applied
sciences
Article
Effect of Soil-Structure Interaction on the Seismic
Response of Existing Low and Mid-Rise RC Buildings
Ibrahim Oz 1, * , Sevket Murat Senel 2, *, Mehmet Palanci 3
1
2
3
*
and Ali Kalkan 2
Department of Civil Engineering, Kirsehir Ahi Evran University, 40100 Kirsehir, Turkey
Department of Civil Engineering, Pamukkale University, 20160 Pamukkale, Turkey; akalkan@pau.edu.tr
Department of Civil Engineering, Istanbul Arel University, 34537 Istanbul, Turkey;
mehmetpalanci@arel.edu.tr
Correspondence: ibrahim.oz@ahievran.edu.tr (I.O.); smsenel@pau.edu.tr (S.M.S.)
Received: 23 October 2020; Accepted: 19 November 2020; Published: 25 November 2020
Abstract: Reconnaissance studies performed after destructive earthquakes have shown that seismic
performance of existing buildings, especially constructed on weak soils, is significantly low.
This situation implies the negative effects of soil-structure interaction on the seismic performance
of buildings. In order to investigate these effects, 40 existing buildings from Turkey were selected
and nonlinear models were constructed by considering fixed-base and stiff, moderate and soft soil
conditions. Buildings designed before and after Turkish Earthquake code of 1998 were grouped as old
and new buildings, respectively. Different soil conditions classified according to shear wave velocities
were reflected by using substructure method. Inelastic deformation demands were obtained by using
nonlinear time history analysis and 20 real acceleration records selected from major earthquakes were
used. The results have shown that soil-structure interaction, especially in soft soil cases, significantly
affects the seismic response of old buildings. The most significant increase in drift demands occurred
in first stories and the results corresponding to fixed-base, stiff and moderate cases are closer to each
other with respect to soft soil cases. Distribution of results has indicated that effect of soil-structure
interaction on the seismic performance of new buildings is limited with respect to old buildings.
Keywords: soil-structure interaction; nonlinear analysis; direct time history analysis; existing
buildings; seismic performance
1. Introduction
The determination of the seismic performance of existing buildings has gained very much
interest in recent years, and today there are a greater number of specifications and regulations
containing provisions on this issue [1]. The seismic behavior of a building is directly related to the
interaction between the three interconnected systems, which are superstructure, foundation and soil
medium surrounding the foundation system [2]. Advances and experiences in earthquake engineering,
reconnaissance surveys after strong earthquakes and academical studies about soil-structure interaction
(SSI) have shown that old buildings designed by limited knowledge are far from meeting the current
standards and performance objectives of new designs. Although there were studies in literature
suggesting the use of force-based computational approaches for the modeling of SSI [3], the application
of these methods has been very limited, and they have not found significant use in practice [1].
Particularly over the last two decades the widespread use of displacement-based methods,
which include nonlinear calculations such as static pushover analysis, provide to investigate SSI
beyond the elastic limits [3,4]. Realistic estimations of both displacement capacities and seismic drift
demands became possible by using nonlinear analysis methods. The damage observations and detailed
structural analyses have shown that SSI could significantly alter both the capacity and demand-related
Appl. Sci. 2020, 10, 8357; doi:10.3390/app10238357
www.mdpi.com/journal/applsci
Appl. Sci. 2020, 10, 8357
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structural parameters (e.g., vibration period, drift capacity, etc.) and hence the seismic performance of
buildings [5,6]. All these observations and findings have shown that SSI effects should be considered
necessary for the design and assessment of buildings.
Earlier studies of SSI contained complex arithmetic formulas relating to wave propagation in
several directions [1], and this approach made these studies difficult to comprehend. SSI is not covered
in the undergraduate level and therefore, it is difficult for many engineers to apply these methods in
design phase. While regulations and documents about SSI are available for engineers in countries
such as USA [7], these sources have guided earthquake engineers only to a limited extent. In many
countries, there are still no mandatory code regulations and directions that enforce the engineers to
consider the SSI effects in design and assessment of buildings.
SSI analyses are performed to investigate the effect of various soil conditions on the response
of structures under seismic actions. There are two approaches for the calculation of SSI, namely the
“direct” and “substructure” methods [8]. In the direct method, the structure and soil are modeled
within a single finite element network in which the nonlinearities of the superstructure and the soil are
represented as a whole, and structure and soil are analyzed together. On the other hand, direct method
requires considerable calculation efforts and analysis duration, and therefore, it is not suitable when
assessing a lot of buildings, as in the case of this study. The combined use of nonlinear time history
analysis and direct method makes this situation more complicated. In the “substructure method,”
on the other hand, the soil and the structure are considered as distinct systems. The behavior of the
foundation and soil is represented by dynamic stiffness and damping coefficients and the effect of
interaction between the soil and foundation is transmitted to the structure by means of dashpots and
springs. This method considerably shortens the duration of analysis since the soil is not modeled
directly. It is thus more favorable to use the substructure method in the studies when dealing with
a large number of buildings. In this study, a lot of buildings (40 buildings) were considered and
seismic response of these buildings under various soil conditions was investigated by using nonlinear
time history analyses. Therefore, substructure method is preferred to investigate effect of SSI by
considering the required efforts. Academical studies considering the SSI have increased in the United
States towards the end of the 2000s and some of them were summarized in the FEMA-440 report [3].
In this report, regulations and expressions are presented to explain how SSI can be considered in
nonlinear static analyses. The findings of these studies were also included in US code specifications [4].
However, the expressions in FEMA-440 [3] and the ASCE-2007 [4] regulations are not recommended
for nonlinear time history analyses and therefore this situation required new studies on this subject.
The results of subsequent studies related with the SSI in performance-based earthquake engineering
were summarized in 2012 and the method which can be used in non-linear time history analysis was
proposed [1]. This approach was also used in this study during the analyses of selected building
models and SSI was represented based on the expressions taken from these studies.
There are many other studies addressing the non-building type of structures in the literature.
Gazetas [9] proposed algebraic formulas and tables that could be used to calculate the dynamic
properties of foundations of different shapes. Mylonakis and Gazetas [6] discussed whether SSI effects
could be beneficial for structures. They have compared the seismic behavior of structures calculated
by using traditional methods and by considering SSI effects. The authors showed that an increase
in the natural vibration period may not always lead to a lower spectral acceleration response and
noted that this may result in an unsafe structural assessment. Mylonakis et al. [10] studied the seismic
analysis and design of bridge piers and proposed simple expressions for the calculation of kinematic
effects. Fatahi et al. [11] examined the seismic performance of empirical buildings with SSI and
showed that the seismic performance of buildings varied significantly depending on the soil conditions.
Shehata et al. [5] investigated the variations in SSI effects depending on the use of different demand
calculation methods in multi-story buildings. Their research has shown that seismic performance
evaluations are not within the reliable limits if the effects of SSI are ignored. Increasing number of
academical studies and engineering reports imply that in the next generation codes SSI modeling
Appl. Sci. 2020, 10, 8357
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will necessarily be required and consideration of SSI effects in design will be mandatory. However,
buildings constructed before these findings will still be the weak point of the cities that are prone to
seismic risk.
Turkey is an earthquake-prone country and the majority of existing building stock, which consist of
low and mid-rise reinforced concrete (RC) buildings, were designed without considering SSI. Therefore,
the main purpose of the present study is to investigate the effects of SSI on the seismic response
of existing buildings. For this purpose, 40 RC buildings selected from Turkey were investigated.
TEC-2007 [12] and TBEC-2018 [13] include the regulations which define the seismic performance
assessment of existing buildings. However, both Turkish earthquake codes do not comprise the
definitions or formulations which explain how to model SSI in design and assessment.
In this study, residential RC buildings that constitute three-, four-, five- and six-story buildings
were selected, and they were mainly classified into two groups as “old” and “new” buildings according
to their construction dates [14]. TEC-1998 [15] is accepted as the reference code to distinguish buildings
since this code applied the capacity design principle at the first time and considerably increased the
design forces and limited the displacement demands in terms of drift ratios. This situation significantly
differs the strength and stiffness capacity of existing buildings constructed before and after TEC-1998
in Turkey. Moreover, mandatory building control law, earthquake insurance and improvements in the
workmanship and material qualities after the 1999 Marmara earthquakes increased the safety of newer
buildings with respect to old ones.
Design projects of these new and old buildings (20 new, 20 old) were obtained from the
municipality archives in Denizli city. Moment-curvature analyses were performed for beams and
columns and member damage limits were determined by using the strain-based definitions of Turkish
Earthquake Code. Both 2007 and 2018 codes use the strain base damage assessment and, in both codes,
ultimate concrete compression strain (which is the major parameter that controls damage capacity
of the RC members) is limited to 1.8%. Non-linear building models were obtained by assigning the
plastic hinges to the critical sections of RC members. Capacity curves of inelastic building models were
obtained by using static pushover analyses and drift demands were calculated by using non-linear
time history analyses.
In fact, the aim of this study is not to evaluate or compare the non-linear modeling rules or
assumptions of any codes. The main objective of this study is to investigate and compare the effect of
SSI on the seismic capacity and demand calculations of existing buildings constructed on the various
soil conditions changing from stiff to soft. The main idea is to compare building capacity curves,
inelastic deformation demands, inter-story drift demands and overall seismic response of existing
buildings which have different story numbers, different stiffness and strength capacities, and different
soil conditions.
For this purpose, four different soil conditions were considered. Response of buildings
under fixed-base, stiff, moderate and soft soil cases were investigated. As mentioned previously,
the “Substructure Method” was employed to explore the effects of the SSI. In order to determine
the seismic demand generated by buildings on different soil conditions, 20 acceleration records
selected from major earthquakes were used. Accordingly, 3200 dynamic nonlinear time history
analyses (40 buildings, 4 different soil profiles and 20 acceleration records) were performed for
three-dimensional multi-story buildings models. Additionally, nonlinear static pushover analyses
were carried out to identify the effect of SSI on the capacity curves of selected buildings and the results
were compared.
2. Nonlinear Modeling of Existing Buildings
The majority of existing residential building stock of Turkey is composed of low and mid-rise RC
buildings. Therefore, in this study buildings were selected to reflect this situation and story numbers of
selected existing buildings vary between three and six. In the study, buildings were grouped according
to their story numbers and construction dates and each story group has five buildings. Distribution of
Appl. Sci. 2020, 10, 8357
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the story numbers and construction dates of selected buildings are presented in Table 1. It should be
stated that construction date of buildings has a crucial role since improvements in the workmanship
and material qualities increased the safety of new buildings. In both seismic codes, a force-based design
approach was used. However, capacity design principles were not considered in TEC-1975. One of
the most important differences between the codes is also that TEC-1998 enforced the use of “ultimate
strength design” for the analysis and design of RC cross-sections and this method is essential for the
application of capacity design principles. In TEC-1975, design spectrum was not defined, but lateral
seismic forces were calculated according to earthquake zone coefficient (Co ), seismic weight (W),
structural configuration system type (K), soil condition (S) and importance factor (I). Maximum lateral
force demand was recommended as 10% of seismic weight for the design of structures (Co = 0.1).
In both seismic codes, soil conditions were only considered to calculate corner periods of the spectrum.
Minimum allowable concrete strength was equal or higher than 16 MPa in TEC-1975, but this value
was increased to 20 MPa in TEC-1998. In TEC-1975, S220 steel class which has a yield strength of
220 MPa was allowed, but in TEC-1998, minimum S420 steel which has a yield strength of 420 MPa
was recommended. It can be said that new buildings have a greater stiffness, strength and ductility
capacity with respect to old buildings. By using such kind of classification, it is aimed to investigate
the effect of SSI on the new (98+) and old buildings (98−).
Table 1. Number of old and new existing buildings for which a soil-structure interaction (SSI) model
has been developed.
