See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/325967536
Seismic Fragility Analysis Of RC Frames On Steep Slopes Under Near-fault
And Far-field Ground Motions
Conference Paper · June 2018
CITATIONS
READS
5
404
3 authors, including:
Jun Xu
Wang Guojue
Xihua University
Chongqing University
15 PUBLICATIONS 38 CITATIONS
15 PUBLICATIONS 81 CITATIONS
SEE PROFILE
All content following this page was uploaded by Wang Guojue on 25 June 2018.
The user has requested enhancement of the downloaded file.
SEE PROFILE
SEISMIC FRAGILITY ANALYSIS OF RC FRAMES ON STEEP
SLOPES UNDER NEAR-FAULT AND FAR-FIELD GROUND MOTIONS
Yingmin LI1, Jun XU 2, Guojue WANG3
ABSTRACT
Reinforced concrete frames on steep slopes (RCFSS), which are usually constructed with two ground levels, are
very common in mountainous or hilly regions. Due to the discontinuity of structural configuration, a sudden
change of structural stiffness and mass exists in the upper ground floor of RCFSS. Thus, the RCFSS are more
vulnerable to rare or mega earthquakes than RC frames on flat ground. In this study, two typical multi-story
RCFSS with and without an earthing tie beam in the upper ground floor were designed according to the seismic
design code of China. Fragility curves of the two RCFSS under both near-fault and far-field ground motions
were developed using nonlinear time history analysis. Following the performance-based evaluation approach, 40
earthquake ground motions (20 near-fault and 20 far-field ground motions) were utilized to evaluate the
likelihood of exceeding the seismic capacity of the frames. The results indicate that the RCFSS with an earthing
tie beam exhibit less fragility at different damage states under both near-fault and far-field ground motions.
Keywords: RC frames on steep slopes; Seismic fragility; Performance-based seismic design; Earthing tie beam
1. INTRODUCTION
The supply of land suitable for development is limited in cities especially those located in
mountainous or hilly regions. In order to increase the usage of land and to accommodate the growing
populations, the RC frame buildings, which are constructed on steep slopes with two ground levels
(Upper G.L. and Lower G.L., see Figure 1), are commonly constructed in mountainous or hilly regions.
According to previous seismic damage researchers (Wang et al. 2009; Sharma et al. 2013; Qu et al.
2015; Pan et al. 2017), the RCFSS suffered more seismic damages in rare or mega earthquakes than
RC frames on flat ground did, due to their vertical structural irregularities both in stiffness and mass.
In RCFSS, columns within the upper ground story are divided into upper base columns and non-base
columns (see Figure 1 b) by different column-end-restraint conditions. When the RCFSS suffered
horizontal seismic excitations, the distribution of column shear is highly uneven in the upper ground
story and the upper base columns bore much more shear and moment than other columns did due to
the short column effects. Thus, upper base columns would collapse firstly, which finally resulted in
half-story collapse failure mode of the RCFSS (Yang 2014). In order to balance the column shear
within the upper ground floor and to minimize the short column effect, earthing tie beams (see
Figure 1b), which are connected with the upper and lower parts of the structure, are introduced by
structural engineers.
Most of the previous research only focused on the influence of structural configurations (Wu et al.
2014; Xu et al. 2017) or ground motion inputs (Ling 2016) on the seismic fragility of RCFSS. This
study aims to investigate the influence of earthing tie beams on the seismic fragility of RCFSS, which
has not been adequately addressed for both near-fault and far-field ground motions so far. Two typical
6-story 3-bay RCFSS with and without an earthing tie beam were designed according to the current
Code for seismic design of buildings (GB 50011-2010). Moreover, fragility curves were generated to
1
Professor, School of Civil Engineering, Chongqing University, Chongqing, China, liyingmin@cqu.edu.cn
PhD student, School of Civil Engineering, Chongqing University, Chongqing, China, junxusc@gmail.com
3
PhD student, School of Civil Engineering, Chongqing University, Chongqing, China, wangguojue@gmail.com
2
examine the influence of earthing tie beams on the seismic fragility of RCFSS under near-fault and
far-field ground motions at different seismic fortification levels.
(a) Side view
(b) Main structural components
Figure 1. Typical RCFSS (National Engineering Technology Research Center for Inland Waterway
Regulation, Chongqing, China)
2. DESIGN AND ANALYTICAL MODELS
Two typical 6-story 3-bay RCFSS with and without an earthing tie beam in the regions with SFI=8
(SFI: seismic fortification intensity, PGA=0.2 g), Site Class II, Seismic Design Group I (see GB
50011-2010) were designed using PKPM software in this study. The plan and elevation of different
structural configurations are illustrated in Figure 2 and Figure 3. The story height of the lower ground
floor was 4.2 m, meanwhile, the story height of other floors was 3.6 m. The dead load (including the
weight of the slab) and the live load applied on the slab were 5.0 kN/m2 and 2.0 kN/m2, respectively.
