for the static analysis of the four-story frames. On the other hand, macro numerical
models are used to perform complete cyclic and time history analyses for all models. In case of macro models, fiber-based finite
element modeling has received special attention in recent years. There are two approaches for macro modeling, which include lumped
and distributed plasticity models. In the lumped plasticity model, rotational spring elements are usually applied at both ends of the
structural members to simulate the inelastic deformation of the plastic hinges. In this case, the entire length of the structural element,
except for the plastic hinges at its two ends, remains in an elastic state. On the contrary, in the distributed plasticity model, nonlinear
behavior is assigned to all sections of the structural element. In this case, several weighted integral points are distributed throughout
the length of the structural element. At each integral point, a nonlinear fiber section is defined for concrete and reinforcing steel bars.
Accordingly, for the distributed nonlinear model, a more accurate description of the nonlinear behavior of structural elements is
provided, compared to the lumped model. Hence, in this study, a distributed plasticity approach is applied in the form of fiber-based
finite element models in OpenSees software [77] for conducting large scale nonlinear cyclic and dynamic analyses.
In Fig. 7, key aspects of the fiber-based finite element modeling in the OpenSees software for a typical specimen are demonstrated.
To model RC members such as walls, columns, and beams, the displacement-based beam-column element with fiber sections is used.
This element uses the distributed plasticity model for describing the nonlinear behavior of the RC structural members. In Fig. 7c, the
fiber sections are presented for each of the elements. In these sections, the concrete02 material available in OpenSees library is applied
to simulate the nonlinear behavior of the concrete fibers. It is worth mentioning that the stress-strain relationship presented in Fig. 5a
were used to define the nonlinear behavior of concrete in fiber-based numerical models. A hysteretic material with the parameters
reported in Table 5 is used to model the reinforcing bars and slit steel connectors. Previous studies [57,58] reveal that by using
hysteretic material, strength and stiffness degradations in the cyclic behavior of the elements will be simulated. It is worth mentioning
that the parameters shown in Table 5 should be determined in such a way that the cyclic behavior of the numerical models can be
confirmed by comparing them with the experimental data. To simulate the rocking behavior of the column bases, ten zero-length
spring elements were used, whose axial stiffness was determined in accordance with the relationship proposed by Qureshi and
Warnitchai [78]. As mentioned earlier, wall-beam steel connections are expected to exhibit elastic behavior. Accordingly, an elastic
beam-column element was utilized for modeling the wall-beam steel connections. Also, the slit steel connectors used in the column
bases were modeled by zero-length spring elements.
Due to small free span of the beams between the walls and weak wall-strong beam design philosophy, the beams are expected to
remain elastic and have significant shear stiffness (this will be presented later in Section 6.1). Therefore, for the adjacent beam ele­
ments, the shear behavior is taken into account by displacement-based beam-column element with nodal shear springs (see Fig. 7d).
The shear stiffness of these nodal springs is calculated according to the following equations [79].
Kshear =
G c Ac
fs lb
(2b)
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Fig. 7. Fiber-based finite element model in OpenSees.
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Table 5
Parameters of hysteretic materials used in fiber-based OpenSees models [58].
element
pinchX
pinchY
damage1
damage2
beta
Reinforcing bars
Slit steel connector
0.001
0.10
0.25
0.55
0.03
0.01
0.0
0.0
0.0
0.0
Gc =
Ec
6
, ν = 0.2; fs =
5
2(1 + ν)
(3b)
Where, lb is the length of beam element and Ec is the elastic modulus of concrete.
It is clear from these equations that as the free span length of the beams decreases, the shear stiffness of the beam becomes
significant.
5.2. Verifications
Two experimental models were selected to verify the assumptions used for the simulated numerical models. To validate the rocking
Fig. 8. Experimental [80] and numerical models of the S16-5.5-0.1 specimen.
