1. Introduction
In Korea, countermeasures against earthquakes, such as seismic capacity evaluations
and/or retrofitting schemes for buildings, especially existing low-rise reinforced
concrete (RC) buildings, have not been implemented comprehensively because Korea had
not experienced many destructive earthquakes. However, more than 1,200 low- or moderate-intensity
earthquakes have occurred in the coastal and inland regions of Korea over the past
20 years. The recent occurrence of moderate earthquakes in Korea, such as the 2016
Gyeongju Earthquake, with M=5.8, and the 2017 Pohang Earthquake, with M=5.4, pointed
to the importance of future earthquake preparedness measures becoming widely recognized
in Korea.
It is very important to assess the seismic risk of existing Korean buildings to mitigate
earthquake damage and provide effective earthquake preparedness measures against future
earthquakes. For this purpose, it is essential to develop a methodology to estimate
the seismic capacity of buildings and their vulnerability, and to predict potential
losses due to earthquakes.
Against this research background, we conducted the seismic capacity evaluation of
14 existing low-rise RC public buildings in Korea based on the Japanese Standard for
Evaluation of Seismic Capacity of Existing Reinforced Concrete Buildings (JBDPA 2005,
2017; Lee et al. 2002) to obtain the fundamental data for evaluating the seismic capacity
of existing low-rise RC buildings in Korea, as described in previous research (Lee
et al. 2018). Their seismic capacities are evaluated by the first and the second level
procedure specified in the Japanese Standard. We then investigated the distribution
of the seismic capacity index IS of existing 14 typical RC buildings in Korea, especially
the distribution of the ductility index (F) of each building, as depicted in Fig. 1 (Lee et al. 2018). The Standard defines the ductility index (F) of a building by
the expected ductility which is primarily based on the shear-to-flexural capacity
ratio ($V_{Su}/V_{M u}$). The result found in Fig. 1 showed that F-index for half buildings investigated in this study varies from 1.8
to 2.6, which corresponds to $\mu$=1.6 to 3.3.
Fig. 1 Ductility index distribution of existing low-rise RC buildings in Korea (Lee
et al. 2018)
It should be pointed out, however, that the ductility expected in these buildings
may need to be re-examined, since most buildings investigated herein have the hoop
spacing wider than 300 mm, and such high ductility calculated by the Standard may
be overestimated. This finding may result in lower seismic capacities and higher seismic
vulnerability of Korean buildings than presented in the research paper (Lee et al.
2018), and revealed that the ductility index (F) should be modified for accurately
estimating the seismic capacity of existing low-rise RC buildings in Korea.
The main objective of this study was to propose a method to evaluate the seismic capacity
of existing low-rise RC buildings in Korea by reviewing the applicability of the Japanese
Standard for Evaluation of Seismic Capacity of Existing Reinforced Concrete Buildings
(JBDPA 2005, 2017). To achieve this, we focused on the following two subjects:
(1) Proposal for a basic structural index suitable for evaluating existing RC buildings
in Korea
$\quad$- Proposal of equations to determine the ultimate horizontal flexural and shear
strength based on test results from Korean RC buildings
$\quad$- Proposal of average shear stresses of Korean buildings based on statistical
data
(2) Seismic capacity of Korean RC buildings based on the proposed basic strength index
$\quad$- Comparison of Korean RC buildings in terms of seismic capacity according
to the proposed basic strength index and the Japanese Standard
$\quad$- Seismic vulnerability and probabilistic assessment of structural damage ratios
of Korean RC buildings due to earthquakes
2. Proposal of Basic Structural Index for Evaluating Existing Korean RC Buildings
As shown in Fig. 2, in this section, we modify the equations for the ultimate flexural and shear strength
of the columns and walls. These are basic components of the basic structural index
that are used when applying the second level procedure of the Japanese Standard (JBDPA
2005, 2017; Lee et al. 2002).
Fig. 2 Flowchart of the proposed basic structural index, which is suitable for evaluating
Korean reinforced concrete (RC) buildings
These modifications are proposed based on the results of tests of columns and walls
in Korean buildings. We propose ultimate flexural and shear strength equations. The
ultimate average shear stress of the columns and walls was evaluated using the first
level procedure, based on statistical data on the structural characteristics of Korean RC buildings.
