Ade Faisal, Afiful Anshari, Fadzli Mohamed Nazri, Moustafa Moufid Kassem

Corresponding email: adefaisal@umsu.ac.id

Corresponding email: adefaisal@umsu.ac.id

**Published at : ** 04 Apr 2023

**Volume :** **IJtech**
Vol 14, No 2 (2023)

**DOI :** https://doi.org/10.14716/ijtech.v14i2.4989

Faisal, A., Anshari, A., Nazri, F.M., Kassem, M.M., 2023. Near-Collapse Probability of RC Frames in Indonesia Under Repeated Earthquakes Containing Fling-Step Effect.

212

Ade Faisal | Program Studi Teknik Sipil, Universitas Muhammadiyah Sumatera Utara, Jl. Mukhtar Basri No.3, Medan 20238, Indonesia |

Afiful Anshari | Program Studi Teknik Sipil, Universitas Muhammadiyah Sumatera Utara, Jl. Mukhtar Basri No.3, Medan 20238, Indonesia |

Fadzli Mohamed Nazri | School of Civil Engineering, Engineering Campus, Universiti Sains Malaysia, 14300, Nibong Tebal, Penang, Malaysia |

Moustafa Moufid Kassem | School of Civil Engineering, Engineering Campus, Universiti Sains Malaysia, 14300, Nibong Tebal, Penang, Malaysia |

Abstract

The velocity pulse and displacement
fling-step pulse signatures may be present in a near-field earthquake ground
motion record. It is generally known that near-field ground motion with pulse
effects accelerated the building drift. The damage of building can also occur
as a result of two or three earthquakes within the building's lifespan. The
repeated earthquakes could cause minor to severe damage to the building,
including structural collapse. This includes earthquakes with fling-step pulse,
which impact is underexamined in the existing studies. Therefore, the objective
of this study is to assess the impact of repeated earthquakes with displacement
of the fling-step pulse on the near-collapse probability of 5-, 10-, 15 and 20-story concrete frames.
Based on the response modification factor R = 8, 5, and 3, the frames are
classified as special, intermediate, and ordinary, respectively. The result
shows that the near-collapse probability of repeated earthquakes is more likely
to occur on the concrete frames which reaches intensity measure of 27.0% than
the effect of single earthquakes.

Incremental dynamic analysis; Interstory drift; Nonlinear response history analysis; Probability of near-collapse

Introduction

Indonesia is flanked by tectonic plates and is repeatedly experiencing
devastating earthquakes due to plate movement. The collision of Eurasian and
Indo-Australian plates has produced devastating earthquakes of the West coast
of Sumatera, i.e. Mw > 9.0 in the Northern part (Prakoso
*et al.,* 2017) and Mw > 8.0 in the Southern part (Mase, 2018). In the Lombok region of central
Indonesia, the collision of these plates has caused earthquakes with Mw >
7.0 (Pramono *et al.,* 2018). These
types of earthquakes tend to occur repeatedly in the same tectonic region with
return periods of hundreds or tens of years, or even shorter. One of the
instances is the Mw 6.4 earthquakes that is followed by Mw 6.8 one which struck
the Lombok region on 07/29/18 and 08/05/2018, respectively (Pramono *et al.,* 2018).

A study of
reinforced concrete (RC) frames subjected to high vibration found a clear link
between interstory drift and structural failure. When the interstory drift
reaches 3% in a 10-story RC building, the column sustains initial damage (Dymiotis *et al.*, 1999). *et
al.*, 2017; Hatzivassiliou
and Hatzigeorgiou,
2015;).

The
fragility curves of 9 RC frames, which are designed according to the seismic
code, are investigated by Kalantari and Roohbakhsh
(2019). In this study, the near-collapse and collapse limit states due
to repeated earthquakes are evaluated as
well. Oggu and Gopikhrisna (2020)
investigates the probability of collapse of regular and irregular RC structures
affected by repeated earthquakes. It shows that the intensity measure for the
probability of collapse (IM) of the regular structure is 3.33% less than IM caused by a single earthquake. More recently, Di Sarno and Pugliese (2021) reports that the
effect of repeated earthquakes on the existing RC structures increases seismic
vulnerability to 17%. Nevertheless, a lower IM result is also found in the
study of the probability of collapse due to repeated earthquakes in an existing
4-story RC structure in comparison with the effect of a single earthquake (Aljawhari *et al.*, 2021).