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CFST columns with slit steel connectors, the experimental model of the S16-5.5-0.1 specimen tested by Liu et al. [80] was used. The
configuration of this experimental specimen is depicted in Fig. 8a. As can be seen, this specimen consists of a CFST column connected to
the foundation by slit steel dampers. Therefore, it can be found that the details of the S16-5.5-0.1 specimen are very similar to the
boundary column proposed in the IDWC system. In accordance with the modeling assumptions mentioned in the previous section, two
finite element models were developed in Abaqus and OpenSees for the S16-5.5-0.1 specimen. In Fig. 8b, the boundary conditions and
meshing of the Abaqus finite element model are shown. It is worth noting that a displacement-control lateral load, with the cyclic
loading history presented in Liu et al. [80], is applied at the top of the column. Fig. 9 compares the results of the numerical models with
those of the experimental model for the S16-5.5-0.1 specimen. From Fig. 9a, it is clear that the hysteresis behavior presented by the
numerical simulation is in very good agreement with the results of the experimental test. In this case, the maximum lateral force
estimated by Abaqus and OpenSees models differed by 5.5% and 3.6% from the experimental result, respectively. Also, due to the use
of hysteretic material for the slit steel connectors, the fiber-based OpenSees model closely matched the hysteretic behavior of the
experimental model. Also, in Fig. 9b, the damage pattern of the Abaqus finite element model is compared with that in the experimental
specimen. As can be seen, the Abaqus model accurately simulates the plastic deformation of the slit steel dampers and rocking motion
at the column base.
For verification of the numerical modeling of inclined precast walls with bolted steel connections, an experimental specimen tested
by Han et al. [55] was selected. Fig. 10 shows the details of this experimental specimen, known as TPSW. As can be seen, the details
used in the bolted steel connection of the TPSW specimen are very similar to the wall-frame joints of the proposed IDWC system. The
normal precast wall panel of the TPSW specimen has a height-to-length ratio greater than two, which normally leads to a
flexure-dominated behavior. In a flexure-dominated wall, the inelastic response of the system is concentrated in boundary elements
that resist axial strain demands. In other words, the structural behavior of the flexure-dominated walls is strongly dependent on the
axial response of the boundary elements [81]. Therefore, it makes sense to select the TPSW specimen for verifying the inclined
demountable walls which may be predominantly subjected to axial load. For the TPSW specimen, Abaqus and OpenSees numerical
models were developed according to the modeling assumptions mentioned in the previous section. Fig. 11 illustrates the boundary
conditions and meshing of the Abaqus model developed for the TPSW specimen. As shown in Fig. 11, cyclic lateral load, with the same
loading history as that used in the test [55], was applied to the upper beam of the TPSW specimen. Fig. 12 compares the results of the
numerical models with the experimental response of the TPSW specimen. From Fig. 12a, it can be seen that the predicted hysteresis
behaviors of the numerical models are in relatively good agreement with those of the experimental model. Compared to the experi­
mental results, the maximum lateral force predicted by the Abaqus and OpenSees models differ by only 1 and 9%, respectively. Also,
looking at Fig. 12b, it is evident that the crack propagation predicted by the Abaqus model is similar to that observed in the exper­
imental model.
Overall, the numerical modeling of both the rocking-based CFST columns and inclined demountable walls was verified by
experimental data from past studies. Based on the results, it can be confirmed that the assumptions used in the numerical modeling are
justified. Hence, the developed numerical models can be argued to be efficient in evaluating the seismic performance of IDWC systems.
6. Results
6.1. Cyclic behavior of the IDWC models
In this section, the results of nonlinear static analysis are presented. As explained in the previous section, Abaqus numerical models
were used to simulate the crack propagation in the four-story models. In Fig. 13, crack propagations of the four-story IDWC and vertical
demountable wall models are compared with the results of conventional shear wall model when subjected to a monotonically
Fig. 9. Comparison between the results of experimental and numerical models for S16-5.5-0.1 specimen [80].
