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Effects of frequency contents of aftershock ground motions on reinforced concrete (RC) bridge columns
Soil Dynamics and Earthquake Engineering 97 (2017) 48–59
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Effects of frequency contents of aftershock ground motions on reinforced concrete (RC) bridge columns Moochul Shina, Byungmin Kimb,
MARK
⁎
a
Department of Civil and Environmental Engineering, Western New England University, 1215 Wilbraham Rd.,Springfield, MA 01119, USA School of Urban and Environmental Engineering, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Eonyang-eup, Ulju-gun, Ulsan 44919, Korea b
A R T I C L E I N F O
A BS T RAC T
Keywords: Aftershock Bridge RC Column Time history analysis Nonlinear analysis Spectral match
This study focuses on exploring effects of frequency contents of aftershock ground motions on seismic responses of reinforced concrete (RC) bridge columns. It has been well recognized that RC columns damaged by a sizeable main shock event become more vulnerable to following aftershocks. Therefore, it is essential to use proper main shock-aftershock sequential ground motions in seismic analyses to ensure the safety and integrity of infrastructure. Using frequency –invariant scaling factors, conventional methods were developed in the past. These methods combine sequential ground motions when performing a time history nonlinear analysis. However, these conventional methods neglect frequency contents of aftershock ground motions, which are usually different from those of main shock ground motions. This research demonstrates the importance of properly representing aftershock ground motions in estimating seismic responses of RC columns, and presents the differences in frequency contents between aftershock ground motions and the corresponding main shock ground motions. Time history seismic analyses using a finite element analysis program OpenSees are carried out. First, main shock motions recorded during the 1994 Northridge, California, the United States of America, the 1997 Umbria-Mache, Italy and the 1999 ChiChi, Taiwan earthquakes are used in this study. Then, the corresponding aftershock motions are selected or obtained: (1) from recordings during the seismic events, (2) by scaling main shock (which represents a traditional method), or (3) by spectrally matching main shock motions to the aftershock motions. The peak displacements and residual displacements of the RC columns using the spectrally matched motions are closer to those results using real aftershock motion records, as opposed to using the scaled motions. This demonstrates that the frequency contents of aftershock ground motions have significant impacts on the seismic responses of RC columns.
1. Introduction Aftershock ground motions can cause substantial harm to already damaged structures by a main shock [e.g, 1–4]. When the Christchurch earthquake in New Zealand occurred in 2011, the aftershocks caused severe damages in the area structurally and economically [4,5]. In order to ensure safety and integrity of infrastructure, precisely characterizing and obtaining sequential ground motions (i.e. main shockaftershocks) is of great concern in the earthquake engineering field. However, there have been only a few limited approaches to estimate aftershock ground motions for main shock-aftershock sequential analyses of structures. First approach is to use sequential ground motions recorded at same stations. Some studies have tried to explore the influence of the aftershocks on seismic responses of structures or
⁎
structural components such as buildings, dam, frames, etc. using sequential ground motions [6–11]. Ruiz-García [6] conducted numerical analyses on structures using recorded main shock and aftershock motions in Mexico, and reported that the structural responses would change due to the different predominant periods in aftershock ground motions. A study by Hatzigeorgiou and Liolios [7] used sequential seismic ground motions recorded in the U.S. to examine the seismic performances of reinforced concrete (RC) frame structures. However, actual aftershock records are not always available for use, especially for the forward prediction. Second approach to acquire aftershock ground motions is to scale main shock ground motions using frequencyinvariant scaling factors [12,13]. Some researchers generated sequential ground motions by randomly selecting them among a set of traditional main shock records and scaling them up/down for their
Corresponding author. E-mail address: [email protected] (B. Kim).
http://dx.doi.org/10.1016/j.soildyn.2017.02.012 Received 15 April 2016; Received in revised form 25 February 2017; Accepted 26 February 2017 0267-7261/ © 2017 Elsevier Ltd. All rights reserved.