2.1 Ultimate strength equations for columns
2.1.1 Ultimate flexural strength of a rectangular column
Fig. 3 shows the relationship between the ultimate flexural strength of columns (subsequently
referred to as $_{c}M_{u}$), obtained using experimental evaluations of the horizontal
behavior of columns of Korean RC buildings (Lee 2011; Yi et al. 2000), and $_{c}M_{u}$,
calculated using Equation 1, which is quoted from the Japanese Standard.
Fig. 3 Relationship between cMu values of columns obtained experimentally and computed
using Equation 1
where $N_{\max}$ is the axial compressive strength of a column ($b DF_{c}+ a_{g}σ_{y}$,
[N]); Nmin is the axial tensile strength of a column ($-a_{g}σ_{y}$, [$N$]); $N$ is
the axial force on the section [N]; at is the tensile reinforcement area [mm2]; $a_{g}$
is the total longitudinal reinforcement area [mm2]; $b$ is the width of compression
face of a column [mm]; $D$ is the cross-sectional depth of a column, [mm]; $σ_{y}$
is the yield strength of the longitudinal reinforcements [MPa]; and $F_{c}$ is the
compressive strength of the concrete [MPa].
As shown in the figure, the flexural strength ratios ($_{testc}M_{u}/_{calcc}M_{u}$)
were approximately distributed between +10 % and -10 %, and the linear correlation
coefficient ($R$) between the experimental and theoretical values of $_{c}M_{u}$ was
0.97. The value of $_{c}M_{u}$ calculated using Equation 1 is in good agreement with the results of the experiments, in which Korean RC columns
were tested. Thus, the values of $_{c}M_{u}$ for existing Korean RC buildings calculated
by Equation 1 may be assumed to be reliable.
2.1.2 Ultimate shear strength equation of rectangular column
The following is an empirical equation derived for beams (Arakawa 1960). It was subsequently
modified to include the effect of the axial load and seismic safety of the shear strength,
as follows:
where $p_{t}$ is the tension reinforcement ratio [%]; $p_{w}$ is the transverse shear
reinforcement ratio; $_{s}σ_{cy}$ is the yield strength of the transverse shear reinforcement
[MPa]; $σ_{o}$ is $N / b D$ [MPa]; $d$ is the distance from the compressive face to
the centroid of the tensile reinforcement [mm]; $M / V$ is the shear span [mm],: which
may be taken as half of the clear height in the case of columns; and $j$ is $7/8d$.
According to the AIJ (2018), the coefficient of Equation 2, 0.053, which is used to calculate the minimum ultimate shear strength of columns
(subsequently referred to as $_{c}V_{Su}$), was derived from the product of the coefficient
of Equation 3, i.e., 0.068 (which calculates the mean of $_{c}V_{Su}$) and the shear strength ratio
($_{testc}V_{Su}/_{calcc}V_{Su-mean}$), i.e., 0.8, which corresponds to -5 % of the
distribution of the shear strength ratios approximated by the normal probability density
function. Thus, Equation 2 may provide safer estimates of $_{c}V_{Su}$ because it uses a lower boundary than
Equation 3.
Fig. 4 shows a histogram of the shear strength ratios ($_{testc}V_{Su}/_{calcc}V_{Su-mean}$),
where $_{testc}V_{Su}$ are experimental results from Korean RC columns and the values
of $_{calcc}V_{Su-mean}$ were calculated using Equation 3. Although Equation 3 calculates the mean of $_{c}V_{Su}$, the mean of $_{testc}V_{Su}/_{calcc}V_{Su-mean}$
was approximately 1.2, as shown in Fig. 4. It should be noted that, according to our experimental results, the equation for
$_{c}V_{Su}$ according to the Japanese Standard generally provided an overestimate,
and may require modification to provide reasonable estimates of the shear strength
of Korean columns.
Based on the procedures presented in AIJ (2018), we modified Equation 4 to evaluate $_{c}V_{Su}$ for Korean RC columns. The coefficient in Equation 4, 0.042, was derived by multiplying the coefficient from Equation 3, 0.068, by the shear strength ratio, 0.62, which corresponds to -5 % of the distribution
for the shear strength ratio, which was approximated by the normal probability density
function, as shown in Fig. 9.