The earthquake
ground motion can be divided into two groups: far field motion (FF) and
near-field motion (NF) (Faisal, Riza, and Hadibroto,
2018; Kalkan and Kunnath, 2006). The near-field ground motion is defined as the
earthquake ground motion that is recorded in a seismic station that is less
than 15 kilometers away from the ruptured fault zone. It has distinct
signatures in both its velocity and displacement forms, (Figure 1), which is
unobservable in the far-field motion. Numerous sources already discussed the
major impact of near-field ground motion with pulse (or fling-step) on the
multi-story RC frames (e.g., Rashidi *et al.*,
2019; Champion and Liel, 2012; Majid *et al.*, 2010; Zahid, Majid, and Faisal, 2017).
However, these studies do not particularly explain the effect of the
displacement fling-step pulse on the concrete frames.

**Figure
1 **a)
far-field earthquake, b) near-field earthquake with velocity pulse effect, and
c) near-field earthquake with the displacement fling-step effect

In addition,
the influence of a repeated near-field earthquake propagates a bigger drift as
compared to the effect of a single earthquake. Again, the effect of multiple
earthquakes incorporating only near-field ground motion is not properly
investigated yet, especially the impact of multiple earthquakes containing the
displacement fling-step pulse on the RC frames. This is, partially, due to the
limited available records. Therefore, the aim of this research is to determine
the likelihood of near-collapse of the RC frames when subjected to a sequence
of near-field earthquakes containing the displacement fling-step effect. The
case study is based on the RC frames that are designed and built in Indonesia.

Experimental Methods

*2.1. RC Frame
Model*

The evaluated
archetype moment resisting frames consists of 5-, 10-, 15- and 20-story RC
structures with regular shape of floor plans, masses, and stiffness (Figure 2a
and 2b). This study assumes that the RC special moment resisting frame (MRF)
with R = 8 is constructed on soft soil in Banda Aceh City, Indonesia, whilst
the intermediate and ordinary MRFs with R = 5 and 3, respectively, are
constructed on medium and hard soils in the same city. The structural model's
plan view and the model's frame section are shown in Figure 2. The length of
all beams are equivalent at 6.0 m, and the height of all columns is 3.5 m, with
the exception of the bottom floor, where the column height is 4.5 m. The
concrete and rebar yield strengths used in all models are fc' 40 MPa and fy 400
MPa. The natural period of the structural model is 0.41 s, 0.80 s, 1.16 s, and
1.58 s for 5-, 10-, 15-story, and 20-story RC frames, respectively.

*2.2. Elements
Strength *

The element strength and deformation capacity, which is
commonly calculated through the concrete section analysis, is defined based on
the FEMA method. Although the internal elastic of the element is designed by
flexural force, the yield flexural strength (My) of the element is calculated
using the empirical value of 1.13My provided by Haselton
*et al.* (2010) to be the maximum flexural force. In order to
comply with the code requirement for a strong column weak beam mechanism, the
element's flexural forces are adjusted. The Modified-Takeda hysteresis rule is
employed to control the material nonlinearity during cycle loads (Figure 2c).
The unloading and reloading parameters for beam and column members based on
some experimental works on the RC structures are selected, namely *=* 0.3
and * *= 0.6, respectively,
as suggested by Fardis (2007).

**Figure 2** a) The plan view, b) 2D
frame models, and c) Modified-Takeda hysteresis and its backbone curve for
lumped plasticity model of nonlinear inelastic elements.