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Fig. 10. Experimental details of the TPSW specimen [55].
Fig. 11. Finite element modeling of the TPSW specimen in Abaqus.
increasing lateral load. For the conventional wall model, with the formation of a plastic hinge, the lower part of the wall boundary and
the web of the wall undergo extensive cracking. In particular, with the development of extensive cracks in the boundary zones,
concrete walls may become unstable and suffer irreparable damage, thus leading to demolition. In contrast, for IDWC and vertical
demountable wall models, the rocking-base columns, which serve as the boundary elements, are free from any damage. This is due to
the use of a rocking mechanism at the base of the columns, which stabilizes the IDWC system. Also, as can be seen, all cracks are
concentrated in the inclined replaceable walls of the IDWC models. The crack concentration is especially evident in the walls of the first
story. In this case, it is only necessary to replace the walls of the first story with new ones, which in turn reduces the repair costs and
increases the seismic resilience of the structure. By comparing the crack propagation results of the demountable wall models with each
other, the models with inclined demountable wall units exhibit more pronounced nonlinear behavior than the vertical demountable
walls due to higher axial strain demands. This can increase the energy dissipation capacity in models with inclined wall segments.
In general, the inclined configuration is the Authors’ preference because it is apparent in Fig. 13 that, in comparison to the vertical
wall, the inclined walls have greater concentration of nonlinear strains in the bottom storey; thereby potentially reducing damage to
the walls in the upper stories and requiring fewer wall units to be replaced following a major earthquake. However, given there is
insignificant difference between the overall behaviours of the models with inclined and vertical walls, choosing vertical configuration
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Fig. 12. Comparison between the results of finite element models and the experimental data of the TPSW specimen [55].
does not seem to compromise the gains offered by the demountable wall system in comparison with the traditional monolithic system.
Also, from Fig. 13, it can be seen that no damage is experienced in the beams of the proposed models with demountable walls. In
justification of this result, it can be said that the beams are restrained by the upper and lower wall segments, and as a result, the free
span of the beams is reduced. In this case, the beams are less deformed and remain almost elastic. However, it is worth noting that the
design characteristics of the beams should be considered based on the weak wall-strong beam design philosophy. Overall, these results
demonstrate that the frame adjacent to the detachable walls remains stable and prevents any collapse of the proposed system when
subjected to severe earthquakes.
Figs. 14–16 illustrate the hysteresis behavior of the studied models subjected to cyclic loading. From these figures, it is clear that the
conventional wall models, due to the inevitable damage at the base of the walls, show a significant strength degradation after 2% roof
drift. On the contrary, the hysteresis behavior of IDWC models does not show any deterioration of strength or stiffness even up to 3.5%
roof drift. This is mainly because of the use of CFST columns with a rocking base, which remain undamaged. It is worth noting that the
models continue to respond stably until the ultimate drift ratio. Herein, the ultimate drift ratio refers to the point where either the
maximum drift is reached or the lateral strength in the post-peak branch is reduced to less than 80% of the maximum lateral strength
[58] and represents the failure of the studied models. As can be seen, for all cases, the ultimate drift of the IDWC and vertical
demountable wall models is higher than that of the conventional wall models. For example, for 10-story models, the ultimate drift ratio
of CW10, VD10, ID110, ID210, ID310, ID410 is equal to 2.02%, 3.48%, 3.48%, 3.49%, 3.5%, 3.5%, respectively. These results indicate
that the conventional wall models fail earlier than the demountable wall models. The earlier failure of conventional concrete walls is
due to the fact that the wall boundary elements undergo significant inelastic deformation, which increases the tensile strain demands
in the reinforcements (see Fig. 13). Also, from Fig. 14, it can be seen that the results of the Abaqus models have a relatively good match
with the results of the OpenSees models.