Number of Stories
Old Buildings (98−)
New Buildings (98+)
3
4
5
6
5
5
5
5
5
5
5
5
The structural properties of buildings, such as section dimensions, reinforcement details,
material properties, dead and live loads acting on the buildings were determined according to
their design projects. Investigation of RC design projects have revealed that concrete strength of old
buildings is mainly 16 MPa, and design projects of these buildings have shown that S220 steel class
with a yield strength (fy ) of 220 MPa is used for both longitudinal and transverse reinforcement. It was
also observed that stirrups were not used in the cross-section of members, and transverse reinforcement
spacing of the members was mainly 200 mm and this was even inadequate according TEC-1975 design
rules. Furthermore, design projects of buildings have shown that section dimensions of the columns
were reduced in the upper stories. Buildings designed according to TEC-1998 or higher have identical
steel class (S420) which yield strength is 420 MPa. However, concrete strengths were changed from
project to project. For this reason, concrete strength of new buildings is not identical, and they were
modeled according to their own concrete strengths. It was also observed that confinement details of
code provisions were applied to beam and columns in new buildings. In addition, column dimensions
were not reduced along the building height. In Figure 1 shows some pictures from the design projects
of a sample four-story building and a photo from field investigation is shown.
Strength and deformation capacities of members at critical sections were determined via
moment-curvature analyses. Stress-strain behavior of confined concrete was represented by Modified
Kent-Park model [16]. Since the purpose of the study is concentrated on the capacity and seismic
demand estimation of buildings, intermediate damage limits (Immediate Occupancy and Life Safety)
of structural members were not used. Collapse limits of members were obtained according to the
strain-based damage definition given in Equation (1). In this equation, limits were calculated depending
on the compression strains of confined concrete (εcc ) and tensile strain (εs ) of steel. Compression strain
regarding collapse limit is formulated by the amount of transverse reinforcement. In the equation,
confined concrete strain limits are expressed depending on the ratio of existing (ρs ) to required (ρsm )
Appl. Sci. 2020, 10, 8357
5 of 21
volumetric transverse reinforcement ratio of members. While performing moment-curvature analyses,
both elongation in steel and compression in concrete were checked and collapse limit was determined
according to whichever came first. In other words, minimum curvature values were determined from
both expressions as indicated in Equation (1). In addition to flexural capacity of beams and columns,
Appl. Sci.
2020, 10, of
x FOR
PEER REVIEW
shear
capacity
members
was also checked for the possible shear failure of RC members [17]. 5 of 22
(a)
(b)
(c)
Figure 1. Field
Field investigations
investigations and photos of design projects ((a): Building
Building picture, (b): Plan
Plan of
of building,
building,
(c): reinforcement details in the RC project).
" capacities of members at
! critical! sections were #determined via
Strength and deformation
ρs
moment‐curvature
analyses.
Stress‐strain
was) represented (1)
by
φcollapse
= min φ@
εcc = 0.004behavior
+ 0.014 of confined
≤ 0.018 ; concrete
φ@(εs = 0.06
ρsm
Modified Kent‐Park model [16]. Since the purpose of the study is concentrated on the capacity and
seismic
demand estimation
ofBuildings
buildings, intermediate damage limits (Immediate Occupancy and Life
3. SSI Modeling
of Selected
Safety) of structural members were not used. Collapse limits of members were obtained according to
The effect of damage
SSI is much
more significant
low-rise (1).
andIn
stiffer
respect
high-rise
the strain‐based
definition
given in in
Equation
this buildings
equation,with
limits
weretocalculated
long
period
structures
[1].
Buildings
considered
in
this
study
are
not
high-rise
structures,
and
therefore
depending on the compression strains of confined concrete (εcc) and tensile strain (εs) of steel.
it
is expected that
SSIregarding
would alter
the response
examinedby
buildings.
Theof
existing
Turkish
earthquake
Compression
strain
collapse
limit is of
formulated
the amount
transverse
reinforcement.
code
regulations
do
not
require
engineers
to
consider
SSI
effects,
whether
designing
new
buildings
In the equation, confined concrete strain limits are expressed depending on the ratio of existing (ρor
s)
determining
the
seismic performances of existing buildings. Instead, the regulations mentioned above
to required (ρ
sm) volumetric transverse reinforcement ratio of members. While performing moment‐
recommended
the “Fixed-Base
Approach”
forand
both
design and in
evaluation
buildings.
mentioned
curvature analyses,
both elongation
in steel
compression
concrete of
were
checkedAs
and
collapse
before,
the
primary
aim
of
this
paper
is
to
determine
SSI
effects
on
the
superstructures
by
considering
limit was determined according to whichever came first. In other words, minimum curvature values
the
“Substructure
Method.”
of theassubstructure
can
beInfound
in the
[8,18].
were
determined from
both Details
expressions
indicated inmethod
Equation
(1).
addition
to literature
flexural capacity
“Inertial
Interactions”
and
“Kinematic
Interactions”
are
two
components,
and
they
should
of beams and columns, shear capacity of members was also checked for the possible shear failure be
of
considered
in [17].
modeling of structures according to substructure method. Inertial interaction refers to the
RC members
displacements and rotations occurring at the foundation level of the superstructure due to shear and
𝜌
@ 𝜀 illustration
0.004 of
0.014
; @degree
𝜀
0.06
 effects. A𝑚𝑖𝑛
moment related
schematic
deformations0.018
for single
of freedom system
(1)
𝜌
(SDOF) caused by the lateral forces is shown in Figure 2. As a result of this interaction, an elongation
of the natural vibration period of the structure is expected. Accordingly, this situation may have a
3. SSI Modeling
Selected
dramatic
effect onof
the
seismic Buildings
response of the structure. The ratio vibration periods of fixed base to SSI
system
SDOF
can approximately
be in
calculated
Equation
(2).
Thefor
effect
of system
SSI is much
more significant
low‐riseby
and
stiffer buildings
with respect to high‐
rise long period structures [1]. Buildings considered
in this study are not high‐rise structures, and
s
2
T0 the response
k ofkhexamined
buildings. The existing Turkish
therefore it is expected that SSI would alter
= 1+ +
(2)
T engineers
kzto consider
k yy
earthquake code regulations do not require
SSI effects, whether designing new
buildings or determining the seismic performances of existing buildings. Instead, the regulations
mentioned above recommended the “Fixed‐Base Approach” for both design and evaluation of
buildings. As mentioned before, the primary aim of this paper is to determine SSI effects on the
superstructures by considering the “Substructure Method.” Details of the substructure method can
be found in the literature [8,18].
“Inertial Interactions” and “Kinematic Interactions” are two components, and they should be
and moment related effects. A schematic illustration of deformations for single degree of freedom
system (SDOF) caused by the lateral forces is shown in Figure 2. As a result of this interaction, an
elongation of the natural vibration period of the structure is expected. Accordingly, this situation
may have a dramatic effect on the seismic response of the structure. The ratio vibration periods of
Appl. Sci. 2020, 10, 8357
6 of 21
fixed base to SSI system for SDOF system can approximately be calculated by Equation (2).

m
F
m
F
m
z

uf
h
y
k
x
k
kx
θ
kyy
kz
(b)
(a)
Figure
Typical lateral
Figure 2.
2. Typical
lateral deformation
deformation of
of single
single degree
degree of
of freedom
freedom system
system (SDOF)
(SDOF) model
model according
according to
to
(a)
fixed
base,
(b)
SSI
system.
(a) fixed base, (b) SSI system.
In Equation (2), T’ denotes the elongated period, k is the stiffness of the structure, kz is the stiffness
2 be taken as two-thirds of the structure
of the vertical spring, h is the effective modal
which𝑘ℎcan
𝑇 height, 𝑘
(2)
1
height, and kyy is the stiffness of the rotational
spring
about
the
𝑇
𝑘𝑧 𝑘𝑦𝑦 y-axis.
On the other hand, kinematic interaction defines the reduction in free-field ground motions at the
(2), T’ denotes
the elongated
k is
of The
the structure,
kz is the
base In
dueEquation
to stiff foundation
elements
located onperiod,
or inside
thethe
soilstiffness
medium.
variation between
stiffness ofand
thefoundation
vertical spring,
h is
the effective
height,by
which
can befunction
taken as representing
two‐thirds of the
free-field
input
motion
(UFIM )modal
is expressed
a transfer
structure
height, andtokyy
is the stiffness
of Two
the rotational
spring
about
thereductions.
y‐axis.
ratio
of foundation
free-field
motion.
components
cause
these
The first one is
On the
other
hand, kinematic
interaction
definesofthe
reduction
in free‐field
at
the “Base
Slab
Averaging”
which defines
transition
spatially
variable
groundground
motionsmotions
from soil
the base due
to stiff foundation
elements
on or inside
thecaused
soil medium.
variation
between
medium
to foundation
due to the
stiffnesslocated
and strength
changes
by the The
foundation
system
[1].
free‐field
and
input motion
(UFIM
is expressed
by a level
transfer
function
representing
the
The
second
onefoundation
is the “Embedment
Effects”
in) which
foundation
motions
are reduced
because
ratio
of foundation
to free‐field
motion.
Two components
cause these
The three
first one
is the
of
ground
motion reduction
along
the depth
of the foundation.
In thereductions.
present study,
different
“Base
Slabwere
Averaging”
defines
transitionand
of spatially
variable
ground
from
soil
types
examined,which
namely
stiff, moderate,
soft. It should
be noted
thatmotions
soil types
are soil
not
medium to
due
to the stiffness
and strength
changes
caused
byare
theonly
foundation
[1].
classified
asfoundation
A, B or D as
described
in the majority
of seismic
codes,
they
used tosystem
represent
The second
is the “Embedment
Effects”
in which
foundation
level motions to
arethese
reduced
because
different
soilone
characteristics.
Mean shear
wave
velocities
(V s30 ) corresponding
soil types
in
of
ground
motion
reduction
along
the
depth
of
the
foundation.
In
the
present
study,
three
different
each direction are given in Table 2 [19,20]. Selected V s30 values are determined according to study of
soil typesetwere
examined,
stiff,
soft. It were
should
be noted by
that
soil types
are not
(Pitilakis
al., 2013).
Shearnamely
modulus
ofmoderate,
these soil and
conditions
calculated
using
Equation
(3).
classified
as A, BVor
D
as
described
in
the
majority
of
seismic
codes,
they
are
only
used
to
represent
In
this equation,
defines
the
shear
wave
velocity
of
soil,
G
denotes
the
soil
shear
modulus,
and
ρs
s
differentthe
soil
characteristics.
shear wave
velocities
(Vs30
corresponding
to these
soil types
in
denotes
soil
mass density. Mean
The mechanical
properties
such
as) mass
densities and
Poisson’s
ratios of
each used
direction
arestudy
givenare
in given
Table in
2 [19,20].
soils
in this
Table 3.Selected Vs30 values are determined according to study of
(Pitilakis et al., 2013). Shear modulus of these soil conditions
were calculated by using Equation (3).
s
In this equation, Vs defines the shear wave velocity ofGsoil, G denotes the soil shear modulus, and ρs
V =
(3)
denotes the soil mass density. The mechanical sproperties
ρs such as mass densities and Poisson’s ratios
of soils used in this study are given in Table 3.
Table 2.
2. Mean shear wave velocities for considered
considered soils
soils types.
types.
Table
Shear
Wave
Velocities
Stiff
Shear
Wave
Velocities
(Mean(Mean
V s30 ) Vs30) Stiff
Horizontal
displacement
(x) (m/s)
Horizontal
displacement
(x) (m/s)
Horizontal
displacement
(y) (m/s)
Horizontal
displacement
(y) (m/s)
Vertical
displacement
(z) (m/s)
Vertical
displacement
(z) (m/s)
Rotation
about
x-axisx‐axis
(xx) (m/s)
Rotation
about
(xx) (m/s)
Rotation about y-axis (yy) (m/s)
Rotation about y‐axis (yy) (m/s)
Torsion about z-axis (zz) (m/s)
Torsion about z‐axis (zz) (m/s)
720720
900900
720720
1020
1020
1080
1080
1020
1020
Moderate
Moderate
285
285
360
360
285
285
405
405
430
430
405
405
Soft
Soft
180
180
224
224
180
180
255
255
270
270
255
255
Table 3. Mass densities (ρs ) and Poisson’s ratio of soil types.
Mass density (ρs )
(KN/m3 )
Poisson’s ratio (γ)
Stiff
Moderate
Soft
22
20
18
0.25
0.33
0.42
Appl. Sci. 2020, 10, 8357
7 of 21
Modeling of buildings according to the substructure method is essentially performed in two parts.