Fig. 4 Distribution of shear strength ratios between the experimental and analytical
values (calculated using Equation 3) for Korean columns
Fig. 5 Relationship between $_{c}V_{Su}$ values according to our experiments for Korean
columns and those calculated using Equations 4 and 2
Fig. 5 shows the relationship between the experimental values of $_{c}V_{Su}$ and those
calculated by the proposed equation, Equation 4, and Equation 2, which is quoted from the Japanese Standard. As shown in the figure, Equation 4 estimates $_{c}V_{Su}$ more reasonably by using a lower boundary than Equation 2.
2.2 Ultimate strength equation for walls
2.2.1 Ultimate flexural strength equation for walls with boundary columns
The flexural strength of a wall with boundary columns, $_{w}M_{u}$, is defined by
the Japanese Standard as follows:
where $a_{g}$ is the total area of longitudinal reinforcement in the boundary column
on the tension side [mm2]; $σ_{y}$ is the yield strength of the longitudinal reinforcement
on the tension side [MPa]; $l_{w}$ is the distance between both centroids of the boundary
columns [mm]; $a_{w}$ is the total area of the vertical reinforcements of the wall,
excluding the reinforcement in the boundary columns [mm2]; $σ_{wy}$ is the yield strength
of the vertical reinforcement of the wall [MPa]; and $N$ is the total axial load of
the boundary column, [N].
Fig. 6 shows the relationship between wMu according to our experiments, in which we evaluated
the horizontal behavior of walls in Korean RC buildings (Yi et al. 2000), and the
values calculated using Equation 5, which is quoted from the Japanese Standard. As we do not have sufficient experimental
data to discuss the relationship between both values of wMu shown in Fig. 6, we cannot draw valid conclusions.
Fig. 6 Relationship between experimental values of $_{w}M_{u}$ and results calculated
using Equation 5
More experimental data should be obtained so that we can propose a suitable value
of $_{w}M_{u}$ for Korean RC walls. As the equation for $_{w}M_{u}$ was derived theoretically,
as shown in AIJ (2018) and JBDPA (2005, 2017), we can assume that the value of $_{w}M_{u}$
calculated using Equation 5 is reliable. This assumption was verified by comparing the results from Equation 5 to the theoretical values calculated using Equation 1, from the Japanese Standard, and experimental values of $_{w}M_{u}$. Thus, in this
study, we calculated $_{w}M_{u}$ for Korean RC walls using Equation 5.
2.2.2 Ultimate shear strength equation for walls with boundary columns
The minimum value of the ultimate shear strength of a wall with boundary columns ($_{w}V_{Su}$)
is calculated using Equation 6 when applying the Japanese Standard. We then modified this equation to evaluate the
behavior and seismic safety of the shear strength of walls based on the mean shear
strength, which is defined by Equation 7, which is derived from $_{w}V_{Su}$ of columns (JBDPA 2005, 2017).
where $p_{te}$ is $100a_{t}/(b_{el})$ [%]; $a_{t}$ is the total area of longitudinal
reinforcement of the tension of the column [mm2]; $b_{e}$ is the equivalent wall thickness
(total cross section area/$l$) [mm]; $l$ is the outer-to-outer distance between two
boundary column [mm]; $h_{w}$ is the height from the floor of the story to the top
of the wall (in the case of a top story or single story wall, $2h_{w}/ l$ is replaced
by $h_{w}/ l$) [mm]; $p_{s}$ is the equivalent wall reinforcement ratio ($a_{w}/ b_{es}$);
$a_{w}$ is the area of one set of lateral reinforcements in the wall [mm2]; $s$ is
the spacing between lateral wall reinforcements [mm]; $_{s}σ_{wy}$ is the yield strength
of the lateral reinforcement in the wall [MPa]; $ΣN$ is the total axial load on the
boundary columns [N]; and $l_{w}$ is the distance between the centroids of the boundary
columns [mm].