The cross-section sizes and reinforcing details of the RCFSS were shown in Table 1 and Table 2. The
reinforcing steel had a standard yielding strength of 400 MPa, whereas the standard cube compression
strength of the concrete was 30 MPa. The infilled walls were not modelled in order to reduce the
complexity of modelling works and increase the efficiency of convergence, however, the effect of the
infilled walls must be considered. Thus, the fundamental periods of the models were shortened using
the reduction factor provided by the code (GB 50011-2010). The shortened fundamental periods of the
models with and without an earthing tie beam were 0.48 s and 0.51 s, respectively.
(a) Upper stories
(b) Lower stories
Figure 2. Plan view of the considered buildings
2
(a) RCFSS w/o tie beam
(b) RCFSS w/ tie beam
Figure 3. Elevation and loads (1.0 DL+0.5 LL) of the considered frames (kN)
Table 1. Cross section sizes and reinforcing details of beams and columns in RCFSS w/o tie beam
Beams
Columns
Bar areas (mm2)
Bar areas (mm2)
Cross
Cross
Floor
Section
Side span
Mid span
Section
Side column
Mid column
(mm×mm) Top
Bottom Top
Bottom (mm×mm) Top
Bottom Top
Bottom
1
987
998
987
998
1019 1019
1019 1019
2
1056 1007
1056 1007
1019 1019
1019 1019
3L
1664 943
2226 888
600×600 1019 1019
1019 1019
3R
300×550 2532 1146
2226 888
3541 3541
3541 3541
4
2119 1036
2038 871
1184 1181
1707 1707
5
1424 955
1509 869
1221 1221
1165 1165
550×550
6
854
879
969
768
843
843
843
843
Table 2. Cross section sizes and reinforcing details of beams and columns in RCFSS w/ tie beam
Beams
Columns
Bar areas (mm2)
Bar areas (mm2)
Cross
Cross
Floor
Section
Side span
Mid span
Section
Side column
Mid column
(mm×mm) Top
(mm×
mm)
Bottom Top
Bottom
Top
Bottom Top
Bottom
1
987
1056
797
1056
1019 1019
1019 1019
2
1056 976
1222 899
1019 1019
1019 1019
3L
1664 1103
2248 1055
600×600 1019 1019
1019 1019
3R
300×550 2532 1734
2248 1055
2387 2387
1336 1336
4
2119 1100
2156 997
1019 1019
1232 1232
5
1424 972
1527 884
1217 1217
1221 1221
550×550
6
854
909
954
799
843
843
843
843
3
The design results (see Table 1 and Table 2) demonstrated that the required bar areas in the upper base
columns had significantly reduced by setting an earthing tie beam.
Based on the design parameters of the models, the analytical models were developed by using
SAP2000 (2010) software. The beams and columns were modelled using beam elements, and the
flexural hinges in beams were modelled with uncoupled moment (M3) whereas for columns the
flexural hinges were modelled with coupled moments (P-M2-M3) according to FEMA 365 (2000). It
should be noted that the earthing tie beam and beams in the upper ground story were modelled with
coupled moments (P-M3) by considering the influence of axial forces in these special structural
members. The M3 hinge was used to simulate the plastic hinge caused by uniaxial moment. Then PM2-M3 and P-M3 hinge were used to simulate the plastic hinges caused by the axial force and
bending moments perpendicular to the element axis.
3. SELECTION OF THE GROUND MOTIONS
The main source of uncertainty exists in the seismic demand of structures is the uncertainty of
earthquake ground motions. In order to obtain a good estimation of the seismic fragility of the models,
totally 40 ground motion records, including 20 near-fault and 20 far-field ground motions were chosen
from the Pacific Earthquake Engineering Research Center (PEER) NGA-West 2 Database (Ancheta et
al. 2014). The near-fault ground motions are defined as those recorded within 20 km of a fault line (Li
and Xie 2007) with strong pulses. The far-field ground motions are defined as those recorded beyond
20 km of a fault line without strong pulses.
Table 3 and Table 4 summarized the name, magnitude, and year of the selected earthquake events and
name of the stations.