In the first part, the motion of the massless foundation system is calculated without the presence
of the superstructure. The second part consists of the application of motion to the structure where
soil properties are simulated by a group of equivalent springs and dashpots [21,22]. Equivalent soil
properties of the foundation-soil interface are represented with springs and dashpots. The stiffness
and damping of these springs and dashpots were calculated according to equations proposed by Pais
and Kaussel [18]. In the present study, stiffer springs (k2 , k3 , k4 ), which were calculated as a function
of interior springs (kz i ) and the stiffness intensity modifiers (Rk,xx –Rk,yy ) along the foundation edges
(Re L and Re B), are used to prevent the underestimation of rotational stiffness (Figure 3). Consequently,
the total stiffness of the foundation was determined. The symbols “L” and “B” represent the dimension
of the foundation system and they are taken as half of the actual dimensions. Re is the foundation
end length ratio which can be taken between 0.3 and 0.5. Damping intensities of dashpots (Figure 3,
cz i ) along the foundation edges were reduced by a damping intensity modifier (Rc,xx –Rc,yy ) to not
overestimate the foundation rotational damping (c2 , c3 , c4 ). A schematic illustration of link and dashpot
assignments
foundation-soil
Appl. Sci. 2020,to
10,the
x FOR
PEER REVIEW interface is shown in Figure 3
8 of 22
Figure
Figure3.3.Calculation
Calculationand
andrepresentation
representationofofstiffness
stiffnessand
anddamping
dampingexpressions
expressionsfor
forthe
thefoundation
foundation
springs
added
to
the
foundation
systems.
springs added to the foundation systems.
Foundation systems of the selected buildings have shallow foundation, and the foundation
Foundation systems of the selected buildings have shallow foundation, and the foundation
dimensions were determined according to design projects of the buildings. Both of the base slab
dimensions were determined according to design projects of the buildings. Both of the base slab
averaging and the embedment effects were taken into account by considering soil shear wave velocities,
averaging and the embedment effects were taken into account by considering soil shear wave
embedment depth of the foundation, and the natural vibration frequencies of structures. The results
velocities, embedment depth of the foundation, and the natural vibration frequencies of structures.
The results indicated that the ground motion reductions (Hu) caused by these effects can be neglected
for selected buildings since they can be considered as low‐ and mid‐rise buildings and they have no
basement. The values calculated for the embedment effects (ωD/Vs) for all of buildings are lower than
0.006 (Figure 4, left). As a result, the calculated ground motion reduction factors (Hu) are very close
Appl. Sci. 2020, 10, 8357
8 of 21
1.0
0.8
0.6
0.4
0.2
0.0
Hu = uFIM/ug
Hu= uFIM/ug
indicated that the ground motion reductions (Hu ) caused by these effects can be neglected for
selected buildings since they can be considered as low- and mid-rise buildings and they have no
basement. The values calculated for the embedment effects (ωD/Vs ) for all of buildings are lower than
0.006 (Figure 4, left). As a result, the calculated ground motion reduction factors (Hu ) are very close to
1 which means that a significant reduction is not needed. A similar situation is also valid for the base
slab averaging effects (Figure 4, right). Consequently, obtained results indicate that selected ground
motions can directly be used for the nonlinear time history analysis of buildings according to both
Appl. Sci. 2020, 10, x FOR PEER REVIEW
9 of 22
cases (Figure 4).
Translation
0
0.4
0.8 1.2
ωD/Vs
1.6
2
1.0
0.8
0.6
0.4
0.2
0.0
Vapp/Vs=10
0
4
8
a0k= ω (BeA)/Vs
12
Figure 4. Ground motion reduction factors: (left) embedment effects, (right) base slab averaging
Figure2012).
4. Ground motion reduction factors: (left) embedment effects, (right) base slab averaging
(NIST,
(NIST, 2012).
4. Effect of SSI on the Capacity and Demand Response of Existing Buildings
4. Effect of SSI on the Capacity and Demand Response of Existing Buildings
In this section, capacity-related parameters such as structural period, yield and ultimate (collapse)
displacement
capacitycapacity‐related
of members and parameters
displacementsuch
demands
of buildings
are evaluated.
In this section,
as structural
period,
yield and ultimate
(collapse) displacement capacity of members and displacement demands of buildings are evaluated.
4.1. Effect of SSI on the Capacity Curves
4.1. Effect
of SSI onmodels
the Capacity
All building
were Curves
analyzed to determine the capacity curves of buildings according to
fixed-based
assumption
and
SSI, analyzed
and total of
(40 buildings
× 4 different
SSIofmodeling)
were
All building
models
were
to160
determine
the capacity
curves
buildingsanalyses
according
to
conducted
via
static
pushover
analysis.
In
this
paper
especially,
the
“Collapse
Prevention”
and
“Yield”
fixed‐based assumption and SSI, and total of 160 (40 buildings × 4 different SSI modeling) analyses
limit
are investigated
since one
of the purposes
of the
current study
is to determine
whether
were states
conducted
via static pushover
analysis.
In this paper
especially,
the “Collapse
Prevention”
and
consideration
of
SSI
alters
the
capacity
curves
of
the
buildings.
“Yield” limit states are investigated since one of the purposes of the current study is to determine
Collapse
prevention
damage
of buildings
by checking damage states of
whether
consideration
of SSI
alterslimits
the capacity
curvesare
of determined
the buildings.
columns,
beams
and
the
story
shear
forces.
To
define
building
collapse
prevention
it is assumed
Collapse prevention damage limits of buildings are determined by checkinglimit,
damage
states of
that
at least
80% and
of beams
in any
story
should
not exceed
the member
limit.
The
of
columns,
beams
the story
shear
forces.
To define
building
collapse collapse
prevention
limit,
it collapse
is assumed
any
column
is
accepted
as
the
collapse
prevention
limit
of
the
buildings.
Shear
force
carried
by
the
that at least 80% of beams in any story should not exceed the member collapse limit. The collapse of
columns
beyond
the yieldaslimit
both ends
were checked
andthe
thebuildings.
contribution
of these
to the
any column
is accepted
the at
collapse
prevention
limit of
Shear
force columns
carried by
the
total
shearbeyond
capacity
ofyield
each limit
story at
was
limited
30%.checked
Collapse
prevention
damageof
limit
is determined
columns
the
both
endsto
were
and
the contribution
these
columns to
according
to eachcapacity
rule andofbuilding
damage
is attained
byCollapse
whichever
gives the lowest
drift
ratio.
the total shear
each story
waslimit
limited
to 30%.
prevention
damage
limit
is
After the
determination
capacity
curves via
static pushover
analysis,
investigated
determined
according
to eachofrule
and building
damage
limit is attained
by authors
whichever
gives the
whether
capacity-related
parameters were altered or not when the SSI was considered. Vibration periods
lowest drift
ratio.
(T), ductility
capacities
(µ)
and of
proportion
drift ratios
corresponding
to yield, and
ultimate
damage
After the determination
capacity of
curves
via static
pushover analysis,
authors
investigated
levels
arecapacity‐related
used to evaluateparameters
and compare
thealtered
effect of
building
capacity
curves. InVibration
order to
whether
were
or SSI
not on
when
the SSI
was considered.
explain
the
details
of
the
applied
procedure,
BO20SN6
was
selected
among
the
considered
buildings.
periods (T), ductility capacities () and proportion of drift ratios corresponding to yield, and ultimate
The
first two
letters
of the
refer to the
the effect
designofcode
of building
the building,
and curves.
“BO” and
“BN”
damage
levels
are used
to building
evaluate name
and compare
SSI on
capacity
In order
are
used to represent
oldof(98−)
and newprocedure,
buildings (98+),
respectively.
The numbers
these
to explain
the details
the applied
BO20SN6
was selected
among following
the considered
letters
indicate
the
order
of
the
building
in
the
inventory.
“SN6”
refers
to
the
story
number
of
the
buildings. The first two letters of the building name refer to the design code of the building, and “BO”
building.
Figure
capacity
curve,
ultimate
damage limits
the BO20SN6
arenumbers
plotted
and “BN”Inare
used5, to
represent
oldyield
(98−)and
and
new buildings
(98+), of
respectively.
The
according
to
each
of
the
soil
classes
considered.
following these letters indicate the order of the building in the inventory. “SN6” refers to the story
number of the building. In Figure 5, capacity curve, yield and ultimate damage limits of the BO20SN6
are plotted according to each of the soil classes considered.
It can be seen from the figure that yield and ultimate damage levels of the building are shifted
left to right from stiff to soft soil types. A similar situation can also be observed for the initial part of
the capacity curve. This situation clearly explains the period elongations from stiff to soft soil profiles.
It should be stated that similar results were observed for all buildings in the inventory.
Appl. Sci.
Sci.2020,
2020,10,
10,x8357
Appl.
FOR PEER REVIEW
of 22
21
109 of
50%
50%
40%
40%
Yield
BO20SN6
Collapse
Prevention
Stiff
Yield
Fixed
Stiff
20%
Moderate
Moderate
10%
BN19SN6
30%
Fixed
Vt/W
Vt/W
30%
20%
Collapse
Prevention
10%
Soft
Soft
0%
0.00%
0.50%
1.00%
/H
1.50%
2.00%
0%
0.00%
2.50%
0.50%
1.00%
/H
1.50%
2.00%
2.50%
Figure 5. Capacity curves and damage limits of selected old and new buildings.
Figure 5. Capacity curves and damage limits of selected old and new buildings.
0.96
1.02
0.58
0.72
0.48
0.62
0.80
0.88
0.43
0.58
0.74
0.82
0.42
0.57
0.73
0.81
T (sec)
It can be seen from the figure that yield and ultimate damage levels of the building are shifted left
In Figure
5, capacity
curves
of BO20SN6
BN19SN6
buildings
corresponding
to different
to right
from stiff
to soft soil
types.
A similarand
situation
can also
be observed
for the initial
part ofsoil
the
conditions
are
presented.
Significant
differences
between
the
strength
and
deformation
capacities
of
capacity curve. This situation clearly explains the period elongations from stiff to soft soil profiles.
selected
shows
the effect
changing
regulations
oninventory.
the old (98−) and new
It shouldbuildings
be stated clearly
that similar
results
were of
observed
for code
all buildings
in the
(98+) In
buildings.
Figure
5
clearly
indicates
that
curves
of
fixed‐base
and
stiff
soil cases
are almost
Figure 5, capacity curves of BO20SN6 and BN19SN6 buildings corresponding
to different
soil
identical
and
capacity
curve
of
moderate
soil
case
is
closer
to
them
with
respect
to
the
soft soil
conditions are presented. Significant differences between the strength and deformation capacities
of
condition.
Variation
of
capacity
curves
imply
that
the
main
difference
occurs
in
the
elastic
slope
of
selected buildings clearly shows the effect of changing code regulations on the old (98−) and new
the
building
and drift
ratios
corresponding
yield
and collapse
limits are
affected
from
(98+)
buildings.
Figure
5 clearly
indicatestothat
curves
of fixed-base
andsignificantly
stiff soil cases
are almost
SSI
in
the
soft
soil
case.
This
figure
also
indicates
that
plastic
drift
capacities
of
the
BO20SN6
building
identical and capacity curve of moderate soil case is closer to them with respect to the soft soil
are
almost unchanged
the movement
of plastic
deformation
capacity,
which
caused
the
condition.
Variation ofand
capacity
curves imply
that the
main difference
occurs
in is
the
elasticbyslope
inertial
interaction
between
structure
and
soil,
can
be
explained
by
shifting
instead
of
increasing.
of the building and drift ratios corresponding to yield and collapse limits are significantly affected
Previous
have
indicated
this also
inertial
interaction,
and hence
elongationofof
the
natural
from SSI studies
in the soft
soilalso
case.
This figure
indicates
that plastic
drift capacities
the
BO20SN6
vibration
period
of
the
buildings
[23].
building are almost unchanged and the movement of plastic deformation capacity, which is caused by
The studies
of Velestos
and structure
Nair [24] and
and soil,
Bielak
[25]
dimensionless
the inertial
interaction
between
can
be investigated
explained bythe
shifting
instead ofparameters
increasing.
that
control
the
vibration
period
of
the
systems
in
SSI,
and
they
showed
that
the
most
important
Previous studies have also indicated this inertial interaction, and hence elongation of the
natural
parameter
is
(h/V
sT), which is known as the structure to soil stiffness ratio. For typical reinforced
vibration period of the buildings [23].
concrete
buildings
on stiff
is usually
than 0.1 [23].
this ratio increases,
the
Theframe
studies
of Velestos
and soil,
Nairthis
[24]ratio
and Bielak
[25]less
investigated
the As
dimensionless
parameters
elongation
thevibration
natural vibration
also increases.