Fig. 17 demonstrates the backbone curve of the models extracted from the hysteresis responses. As can be seen, for the 4-story
models, the lateral strength of the conventional wall model is higher than that of the demountable wall models. For example, at a
roof drift of 1.5% the lateral strength of the CW4 model is 28%, 28%, 25%, 20% and 21% higher than that of the VD4, ID14, ID24, ID34
and ID44 models, respectively. However, with the increase in the number of stories, the lateral strength of the demountable wall
models became higher than that of the conventional wall model. For example, at a roof drift of 1.5%, the lateral strength of the CW15
model is 17%, 17%, 15%, 14.5% and 18% less than that of the VD15, ID115, ID215, ID315 and ID415 models, respectively.
Fig. 18 shows the initial lateral stiffness of the studied models. The initial lateral stiffness of the models is calculated using the
following equation.
)
(
1 F+y F− y
Ki =
+
(6)
2 δ+y δ− y
Where, F+y , F− y and δ+y , δ− y are the yield strengths and yield displacements in the positive and negative directions of the back-bone
curve, respectively.
From Fig. 18, it can be seen that the initial lateral stiffness of the conventional wall models is higher than that of the demountable
wall models in all cases. For instance, in the case of 10-story models, the initial lateral stiffness of CW10 is 62%, 24%, 181%, 72% and
73% higher than that of VD10, ID110, ID210, ID310 and ID410, respectively. These results are due to the use of small wall panels and
the introduction of a rocking mechanism at the column bases of IDWC models. Previous studies [82–84] show that by weakening the
initial lateral stiffness of the lateral resisting system, the base shear and the floor acceleration are decreased, which will be investigated
in the next section.
Fig. 19 illustrates the amount of energy dissipated at the roof drift cycles of 1, 1.5 and 2% for the different models. Herein, the
energy dissipated in each cycle represents the enclosed area of the force-displacement curve of that cycle. For the 4-story models, the
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Fig. 13. Crack propagation of the 4-story models at 2% roof drift.
conventional wall model has dissipated more energy than the IDWC models and vertical demountable wall model. Conversely, for the
10- and 15-story models, the demountable wall models dissipated more energy than the conventional wall models. For instance, in the
case of 15-story models with a roof drift of 1.5%, the energy dissipated by the CW15 model is 37.2%, 37.3%, 31.7%, 32.7% and 40%
less than that of the VD15, ID115, ID215, ID315 and ID415 models, respectively. Also, by comparing amongst the different IDWC
models, it can be seen that ID3i and ID4i have a higher energy dissipated capacity. In general, it can be figured out that the energy
dissipation capacity of the proposed IDWC system is enhanced as the number of stories increases. This result can be attributed to the
increase in the number of walls experiencing nonlinear behavior along the height of the IDWC models.
6.2. Time history response of the studied models
In this section, the main results extracted from the time history analysis are presented. Fig. 20 shows the maximum roof drift ratio of
the models subjected to different ground motion records. Herein, the roof drift ratio denotes the ratio of roof displacement to the total
height of the models. By looking at Fig. 20a, it is evident that CW4 has the lowest value of the maximum roof drift in all cases, while the
highest roof drift belongs to ID14. These results can be attributed to the significantly higher stiffness of the conventional wall system in
four-story models. On the contrary, for 10- and 15-story models, the proposed demountable wall models show in general slightly
smaller roof drift ratio compared to the conventional model in most cases. The greatest difference was observed for earthquake record
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Fig. 14. Hysteresis behavior of the 4-story models.
Fig. 15. Hysteresis behavior of the 10-story models.
7 scaled to MCE level, with the roof drift ratio of the CW15, VD15, ID115, ID215, ID315 and ID415 models being 1.91%, 1.42%, 1.32%,
1.32%, 1.23% and 1.16%, respectively. This noteworthy trend can be attributed to the difference in correlation between the building
height and stiffness as well as the energy dissipation capacity for the conventional and demountable wall systems. For example, as can
be seen in Fig. 18, the stiffness of the IDWC and vertical demountable wall models are significantly less than that of the conventional
model for 4-storey height, whereas the difference rapidly decreases for the taller models (being almost comparable for the 15 story
models). On the other hand, as seen in Fig. 19 the energy dissipation capacity of the conventional wall is greater than the demountable
walls for the 4-storey models, whereas the hierarchy is reverse for taller (10, 15 story) models.