Soil Dynamics and Earthquake Engineering 97 (2017) 48–59
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Fig. 1. Schematics of the tested columns: (a) Kawashima et al. [22], (b) Lehman and Moehle [23], (c) Chai et al. [24], and (d) schematic of the numerical column model of Kawashima et al.’s column and (e) fiber section of the numerical column models.
analyses. [7,13,14]. Researchers are aware of the limitations of these conventional approaches using main shocks to obtain aftershocks for seismic analyses, since the frequency contents of aftershock ground motions are usually different from those of main shock ground motions. Conte 1992 [15] and Conte and Peng, 1997 [16] demonstrated that the nonstationary frequency contents of earthquake motions could make significant impacts on responses of inelastic structures using a time-varying stochastic earthquake model. A group of researchers studied the effects of different characteristics earthquake ground motions, which inherently include different waves, on steel frame (bi-linear) structures [17]. In their studies, they took into accounts the nonstationary nature of the frequencies of different seismic waves. Then, Moustafa and Takewaki [18,19] continually investigated structural responses of inelastic structures when they are subjected to random sequential motions using a simple stochastic model for the repeated motions, and the characteristics of sequential ground motions. It is well known that long period components of the ground motions from smaller magnitude earthquakes are generally smaller than those from larger earthquakes. Therefore, the ground motions from the aftershocks (whose magnitudes are usually smaller than main shocks)
Table 1 The geometrical and mechanical properties of the tested columns. Kawashima et al.
Lehman and Moehle
Chai et al.
Diameter of the cross section (mm)
400
609.6
609.6
Effective height (mm) Slenderness ratio Vertical force (kN)
1350
2438.4
3657.6
3.4: 1 185
4:1 653
6:1 1778
Yielding strength of longitudinal reinforcement (MPa)
374
483
315
Yielding strength of transverse reinforcement (MPa)
363
666
352
Compressive strength of concrete (MPa)
30
30
33
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Fig. 2. Comparison of the force-displacement relationships of: (a.1) Kawashima et al.; (b) Lehman and Moehle; (c) Chai et al.; and (a.2) the strain of one of the longitudinal reinforcement of Kawashima et al. Table 2 Selected sequential main shock-aftershock pairs with record sequence numbers (RSN) of the NGA-West2 database. Earthquake Name
Main shock Magnitude
Main shock RSN
Aftershock Magnitude
Aftershock RSN
Station Name
1994 1994 1994 1994 1994 1994 1997 1997 1997 1997 1999 1999 1999 1999 1999 1999
6.7 6.7 6.7 6.7 6.7 6.7 6.0 6.0 6.0 6.0 7.6 7.6 7.6 7.6 7.6 7.6
1004 1039 1044 1052 1085 1086 4349 4349 4345 4352 1507 1512 1512 1513 1513 1549
5.3 6.0 5.2 5.2 5.3 5.3 5.5 5.6 5.5 5.5 6.2 6.2 6.3 5.9 6.3 6.2
3771 1681 1670 1671 1737 3767 4364 4385 4362 4367 2622 2628 3473 2391 3474 2658
LA - Sepulveda VA Hospital Moorpark - Fire Sta Newhall - Fire Sta Pacoima Kagel Canyon Sylmar - Converter Sta East Sylmar - Olive View Med FF Colfiorito Colfiorito Assisi-Stallone Nocera Umbra TCU071 TCU078 TCU078 TCU079 TCU079 TCU129
Northridge Northridge Northridge Northridge Northridge Northridge Umbria Marche, Umbria Marche, Umbria Marche, Umbria Marche, Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan
Italy Italy Italy Italy
bridge columns under main shock-aftershock sequential loading conditions. In addition, the study investigates the feasibility of the use of main shock ground motions to generate subsequent motions by spectrally matching the frequency contents of main shocks to those of aftershock motions for sequential seismic analyses. Main shock and aftershock earthquake ground motion pairs recorded during the 1994 Northridge, California, the United States of America, the 1997 UmbriaMache, Italy and the 1999 Chi-Chi, Taiwan earthquakes are selected for the seismic structural analyses using the program OpenSees [21]. To
are weak at long periods, which results in difference in frequency contents in ground motions for main shocks and aftershocks. Given the same magnitudes between main shocks and aftershocks, Atkinson [20] reported that the short-period spectral accelerations from aftershock earthquakes are smaller than those from main shocks using the Eastern North America earthquake records. A RC column is one of the important components of a lifeline structure. This study focuses on the effects of frequency contents of aftershock motions on seismic responses of reinforced concrete (RC)