*2.2. Rotation Capacity*

The
yield rotation of the
member was obtained by the ratio of *M*_{y} with elastic rotation
stiffness (*K*_{0}=6*EI/L*) of the member. The post-yield
stiffness ratio or bi-factor (*r*) of the member’s hysteresis rule was
estimated based on the ratio of the capping moment and yield moment (*M*_{c}/M_{y})
and ductility of plastic rotation capacity as follows:

This
study employs plastic rotation capacity rad
for special MRF, whereas = 0.02 rad for medium and ordinary MRFs, as
proposed by Haselton *et al.* (2010).
The post capping rotation, = 0.02 rad
for medium and ordinary MRFs, as proposed by Haselton
*et al.* (2010). The post capping rotation, , uses 0.06 based on the average
value in Zareian
and Krawinkler (2010). The ratio of *M*_{c}/M_{y} reflects the strength
hardening of RC members, which is taken as *M*_{c}/M_{y}=1.13
based on the average value in Haselton *et al.*
(2010), and as suggested by FEMA-P695 (FEMA,
2009).

*2.3.
Strength Degradation*

This
study considers the strength degradation of the member up to residual strength
of 1% of the initial strength (yield moment) at the ultimate rotation
ductility, The strength at 1% of the
initial strength is sufficiently very low to represent strength at collapse
state (Carr, 2010). The capping rotation ductility, is defined through Equation 2;
whereas ultimate rotation ductility, is obtained based on yield
rotation (), plastic rotation capacity (), and post-capping rotation
capacity (), as follows:

*2.4. Ground Motions and Intensity Measure*

Generally, there are 2 types of ground
motions employed in earthquake sequence study on the structural response,
namely as-recorded mainshock-aftershock and artificial repeated earthquake.
Since the as-recorded mainshock-aftershock sequences for motions containing
fling-step pulse are scarce, therefore, the ground motion used in this study is
artificially repeated earthquakes. These ground motions are selected from the
available records in *Pacific Earthquake
Engineering Research *(PEER)* Next
Generation Attenuation *(NGA) and COSMOS. The selection criteria are based
on magnitude, near-field source-to-site distance (15 km), fault mechanism,
and soil type. Table 1 shows the selected records containing near-field motion
with fling-step effects.

**Table 1** List of selected records of near-field ground motion containing
fling-step pulse effect sourced from PEER NGA and COSMOS

Record No |
Year |
Earthquake |
M |
Station |
Dist.(km) |
PGA (g) |
PGV (cm/s) |
PGD (cm) |