Fig. 21 demonstrates the median value of the peak inter-story drifts for all cases. It can be observed in this figure that all models
incur inter-story drift ratios less than 2% and 2.5% for DBE and MCE events, respectively. Also, by observing the results of the 10- and
15-story models, it can be seen that all IDWC and vertical demountable wall models have far less drift in the upper stories compared to
the conventional models. In other words, a more uniform distribution of inter-story drift is provided for all demountable wall models
by increasing the height of building frames. These results are more evident for the ID3i and ID4i models that can be attributed to the
fact that the IDWC system behaves similar to braced frames (with multiple eccentric braces provided by the wall segments). Note that
frames typically deform in a mode that has higher drifts at the lower stories, and with the inclined walls bracing the frames, the drifts
become more uniform across the height. On the contrary, conventional walls of medium to high-rise buildings respond in a cantilever18
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Fig. 16. Hysteresis behavior of the 15-story models.
Fig. 17. Backbone curves of the studied models.
Fig. 18. Initial stiffness of the studied models.
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Fig. 19. Energy dissipated by the models at 1%, 1.5% and 2% drifts.
mode characterized by higher drifts in the upper stories. However, this is not the case for 4-story models. Because the results of 4-story
models show that at the lower stories, the inter-story drifts of IDWC models are higher than those of the conventional model.
For a more useful comparison, Fig. 22 depicts the maximum value of the median inter-story drift ratios for all models subjected to
DBE and MCE events. For all cases of 4-story models, the CW4 has the lowest value of inter-story drift and the ID24 has the highest one.
For example, under MCE events, the maximum inter-story drift of CW4 is 54%, 54%, 57%, 13% and 21% smaller than that of the VD4,
ID14, ID24, ID34 and ID44, respectively. On the contrary, for the 10- and 15-story models under DBE and MCE events, the IDWC and
vertical demountable wall models experienced less inter-story drift than the conventional model. For example, for the 15-story models
under the MCE events, the maximum inter-story drift of CW15 is 29%, 25%, 29%, 30% and 43% higher than that of VD15, ID115,
ID215, ID315 and ID415, respectively. According to these results, it can be seen that as the number of stories increases, the ID4i model
performs better than other models in terms of inter-story drift response.
Fig. 23 illustrates the median values of peak floor acceleration for the studied models under DBE and MCE events. For all cases, the
IDWC and vertical demountable wall models experience much lower floor accelerations compared to the conventional experimental
models. For example, under MCE events, the maximum floor acceleration of the CW10 model is 71%, 40%, 53%, 53% and 57% higher
than that of the VD10, ID110, ID210, ID310 and ID410 models, respectively. These results are mainly due to the lower initial lateral
stiffness of the proposed demountable wall models compared to the conventional models, as predicted in the previous section. It is
worth mentioning that the reduction of floor acceleration is the most important advantage of the IDWC system, as it can significantly
reduce damage to acceleration-sensitive nonstructural elements (e.g. ceilings, pipes, electrical/mechanical equipment, services etc.)
[85].