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summarized in Table 1. More details of the tested columns can be found in their studies [22–24]. For developing numerical columns, total four nonlinear displacement-based beam-column elements were used, while nonlinear constitutive material models were assigned to each fiber: core concrete (Concrete01 or Concrete 04), cover concrete (Concrete01 or Concrete04) and longitudinal reinforcement (Steel 02), respectively. Mander et al.’s concrete model [25] was used for the constitutive model of concrete for the columns tested by Lehman and Moehle and Chai et al., while the concrete model developed by Kawashima et al. was used to describe the constitutive behavior of concrete of Kawashima et al.’s column. Five elements and six nodes were used to build the corresponding numerical column models. Four of them were inelastic beam-column elements while an elastic beamcolumn element was selected for the top portion of the columns. Fig. 1.d shows the schematic of the numerical column model of Kawashima et al.’s column as an example. A lumped mass was assigned to the top node of each column, which represents the weight of a superstructure. More details of one numerical column model can be found in a study by Andrawes et al. [26]. The numerical column models were subjected to the same cyclic loading protocols that were adopted during each experimental test. Fig. 2 compares the force-displacement relationships between the experiment and the numerical analysis of each column. Especially local strain results were compared with the strain values obtained from one strain gage placed on the longitudinal reinforcement at the height of 525 mm from the top of the footing for Kawashima et al.’s column (see Fig. 1(a)). The results of the numerical columns agreed well with the experimental results of all three numerical columns including the strain from the Kawashima et al.’s column. The maximum lateral force of the numerical models was 104.0%, 104.2% and 100.6% to that of the tested Kawashima et al., Lehman and Moehle, and Chai et al.’s columns, respectively. The George E. Brown, Jr. Network for Earthquake Engineering Simulation's data bases available the NEEShub [27] is used to collect the digitalized test data for the Lehman and Moehle and Cahit et al.'s columns.
Fig. 3. Ratios of spectral accelerations of aftershocks (SaAS) to those of main shocks (SaMS) after normalizing them by PGA values. The blue line represents a mean ratio.
generate sequential motions, structural responses are evaluated using three different methods: 1) using the synthetic aftershock ground motions obtained by repeating/scaling main shock motions (a traditional method), 2) using spectrally matching main shock motions, and 3) by using actual aftershock ground motion recordings. Those responses are compared to one another to investigate the frequency effects of sequential motions on RC structures. 2. Modeling and validation 2.1. Modeling The finite element program OpenSees was used to develop numerical models of three reinforced concrete (RC) bridge columns: (1) a RC column performed by Kawashima et al. [22], (2) a RC column by Lehman and Moehle [23], and (3) a RC column tested by Chai et al. [24]. A quasi-static cyclic testing was carried out for each column. Fig. 1 shows schematics of the tested bridge columns. The diameters of the tested circular columns by Kawashima et al., Lehman and Moehle and Chai et al. were 400 mm, 609.6 mm and 609.6 mm, respectively. The effective heights of each column where the lateral cyclic force was applied were 1350 mm, 2438.4 mm and 3657.6 mm, respectively. Approximate 5~18% of the RC crosssections were applied as vertical forces. Since applying a high vertical force is practically challenging, this range was considered from tests conducted in the past. The geometrical and mechanical properties of each tested column are
3. Selected main shock-aftershock ground motions A number of ground motions recorded during the M6.7 1994 Northridge, California, the United States of America, the M6.0 1997 Umbria-Mache, Italy, and the M7.6 1999 Chi-Chi, Taiwan earthquakes were selected from the Next Generation Attenuation relationships for Western U.S. (NGA-West2) database [28]. These earthquakes have abundant recordings of aftershock earthquakes. We chose aftershock
Fig. 4. (a) Comparisons of predominant periods (Td) of the selected main shock (MS) and aftershock (AS) ground motions, and (b) mean periods (Tm) of MS and AS ground motions.