Table 3. Characteristics of selected near-fault ground motions
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Earthquake
Imperial Valley-06
Imperial Valley-06
Imperial Valley-06
Imperial Valley-06
Imperial Valley-06
Imperial Valley-06
Irpinia Italy-01
Northridge-01
Chi-Chi Taiwan
Chi-Chi Taiwan
Chi-Chi Taiwan
Chi-Chi Taiwan
Chi-Chi Taiwan
Chuetsu-oki Japan
Darfield New Zealand
Darfield New Zealand
Darfield New Zealand
Darfield New Zealand
El Mayor-Cucapah Mexico
El Mayor-Cucapah Mexico
Station
El Centro Array #10
El Centro Array #3
El Centro Array #5
El Centro Array #6
El Centro Differential Array
Holtville Post Office
Sturno (STN)
Sylmar - Olive View Med FF
TCU046
TCU049
TCU051
TCU053
TCU101
Joetsu Kakizakiku Kakizaki
DSLC
Riccarton High School
ROLC
TPLC
El Centro Array #12
Westside Elementary School
4
M
6.53
6.53
6.53
6.53
6.53
6.53
6.9
6.69
7.62
7.62
7.62
7.62
7.62
6.8
7
7
7
7
7.2
7.2
R(km) Year
8.60 1979
12.85 1979
3.95 1979
1.35 1979
5.09 1979
7.50 1979
10.84 1980
5.30 1994
16.74 1999
3.76 1999
7.64 1999
5.95 1999
2.11 1999
11.94 2007
8.46 2010
13.64 2010
1.54 2010
6.11 2010
11.26 2010
11.44 2010
Figure 4. Acceleration spectra of selected near-fault ground motions and design spectrum
Table 4. Characteristics of selected far-field ground motions
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Earthquake
San Fernando
San Fernando
Imperial Valley-06
Loma Prieta
Loma Prieta
Kobe Japan
Duzce Turkey
Hector Mine
Niigata Japan
Chuetsu-oki Japan
Iwate Japan
Iwate Japan
El Mayor-Cucapah Mexico
El Mayor-Cucapah Mexico
El Mayor-Cucapah Mexico
El Mayor-Cucapah Mexico
El Mayor-Cucapah Mexico
Darfield New Zealand
Darfield New Zealand
El Mayor-Cucapah Mexico
Station
LA - Hollywood Stor FF
Whittier Narrows Dam
Calipatria Fire Station
Agnews State Hospital
Salinas - John & Work
Sakai
Sakarya
Amboy
NIGH13
NIG010
AKTH17
YMT017
El Centro-Meloland Geotechnic
Brawley Airport
Holtville Post Office
Meloland_ E Holton Rd.
El Centro-Meadows Union School
DORC
Pages Road Pumping Station
El Centro Array #4
5
M
6.61
6.61
6.53
6.93
6.93
6.9
7.14
7.13
6.63
6.8
6.9
6.9
7.2
7.2
7.2
7.2
7.2
7
7
7.2
R(km) Year
22.77 1971
39.45 1971
24.60 1979
24.57 1989
32.78 1989
28.08 1995
45.16 1999
43.05 1999
39.43 2004
49.19 2007
48.14 2008
36.73 2008
29.00 2010
41.48 2010
36.52 2010
30.63 2010
28.30 2010
32.91 2010
24.55 2010
35.46 2010
Figure 5. Acceleration spectra of selected far-field ground motions and design spectrum
Figure 4 and Figure 5 show the comparison of the scaled acceleration spectra from selected ground
motions and design spectrum, from which it can be seen that the mean spectrum of the selected ground
motions matched the target spectrum specified in the GB 50011-2010 well. In this study, only one
horizontal direction was considered.
4. FRAGILITY ANALYSIS OF RC FRAMES ON STEEP SLOPES
Incremental dynamic analysis (IDA) is used for estimating the seismic performance of structures
under several ground motions. This method was proposed by Vamvatsikos and Cornell (2002) and
used for seismic vulnerability evaluation of building structures in hilly areas (Ling 2016; WelshHuggins et al 2017). The spectral acceleration Sa (T1 , 5%) was considered as the intensity measure
(IM) and maximum inter-story drift ratio  max for damage measure (DM). Each ground motion was
scaled monotonically with respect to the individual Sa (T1 , 5%) based on the corresponding elastic
fundamental period of each frame. The Sa (T1 , 5%) value is 0.1 g initially, then increased gradually
until collapse of the frame is observed by the hunt&fill tracing algorithm (Vamvatsikos and Cornell
2002). The frame models can be considered as collapsed when the analytical results meet any of the
following criteria: 1) dynamic instability of the frame occurs, the maximum inter-story drift is lower
than 10%, meanwhile the slope of IDA curve is less than 20% of its initial value; 2) the maximum
inter-story drift exceeds 10%. The IDA curves of the RCFSS are shown in Figure 6 and Figure 7.