Another important parameter of seismic response used for evaluating the seismic resilience of structures is residual drift. The higher
the residual drifts a structure experiences, the more challenges it will face in recovering after a severe earthquake. Accordingly, Fig. 24
compares the maximum roof residual drift ratios of the models under the seven earthquakes used. Herein, the roof residual drift ratio
represents the ratio of roof displacement at the end of the analysis to the total height of the models. From Fig. 24, it is evident that in
most cases, the conventional models have the highest residual drift and the ID4i model has the least. For example, under earthquake
record 1 scaled to MCE intensity, the roof residual drift ratios of the CW10, VD10, ID110, ID210, ID310 and ID410 models are equal to
0.26%, 0.06%, 0.08%, 0.02%, 0.04% and 0.004%, respectively. These results confirm that by using CFST columns with a rocking
mechanism at the base, the deterioration of strength and stiffness in the hysteresis behavior of IDWC and vertical demountable wall
models is mitigated, thus leading to a significant reduction in residual drifts. It can also be seen that with the increase in the number of
stories, due to the effect of gravity loads on the boundary columns, the residual drifts decrease in the proposed demountable wall
models.
Fig. 25 shows the median values of peak base shear for the studied models. It is clear from this figure that in general, the con­
ventional models incur a higher base shear demand than the IDWC and vertical demountable wall models. For example, for 10-story
models under MCE earthquakes, the base shear of the CW10 model is 76%, 80%, 81%, 60% and 73% higher than that of the VD10,
ID110, ID210, ID310 and ID410 models, respectively. These results confirm that by reducing the initial lateral stiffness of the IDWC
and vertical demountable wall models, the floor acceleration and base shear are reduced significantly compared to the conventional
model.
6.3. Incremental dynamic analysis results
Incremental Dynamic Analysis (IDA) [86] is a common method used to predict performance of a building under seismic ground
motions of different intensity, starting from the elastic state to the dynamic instability or collapse point. For this purpose, a structural
model is subjected to different ground motion records, with multiple levels of intensity. In other words, for each seismic intensity level,
a nonlinear time history analysis is performed and structural response is measured. After completing multiple time history analyses of a
structural model, an IDA curve (i.e. a plot of ground motion intensity measure vs. maximum structural response, known as engineering
demand parameter EDP) is generated for each earthquake record. The 5%-damped spectral acceleration of each record at the
fundamental period of the building, Sa (T1 , 5%), is widely used as the intensity measure (IM), and maximum inter-story drift ratio is
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Fig. 20. Maximum roof drift ratio for the studied models.
considered as the engineering demand parameter (EDP). Here, to perform IDA for the studied models, the seven ground motion records
reported in Table 4 are used.
Figs. 26–28 illustrate the IDA curves for the studied models under different ground motion records. As shown in these figures, each
IDA curve is generated by interpolating the IM and EDP points for each earthquake record. Also from these figures, it can be seen that
on each IDA curve, the collapse prevention point is marked by a red circle. The collapse prevention point represents the point where the
slope of the curve reduces to less than 20% of the initial slope [86].
From the IDA curves, the collapse margin ratio (CMR) can be determined. CMR is a primary and very important parameter in
determining the collapse safety of a building. This ratio is determined based on FEMA-P695 [87] as follow.
CMR =
̂
S CT
SMT
(4b)
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Fig. 21. Median values of peak inter-story drift ratios of studied models under (a) DBE and (b) MCE events.
Where, ̂
S CT denotes the value of 5%-damped spectral acceleration at the fundamental period of the structure by which the 50% of the
records result in the collapse of structure, and SMT represents the 5%-damped spectral acceleration of the MCE ground motions at the
fundamental period of the structure.
Figs. 26–28 indicate the CMR values for different models. In general, it can be seen, for all cases, the highest value of CMR is for ID3i
and ID4i models. For example, for 15-story models, the CMR value of ID415 is 53.5%, 22.8%, 35.8%, 32.3% and 2.33% higher than
that of CW15, VD15, ID115, ID215 and ID315, respectively. These results can be attributed to less damage in CFST columns and higher
energy dissipation capacity for ID3i and ID4i models (see Figs. 13 and 19). According to these results, it can be seen that the inclined
demountable wall models, especially for 10- and 15-story frames, have a higher collapse capacity than conventional concrete wall
models. It is worth mentioning that the numerical models developed to perform dynamic analysis are affected by epistemic and
aleatory uncertainties. In fact, these factors can affect the fragility curves as well as the collapse capacity of the building. However,
considering that the present paper is a comparative study, the effects of epistemic and aleatory uncertainties are assumed to be similar
for all numerical models.