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Fig. 5. (a) Main shock and aftershock spectral accelerations, and (b) acceleration time series of the M6.7 Northridge, California, earthquake recorded at the LA-Sepulveda VA Hospital station, as well as those of the main shock motion spectral matched to the aftershock motion.
Fig. 6. Seismic responses of the RC column (Kawashima et al.) under the M6.7 1994 Northridge main shock and aftershock ground motions recorded at the LA – Sepulveda VA Hospital station: (a) time histories of the top displacement, (b) lateral force and displacement relationships, and (c) time histories of a strain of a longitudinal rebar.
and record sequence number (RSN) of the selected main shockaftershock pairs. Fig. 3 shows ratios of spectral accelerations (Sa) of the selected
ground motions recorded at the stations at which the selected main shock motions were recorded. Total 16 main shock-aftershock ground motion sets were selected herein. Table 2 summarizes the magnitudes 52
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Table 3 The maximum displacements during the aftershock ground motions for Kawashima et al.’s column. 1 g of PGA
1 g of Sa at T1
Sequential motion sets (MS. RSN-AS. RSN)
Td-MS (sec)
Td-AS (sec)
Max.disp MS-AS (mm)
Max.disp MS-MS (mm)
Max.disp MS-SM (mm)
Max.disp MS-AS (mm)
Max.disp MS-MS (mm)
Max.disp MS-SM (mm)
1004–3771 1039–1681 1044–1670 1052–1671 1085–1737 1086–3767 4349–4364 4349–4385 4345–4362 4352–4367 1507–2622 1512–2628 1512–3743 1513–2391 1513–3474 1549–2658
0.28 0.26 0.32 0.5 0.38 0.36 0.08 0.08 0.32 0.16 0.26 0.16 0.16 0.2 0.2 0.24
0.22 0.3 0.38 0.38 0.12 0.28 0.24 0.32 0.28 0.18 0.14 0.3 0.16 0.2 0.26 0.18
56.80 100.53 69.44 101.84 70.61 54.11 145.87 127.73 61.82 32.12 18.59 138.07 177.42 54.60 88.80 44.06
80.82 68.19 101.66 119.48 105.77 139.68 94.01 94.01 54.05 55.89 71.19 111.10 111.11 192.98 192.98 71.45
52.41 100.15 67.82 113.46 67.76 74.46 130.60 95.10 43.51 28.36 17.56 113.21 128.53 70.93 107.18 43.29
16.95 65.06 44.12 72.15 23.12 33.17 18.84 19.57 23.47 9.74 13.38 18.07 24.68 25.16 37.51 25.31
29.30 30.64 37.32 132.36 48.50 125.70 10.89 10.89 22.69 11.84 20.18 16.79 16.79 58.39 58.39 44.12
16.97 54.44 42.54 83.86 29.17 41.45 20.63 16.62 16.95 8.33 10.81 16.07 15.55 15.17 34.23 29.19
Table 4 The 2nd Residual displacements during the aftershock ground motions for Kawashima et al.’s column. 1 g of PGA Sequential motion sets (MS. RSN-AS. RSN)
Tm-MS
Tm-AS
(sec)
1004–3771 1039–1681 1044–1670 1052–1671 1085–1737 1086–3767 4349–4364 4349–4385 4345–4362 4352–4367 1507–2622 1512–2628 1512–3743 1513–2391 1513–3474 1549–2658
0.46 0.47 0.53 0.66 0.76 0.76 0.54 0.54 0.34 0.24 0.33 0.43 0.43 0.49 0.49 0.35
1 g of Sa at T1
(sec)
2nd Residual disp. MS-AS (mm)
2nd Residual disp. MS-MS (mm)
2nd Residual disp. MS-SM (mm)
2nd Residual disp. MS-AS (mm)
2nd Residual disp. MS-MS (mm)
2nd Residual disp. MS-SM (mm)
0.28 0.55 0.44 0.53 0.34 0.31 0.60 0.64 0.32 0.19 0.20 0.44 0.56 0.28 0.38 0.39
8.80 15.95 −5.88 12.25 18.92 11.91 0.09 1.94 12.06 8.25 −0.93 4.71 14.82 24.50 22.48 11.52
13.69 13.03 1.13 4.67 1.60 −3.38 7.06 7.06 8.65 1.35 1.74 3.30 3.30 36.96 36.96 13.46
10.57 18.10 1.77 3.23 10.91 15.56 −0.79 1.21 4.65 7.87 −1.56 0.38 1.52 33.32 34.84 12.06
−1.51 9.61 4.03 17.93 6.61 25.99 0.18 −1.39 −1.57 0.15 −2.21 −0.15 1.10 −5.75 −5.83 3.05