Fig. 7 shows a histogram of the shear strength ratios ($_{testw}V_{Su}/_{calcw}V_{Su-mean}$),
where the values of $_{testw}V_{Su}$ were obtained experimentally, and $_{calcw}V_{Su-mean}$
was calculated using Equation 7. Though Equation 6 defines the mean of $_{w}V_{Su}$, the mean value of $_{testw}V_{Su}/_{calcw}V_{Su-mean}$
was approximately 0.86, as shown in Fig. 7. Note that the Japanese Standard equation for $_{w}V_{Su}$ generally underestimates
the results of experiments on Korean walls, and may need to be modified to reasonably
estimate the shear strength of Korean RC walls with boundary columns.
Fig. 7 Distribution of the ratios of experimentally measured shear strength to the
values calculated using Equation 7
Fig. 8 Relationship between the experimental values of $_{w}V_{Su}$ and those calculated
using Equations 8 and 6
We modified Equation 8 to provide reasonable estimations of $_{w}V_{Su}$ for Korean RC walls, based on the
procedure used for $_{c}V_{Su}$. The coefficient of Equation 8, of 0.037, was obtained by multiplying the coefficient from Equation 7, 0.068, by the shear strength ratio, 0.55, which corresponds to -5 % of the distribution
curve of the shear strength ratio. We approximated this by the normal probability
density function, as shown in Fig. 7.
Fig. 8 shows the relationship between the experimental values of $_{w}V_{Su}$, those calculated
using Equation 8, and those obtained using Equation 6 from the Japanese Standard. As shown in the figure, Equation 8 clearly provides more reasonable estimates of $_{w}V_{Su}$ than Equation 6 for Korean buildings because it uses a lower boundary.
2.3 Ultimate average shear stress of rectangular columns
Table 1 shows the values of the parameters used to estimate the unit average shear stresses
of columns based on the first level procedure. These values were determined statistically
based on both technical and engineering considerations. We obtained statistics from
7,256 columns of 26 Korean RC buildings, such as histograms of the tension reinforcement
ratios ($p_{t}$) and the transverse shear reinforcement ratios ($p_{w}$) of the columns,
as shown in Figs. 9 and 10, respectively.
Table 1 Parameters used to estimate the unit average shear stress of columns based
on the first level procedure
|
Variable
|
Korean
buildings
|
Japanese buildings
(JBDPA
2005, 2017)
|
|
Compressive strength of concrete, $F_{c}$, [MPa]
|
18
|
20
|
|
Yield strength of longitudinal reinforcement, $σ_{y}$, [MPa]
|
240
|
300
|
|
Yield strength of shear reinforcement, $_{s}σ_{cy}$, [MPa]
|
240
|
300
|
|
Tension reinforcement ratio, $P_{t}$, [%]
|
0.55
|
0.4
|
|
Shear reinforcement ratio, Pw, [%]
|
0.13
|
0.1
|
|
Axial stress,
($σ_{o}= N/b D$), [MPa]
|
2
|
2
|
Column strength was evaluated using the first level procedure based on the average
shear stress and cross-sectional area of each column, which we classified into the
following groups;
(1) Short columns with clear height-to-depth ratios less than 2
(2) Short columns with clear height-to-depth ratios between 2 and 6
(3) Short columns with clear height-to-depth ratios greater than 6
Based on the Japanese Standard, we took the unit average shear stress of columns to
be 1.5, 1.0, and 0.7 MPa for height-to-depth ratios less than 2, between 2 and 6,
and greater than 6, respectively. These values were selected conservatively after
analyzing the parameters shown in Table 1, which were used to evaluate Japanese buildings. We mainly considered shear and flexural
failure modes in these calculations.
Fig. 9 Distribution of tension reinforcement ratios of Korean RC columns
Fig. 10 Distribution of shear reinforcement ratios of Korean RC columns
Fig. 11 Unit shear stresses of rectangular columns according to the first level procedure
Fig. 11 shows the shear stress values computed to determine suitable unit shear stresses
for Korean columns and those adopted by the Japanese Standard. In the figure, $_{c}τ_{M
u}$ and $_{c}τ_{Su}$ represent unit shear stresses at the flexural and shear failure
modes for the clear height-to-depth ratio; these were calculated using the values
in Table 1 based on Equations 9 and 10, which were derived from Equations 1 and 4, respectively.
where $_{c}V_{M u}$ is the shear strength in the flexural failure mode, defined as
$2M u /h_{o}$ [kN]; $_{c}R_{h}$ is the clear height ($h_{o}$)-to-depth ($D$) ratio;
and $_{c}V_{Su}$ is the ultimate shear strength in the shear failure mode [kN].