1 |
1999 |
Chi-Chi |
7.6 |
TCU052 |
1.8 |
0.35 |
178.00 |
493.52 |

2 |
1999 |
Chi-Chi |
7.6 |
TCU068 |
3.0 |
0.50 |
277.56 |
715.82 |

3 |
1999 |
Chi-Chi |
7.6 |
TCU074 |
13.8 |
0.59 |
68.90 |
193.22 |

4 |
1999 |
Chi-Chi |
7.6 |
TCU084 |
11.4 |
0.98 |
140.43 |
204.59 |

5 |
1999 |
Chi-Chi |
7.6 |
TCU129 |
2.2 |
0.98 |
66.92 |
126.13 |

6 |
1999 |
Kocaeli |
7.4 |
Yarimca |
3.3 |
0.23 |
88.83 |
184.84 |

7 |
1999 |
Kocaeli |
7.4 |
Izmit |
4.3 |
0.23 |
48.87 |
95.49 |

8 |
1999 |
Chi-Chi |
7.6 |
TCU102 |
1.2 |
0.29 |
84.52 |
153.88 |

9 |
1999 |
Chi-Chi |
7.6 |
TCU089 |
8.3 |
0.34 |
44.43 |
193.90 |

10 |
1999 |
Chi-Chi |
7.6 |
TCU049 |
3.3 |
0.27 |
54.79 |
121.77 |

11 |
1999 |
Chi-Chi |
7.6 |
TCU067 |
1.1 |
0.48 |
94.31 |
181.25 |

12 |
1999 |
Chi-Chi |
7.6 |
TCU075 |
3.4 |
0.32 |
111.79 |
164.36 |

13 |
1999 |
Chi-Chi |
7.6 |
TCU076 |
3.2 |
0.33 |
65.93 |
101.65 |

14 |
1999 |
Chi-Chi |
7.6 |
TCU072 |
7.9 |
0.46 |
83.60 |
209.67 |

15 |
1999 |
Chi-Chi |
7.6 |
TCU065 |
2.5 |
0.76 |
128.32 |
228.41 |

16 |
1999 |
Chi-Chi |
7.6 |
TCU078 |
8.3 |
0.43 |
41.88 |
121.23 |

17 |
1999 |
Chi-Chi |
7.6 |
TCU082 |
4.5 |
0.22 |
50.49 |
142.78 |

18 |
1999 |
Chi-Chi |
7.6 |
TCU128 |
9.1 |
0.14 |
59.42 |
91.05 |

19 |
1999 |
Chi-Chi |
7.6 |
TCU071 |
4.9 |
0.63 |
79.11 |
244.05 |

20 |
1994 |
Northridge-01 |
6.7 |
LA-Sepulveda |
6.7 |
0.46 |
13.80 |
26.13 |

The intensity measure (IM)
employed in this study is *RSA*(*T*_{1}). All the selected records
are scaled up and down by referring to the elastic designed spectral
acceleration (Figure 3a) at the natural period of the model considered, *RSA*(*T*_{1}),
as demonstrated in Figure 3b. The design spectra for Banda Aceh City is
depicted in Figure 3a, which is developed based on the Indonesian seismic code
(SNI 1726:2012) (BSN, 2012). The Indonesian code is originally adopted
from standard ASCE/SEI 7-10 (ASCE, 2013). In order to model the
artificial repeated earthquakes, all the scaled ground motions are then paired
randomly by adding the 50 seconds of zero motions in between two, and/or three
scaled motions (Figure 3c) to make the free vibration on the structure exhibit
properly before the next earthquake motion started. The study used single, 2-
and 3-times repeated earthquakes to be induced on the RC moment resisting
frames (MRF) model.

*2.5. Structural Analysis and Collapse Limit
State*

In the design phase, the two dimensional of 3-, 10-, 15 and 20-story RC frames are analyzed with the response spectrum method to get the design flexural force. The elastic design phase complies with the Indonesian Standard SNI 1726:2012 (BSN, 2012), which is nearly identical with the ASCE/SEI 7-10 (ASCE, 2013). The 2D nonlinear inelastic response history analysis with lumped plasticity model is conducted to define the near-collapse state of the system using Ruaumoko 2D v.4.0 (Carr, 2010). This analysis is done in line with the seismic performance assessment guideline as stipulated in FEMA P-695 (FEMA, 2009).

**Figure 3** Model of earthquake ground motion: a) Elastic design spectra for
Banda Aceh City, b) Illustration of the ground motion scaling process, (c)
example of 3 times repeated earthquakes

The
incremental dynamic analysis (IDA) (Vamvatsikos
& Cornell, 2002) is utilized to define the interstory drift (IDR)
for the near collapse state, which is the same as the engineering demand
parameter (EDP). In the IDA, the IM = *RSA*(*T*_{1}) is repeatedly scaled in
order to find the IM level at which each ground motion causes EDP’s failure
criterion such as near-collapse or collapse. The near-collapse limit state of
IDR = 2.0% is employed based on the requirement stipulated in Indonesian
seismic code, as well as in ASCE 7-10. From IDA, the following parameters namely, , median and standard deviation, respectively, are
defined by fitting the interpolated IM through the method of moments as follow:

*2.6. Probability of Near Collapse*

The probability of near collapse (or any limit state of interest) is commonly expressed by the fragility function, which is developed through a log normal cumulative distribution function as follows:

where *P*[*D **d *|*R=RSA*(*T*_{1})] is the probability of reaching or exceeding the
collapse state (the so-called probability near collapse), while the
structure is induced by a ground motion with *R*=*RSA(T*_{1}); is the standard
lognormal cumulative distribution function; is the median of the ground motion that will cause collapse; and _{ }is the standard deviation of the
ground motion that will cause near-collapse. In developing the fragility
function, the result from the IDA doesn’t always achieve the targeted collapse
limit state. A statistical tool proposed by Baker
(2015) is useful to repair the data in order to estimate the fragility
function. The study also adopts the recommendation of FEMA P-58 guidelines in
order to always increase the logarithmic standard deviation (by adding = 0.1). It is done so since the uncertainty
in the analytically-based fragility curve could not adequately and accurately
represent the true variability (Porter, Kennedy, and
Bachman, 2007).