0.49 2.55 4.51 14.63 11.40 16.08 −0.44 −0.44 −1.32 0.17 −2.45 −0.33 −0.33 −8.76 −8.76 7.78
−1.28 9.46 4.74 14.26 8.62 22.46 −1.68 −0.11 −1.31 0.15 −2.44 −0.44 −0.46 −6.60 −5.65 4.99
Fig. 7. Time history displacements of the RC column (Kawashima et al.) under: (a) the 1997 Umbria-Marche earthquake motions measured at the Nocera Umbra station, and (b) the 1999 Chichi earthquake motions measured at the TCU 129 station.
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Fig. 8. Time history displacements of the RC column under: (a) the 1994 Northridge motions at the LA–Sepulveda VA Hospital station, (b) 1997 Umbria-Marche motions at the Nocera Umbra station, and (c) 1999 Chichi motions at the TCU129 station.
column, (2) Lehman and Moehle's column and (3) Chai et al.’s column. The numerical columns were subjected to three different sequential ground motions: (1) actual main shock and after shock ground motions recorded at same stations (MS-AS), (2) repeating/scaling main shocks to represent aftershocks (MS-MS), or (3) spectrally matching main shock motions to the aftershock motions (MS-SM). The maximum displacement and the relative residual displacement (i.e. the final (2nd) residual displacement –1st residual displacement) during these three sequential ground motions were considered as seismic responses. The main shock ground motions were spectrally matched to the aftershock ground motions by using a program SeismoMatch v2.1.2 [30] over a period range of 0.02 s through 2.00 s Fig. 5 shows main shock and aftershock motions of the M6.7 Northridge, California, earthquake recorded at the LA-Sepulveda VA Hospital station, as well as those of the main shock motion spectral matched to the aftershock motion. The spectral shape of the aftershock motion is quite different from that of the main shock motion as shown in Fig. 5(a). The spectrally matched main shock motion is similar to the aftershock motion over an entire period range. The acceleration time series of the main shock motion spectrally matched to the aftershock motion still resemble those of the main shock motion as shown in Fig. 5(b).
aftershocks to those of the corresponding main shocks. The spectral accelerations were normalized by peak ground accelerations (PGA) to evaluate the variation of spectral accelerations at different periods. It is worth noting that Sa of aftershocks (SaAS) is generally smaller than those of main shocks (SaMS) at periods longer than approximately 2.0 s Fig. 4 shows predominant periods (Td) and mean periods (Tm) of the selected main shock and aftershock ground motions. The predominant period is the period at which the maximum spectral acceleration occurs in an acceleration response spectrum calculated at 5% damping. Rathje et al. [29] proposed the mean period which can be estimated by:
Tm =
∑ Ci2 / fi ∑ Ci2
,
(1)
where Ci is the Fourier amplitude, and fi represents the discrete Fourier transform frequencies between 0.25 and 20 Hz. The predominant periods for main shock and aftershock motions are different, but do not show a clear trend (Fig. 4a). However, 10 out of 16 aftershock motions have shorter mean periods than those for main shock motions (Fig. 4b), which is consistent with the observation in Fig. 3. The average mean period of the aftershock motions is approximately 0.40 s, while that of the main shock motions is about 0.49 s.