Forthey
thisshowed
reason, that
elongation
of important
vibration
that controlofthe
period of period
the systems
in SSI, and
the most
period
resulting
from
inertial
interaction
should
be
taken
into
consideration
when
assessing
the
parameter is (h/Vs T), which is known as the structure to soil stiffness ratio. For typical reinforced
seismic
of structures
since
period of
building
affects
theratio
displacement
concretebehavior
frame buildings
on stiff
soil,the
thisvibration
ratio is usually
lessthe
than
0.1 [23].
As this
increases,
demand.
the elongation of the natural vibration period also increases. For this reason, elongation of vibration
The
naturalfrom
period
of theinteraction
buildings should
in the inventory
are consideration
determined for
eachassessing
soil typethe
and
story
period
resulting
inertial
be taken into
when
seismic
groups
the analyses,
mean period
fixed‐base
and
periods
due to
behaviorfrom
of structures
since and
the vibration
periodvalues
of the of
building
affects
theelongated
displacement
demand.
different
soil
classes
are
shown
in
Figure
6.
Figure
7
also
shows
that
vibration
periods
increase
with
The natural period of the buildings in the inventory are determined for each soil type and story
increasing
story
numbers
as
expected.
This
situation
is
valid
for
all
soil
types.
Comparison
of
values
groups from the analyses, and mean period values of fixed-base and elongated periods due to different
in
Figures
andshown
7 haveinshown
the elongation
of the
vibration
period
is much
more
significant
in
soil
classes6are
Figurethat
6. Figure
7 also shows
that
vibration
periods
increase
with
increasing
the
soft
soil
case
and
this
behavior
is
identical
both
in
new
(98+)
and
old
(98−)
buildings
(Figure
7).
story numbers as expected. This situation is valid for all soil types. Comparison of values in Figures 6
and 7 have shown that the elongation of the vibration period is much more significant in the soft soil
4 buildings
5
6 (Figure 7).
case and this behavior is identical both in new (98+) and old3(98−)
In addition to vibration
1.2 periods, elongation of displacement capacities corresponding to yield
and collapse limits (as shown
1.0 in Figure 5) were also investigated for all buildings and soil conditions.
0
Relation between elongation
0.8 of the vibration periods (T /T) and change in the yield drift ratios
(∆y 0 /∆y ) depending on the SSI
are illustrated in Figure 8. In this figure, T0 and ∆y 0 notations represent
0.6
the vibration periods and yield displacements of stiff, moderate and soft soil cases, respectively.
0.4
T and ∆y notations, on the other hand, correspond to fixed-base case. Strong correlation between
0.2
(T0 /T) and (∆y 0 /∆y ) values explains the effect of SSI on the capacity (yield displacement) and demand
0.0
(period)-related structural parameters
Fixed of the buildings.
Stiff
Moderate
Soft
Soil Class
Figure 6. Distribution of mean vibration periods according to story numbers and soil types.
The natural period of the buildings in the inventory are determined for each soil type and story
groups from the analyses, and mean period values of fixed‐base and elongated periods due to
different soil classes are shown in Figure 6. Figure 7 also shows that vibration periods increase with
increasing story numbers as expected. This situation is valid for all soil types. Comparison of values
in Figures 6 and 7 have shown that the elongation of the vibration period is much more significant in
Appl. Sci. 2020, 10, 8357
10 of 21
the soft soil case and this behavior is identical both in new (98+) and old (98−) buildings (Figure 7).
3
4
5
T (sec)
1
0.8
0.6
0.4
0.6
0.2
0.4
0.0
0.2
0
3 St
Moderate
Soft
4 St
5 St
6 St
Appl. Sci. 2020,
10, x 5FOR PEER
0
10 REVIEW15
98-
1.2
Fixed
Stiff
Fixed
1.4
0.96
1.02
11 of 22
0.58
0.72
0.8
0.48
0.62
0.80
0.88
1.2
Fixed
1
T (sec)
T (sec)
98+
0.43
0.58
0.74
0.82
1.0
1.4
0.42
0.57
0.73
0.81
Appl. Sci. 2020, 10, x FOR PEER REVIEW
1.2
6
Stiff
0.8
Moderate
0.6
0.4
Stiff
Moderate
0.2
Soil Class
3 St
0
0
20
Soft
Soft
4 St
5
6 St
5 St
10
15
20
Figure 6. Distribution
of mean vibration periods according to story numbers
and soil types.
Building Number
Building Number
Figure 6. Distribution
of mean vibration periods according to story numbers
and soil types.
1.4
11 of 22
1.4
98+
98Figure 7. Distribution of vibration periods for all models according
to story numbers and soil types.
Fixed
1.2
1.2
Fixed
1
1
Stiff
T (sec)
T (sec)
In addition to vibration periods, elongation
of displacement
capacities corresponding to yield
Stiff
0.8
0.8
Moderate
and 0.6
collapse limits (as shown in Figure 5) were also investigated
for all buildings and soil conditions.
0.6
Moderate
Relation
between elongation of the vibration periods (T′/T)
and change in the yield drift ratiosSoft
(y′/y)
0.4
0.4
Soft
0.2 figure, T′ and y′ notations represent the
0.2
depending
on the SSI are5 illustrated
in Figure 8. In this
6 St
3 St
St
4 St
3 St
6 St
4 St
5 St
0
0
vibration
periods and yield displacements of stiff, moderate
and soft soil cases,
respectively. T and
0
5
10
15
20
0
5
10
15
20
y notations, on the other
between (T′/T) and
Building Number
Buildinghand,
Numbercorrespond to fixed‐base case. Strong correlation
(y′/y) values explains the effect of SSI on the capacity (yield displacement) and demand (period)‐
Figure 7. Distribution of vibration periods for all models according to story numbers and soil types.
Figure
7. Distribution
of vibration
for all models according to story numbers and soil types.
related
structural
parameters
of the periods
buildings.
y'/y
In addition to vibration
periods, elongation of displacement capacities corresponding to yield
2.6
R² = 0.88
and collapse limits (as shown in Figure 5) were also investigated for all buildings
and soil conditions.
2.2
Relation between elongation
of the vibration periods (T′/T) and change in the yield drift ratios (y′/y)
depending on the SSI are illustrated in Figure 8. In this figure, T′ and y′ notations represent the
1.8yield displacements of stiff, moderate and soft soil cases, respectively. T and
vibration periods and
y notations, on the other hand, correspond to fixed‐base case. Strong correlation between (T′/T) and
1.4
(y′/y) values explains the effect of SSI on the capacity (yield displacement) and demand (period)‐
related structural parameters of the buildings.
1.0
2.6
0.6
1.00
1.20
T'/T
1.40
1.60
1.80
y'/y
2.2
0.2
0.80
1.8
R² = 0.88
Figure
Correlation of
Figure
8. Correlation
of shifted
shifted yield
yield points
points and
and elongated
elongated vibration
vibration periods.
periods.
1.48.
The
The effect
effect of
of SSI
SSI
on the
the plastic
plastic deformation
deformation capacity
capacity of
of buildings
buildings is
is also
also investigated.
investigated. For
For this
this
1.0on
0 ) were divided into
purpose,
plastic
drift
capacities
corresponding
to
stiff,
moderate
and
soft
cases
(∆
p
purpose, plastic drift capacities corresponding to stiff, moderate and soft cases (p′) were divided
the
of fixed-base
of results
is presented
in Figure
9. Variation
of ∆p 0 /∆of
p ) and
p
0.6 case (∆
intoratios
the ratios
of fixed‐base
case
(p)distribution
and distribution
of results
is presented
in Figure
9. Variation
values
indicates
that
effects
of
SSI
on
the
plastic
deformation
capacity
of
buildings
are
insignificant
and
p′/p values indicates that effects of SSI on the plastic deformation capacity of 0buildings are
0.2between plastic deformation capacities and period elongations (T /T) due to SSI.
there
is no correlation
insignificant
and there
is no correlation between plastic deformation capacities and period
0.80
1.00
1.20
1.40
1.60
1.80
Effect
of
this
situation
elongations (T′/T) due to SSI. can also be examined from the ductility capacities of buildings.
T'/T
Increasing yield displacements and similar plastic drift capacities requires to decrease ductility
capacities of buildings.
This disadvantage
related
with
SSI was
also reported
Figure 8. Correlation
of shifted yield
points
andthe
elongated
vibration
periods. by Shakib and
Homei [26]. In order to investigate the extent of this problem, changes in the ductility ratios depending
0 /T) values are presented in Figure 10. Figure 10 clearly shows the considerable decrease in
on the
(Teffect
The
of SSI on the plastic deformation capacity of buildings is also investigated. For this
building
ductility
capacities
(µ0 /µ)
due to effect of
[21,22,26].
purpose, plastic drift
capacities
corresponding
to SSI
stiff,
moderate and soft cases (p′) were divided
into the ratios of fixed‐base case (p) and distribution of results is presented in Figure 9. Variation of
p′/p values indicates that effects of SSI on the plastic deformation capacity of buildings are
insignificant and there is no correlation between plastic deformation capacities and period
elongations (T′/T) due to SSI.
1.4
R² = 0.05
1.2
1.0
p'/p
p'/p
Appl. Sci. 2020, 10, 8357 0.8
Appl. Sci. 2020, 10, x FOR PEER REVIEW
11 of 21
12 of 22
0.6
0.4
1.4
0.2
1.2
0.0
1.0
0.80
0.8
R² = 0.05
1.00
1.20
1.40
1.60
1.80
T'/T
0.6
Figure 9. Correlation of shifted plastic limits and elongated vibration periods.
0.4
0.2 can also be examined from the ductility capacities of buildings. Increasing
Effect of this situation
yield displacements 0.0
and similar plastic drift capacities requires to decrease ductility capacities of
buildings. This disadvantage
SSI was also
by Shakib1.80
and Homei [26]. In
0.80 related
1.00with the1.20
1.40reported1.60
order to investigate the extent of this problem, changes
T'/Tin the ductility ratios depending on the (T′/T)
values are presented in Figure 10. Figure 10 clearly shows the considerable decrease in building
Figure 9.
9. Correlation
Correlation of
of shifted plastic
plastic limits
limits and
and elongated
elongated vibration
vibration periods.
Figure
periods.
ductility capacities
(μ′/μ)
due to effectshifted
of SSI [21,22,26].
'/
Effect of this situation can also be examined from the ductility capacities of buildings. Increasing
1.2
yield displacements and similar plastic drift capacities requires to decrease
ductility capacities of
R² = 0.74
buildings. This disadvantage
related
with
the
SSI
was
also
reported
by
Shakib
and Homei [26]. In
1.0
order to investigate the extent of this problem, changes in the ductility ratios depending on the (T′/T)
values are presented
0.8in Figure 10. Figure 10 clearly shows the considerable decrease in building
ductility capacities (μ′/μ) due to effect of SSI [21,22,26].
0.6
1.2
0.4
R² = 0.74
'/
1.0
0.2
0.8
0.0
0.60.80
1.00
1.20
T'/T
1.40
1.60
1.80
0.4 10.
Figure
10. Decrease
Decrease in
in structure
structure ductility
ductility capacities
capacities with
with SSI
SSI effects.
effects.
Figure
4.2. Effect of SSI on the
0.2Displacement Response of Existing Buildings
4.2. Effect of SSI on the Displacement Response of Existing Buildings
To investigate the effect of SSI on the displacement response of buildings, nonlinear dynamic
0.0 effect of SSI on the displacement response of buildings, nonlinear dynamic
To investigate the
analyses were performed. For this purpose, 20 real strong ground motions were selected [27].
0.80For this1.00
1.60 were1.80
analyses were performed.
purpose, 201.20
real strong1.40
ground motions
selected [27]. Some
Some attributes of selected records are given in Table
4. Response spectrum of selected records and
T'/T
attributes of selected records are given in Table 4. Response spectrum of selected records and their
their mean is drawn in Figure 11. The maximum spectral acceleration of the mean spectrum is around
mean is drawn in Figure
maximum
spectral acceleration
of the mean
spectrum is around 1.14
Figure11.
10.The
Decrease
inare
structure
effects.
1.14 g and elastic spectral
accelerations
higherductility
than 1 gcapacities
betweenwith
the SSI
periods
of 0.2 s to 0.6 s.
g and elastic spectral accelerations are higher than 1 g between the periods of 0.2 s to 0.6 s.