In this study, we selected the values of unit shear stress by applying the first level
procedure to Korean RC columns based on the values of $_{c}τ_{M u}$ and $_{c}τ_{Su}$
shown in Fig. 11, as follows:
(1) 1.4 MPa for Short columns with clear height-to- depth ratios less than 2
(2) 0.9 MPa for Short columns with clear height-to- depth ratios between 2 and 6
(3) 0.6 MPa for Short columns with clear height-to- depth ratios greater than 6
2.4 Ultimate average shear stress of wall
Fig. 12 shows a typical cross section of walls with boundary columns, which we used to estimate
unit average shear stresses when applying the first level procedure. The values shown
were selected based on statistics of 26 RC buildings. The strength of walls with boundary
columns was evaluated using the first level procedure based on the unit average shear
stress and cross- sectional area of the walls. We set the unit average shear stress
to 3.0 MPa when applying the Japanese Standard.
Fig. 12 Typical cross section of Korean walls with boundary columns
Fig. 13 Unit shear stresses of walls with boundary columns
Fig. 13 shows the average shear stresses of walls, which we calculated to assess appropriate
unit shear stresses for Korean walls, and the corresponding values for the Japanese
Standard. In the figure, $_{w}τ_{M u}$ and $_{w}τ_{Su}$ represent unit shear stress
at the flexural and shear failure modes, respectively, of the walls according to the
clear height-to-depth ratio. These values were calculated using Equations 10 and 11, which we derived from Equations 4 and 7, respectively. We modified these equations to reflect the typical cross section,
which is shown in Fig. 13.
where $_{w}τ_{M u}$ is the shear strength at the flexural failure mode, defined as
$2_{w}M_{u}/ tl_{w}h_{w}$ [kN]; $_{w}R_{h}$ is $h_{w}/ l_{w}$; and $_{w}V_{Su}$ is
the ultimate shear strength in the shear failure mode [kN].
Based on the values of $_{w}τ_{M u}$ and $_{w}τ_{Su}$ shown in Fig. 13, we determined the unit shear stress, of 2.0 MPa, using the first level procedure
for Korean RC walls with boundary columns. These calculations were based on both technical
and engineering considerations.
3. Evaluation of Seismic Capacity and Safety of RC Buildings in Korea Based on the
Proposed Basic Structural Index
In this section, we describe the relationship between the $I_{S}$ of existing RC buildings
in Korea evaluated based on the proposed basic structural index (called the proposed
method hereafter) and the Japanese Standard. We also applied a probabilistic method
to estimate the structural damage ratios due to future earthquakes. The Korean buildings
investigated in this study, on the other hand, were summarized in the previous research
(Lee et al. 2018). The evaluation results of seismic capacity based on the Japanese
Standard were shown in our previous research (Lee et al. 2018). These are 14 typical
RC public buildings, with between three and five stories, which were constructed before
the code revision in 1988. Most of the concrete used in the construction of these
buildings has a design strength of 18 MPa or 21 MPa, and the typical column cross
section is 400 mm×400 mm. The hoops are arranged with spacings of more than 300 mm.
3.1 Relationship between seismic capacity estimated by the proposed method and the
Japanese Standard
Figs. 14 and 15 show the relationship between the seismic capacity indices ($I_{S}$) estimated using
the first and the second level procedures of the proposed method and the Japanese
Standard. When calculated using the first level procedure, shown in Fig. 14, $I_{S}$ values generally indicate that capacity is 20 % lower when calculated using
the proposed method rather than that of the Japanese Standard. This is because the
unit average shear stress of the columns according to the first level procedure of
the proposed method and Japanese Standard was 0.6 and 0.7 MPa (for columns of $Rh$>6),
respectively, and the respective values for walls with boundary columns were 2.0 and
3.0 MPa).
Fig. 14 Relationship between $I_{S}$ values (according to the first level procedure)
of Korean buildings when calculated using the proposed method and the Japanese Standard
Fig. 15 Relationship between $I_{S}$ values (according to the second level procedure)
of Korean buildings when calculated using the proposed method and the Japanese Standard
When using the second level procedure, $I_{S}$ values of the proposed method are generally
15 % lower than those of the Japanese Standard, as shown in Fig. 15. This is because we used lower bounds, as shown in Equations 4 and 8, when using the proposed method to evaluate suitable ultimate shear strength for
Korean columns and walls.