(a) RCFSS w/o tie beam
(b) RCFSS w/ tie beam
Figure 6. IDA curves for RCFSS under near-fault ground motions
6
(a) RCFSS w/o tie beam
(b) RCFSS w/ tie beam
Figure 7. IDA curves for RCFSS under far-field ground motions
The logarithmic correlation between median engineering demand parameters (EDP) and the selected
IM are shown in Equation 1, which was regressed by cloud approach from the IDA results.
ln( Dnf_w/o )  - 4.2579  1.2213 ln( Sa )

ln( Dnf_w /)  - 4.3130  1.2128 ln( Sa )

ln( Dff_w/o )  - 4.1994  1.1966 ln( Sa )
ln( D )  - 4.3704  1.1932 ln( S )
ff_w/
a

(1)
Where Dnf_w/o , Dnf_w/ are the median estimate of the demand of the RCFSS without and with an
earthing tie beam under near-fault ground motions, respectively; Dff_w/o , Dff_w/ are median estimate of
the demand of the RCFSS without and with an earthing tie beam under far-field ground motions,
respectively.
According to HAZUS-MH 2.1 and GB 50011-2010, the damage states for 6-story RCFSS can be
defined as four levels: Slight Damage (SD), Moderate Damage (MD), Extensive Damage (ED), and
Complete Damage (CD). Their maximum inter-story drift ratio at the threshold of damage states are
listed in Table 5.
Table 5. Definition of structural damage states
Damage state
Maximum inter-story drift
Slight
0.4%
Moderate
1%
Extensive
2%
Complete
4%
Fragility curves, which represent the cumulated probability of exceeding predefined damage states
(see Table 5) under given seismic excitation intensities, are derived from Equation 2 using linear
regression results in Equation 1. Fragility curves at different damage states are shown in Figure 8 and
Figure 9.
 ln( Dˆ /Cˆ )
Pf  Φ 
 2  2
c
d





(2)
Where Φ is the lognormal-cumulative distribution function, Ĉ is the median deviation of structural
anti-seismic capacity in a specified limiting condition, D̂ is the median deviation of structural seismic
7
demand, and
c2  d2 is the standard deviation of the damage measures, and when Sa is selected as
IM, c2  d2 =0.4 .
The fragility of different seismic fortification levels specified in GB 50011-2010 can be computed
using Equation 3 and listed in Table 6 and Table 7.
Sa (T1 ,  ）
= (T1 ,  ） g
(3)
Where Sa (T1 ,  ）,  (T1 ,  ）, g and  are spectral acceleration at different fortification levels, the
maximum influence coefficient at the fundamental period T1 , gravity acceleration, and damping ratio
(5%), respectively.
Figure 8. Fragility curves for RCFSS under near-fault ground motions
Table 6. Seismic fragility matrix for the given 3 seismic fortification levels under near-fault ground motions
Levels
Frequent EQ
Fortificate EQ
Rare EQ
Damage state （%）
Moderate
Extensive
w/o
w/
w/o
w/
0.00 0.00
0.00 0.00
0.48 0.52
0.00 0.00
31.85 32.30
1.37 1.42
Sa (T1, 5%) [g]
w/o
0.11
0.32
0.64
Slight
w/
w/o
w/
0.12 0.03 0.03
0.34 38.33 39.36
0.68 96.55 96.65
Figure 9. Fragility curves for RCFSS under far-field ground motions
8
Complete
w/o
w/
0.0
0.0
0.0
0.0
0.0
0.0
Table 7. Seismic fragility matrix for the given 3 seismic fortification levels under far-field ground motions
Levels
Sa (T1, 5%) [g]
Frequent EQ
Fortificate EQ
Rare EQ
w/o
0.11
0.32
0.64
w/
0.12
0.34
0.68
Slight
w/o
w/
0.07 0.03
46.78 35.93
97.68 95.61
Damage state （%）
Moderate
Extensive
w/o
w/
w/o
w/
0.00 0.00
0.00 0.00
0.89 0.40
0.00 0.00
38.26 27.98
2.11 1.03
Complete
w/o
w/
0.00 0.00
0.00 0.00
0.01 0.00
In Figure 8 and Figure 9, we compared fragility curves for RCFSS models with different
configurations and under different seismic inputs. It can be observed that RCFSS with an earthing tie
beam experienced less fragility at each damage states. We also observed an important difference
between the seismic fragility of RCFSS under different types of ground motions inputs. When the
RCFSS were excited by far-field ground motions, the influence of the earthing tie beam on the seismic
fragility of RCFSS was significant. On the other hand, the earthing tie beam only had a slight
influence on the seismic fragility of RCFSS while excited by near-fault ground motions.