Effect of SSI on the displacement response of existing buildings was investigated by two different
4.2. Effect of demand
SSI on theparameters
Displacement
Response
Existing
Buildings
earthquake
(EDPs):
roofofand
inter-story
drift ratios. Roof displacement is one of
Table 4. General properties of selected real earthquake records.
the most
widely used
andon
it the
has displacement
wide applicability,
especially
for determining
thedynamic
seismic
To investigate
theparameters
effect of SSI
response
of buildings,
nonlinear
Vmax/Aaccording
max
performance
structures.For
However,
seismic
performance
of buildings
is determined
to
analyses Name
wereofperformed.
this
purpose,
20
real
strong
ground
motions
were
selected
[27].
Some
of Acceleration Depth (km) PGA (g) PGV (cm/s) PGD (cm)
(s)
different
seismic
intensity
or
earthquake
levels.
Different
earthquake
levels
can
be
recommended
attributes of selected records are given in Table 4. Response spectrum of selected records and their
CAP‐RIO270
18.50 spectral
0.39acceleration
40.58of the in
47.44
for
different
performance
according
to building
importance
the spectrum
modern0.11
seismic
codes.
mean
is drawn
in Figure 11.levels
The maximum
mean
is around
1.14
CHI‐TCU74N
13.67
0.35
39.54
49.12
Earthquake
onaccelerations
the other hand,
are described
according
different
exceeding
g and elastic levels,
spectral
are
higher
than
1 g between
thetoperiods
of 0.2
s to0.12
0.6 s.probability
CHI‐TCU95W
43.44drift demand
0.38 ratios
59.39
0.16investigated
levels. Considering
this situation, roof
of existing80.09
buildings are
COA‐PLE045
0.59
59.38
14.36
0.10
Table 4.For
General
properties
selected realexceedance
earthquake records.
in a probabilistic
manner.
this 8.50
purpose, of
cumulative
probability
of
drift ratios is
calculated from the displacement demands of buildings which are subjected to 20 real earthquake
Vmax/Amax
Name
oftoAcceleration
Depth (km)
(g) PGV
(cm/s) PGD
(cm)
records. In
order
generalize obtained
results,PGA
cumulative
exceeding
probabilities
are provided for
(s)
different building groups (new and old), story numbers and soil type which are modeled according to
CAP‐RIO270
18.50
0.39
40.58
47.44
0.11
the substructure method.
CHI‐TCU74N
13.67
0.35
39.54
49.12
0.12
CHI‐TCU95W
43.44
0.38
59.39
80.09
0.16
COA‐PLE045
8.50
0.59
59.38
14.36
0.10
LOM‐BRN090
10.30
0.50
43.79
13.03
0.09
LOM‐CYC285
21.80
0.48
43.91
81.28
0.09
LOM‐G03090
14.40
0.37
43.08
25.31
0.12
LOM‐SAR000
13.00
0.51
41.26
16.42
0.08
Appl. Sci. 2020, 10,
8357
NOR‐CNP196
15.80
0.42
57.01
67.59
0.14
NOR‐LOS000
13.00
0.41
44.84
20.16
0.11
NOR‐LOS270
13.00
0.48
44.52
15.25
0.09
Table 4. General properties of selected real earthquake records.
NOR‐MU2035
20.80
0.62
41.93
16.57
0.07
Name
of
NOR‐MUL009
19.60
0.42
55.74
55.98
0.14
Depth (km)
PGA (g)
PGV (cm/s)
PGD (cm)
Vmax /Amax (s)
Acceleration
NOR‐ORR090
22.60
0.57
53.72
37.60
0.10
CAP-RIO270
0.11
NOR‐ORR360 18.50
22.600.39
0.51 40.58 51.32 47.44 31.36
0.10
CHI-TCU74N
0.12
NOR‐SAT180 13.67
13.300.35
0.48 39.54 65.88 49.12102.17
0.14
CHI-TCU95W
43.44
0.38
59.39
80.09
0.16
NPAL‐NPS210
8.20
0.59
72.12
13.45
0.12
12 of 21
COA-PLE045
8.50
0.59
59.38
14.36
0.10
KOC-DZC270
12.70
0.36
61.02
252.44
0.17
Effect
of SSI on the displacement
response of 41.40
existing buildings
by two
LAN-CLVTR
21.20
0.42
22.07 was investigated
0.10
LOM-BRN000
10.30
0.45
50.43
16.20
0.11
different earthquake demand parameters (EDPs): roof and inter‐story drift ratios. Roof displacement
10.30parameters
0.50
43.79 applicability,
13.03 especially0.09
is one ofLOM-BRN090
the most widely used
and it has wide
for determining
LOM-CYC285
21.80
0.48
43.91
81.28
0.09
the seismic performance of structures. However, seismic performance of buildings
is determined
LOM-G03090
14.40
0.37
43.08
25.31
0.12
according
to different seismic
or earthquake
levels. Different
LOM-SAR000
13.00intensity 0.51
41.26
16.42 earthquake
0.08levels can be
recommended
for different15.80
performance0.42
levels according
in the modern
NOR-CNP196
57.01 to building
67.59 importance0.14
NOR-LOS000
13.00 on the other
0.41 hand, are
44.84
20.16
0.11
seismic codes.
Earthquake levels,
described according
to different
exceeding
NOR-LOS270
13.00
0.48
44.52
15.25
0.09
probability levels. Considering this situation, roof drift demand ratios of existing buildings are
NOR-MU2035
20.80
0.62
41.93
16.57
0.07
investigated in a probabilistic manner. For this purpose, cumulative exceedance probability of drift
NOR-MUL009
19.60
0.42
55.74
55.98
0.14
ratios is NOR-ORR090
calculated from the
displacement
of buildings 37.60
which are subjected
to 20 real
22.60
0.57demands 53.72
0.10
earthquake
records. In order
to generalize
obtained results,
probabilities are
NOR-ORR360
22.60
0.51
51.32 cumulative
31.36 exceeding 0.10
13.30 groups 0.48
65.88story numbers
102.17 and soil 0.14
providedNOR-SAT180
for different building
(new and old),
type which are
NPAL-NPS210
8.20
0.59
72.12
13.45
0.12
modeled according to the substructure method.
2.5
CAP-RIO270
CHI-TCU95W
KOC-DZC270
LOM-BRN000
LOM-CYC285
LOM-SAR000
NOR-LOS000
NOR-MU2035
NOR-ORR090
NOR-SAT180
Mean
Sa (g)
2.0
1.5
1.0
0.5
CHI-TCU74N
COA-PLE045
LAN-CLVTR
LOM-BRN090
LOM-G03090
NOR-CNP196
NOR-LOS270
NOR-MUL009
NOR-ORR360
NPAL-NPS210
0.0
0.0
1.0
2.0
T (sn)
3.0
4.0
Figure 11.
11. Response
Response spectrum
spectrum of
of selected
selected real
real ground
ground motion
motion records
Figure
records used
used in
in this
this study.
study.
In
In order
order to
to determine
determine cumulative
cumulative probability
probability of
of exceedance
exceedance curves,
curves, maximum
maximum displacement
displacement
demands
of
each
building
at
roof
level
were
determined
and
these
demands
were
collected
in theindata
demands of each building at roof level were determined and these demands were collected
the
pool.
In
each
data
pool
100
drift
ratios
(5
buildings
×
20
acceleration
records)
corresponding
to each
data pool. In each data pool 100 drift ratios (5 buildings × 20 acceleration records) corresponding
to
story
groupgroup
of new
and old
werewere
obtained
andand
thenthen
theythey
were
ranked
from
minimum
to
each story
of new
andbuildings
old buildings
obtained
were
ranked
from
minimum
maximum.
Minimum
and maximum
values in
the data
drift ratiosthe
corresponding
to maximum.
Minimum
and maximum
values
in pool
the represent
data pooltherepresent
drift ratios
probability of exceeding 100% and 0%, respectively. In order to compare the drift demands between
the fixed-base and SSI approaches, different exceedance probability levels were also considered.
For this purpose, drift ratios corresponding to probability of exceeding 50% and 10% levels were used.
Cumulative exceedance probabilities of three- to six-story buildings are plotted in Figures 12–15. It can
be seen from the figures that roof drift probabilities of the fixed-base approach and stiff soil conditions
are very similar, and they are mostly overlapped. Drift demands of moderate soil condition are closer
to fixed-base and stiff soil cases with respect to soft soil condition. These figures clearly show that roof
90%
100%
80%
90%
80%
90%
70%
80%
70%
80%
98+
60%
70%
98+
50%
60%
40%
50%
30%
40%
20%
30%
10%
20%
0%
10%
0.0%
0%
0.0%
100%
0.5%
0.5%
1.5%
2.0%
1.5%
2.0%
98-
60%
70%
98-
50%
60%
40%
50%
30%
40%
20%
30%
10%
20%
0%
10%
0.0%
0%
0.0%
0.5%
0.5%
1.0%
/H
1.0%
/H
Fixed
Stiff
Fixed
Moderate
Stiff
Soft
Moderate
1.5% Soft
2.0%
1.5%
2.0%
Figure 12. Cumulative exceedance probability curves of the three‐story buildings.
Figure 12. Cumulative exceedance probability curves of the three-story buildings.
Figure 12. Cumulative exceedance probability curves of the three‐story buildings.
100%
90%
100%
90%
100%
80%
90%
80%
90%
70%
80%
Probability
Probability
1.0%
/H
1.0%
/H
Fixed
Stiff
Fixed
Moderate
Stiff
Soft
Moderate
Soft
Probability
Probability
90%
100%
98+
60%
70%
98+
50%
60%
40%
50%
30%
40%
20%
30%
10%
20%
0%
10%
0.0%
0%
0.0%
Fixed
Stiff
Moderate
Fixed
Soft
Stiff
Moderate
Soft
70%
80%
Probability
Probability
Probability
Probability
corresponding probability of exceeding 100% and 0%, respectively. In order to compare the drift
also considered. For this purpose, drift ratios corresponding to probability of exceeding 50% and 10%
demands between the fixed‐base and SSI approaches, different exceedance probability levels were
levels were used. Cumulative exceedance probabilities of three‐ to six‐story buildings are plotted in
also considered. For this purpose, drift ratios corresponding to probability of exceeding 50% and 10%
Figures 12–15. It can be seen from the figures that roof drift probabilities of the fixed‐base approach
levels were used. Cumulative exceedance probabilities of three‐ to six‐story buildings are plotted in
and stiff soil conditions are very similar, and they are mostly overlapped. Drift demands of moderate
Figures 12–15. It can be seen from the figures that roof drift probabilities of the fixed‐base approach
Appl.
2020, 10, 8357
of 21
soil Sci.
condition
are closer to fixed‐base and stiff soil cases with respect to soft soil condition.13These
and stiff soil conditions are very similar, and they are mostly overlapped. Drift demands of moderate
figures clearly show that roof demands gradually increase due to SSI, and the most significant effect
soil condition are closer to fixed‐base and stiff soil cases with respect to soft soil condition. These
of SSI is observed on soft soil case in all story groups of new and old buildings.
figures clearly
show
that roof
gradually
increase
due effect
to SSI,ofand
most significant
effect
demands
gradually
increase
duedemands
to SSI, and
the most
significant
SSIthe
is observed
on soft soil
of SSI
is story
observed
on soft
soiland
caseold
in all
story groups of new and old buildings.
case
in all
groups
of new
buildings.
100%
100%
98-
60%
70%
50%
60%
98-
40%
50%
30%
40%
20%
30%
10%
20%
Fixed
Stiff
Fixed
Moderate
Stiff
Soft
Moderate
1.5% Soft2.0%
0%
10%
1.0%
1.5%
2.0%
0.0%
0.5%
1.0%
0%
/H
/H
0.5%
1.0%
1.5%
2.0%
0.0%
0.5%
1.0%
1.5%
Figure 13. Cumulative
exceedance
probability
curves
of
the
four-story
buildings.
/H
/H
Figure 13. Cumulative
exceedance probability curves of the four‐story buildings.
0.5%
Figure 13. Cumulative exceedance probability curves of the four‐story buildings.
2.0%
100%
100%
90%
90%
80%
80%
70%
70%
60%
60%
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
0%
0%0.0%
0.0%
1415ofof2122
15 of 22
98+
98+
0.5%
0.5%
1.0%
1.0%
/H
/H
Probability
Probability
Probability
Probability
Appl.Sci.