Results and Discussion

This
section is discussed based on the median value of probability near collapse, , to
capture the increment of effect of the repeated earthquake on the system.
Moreover, the standard deviation of the cumulative distribution of IM=*RSA*(*T*_{1}), , is also used to discuss the decrease of IM
required to produce near-collapse state. This value will affect the slope of
the diagonal line of fragility curve. The result of * *and that are used to construct the fragility curve is
provided in Table 2. The
table indicates that is found within the range of 0.16 to 0.33
for all MRFs considered in the study. Porter, Kennedy, and
Bachman (2007) find that commonly is
within the range of 0.2 to 0.6, after adding the uncertainty factor whereas Baker (2015) explains that = 0.4 is
commonly used to develop the fragility function, without the uncertainty
factor. Basone *et
al.* (2017) assess the seismic fragility curve of RC buildings with
T1 =0.34 s and find the standard deviation for the dataset, which ranged from
0.29 to 0.60. They evaluate the RC building up to the collapse state. Porter et
al. also explains that the quality of the dataset is high if the or differences
are found to be ³ 20%. The and listed
in Table 2 clearly demonstrates the
value difference, as indicated by Porter et al. Therefore, it can be said that
the * *and resulted
from this study is well defined, thus it is capable to produce high quality
fragility functions.

Figures 4 - 6 have depicted the fragility
curve of the 5-, 10-, 15-, and 20-story of special (R=8), intermediate (R=5),
and ordinary (R=3) MRFs under the effect of single earthquake (1XE), 2-times
earthquake (2XE) and 3-times earthquakes (3XE). Overall, the figures clearly
demonstrate that as the number of stories and R increased, the IM required to
produce near-collapse state decreased. This rule of thumb confirms that the
process conducted in this study is in the right path. Figure 4a indicates that IM = *RSA*(*T*_{1}) = 2.63
g is required to achieve the probability of near-collapse for 5-story ordinary
MRF. This IM is slightly decreased to
2.38 g and 2.30 g for 2XE and 3XE, respectively, to achieve near-collapse
probability. A similar condition is also indicated in 10- and 20-story ordinary
MRFs in achieving the probability near-collapse (Figures 4b and 4c). For this
ordinary MRF, the maximum effect of 2XE and 3XE is found to be exhibited on the
15-story and 20-story MRFs, respectively. In average, the 2XE has influenced
the response of 15-story MRF to be 14.48% more likely than 1XE in achieving the
near-collapse state, whereas 3XE has affected 20-story MRF of 24.4% more likely
than 1XE (Figures 4c and 4d).

**Figure
6** Probability
of near collapse for 5-, 10-, 15-, and 20-story RC frames for R = 8 induced by
repeated earthquake with fling-step effects

The near-collapse
probability for intermediate and special MRFs is depicted in Figures 5 and 6,
respectively. The figures indicate that the effect of R pushes the diagonal
line of the fragility curve to the left to become a vertical-like line. These
conditions mean that lower IM is more likely achieve the near-collapse
EDP. In the case of intermediate MRF,
the study finds that 2XE produces the maximum effect on the 20-story MRF
(Figure 5d). The 2XE makes the decrement of IM reached 27.0% in achieving near-collapse
EDP, whereas 3XE has maximum affection on the 15-story MRF, which is about
11.13 % more likely than the IM of 1XE (Figure 5c). Similar trend is indicated
for special MRFs affected by single and repeated earthquakes in Figure 6. The
IM of probability near collapse is clearly decreased as the number of the story
increased.

In Table
2, the median for special and intermediate MRFs, which have fundamental periods
of *T*_{1} = 0.41 s to 1.58 s,
are found within the range of = 0.36 to 2.10. This result is much lower than the
median IDA result of *m* = 0.98 to 5.36 for the collapse capacity of modern
ductile concrete MRF with *T*_{1}
= 0.42 s to 1.69 s done by Champion and Liel (2012).
It is obviously lower since this study is based on the near-collapse state,
which is not the collapse state as reported in Champion and Liel’s study. In
fact, this study also found the collapse state median IDA of = 0.71
to 4.67, which would be discussed in the upcoming paper.