Table 6 and Table 7 summarized the seismic fragility matrix for the given seismic fortification levels
according to the code (GB 50011-2010). It is seen that all the probability of exceeding damage state
ED at rare earthquake level are under 10%, which meet the seismic performance requirements, as well
as “no collapse under rare earthquakes”.
5. CONCLUSIONS
This study developed fragility curves for RCFSS with and without an earthing tie beam under both
near-fault and far-field ground motions. Based on the analytical results, the following conclusions can
be drawn:
The seismic fragility of RCFSS could be improved to some extent with an earthing tie beam. In
addition, the seismic fragility improvement of the earthing tie beam is more obviously on the RCFSS
under far-field ground motions than those under near-fault ground motions. The performance
objectives for RCFSS designed according to the Code for seismic design of buildings (GB 50011-2010)
could be implemented with acceptable reliabilities.
6. ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China (Nos. 51638002 and
51478067). The authors would like to thank Dr. Jiulin Bai and PhD student Peiwen Shen of
Chongqing University, and Dr. Wenwen Luo of Chongqing University of Science and Technology, for
their constructive suggestions and design experience that greatly helped to improve the quality of this
article.
7. REFERENCES
Ancheta T D, Darragh R B, Stewart J P, et al. (2014) NGA-West2 Database. Earthquake Spectra, 30(3): 9891005.
Computers and Structures, Inc. (2010) SAP 2000: Linear and nonlinear static and dynamic analysis of three
dimensional structures. CSI, Berkeley, CA.
FEMA-356 (2000). Prestandard and commentary for seismic rehabilitation of buildings. FEMA, Washington,
D.C.
HAZUS-MH 2.1 earthquake model technical manual (2017). FEMA, Mitigation Division, Washington, D.C.
9
GB 50011-2010 (2015). Code for seismic design of buildings. China Architecture & Building Press, Beijing,
China.
Ling L (2016). Failure mode under strong earthquake and fragility analysis of typical RC frame structures on
slope, Ph.D. Thesis, School of Civil Engineering, Chongqing University, Chongqing, China.
Li S, Xie LL (2007). Progress and trend on near-field problems in civil engineering. Acta Seismologica Sinica,
20(1), 105-114.
Pan Y, Wang ZK, Shi SJ, et al. (2017) Investigation and analysis on seismic damage of residential buildings
along highway from Kathmandu to Zhangmu in Ms 8.1 Gorkha earthquake. Journal of Hunan University
(Natural Science), 44(3): 35-44.
Qu Z, Yang YQ (2015). Seismic damages to owner-built dwellings in the 2015 earthquake sequence in Nepal.
Earthquake Engineering and Engineering Dynamics, 35(04): 51-59.
Sharma M L, Sinvhal A, Singh Y, et al. (2013) Damage survey report for Sikkim earthquake of 18 September
2011. Seismological Research Letters, 84(1): 49-56.
Vamvatsikos D, Cornell CA (2002). Incremental dynamic analysis. Earthquake Engineering & Structural
Dynamics, 31(3): 491-514.
Wang LP, Li YM, Zheng N, et al. (2009) Seismic damage investigation on typical slope building in Wenchuan
earthquake. Journal of Xi'an University of Architecture & Technology (Natural Science Edition), 41(06): 822826.
Welsh-Huggins S J, Rodgers J, Holmes W, et al. (2017) Seismic vulnerability of reinforced concrete hillside
buildings in Northeast India, 16th World Conference on Earthquake, Santiago, Chile.
Wu YT, Lin XB, Li YM, et al. (2014) Seismic collapse-resistant capacity of moment frames supported by
stepped foundation in mountainous city. Journal of Building Structures, 2014, 35(10): 82-89.
Xu G, Li AQ, Chen SF (2017). Seismic vulnerability analysis of moment frames supported by stepped
foundation. Journal of Disaster Prevention and Mitigation Engineering, 37(03): 341-347.
Yang BT (2014). Quasi-static experimental study on seismic performance of typical mountain cliff-structure,
M.S. Thesis, School of Civil Engineering, Chongqing University, Chongqing, China.
10
View publication stats