Sci.2020,
2020,10,
10,8357
x FOR PEER REVIEW
Appl.
Appl. Sci. 2020, 10, x FOR PEER REVIEW
Fixed
Stiff
Fixed
Moderate
Stiff
Soft
Moderate
Soft
1.5%
1.5%
2.0%
2.0%
100%
100%
90%
90%
80%
80%
70%
70%
60%
60%
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
0%
0%0.0%
0.0%
9898-
Fixed
Stiff
Fixed
Moderate
Stiff
Soft
Moderate
Soft
0.5%
0.5%
1.0%
1.0%
/H
/H
1.5%
1.5%
2.0%
2.0%
100%
100%
90%
90%
80%
80%
70%
70%
60%
60%
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
0%
0%0.0%
0.0%
98+
98+
Fixed
Stiff
Fixed
Moderate
Stiff
Soft
Moderate
Soft
0.5%
0.5%
1.0%
1.0%
/H
/H
1.5%
1.5%
2.0%
2.0%
Probability
Probability
Probability
Probability
Figure 14. Cumulative exceedance probability curves of the five‐story buildings.
Figure 14. Cumulative exceedance probability curves of the five-story buildings.
Figure 14. Cumulative exceedance probability curves of the five‐story buildings.
100%
100%
90%
90%
80%
80%
70%
70%
60%
60%
50%
50%
40%
40%
30%
30%
20%
20%
10%
10%
0%
0%0.0%
0.0%
9898-
Fixed
Stiff
Fixed
Moderate
Stiff
Soft
Moderate
Soft
0.5%
0.5%
1.0%
1.0%
/H
/H
1.5%
1.5%
2.0%
2.0%
Figure
Figure15.
15.Cumulative
Cumulativeexceedance
exceedanceprobability
probabilitycurves
curvesofofthe
thesix-story
six‐storybuildings.
buildings.
Figure 15. Cumulative exceedance probability curves of the six‐story buildings.
Distribution
Distributionofofresults
resultsalso
alsoshows
showsthat
thatprobabilistic
probabilisticroof
roofdisplacement
displacementdemands
demandsininold
oldbuildings
buildings
(98−)
are
new
(98+),
On
hand,
the
of results
also
that
probabilistic
roof
displacement
demandsamong
in
old buildings
(98−)Distribution
aregreater
greaterthan
than
newones
onesshows
(98+),as
asexpected.
expected.
On the
theother
other
hand,differences
differences
among
theroof
roof
demand
curves
of
especially
in
fiveand
six-story
buildings
are
relatively
low
with
respect
to
other
(98−)
are
greater
than
new
ones
(98+),
as
expected.
On
the
other
hand,
differences
among
the
roof
demand curves of especially in five‐ and six‐story buildings are relatively low with respect to other
ones.
words,
the the
effect
of five‐
SSIofisand
much
more
in low-rise
having
relatively
demand
curves
of especially
in
six‐story
buildings
are
relatively
low with
respect
tohaving
other
ones.InInother
other
words,
effect
SSI
is
muchpronounced
more pronounced
in buildings
low‐rise
buildings
higher
stiffness
capacities
and
strength
This
situation
is muchisinmore
evident
in threeand
ones.
In
other
words,
thecapacities
effect
ofand
SSIratios.
is much
more
pronounced
low‐rise
relatively
higher
stiffness
strength
ratios.
This
situation
much
morebuildings
evident
inhaving
three‐
four-story
new
buildings
(98+).
All
these
investigations
have
shown
that
relative
effect
of
SSI
especially
relatively
highernew
stiffness
capacities
ratios. This situation
is much
evident
in of
three‐
and four‐story
buildings
(98+).and
Allstrength
these investigations
have shown
thatmore
relative
effect
SSI
inand
softfour‐story
soil case
isnew
much
more
significant
stifferinvestigations
andinstronger
buildings.
(98+).
Allin
these
have
shownbuildings.
that relative effect of SSI
especially
in soft
soilbuildings
case
is much
more
significant
stiffer and
stronger
Numerical
evaluations
results
have
indicated
probabilistic
roof
drift
especially
in soft
soil case isofof
much
more
significant
inthat
stiffer
and stronger
buildings.
Numerical
evaluations
results
have
indicated
that
probabilistic
roof
driftratios
ratioscalculated
calculatedfor
for
soft
soil
case
can
be
1.3
to
1.7
times
greater
than
that
of
fixed-base
case
in
three-story
new
buildings.
Numerical
results
have indicated
that
probabilistic
drift ratiosnew
calculated
for
soft soil
case canevaluations
be 1.3 to 1.7oftimes
greater
than that of
fixed‐base
case roof
in three‐story
buildings.
However,
these
ratios
decrease
toto1.2
toto1.3
three-story
old
on
soft
soil case
can
be 1.3
to 1.7 times
greater
than
that of fixed‐base
casedepending
in three‐story
new
buildings.
However,
these
ratios
decrease
1.2
1.3inin
three‐story
oldbuildings
buildings
depending
onthe
theprobability
probability
ofHowever,
levels
(50%,
10%
ratios
buildings
range
these
ratios
decrease
to maximum
1.2
to 1.3 in(0%)).
three‐story
old buildings
depending
on
the probability
ofexceeding
exceeding
levels
(50%,
10%and
and
maximum
(0%)).The
Thesame
same
ratiosininsix-story
six‐storyold
old
buildings
range
from
1.05
to
1.2.
These
numerical
comparisons
indicate
that
the
relative
effect
of
SSI
is
much
of
exceeding
levels
(50%,
10% and comparisons
maximum (0%)).
The same
ratios
in six‐story
old
buildings
range
from
1.05 to 1.2.
These
numerical
indicate
that the
relative
effect of
SSI
is muchmore
more
effective
ininto
stiffer
low-rise
buildings.
ItItcan
that
results
from
1.05
1.2. and
These
numerical
comparisons
indicate
that
the relative
effect
of SSI is
muchshow
more
effective
stiffer
andstronger
stronger
low‐rise
buildings.
canbe
beadmitted
admitted
thatthe
theobtained
obtained
results
show
consistency
results
obtained
from
similar
effective
inwith
stiffer
and
stronger
low‐rise
buildings.
It can in
beinliterature
admitted
that
consistency
withthe
the
results
obtained
from
similarstudies
studies
literature[21].
[21].the obtained results show
consistency with the results obtained from similar studies in literature [21].
0
0
0.0%
1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
Story
Story
Story
Story
Story
Story
In addition
to evaluation
of inter‐story
roof drift ratios,
effectsare
ofplotted
SSI on the
inter‐story
drift ratios
areand
also
discussed.
In Figures
16–23, mean
drift ratios
for different
building
groups
discussed.
In
Figures
16–23,
mean
inter‐story
drift
ratios
are
plotted
for
different
building
groups
and
soil types. While calculating the inter‐story drift ratios, the same method was applied. One hundred
soil types.drift
While
calculating
inter‐story
drift ratios,
the
same method
was were
applied.
One
inter‐story
ratios
obtainedthe
from
five buildings
and 20
acceleration
records
used
andhundred
values
inter‐story drifttoratios
obtainedoffrom
five buildings
20 acceleration
records were
used
and values
corresponding
probability
exceeding
levels and
of 50%,
10% and maximum
drift
ratios
were
corresponding
to
probability
of
exceeding
levels
of
50%,
10%
and
maximum
drift
ratios
averaged.
method was repeated for each story group. Variation of inter‐story drift ratios15clearly
Appl.
Sci. 2020,This
10, 8357
ofwere
21
averaged.
Thismost
method
was repeated
for depending
each story group.
inter‐story
drift
ratios of
clearly
show
that the
significant
changes
on theVariation
SSI occurofat
the bottom
stories
the
show that[21]
theand
most
changes
depending
on the
SSI occur
at soft
the soil
bottom
of the
buildings
thesignificant
most evident
increments
are again
observed
in the
case.stories
All of these
In
addition
to
evaluation
of
roof
drift
ratios,
effects
of
SSI
on
the
inter-story
drift
ratios
are
also
buildings
[21] and
most evident
increments
are again
in case
the soft
soil
case. All of
these
figures
indicate
thatthe
inter‐story
drift ratios
are increased
in observed
the soft soil
in all
probability
levels.
discussed.
Indrift
Figures
mean
inter-story
drift
ratios
arethan
plotted
forsoil
different
groups
and
figures indicate
that16–23,
inter‐story
drift
ratios
are are
increased
in
the0.5%
soft
case
inbuilding
all probability
levels.
Inter‐story
ratios
at 50%
probability
level
lower
and
the difference
between
the
soil
types.
While
calculating
the
inter-story
drift
ratios,
the
same
method
was
applied.
One
hundred
Inter‐story
drift
ratios
at
50%
probability
level
are
lower
than
0.5%
and
the
difference
between
the
soil types in terms of story drift ratios is not obvious.
inter-story
drift
ratios
obtained
from
five
buildings
and
20
acceleration
records
were
used
and
values
soil Drift
typesratios
in terms
of story drift
is not obvious.
corresponding
toratios
probability
of exceeding 10% are higher than that of 50% ratios and
corresponding
to probability
of exceeding
levels
of
10%ratios
and
drift
were
averaged.
Driftofratios
corresponding
to probability
of 50%,
exceeding
10%maximum
are
higher
thanratios
thatlevel
of
50%
ratios
and
the effect
SSI
becomes
more
apparent.
Inter‐story
drift
at this
probability
can
be close
This
method
was
repeated
for
each
story
group.
Variation
of
inter-story
drift
ratios
clearly
show
that
the
effect
of
SSI
becomes
more
apparent.
Inter‐story
drift
ratios
at
this
probability
level
can
be
close
to 1% in soft soil cases. However, variations of drift demands have indicated that the effect of SSI is
the
changes
depending
theofSSI
occur
at the
bottom
storieswith
of
the
buildings
tomost
1%
insignificant
soft soil
cases.
However,
drift
demands
have
that
the
effect
of[21]
SSI is
not
significant
in upper
stories
andvariations
the on
response
of
upper
stories
is indicated
limited
respect
to bottom
and
the
most
evident
increments
are
again
observed
in
the
soft
soil
case.
All
of
these
figures
indicate
not
significant
in
upper
stories
and
the
response
of
upper
stories
is
limited
with
respect
to
bottom
stories. This situation is similar for all building groups and soil conditions. At this point, it should be
that
inter-story
drift
ratios
arethe
increased
inat
the
soft
soildue
case
allwere
probability
levels.
Inter-story
drift
stories.
This
situation
is by
similar
for all building
groups
and
soil
conditions.
At
this
point,
it should
be
stated
that
drifts
caused
rotations
the
base
toinSSI
extracted
while
calculating
the
ratios
at
50%
probability
level
are
lower
than
0.5%
and
the
difference
between
the
soil
types
in
terms
of
stated thatdrift
drifts
caused
by the
rotations at the base due to SSI were extracted while calculating the
inter‐story
ratios
of first
stories.
story
drift ratios
not obvious.
inter‐story
driftisratios
of first stories.
3
3
3
Fixed
Fixed
Fixed
3
3
3
Fixed
Fixed
Fixed
Stiff
Stiff
Stiff
Stiff
Stiff
Stiff
Moderate
Moderate
Moderate
2
2
2
Moderate
Moderate
Moderate
Soft
Soft
Soft
2
2
2
Soft
Soft
%10
Max
Soft
%50
%10
Max
%50
1
1
1
1
1
1
0
0
0.0%
1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
0
0
0.0%
1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
Figure 16. Mean of inter‐story drift ratios corresponding to different exceedance probability levels for
Figure 16. Mean of inter-story drift ratios corresponding to different exceedance probability levels for
Figure 16. new
Meanbuildings.
of inter‐story drift ratios corresponding to different exceedance probability levels for
three‐story
three-story new buildings.
three‐story new buildings.
1
1
Stiff
Moderate
Moderate
Soft
Soft
%50
%50
0
0
0.0%
1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
3
3
2
2
Fixed
Fixed
Stiff
Stiff
Moderate
Moderate
Soft
Soft
%10
%10
1
1
0
0
0.0%
1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
3
3
2
2
Story
Story
Story
Story
2
2
Fixed
Fixed
Stiff
Story
Story
3
3
Fixed
Fixed
Stiff
Stiff
Moderate
Moderate
Soft
Soft
Max
Max
1
1
0
0
0.0%
1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
Figure
Figure17.