Kalantari and
Roohbakhsh (2019)
found the fragility curve of the 4-story RC structure is based on the
dispersion of *b*= 0.82 to
1.04. Their study also explains that the fragility curve of a 15-story RC
structure is developed based on *b* =
0.96 to 1.07. Aljawhari *et al.* (2021)
reports that the dispersion of *b* =
0.359 is used to generate the fragility curve of a 4-story RC building. In this
study, we obtained *b* =
0.27 for 5-story, and *b* =
0.29 for 15-story RC special MRF. The significant gap shown in result *b* is mainly caused by the handling of the
uncertainty issues (quality of the dataset) for each study. Therefore, the
comparison of those results shall not be made straightforward. However,
statistically, we may refer to Porter, Kennedy, and
Bachman (2007) and Baker (2015) for the
common thresholds of dispersion in developing fragility curves, i.e. *b* = 0.2 to 0.4. It means that the fragility
curves of this study and the one in the study of Aljawahari *et al.* are
the common curves to be used as the probability of the limit state function of
RC structures.

Shokrabadi, Burton, and Stewart (2018) already
explains that the response RC frames with *T*_{1}
= 1.12 s and 1.71 s are increased significantly
to 30% - 50% when aftershock combines with mainshock motions. This increases
the collapse probability to be 1.5
and 3.5 times more likely. The
evaluation of a 4-story regular RC frame made by Oggu
and Gopikhrisna (2020) finds that the probability of the considered IM
decreases to 23.91%, which is smaller than the effect of a single earthquake. Di Sarno and Pugliese (2021) reported that the
effect of repeated earthquakes on existing 4-story RC structures caused the
probability of considered IM to decrease to 17% in comparison with the effect
of a single earthquake. In this study, the probability of IM for 5-story RC
special MRF under repeated earthquakes is decreased to 25.94%, which is smaller
than the effect of a single earthquake. These significant gaps in the
probability of IMs are mainly caused by the different methods of modeling the
repeated earthquake and the selection of ground motion.

Conclusion

The probabilistic seismic assessment of
reinforced concrete (RC) moment resisting frame (MRF) in Indonesia has been
presented. The
assessment makes use of the single, twice, and three times repeated earthquakes
(referred to as 1XE, 2XE, and 3XE) that contain the displacement fling-step
pulse. Four archetype RC frames were considered, namely 5-, 10-, 15-, and 20-story with
response modification factor R = 8, 5, and 3, which represents special,
intermediate, and ordinary MRF. Therefore, this study concluded that repeated
earthquakes is more likely producing near-collapse IM 27.0% earlier than the IM
of single earthquake, particularly on the intermediate MRF. In this case, the
near-collapse probability of ordinary MRF is posed slightly differently with
intermediate MRF. For special MRF, it is found that the near-collapse
probability may increase significantly due to the effect of 2XE and 3XE. It is
indicated by the 22.19% decrement of IM in producing near-collapse EDP, which
was lower than IM for 1XE. In average, the
2XE which might be producing the near-collapse IM of 16.58% is more likely to
occur on the all considered RC frames in comparison with 1XE. This probability
was larger than 3XE effect, which 9.45% more likely to exhibit on the frames
compared with the effect of 1XE. In average, the repeated earthquakes
containing fling-step pulse may increase the near-collapse probability of
special, intermediate, and ordinary RC frames to reach 13.81%, 12.67%, and
12.56%, respectively. In comparison to 1XE, the trends of the effect of 3XE on
this near-collapse probability do not always produce a superior effect when
compared to the effect of 2XE. Indeed, besides the repeated earthquakes
containing filing-step pulse, the variations in considered story heights, R,
and rotation capacity also contributes to the critical effect on the seismic
performance of the structure.

Acknowledgement

We gratefully thank the Fundamental Research grant with contract number
05/II.3-AU/UMSU-LP2M/C/2021 in the year 2021 for sponsoring this study, which
were awarded to the first author. The authors wish to thank the undergraduate students who were involved in this research as
numerators.

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