3.2 Distribution of seismic capacity values
Fig. 16 shows the distribution of $I_{S}$ values of Korean RC buildings evaluated by the
proposed method and the Japanese Standard (Lee et al. 2018). We used the second level
procedure to plot IS in both directions for each building. As shown in Fig. 16, the $I_{S}$ values of Korean buildings have a much narrower distribution when calculated
using the proposed method rather than the Japanese Standard. The $I_{S}$ values calculated
using the proposed method are lower than those calculated using the Japanese Standard.
As mentioned above, this is because our empirical equations approximate the lower
bounds of ultimate shear strength.
Fig. 16 Distribution of $I_{S}$ values of Korean RC buildings evaluated by the proposed
method and the Japanese Standard
3.3 Distribution of Ductility Index
Fig. 17 shows the distribution of the ductility indices (F) of 14 Korean buildings, which
were computed using the proposed method. As mentioned earlier, the Japanese Standard
(JBDPA 2005, 2017) defines the ductility index (F) of a building in terms of the expected
ductility, which is primarily based on the shear-to-flexural capacity ratio ($V_{Su}/
V_{M u}$).
Fig. 17 shows the F-indices of half of the buildings investigated in this study, which varied
between 1.4 and 2.3, corresponding to $\mu$=1.1 to 2.4. The F-indices estimated using
the Japanese Standard ranged from 1.8 ($\mu$=1.6) to 2.6 ($\mu$=3.3), as shown in
Fig. 1. We assumed that the proposed method provides relatively reasonable results for the
ductility indices of Korean RC buildings with hoop spacings wider than 300 mm.
3.4 Probabilistic approach for calculating the structural damage ratio due to future
earthquakes
It is widely recognized that structural safety can rarely be evaluated with certainty
due to uncertainties in ground motion, the ultimate strength and ductility of structures,
and their response to earthquakes etc., so it should be analyzed probabilistically
rather than deterministically. Nakano (1986) and Okada (1985) proposed a methodology
to assess structural damage ratios due to earthquakes, in which they analyzed the
relationship between the seismic capacity and damage ratio due to previous severe
earthquakes in Japan. They applied a probabilistic approach to predict the potential
damage caused by future earthquakes. We applied the basic concept proposed by Nakano
(1986) and Okada (1985) to probabilistically assess structural damage ratios due to
earthquakes.
Fig. 17 Ductility index distribution of Korean RC buildings computed by the proposed
method
3.4.1 Basic concept of assessment of structural damage ratio due to earthquakes
By defining $P_{Is}(x)$ and $P_{ET}(x)$, which are the probability density functions
of IS and the required seismic capacity, respectively, the damage ratio V, i.e., the
ratio of damaged buildings to total buildings, is expressed as follows:
The function $P_{ET}(x)$ is the probability distribution of the required seismic capacity,
which we denote as the $E_{T}$-index. Therefore, the term in the square bracket represents
the probability of failure for structures with $I_{S}$ equal to $x$. Note that the
uncertainty associated with the ground motion is taken into account. We simplify our
discussion by assuming that the seismic capacity of each building is deterministic
in Equation 13. Setting $v(x)$, as shown in Equation 14, the term $v(x)$ can be considered to represent the distribution of the $I_{S}$ values
of damaged buildings.
We estimate the structural damage ratio [$V$] and distribution of $I_{S}$ values of
damaged buildings [$v(x)$] in terms of the probability density function [$P_{Is}(x)$]
for Korean RC buildings, which we approximate by a normal probability density function
(curve-1 in Fig. 18), as shown in Equation 15. We calculated the $E_{T}$-index [$P_{ET}(x)$] using Equation 16, which was derived by Nakano (1986) and Okada (1985) based on a normal probability
density function.