17.Mean
Meanofofinter-story
inter‐storydrift
driftratios
ratioscorresponding
correspondingtotodifferent
differentexceedance
exceedanceprobability
probabilitylevels
levelsfor
for
three-story
old
buildings.
Figure 17. old
Mean
of inter‐story drift ratios corresponding to different exceedance probability levels for
three‐story
buildings.
three‐story old buildings.
Appl.Sci.
Sci.2020,
2020,10,
10,8357
x FOR PEER REVIEW
Appl.
Appl. Sci.
2020, 10,
x FOR PEER REVIEW
Appl. Sci. 2020, 10, x FOR PEER REVIEW
2
2
2
4
4
4
3
3
3
2
2
2
Fixed
Fixed
Fixed
Stiff
Stiff
Stiff
Moderate
Moderate
Moderate
Soft
Soft
Soft
%10
%10
%10
4
4
4
3
3
3
Story
Story
Story
Story
Story
Story
3
3
3
Fixed
Fixed
Fixed
Stiff
Stiff
Stiff
Moderate
Moderate
Moderate
Soft
Soft
Soft
%50
%50
%50
Story
Story
Story
4
4
4
1617
ofof
2122
17
of
22
17 of 22
2
2
2
Fixed
Fixed
Fixed
Stiff
Stiff
Stiff
Moderate
Moderate
Moderate
Soft
Soft
Soft
Max
Max
Max
1
1
1
1
1
1
1
1
1
0
0
00.0% 1.0% 2.0%
0.0% 1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
i/hi
0
0
00.0% 1.0% 2.0%
0.0% 1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
i/hi
0
0
00.0% 1.0% 2.0%
0.0% 1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
i/hi
4
4
4
4
4
4
4
4
4
Figure 18. Mean of inter‐story drift ratios corresponding to different exceedance probability levels for
Figure 18. Mean of inter‐story drift ratios corresponding to different exceedance probability levels for
Figure
Mean
inter‐storydrift
driftratios
ratioscorresponding
correspondingtotodifferent
different
exceedance
probability
levels
Figure
18.18.Mean
ofofinter-story
exceedance
probability
levels
forfor
the
four‐story
new
buildings.
the four‐story new buildings.
the
four‐story
new
buildings.
the four-story new buildings.
2
2
2
Fixed
Fixed
Fixed
Stiff
Stiff
Stiff
Moderate
Moderate
Moderate
Soft
Soft
Soft
%10
%10
%10
3
3
3
Story
Story
Story
2
2
2
3
3
3
Story
Story
Story
Story
Story
Story
3
3
3
Fixed
Fixed
Fixed
Stiff
Stiff
Stiff
Moderate
Moderate
Moderate
Soft
Soft
Soft
%50
%50
%50
2
2
2
Fixed
Fixed
Fixed
Stiff
Stiff
Stiff
Moderate
Moderate
Moderate
Soft
Soft
Soft
Max
Max
Max
1
1
1
1
1
1
1
1
1
0
0
00.0% 1.0% 2.0%
0.0% 1.0% 2.0%
0.0% 1.0%
/hi 2.0%
/hi
/hi
0
0
00.0% 1.0% 2.0%
0.0% 1.0% 2.0%
0.0% 1.0%
/hi 2.0%
/hi
/hi
0
0
00.0% 1.0% 2.0%
0.0% 1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
i/hi
Figure 19. Mean of inter‐story drift ratios corresponding to different exceedance probability levels for
Figure
Figure19.
19.Mean
Meanofofinter-story
inter‐storydrift
driftratios
ratioscorresponding
correspondingtotodifferent
differentexceedance
exceedanceprobability
probabilitylevels
levelsfor
for
Figure
19. Mean
inter‐story drift ratios corresponding to different exceedance probability levels for
the
four‐story
oldofbuildings.
the
old
buildings.
thefour-story
four‐story
old
buildings.
the four‐story old buildings.
Story
Story
Story
3
3
3
2
2
2
5
5
5
4
4
4
3
3
3
2
2
2
Fixed
Fixed
Fixed
Stiff
Stiff
Stiff
Moderate
Moderate
Moderate
Soft
Soft
Soft
%10
%10
%10
5
5
5
4
4
4
Story
Story
Story
4
4
4
Fixed
Fixed
Fixed
Stiff
Stiff
Stiff
Moderate
Moderate
Moderate
Soft
Soft
Soft
%50
%50
%50
Story
Story
Story
5
5
5
3
3
3
2
2
2
Fixed
Fixed
Fixed
Stiff
Stiff
Stiff
Moderate
Moderate
Moderate
Soft
Soft
Soft
Max
Max
Max
1
1
1
1
1
1
1
1
1
0
0
00.0% 1.0% 2.0%
0.0% 1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
i/hi
0
0
00.0% 1.0% 2.0%
0.0% 1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
i/hi
0
0
00.0% 1.0% 2.0%
0.0% 1.0% 2.0%
0.0% 1.0%
i/hi 2.0%
i/hi
i/hi
Figure
Figure20.
20.Mean
Meanofofinter-story
inter‐storydrift
driftratios
ratioscorresponding
correspondingtotodifferent
differentexceedance
exceedanceprobability
probabilitylevels
levelsfor
for
Figure 20. Mean of inter‐story drift ratios corresponding to different exceedance probability levels for
Figure
20. Mean
of
inter‐story drift ratios corresponding to different exceedance probability levels for
the
five-story
new
buildings.
the
five‐story
new
buildings.
the five‐story new buildings.
the five‐story new buildings.
Appl. Sci. 2020, 10, 8357
Appl.Sci.
Sci.2020,
2020,10,
10,xxFOR
FORPEER
PEERREVIEW
REVIEW
Appl.
33
22
Moderate
Moderate
Soft
Soft
%50
%50
44
33
22
55
Fixed
Fixed
Stiff
Stiff
Moderate
Moderate
Soft
Soft
%10
%10
44
Story
Story
Story
Story
44
55
Fixed
Fixed
Stiff
Stiff
Story
Story
55
17 of 21
18of
of22
22
18
33
22
Fixed
Fixed
Stiff
Stiff
Moderate
Moderate
Soft
Soft
Max
Max
11
11
11
00
0.0% 1.0%
1.0% 2.0%
2.0%
0.0%
i/hi
i/h
i
00
0.0% 1.0%
1.0% 2.0%
2.0%
0.0%
i/hi
i/h
i
00
0.0% 1.0%
1.0% 2.0%
2.0%
0.0%
i/hi
i/h
i
Figure21.
21.Mean
Meanof
ofinter‐story
inter‐storydrift
driftratios
ratioscorresponding
corresponding todifferent
differentexceedance
exceedanceprobability
probabilitylevels
levelsfor
for
Figure
Figure
21. Mean
of inter-story
drift ratios
corresponding totodifferent
exceedance probability
levels for
the
five‐story
old
buildings.
thefive-story
five‐storyold
oldbuildings.
buildings.
the
Story
Story
44
33
Moderate
Moderate
Soft
Soft
%50
%50
22
55
44
Moderate
Moderate
Soft
Soft
33
%10
%10
22
66
Fixed
Fixed
Stiff
Stiff
55
44
Story
Story
55
66
Fixed
Fixed
Stiff
Stiff
Story
Story
66
11
11
33
Fixed
Fixed
Stiff
Stiff
Moderate
Moderate
Soft
Soft
Max
Max
22
11
0
00
00
19 of 22
0.0% 1.0%
1.0% 2.0%
2.0%
0.0%
1.0%
2.0%
0.0%
1.0%
2.0%
0.0%
0.0% 1.0% 2.0%
0.0% 1.0% 2.0%
i/h
i
i/hi
i/h
i
i/h
stories are more
critical
in old buildings (98−). However,
in new buildings the SSI
strongly
affected
i/h
i/h
i
i
i
theFigure
response
of
first
stories
and
the
place
of the critical
story
moved
to the
first story.
The
ratio of
Figure
22.
Mean
of
inter‐story
drift
ratios
corresponding
to
different
exceedance
probability
levels
for
22.
Mean
ofof
inter-story
drift
ratios
corresponding
toto
different
exceedance
probability
levels
for
Figure
22.
Mean
inter‐story
drift
ratios
corresponding
different
exceedance
probability
levels
for
increment
is
much
more
significant
in
the
first
stories
of
new
buildings
with
respect
to
old
ones.
the
six‐story
new
buildings.
the six-story new buildings.
Appl. 0
Sci. 2020, 10, x FOR PEER REVIEW
the six‐story new buildings.
Story
Story
Story
6
Distribution
of values
values indicates
indicates6that
that the
the inter‐story
inter‐story
drift ratios
ratios6 of
of stiff
stiff and
andFixed
moderate soil
soil
Fixed drift
Distribution
of
moderate
Fixed
conditions
are
closer
to
the
fixed‐base
case
with
respect
to
ratios
of
soft
soil.
Story
drifts
conditions are closer to the fixed‐base
case with
Stiffrespect to ratios
StiffStory drifts
5 of soft soil.
5
Stiff
5
corresponding
to the
the
soft soil
soil case
case are
are much
much more
more remarkable
remarkable and
and the
the level
level of
of increment
increment isis much
much
corresponding
to
soft
Moderate
Moderate
Moderate
more pronounced
pronounced with
with respect
respect to
to other
other
cases. These
These observations
observations about
about
the effect
effect of
of soil
soil conditions
conditions
4 the
more
4 cases.
4
Soft
Soft
are
compatible
with
the
findings
related
to
the
probabilistic
roof
drift
ratios
presented
in
Figures
12–
Soft
are compatible with the findings related to the probabilistic roof drift ratios presented in Figures 12–
Max
%10
15.
%50
3
3
15.
3
Comparisons
of
probabilistic
inter‐story
drift
ratios
indicate
that there
there are
are considerable
considerable
Comparisons of probabilistic inter‐story drift ratios indicate that
2
2
differences
among
the
maximum
and
other
probabilistic
drift
ratios.
Effect
of
SSI
is
much more
more
2
differences
among the maximum and other probabilistic drift ratios. Effect of SSI is much
evidenton
onthe
themaximum
maximumdrift
driftratios
ratiosand
andresults
resultshave
haveshown
shownthat
thatmaximum
maximumdrifts
driftscan
canapproximately
approximately
evident
1
1 50% drifts
1
be
greater
than
four
times
from
the
and
two
times
from
the
10%
drifts.
Graphical
be greater than four times from the 50% drifts and two times from the 10% drifts. Graphical
distributions
show
that
these
trends
are
almost
similar
in
old
(98−)
and
new
(98+)
buildings,
but
distributions show that these trends are
0 new (98+) buildings, but
0 almost similar in old (98−) and
0
differencesamong
among the
the probabilistic
probabilisticdrift
drift
demands
are
quitesignificant.
significant. 0.0% 1.0% 2.0%
differences
demands
quite
0.0%
1.0%are
2.0%
0.0% 1.0%
2.0% drift ratios
Maximum
inter‐story
of
buildings
resting
on
soft soils
soils are
are mostly
mostly
higher than
than 1.5%
1.5%
i/hiresting on soft
i/h
Maximum inter‐story
drift ratios of buildings
higher
i
i/hi
and maximum
maximum inter‐story
inter‐story drift
drift ratios
ratios are
are generally
generally accumulated
accumulated at
at the
the first
first stories.
stories. This
This situation
situation isis
and
Figure
23.
Mean
of
inter-story
drift
ratios
corresponding
to
different
exceedance
probability
levels
for
much
more
apparent
in
low‐rise
buildings
(three‐
and
four‐story)
independent
from
the
building
much Figure
more 23.
apparent
low‐risedrift
buildings
(three‐ and to
four‐story)
independent
from the
building
Mean ofin
inter‐story
ratios corresponding
different exceedance
probability
levels
for
the six-story
old distribution
buildings.
group.
However,
of
values
has
shown
that
drift
demands
of
especially
upper
stories
are
group.the
However,
distribution
of
values
has
shown
that
drift
demands
of
especially
upper
stories
are
six‐story old buildings.
higher in
in old
old buildings
buildings with
with respect
respect to
to new
new ones
ones (see
(see Figures
Figures 21
21 and
and 23).
23). Critical
Critical stories
stories in
in five‐
five‐ and
and
higher
six‐story
old
buildings
are
the
second
stories
and
SSI
does
not
change
this
situation.