7. Discussions and future studies
As the cyclic loading results demonstrate, the initial lateral stiffness of the proposed IDWC system is lower than that of its con­
ventional monolithic wall counterpart. This reduction in the initial lateral stiffness of the proposed IDWC system is because of the
discrete wall units (rather than an integral web wall) in each story and the rocking connection at the boundary column bases. The
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Fig. 22. Maximum values of inter-story drift ratios for the studied models under (a) DBE and (b) MCE events.
results also indicated that weakening of the initial lateral stiffness of the IDWC system leads to a reduction of the floor acceleration and
base shear demands under severe earthquakes. However, smaller initial lateral stiffness can lead to greater inter-story drifts in IDWC
walls; especially when the height is small. Nevertheless, as the cyclic and time history analyses reveal, the IDWC system has greater
energy dissipation capacity which helps in reducing the inter-story drifts. The increase in the energy dissipation capacity of the IDWC
system originates from two sources; one is rocking CFST columns as boundary elements and the other is inclined walls as seismic fuses.
When a smaller number of inclined walls are used in each floor, these walls are prone to extensive damage and a highly non-linear (i.e.
inelastic) response, which results in an increase in the amount of energy dissipated. This is especially important when the number of
stories increases. In this case, the number of walls with non-linear behavior increases with height, which leads to enhanced energy
dissipation capacity for the IDWC system. It is worth mentioning that the time history analysis results suggested better performance of
the ID3i and ID4i models than other demountable wall models. This can be attributed to the arrangement of the inclined walls in
different models. As can be seen in Fig. 13, the walls in other models are inclined only in one direction in each story, but in ID3 and ID4
models there are inclined walls with tension and compression behavior in each story.
In general, it can be argued that the proposed IDWC system combines the concepts of reduced initial stiffness and additional
damping, which leads to a simultaneous reduction of seismic demands. Experimental and numerical studies [82–84] have shown that
by weakening the initial stiffness and increasing the damping of structural systems, it is possible to simultaneously mitigate damage to
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Fig. 23. Median values of maximum floor acceleration of the studied models subjected to (a) DBE and (b) MCE events.
structural and non-structural elements. In addition to these valuable results, due to the use of rocking-based CFST columns, the IDWC
models experience negligible residual drifts, thus enhancing their seismic resilience.
For practical application of the IDWC system, more study is needed. The following could be the priorities for future studies on this
system:
• Design methods should be developed to optimize the seismic performance of IDWC systems
• As the performance of buildings will be different from the performance of isolated structural walls due to interaction between the
wall, floors and gravity frames [88], future studies should also investigate the performance of complete building systems including
IDWC as the lateral load resisting component together with floors and gravity-resisting columns/frames/walls.
• IDWC systems should be studied in conjunction with non-structural elements to explicitly investigate their relative performance in
IDWC and conventional wall buildings
• As the numerical results demonstrate, the proposed system, with the vertical wall arrangements, still performs better than the
conventional wall system for 10 and 15-story models. Therefore, in future studies, it is suggested to evaluate the optimal method for
height-wise distribution of structural damage in vertical demountable wall models.
• As the IDWC system simultaneously reduces floor acceleration, inter-story drift and residual drift, this system can be a good option
for seismic retrofitting of existing buildings. This could also be explored in future studies.
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Fig. 24. Maximum value of roof residual drift ratio of studied models.