Fig. 18 Structural damage ratios of Korean RC buildings due to earthquakes
Note that the $E_{T}$-index mentioned above is the required seismic capacity of buildings
that were moderately or severely damaged by the 1968 Tokachi-oki and 1978 Miyagiken-oki
earthquakes (Shiga et al. 1968; Shiga 1978). The acceleration due to gravity was assumed
to be approximately 0.23 g at sites and the predominant period was 0.4 s (Lee 2010;
Umemura 1973).
3.4.2 Structural damage ratios due to future earthquakes
Fig. 18 shows the structural damage ratios due to earthquakes and the distribution of IS
values of potentially damaged Korean RC buildings (curve-I). We calculated these values
using Equations 15 and 16 based on the intensities of the 1968 Tokachi-oki and 1978 Miyagiken-oki earthquakes
(Shiga et al. 1968; Shiga 1978). We used in Equation 15 and in Equation 18. Fig. 18 shows the damage ratios due to 0.2 g, 0.15 g and 0.1 g earthquakes, which we calculated
using Equations 13 and 14. We also plotted the mean values of (Equation 13), which we scaled by the ground acceleration.
As shown in Fig. 18, the structural damage ratio of Korean RC buildings is approximately 70 % in the
case of earthquakes with the same intensity as the Tokachi-Oki and Miyagi-KenOki earthquakes,
which we assumed to be approximately 0.23 g. The damage ratios of Korean buildings
due to 0.1 g, 0.15 g, and 0.2 g earthquakes were estimated to be 7 %, 27 %, and 55
%, respectively.
4. Concluding remarks
We proposed a method to evaluate the seismic capacity of RC buildings in Korea by
reviewing the applicability of the Japanese Standard for Evaluation of Seismic Capacity
of Existing Reinforced Concrete Buildings (JBDPA 2017). Our findings can be summarized
as follows:
$\quad$1) Based on the relationship between our experimental results for Korean buildings
and values calculated using the strength equations for the columns and walls from
the Japanese Standard, we determined that we could apply the flexural strength equations
without modification. The shear strength equations were modified based on our experimental
results, following the same procedure as the Japanese Standard, as follows;
$\quad$For column :
$\quad$$_c V_{S u}=\left\{\frac{0.042 p_{t}^{0.23}\left(180+F_{c}\right)}{M /(V d)+0.12}+2.7
\sqrt{p_{w s} \sigma_{c y}}+0.1 \sigma_{o}\right\} b j$
$\quad$For walls :
$\quad$$_{w} V_{S u}=\left\{\frac{0.037 p_{t e}^{0.23}\left(180+F_{c}\right)}{2 h_{w}
/ i+0.12}+2.7 \sqrt{p_{s s} \sigma_{w y}}+0.1 \frac{\Sigma N}{b_{e} l}\right\} b_{e}
l_{e}$
$\quad$2) The following conservative estimates of unit shear stress were selected
when applying the first level procedure to Korean RC columns and walls. The values
are based on the statistics of structural characteristics of existing RC buildings,
using the proposed ultimate strength equations.
$\quad$- 1.4 MPa: for short columns with clear height-to-depth ratios less than 2
$\quad$- 0.9 MPa: for short columns with clear height-to-depth ratios between 2 and
6
$\quad$- 0.6 MPa: for short columns with clear height-to-depth ratios greater than
6
$\quad$- 2.0 MPa: for wall with boundary columns
$\quad$3) The $I_{S}$ values of Korean buildings were distributed much more narrowly
when calculated using the proposed method rather than the Japanese Standard, and $I_{S}$
values estimated by the proposed method were lower than those estimated by the Japanese
Standard.
$\quad$4) We assumed that the ductility indices calculated by the proposed method
are more reasonable for Korean RC buildings with hoop spacings wider than 300 mm than
those obtained using the Japanese Standard.
$\quad$5) The structural damage ratios of Korean RC buildings due to accelerations
of 0.1 g, 0.15 g, 0.2 g and 0.23 g were estimated probabilistically to be 7 %, 27
%, 55 % and 70 %, respectively.
$\quad$6) These findings indicate that the proposed method provides a useful strategy
for identifying Korean buildings with seismic vulnerabilities and recommend urgent
earthquake preparedness measures. In future research, we will determine the value of the seismic index necessary for protecting Korean RC buildings.
This investigation will be based on empirical and analytical studies. We will also
develop technically sound and cost-effective seismic retrofit schemes.