Decrease
in
5. Comparison
of SSI Effects
the Seismic
Existing
six‐story
old buildings
are theon
second
stories Performance
and SSI doesofnot
changeBuildings
this situation. Decrease in
column
dimensions
in
the
upper
stories
and
the
relatively
higher
vibration
periods
caused
by
upper
column dimensions in the upper stories and the relatively higher vibration periods caused by upper
Obtained results clearly show that interaction between soil and the structure affects both
calculation of displacement capacities and demands in existing buildings. This situation implies that
seismic performance of these buildings should also be examined since the performance is determined
by comparing both capacity and demand.
Appl. Sci. 2020, 10, 8357
18 of 21
Drift ratios corresponding to probability of exceeding 10% are higher than that of 50% ratios and
the effect of SSI becomes more apparent. Inter-story drift ratios at this probability level can be close to
1% in soft soil cases. However, variations of drift demands have indicated that the effect of SSI is not
significant in upper stories and the response of upper stories is limited with respect to bottom stories.
This situation is similar for all building groups and soil conditions. At this point, it should be stated
that drifts caused by the rotations at the base due to SSI were extracted while calculating the inter-story
drift ratios of first stories.
Distribution of values indicates that the inter-story drift ratios of stiff and moderate soil conditions
are closer to the fixed-base case with respect to ratios of soft soil. Story drifts corresponding to the soft
soil case are much more remarkable and the level of increment is much more pronounced with respect
to other cases. These observations about the effect of soil conditions are compatible with the findings
related to the probabilistic roof drift ratios presented in Figures 12–15.
Comparisons of probabilistic inter-story drift ratios indicate that there are considerable differences
among the maximum and other probabilistic drift ratios. Effect of SSI is much more evident on the
maximum drift ratios and results have shown that maximum drifts can approximately be greater
than four times from the 50% drifts and two times from the 10% drifts. Graphical distributions show
that these trends are almost similar in old (98−) and new (98+) buildings, but differences among the
probabilistic drift demands are quite significant.
Maximum inter-story drift ratios of buildings resting on soft soils are mostly higher than 1.5%
and maximum inter-story drift ratios are generally accumulated at the first stories. This situation
is much more apparent in low-rise buildings (three- and four-story) independent from the building
group. However, distribution of values has shown that drift demands of especially upper stories
are higher in old buildings with respect to new ones (see Figures 21 and 23). Critical stories in fiveand six-story old buildings are the second stories and SSI does not change this situation. Decrease in
column dimensions in the upper stories and the relatively higher vibration periods caused by upper
stories are more critical in old buildings (98−). However, in new buildings the SSI strongly affected
the response of first stories and the place of the critical story moved to the first story. The ratio of
increment is much more significant in the first stories of new buildings with respect to old ones.
5. Comparison of SSI Effects on the Seismic Performance of Existing Buildings
Obtained results clearly show that interaction between soil and the structure affects both calculation
of displacement capacities and demands in existing buildings. This situation implies that seismic
performance of these buildings should also be examined since the performance is determined by
comparing both capacity and demand.
Calculation of capacity curves revealed that interaction between soil and the structure shifts
the total displacement capacity of buildings instead of increasing them. Assessments performed
after pushover analyses show that plastic deformation capacity of buildings remains almost constant
(Figure 9) while yield displacements increase. Decreasing displacement ductilities corresponding to
soft soils are the indicator of this situation (Figure 10). Changes in the elastic slope of the building
capacity curves also imply the elongations in vibration periods and hence higher seismic displacement
demands in buildings (Figure 5). Figures 12–15 clearly represent this increase in demands from stiff
to soft soil sites. All these capacity- and demand-related changes in the results are the indicator of
possible seismic performance changes in selected buildings.
Seismic performance of investigated buildings was determined by using Turkish Earthquake
Code regulations and the effect of SSI on the collapse risk of old and new buildings was compared.
At this point, it should be reminded again that the aim of this study is not to investigate the seismic
performance of selected buildings according to one specific code regulations. The aim of this study is to
understand whether consideration of SSI can change the capacity and demand calculations (and hence
the performance estimations) of existing buildings. For this reason, the number of collapsed buildings
under various soil conditions was determined and compared.
Appl. Sci. 2020, 10, x FOR PEER REVIEW
20 of 22
Appl. Sci. 2020, 10, 8357
19 of 21
Soft
30.0%
0%
0%
0%
0%
0.0%
0%
0%
0%
1%
10.0%
0%
0%
0%
1%
20.0%
3
4
5
6
98+
3
5
6
25%
28%
29%
17%
19%
23%
40.0%
44%
46%
47%
54%
Moderate
38%
Stiff
48%
50%
55%
56%
Fixed
50.0%
40%
60.0%
0%
0%
0%
2%
Percentage of Collapses
constructions (Figure 5) suppress the deteriorating effects of SSI and the effect of interaction becomes
limited on new buildings.
Figure
24 Earthquake
also shows Code,
that inseismic
each soil
condition seismic
performance
of old
decreases
In
Turkish
performance
of buildings
is determined
bybuildings
using strain-based
by the increasing
of Furthermore,
stories. However,
the ratio of
of damages,
collapsed whether
buildingsinon
soft soil
to fixed‐
damage
assessmentnumber
method.
accumulation
beams
or columns,
base
case
indicates
that
the
relative
effect
of
SSI
is
much
more
significant
in
lower
story
buildings.
In
contributes to damaged columns and the shear capacity of stories are additional factors which are
three‐story
old
buildings
the
ratio
of
collapsed
buildings
on
soft
soils
(38%)
is
greater
than
two
times
considered by the Turkish Earthquake Code for the seismic performance assessment. In Figure 24,
that of the
case
Differences
between
softonand
moderate
more
changes
in fixed‐base
the number
of(17%).
collapsed
buildings
located
stiff
to soft soil
soil cases
sites are
are much
presented.
apparent
with
respect
to
moderate
and
stiff
or
stiff
and
fixed‐base
cases.
Increasing damage trends show that interaction between soil and the structure is much more significant,
Distribution
of collapsed
buildings
is presented
in Figure
24 and
clearly show
that
especially
in soft soils,
and a number
of collapsed
buildings
on soft
soilsthese
sites values
are considerably
higher
seismic
performance
of
especially
older
constructions
is
significantly
affected
from
the
SSI.
Results
than that of others. Figure 24 also reveals that the devastating effects of SSI are much more evident
have
clearly revealed
that damage
risk significantly
increases
in of
soft
soil
cases with (Figure
respect 5)
to
in
old buildings
with respect
to new ones.
Higher seismic
capacities
new
constructions
moderatethe
and
stiff cases. effects of SSI and the effect of interaction becomes limited on new buildings.
suppress
deteriorating
4
98-
Figure
Figure24.
24.Distribution
Distributionof
ofnumber
numberof
ofcollapse
collapseevents
eventsfor
forthe
theexisting
existingbuildings
buildings(%).
(%).
Figure 24 also shows that in each soil condition seismic performance of old buildings decreases by
6. Conclusions
the increasing number of stories. However, the ratio of collapsed buildings on soft soil to fixed-base case
Forty
existing
buildings
before
after in in
1998
when
thebuildings.
modern seismic
design
indicates
that
the relative
effectconstructed
of SSI is much
moreand
significant
lower
story
In three-story
code
of Turkey
implemented
investigated
considering
soil‐structure
interaction.
old
buildings
thewas
ratio
of collapsedwere
buildings
on softby
soils
(38%) is greater
than two
times thatSeismic
of the
response
of
buildings
was
determined
by
using
non‐linear
time
history
analyses
and 20 strong
fixed-base case (17%). Differences between soft and moderate soil cases are much more apparent
with
groundto motions.
between
soil andcases.
the structure was modeled by applying the
respect
moderate Interaction
and stiff or stiff
and fixed-base
substructure
method
and four
different
cases classified
according
shear
wave
velocities
Distribution
of collapsed
buildings
is presented
in Figure
24 and to
these
values
clearly
show were
that
considered.
Seismic
displacement
demands
at
roof
and
story
levels
were
calculated
for
all
buildings
seismic performance of especially older constructions is significantly affected from the SSI. Results
have
under revealed
fixed‐base,
moderate
and soft soilincreases
conditions.
clearly
thatstiff,
damage
risk significantly
in soft soil cases with respect to moderate and
In
addition
to
demand
calculations
by
using
non‐linear time history analyses, capacity curves of
stiff cases.
the buildings were obtained through static pushover analyses. By this method, drift ratios
6.corresponding
Conclusions to yield and ultimate levels were obtained for each soil case and for each building.
Then, displacement demands and building capacities were investigated, the effects of soil‐structure
Forty existing buildings constructed before and after in 1998 when the modern seismic design
interaction on existing buildings under various soil conditions were compared and the results are
code of Turkey was implemented were investigated by considering soil-structure interaction.
summarized below.
Seismic response of buildings was determined by using non-linear time history analyses and
The capacity curves obtained from the static pushover analyses of old and new buildings show
20 strong ground motions. Interaction between soil and the structure was modeled by applying
that the interaction between soil and the structure shifts the total displacement capacity of buildings
the substructure method and four different cases classified according to shear wave velocities were
instead of increasing it. Depending on the weak soil conditions, rotations at base increase and this
considered. Seismic displacement demands at roof and story levels were calculated for all buildings
situation increases the elastic drift ratios corresponding to the yield. In other words, plastic
under fixed-base, stiff, moderate and soft soil conditions.
deformation capacity of buildings remains almost constant while yield displacements increase.
In addition to demand calculations by using non-linear time history analyses, capacity curves of the
Decreasing displacement ductilities are the result of this situation. Changes in the elastic slope of the
buildings were obtained through static pushover analyses. By this method, drift ratios corresponding
buildings also increase the vibration periods and then the displacement demands of the buildings.
to yield and ultimate levels were obtained for each soil case and for each building. Then, displacement
Changes in the seismic demands were investigated by comparing the roof drift ratios
demands and building capacities were investigated, the effects of soil-structure interaction on existing
corresponding to exceedance probabilities of 50%, 10% and maximum. Distribution of values clearly
buildings under various soil conditions were compared and the results are summarized below.
indicated that most critical results were obtained under soft soil conditions, and results obtained from
Appl. Sci. 2020, 10, 8357
20 of 21
The capacity curves obtained from the static pushover analyses of old and new buildings show that
the interaction between soil and the structure shifts the total displacement capacity of buildings instead
of increasing it. Depending on the weak soil conditions, rotations at base increase and this situation
increases the elastic drift ratios corresponding to the yield. In other words, plastic deformation capacity
of buildings remains almost constant while yield displacements increase. Decreasing displacement
ductilities are the result of this situation. Changes in the elastic slope of the buildings also increase the
vibration periods and then the displacement demands of the buildings.
Changes in the seismic demands were investigated by comparing the roof drift ratios corresponding
to exceedance probabilities of 50%, 10% and maximum. Distribution of values clearly indicated that
most critical results were obtained under soft soil conditions, and results obtained from the soft soil
cases were significantly separated from the others. Drift demands of moderate soil cases are closer to
fixed and stiff soil cases with respect to soft soil conditions. Relative demand increase under soft soil
case is much more evident in low story buildings with respect to higher ones.
Investigation of inter-story drift demands showed that first stories are mostly affected from the
weak soil conditions and in all cases most significant demand increase occurs at the first stories.
Increase in the maximum inter-story drift demand is much more evident with respect to ones
corresponding to 50% and 10% exceedance probabilities.
Effect of soil conditions on the number of collapsed buildings is also investigated and compared.
Distribution of results have shown that a number of collapsed buildings are almost similar in fixed-base,
stiff and even in moderate soil cases. However, under soft soil conditions the number of collapsed
buildings increase and the level of increment is much more significant in old and low story buildings.
A distinct increase in the number of collapsed three- and four-story buildings indicates that the fragility
of old and low story buildings on weak soil conditions is much higher. Performance of new buildings,
on the other hand, is not as critical as the old ones. Higher seismic capacities of new constructions
suppress the deteriorating effects of soft soil conditions and reduce the collapse risk of new buildings.
Author Contributions: S.M.S. conceived of the presented idea, supervised the work, and drafted the manuscript.
M.P. contributed to method of analysis and supervised the analytical computations. A.K. and I.O. designed the
nonlinear structural models and analyzed the buildings. All authors have read and agreed to the published
version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.
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