8. Conclusions
In this paper, the use of inclined demountable walls with rocking CFST columns (IDWC) was introduced as a seismic resistant
system. The main goal of the IDWC system was to simultaneously reduce all seismic demands and increase the seismic resilience and
sustainability of building structures. In the IDWC system, several small inclined walls were connected to the beams of each story by
means of bolted steel connections. Due to the structural details of the IDWC system, it was shown that by using inclined walls, the
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Fig. 25. Median values of peak base shear for the studied models.
number of steel joints and the amount of concrete consumed per story were reduced. Also, to increase the energy dissipation capacity of
the system and reduce damage to wall boundary zones, rocking-based CFST columns are used in this system. The IDWC system was
compared with the conventional RC wall system using models of 4-, 10- and 15-stories. At each height level, five different wall ar­
rangements were taken into account to find the best case for improving the seismic performance of the IDWC system. To evaluate the
seismic behavior of the IDWC system, numerical models were developed and verified by using experimental results from previous
studies. Both cyclic and dynamic analyses were performed on the studied models, and the following conclusions can be drawn based on
the results.
• When subjected to a monotonically increasing lateral load, it was shown that for the IDWC models, all damages were concentrated
only in the demountable walls, which could easily be replaced with new ones. However, for the conventional wall model, the
formation of a plastic hinge at the wall base caused significant damage in the wall boundary regions.
• Due to little damage in the rocking boundary columns, the hysteresis behavior of the IDWC models was relatively more stable
compared to their conventional counterparts. This was especially evident in taller walls with a higher number of stories.
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Journal of Building Engineering 75 (2023) 107009
A. Naserpour et al.
Fig. 26. Incremental dynamic analysis curves for 4-story models.
Fig. 27. Incremental dynamic analysis curves for 10-story models.
• The backbone curve of the models illustrated that the initial lateral stiffness of the IDWC models is significantly less than that of the
conventional walls; more so when the height is shorter. The most important reasons for lower stiffness are the use of fewer walls in
each story and the rocking mechanism at the base of the CFST columns.
• As a result, when the height was short (e.g. 4-storey) the IDWC models deformed more resulting in a greater maximum inter-storey
drift compared to the conventional model.
• As the cyclic results showed, with the increase in height, the energy dissipation capacity of the IDWC models was up to 56% higher
than that of the conventional model.
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Journal of Building Engineering 75 (2023) 107009
A. Naserpour et al.
Fig. 28. Incremental dynamic analysis curves for 15-story models.
• Due to the increase in energy dissipation capacity of IDWC models, the maximum inter-story drift in the taller models of 10 and 15storeys (for which the stiffness were comparable) was up to 30% less than that in conventional models when subjected to strong
ground motions. In this case, the best result was obtained for IDWC models when the inclined walls were arranged in different
directions in each story.
• By reducing the initial stiffness of the IDWC models, the floor acceleration and base shear were significantly reduced compared to
the conventional models. According to these results, it can be argued that the IDWC system reduces damage to both drift-sensitive
and acceleration-sensitive non-structural elements.
• The use of rocking connections at the base of the columns caused the permanent drift of the IDWC models to be negligible when
subjected to severe earthquakes. These results were especially evident for the 10- and 15-story models, where the effect of gravity
loads on the boundary columns was greater.
• As shown by the IDA curves, the collapse prevention capacity of the IDWC models was up to 53.5% higher than that of the con­
ventional models.
• In general, it can be declared that the IDWC system, in addition to increasing seismic resilience, simultaneously reduces all seismic
demands. By achieving these features for the proposed IDWC system, damage to structural and non-structural elements is mitigated
in comparison to the conventional RC wall system. Although the proposed system can be a suitable method for the next generation
of buildings, more experimental and numerical studies are needed to generalize its application.
Author statement
Afshin Naserpour: Conceptualization, Methodology, Investigation, Validation, Formal analysis, Software, Writing - original draft,
Writing – review & editing.
Mojtaba Fathi: Conceptualization, Methodology, Supervision, Writing – review & editing.
Rajesh Dhakal: Conceptualization, Methodology, Writing – review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Data availability
No data was used for the research described in the article.
Acknowledgment
The researchers state that there is no acknowledgment for this paper.
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Journal of Building Engineering 75 (2023) 107009
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