4.1. Kawashima et al. Column 4.1.1. Scaled to 1 g of PGA The main period (T1) of Kawashima et al.'s column was found to be 0.18 s, and the 10% of the compressive strength of the cross section was assigned to the top node representing the weight of the super-
4. Main shock-aftershock sequential analysis A series of nonlinear time history analyses were conducted on the three validated numerical RC column models: (1) Kawashima et al.’s 54
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Fig. 9. Lateral force-displacement relationships of the RC column (Kawashima et al.) under: (a) the 1994 Northridge motions at the LA – Sepulveda VA Hospital station, (b) 1997 Umbria-Marche motions at the Nocera Umbra station, and (c) 1999 Chichi motions at the TCU129 station.
than using MS-MS. Similar observations are found in the lateral force and displacement relationships (Fig. 6b) and time histories of a strain of a longitudinal rebar (Fig. 6c). The detailed responses of the simulations were summarized in Tables 3 and 4. These results clearly demonstrate the importance of properly characterizing the frequency contents of aftershock ground motions for main shock-aftershock sequential analyses. Fig. 7(a) and (b) show the time history displacements of the RC column under two sequential ground motions sets; one is from the 1996 Umbria-Marche, Italy earthquake and another one is from the 1999 Chi-Chi, Taiwan earthquake. The seismic responses of the RC column are different between MS-AS and MS-MS analyses, while the responses under the spectrally matched aftershocks (MS-SM) are closer to those under the actual ground motions records (MS-AS). All the simulation results based on 16 different main shock-aftershock sequential ground motion sets show similar trends. More details are discussed in the next section.
structure. All of the selected main shock and aftershock ground motions were scaled to have the peak ground acceleration (PGA) of 1g. Fig. 6 shows seismic responses of the RC column model subjected to three sets of main shock-aftershock ground motions: MS-AS; MSMS; and MS-SM for the 1944 Northridge earthquake. The RSN for main shock and aftershock ground motions are 1004 and 3771, respectively. The main shock ground motions are identical for the three sets of the sequential ground motions, and followed by three different aftershock ground motions. Fig. 6 clearly shows the differences between the seismic responses of the RC column when it was subjected to the actual sequential ground motions (MS-AS) and the main shock ground motion followed by the synthetic aftershock ground motion generated by repeating the main shock motion (MS-MS). The seismic responses of the column are overestimated when it was subjected to a sequential ground motion set using a traditional method as compared to that under the actual main shock-aftershock ground motion. This was due to the fact that the RC column's main period changed when subject to a main shock ground motion and the frequency contents of aftershock ground motions affected the response of the RC column. When the main shock motion is spectrally matched to the aftershock motion, the frequency contents of spectrally matched motion become similar to those of the aftershock motion. The 2nd residual displacement under MS-AS is shifted toward the original position while the 2nd residual displacement under MS-MS is shifted to the opposite direction. The maximum and final residual displacements recorded under MS-SM are closer to those using MS-AS rather
4.1.2. Scaled to the spectral acceleration of 1 g The ground motions were scaled to match the spectral acceleration of 1g at the main period of the original column (T1=0.18 s) in order to further examine the effects of the frequency contents on the seismic responses of the RC column. Fig. 8 shows the time history displacements of the RC column under three sets of earthquake sequential ground motions: the 1994 Northridge, USA; 1997 Umbria-Marche, Italy; and 1999 Chi-Chi, Taiwan earthquakes. All three cases show the 55
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damaged by the main shocks. When the damage is minor, the differences among MS-AS, MS-MS and MS-SM responses are minimal, since the structure still behaves elastically, and the change of the main period of the structure is insignificant. Fig. 8(b) shows a case of the RC column with little damage under the main shock. The residual displacement after the main shock, for instance, is 0.17 mm, while those due to the 1994 Northridge main shock motion at the LA – Sepulveda VA Hospital station and the 1999 Chi-Chi main shock motion at the TCU129 station are −1.29 mm 5.20 mm, respectively (see Fig. 8(a) and (c)). Fig. 9 shows the corresponding force-displacement relationships of the RC column under the same sequential ground motion sets used in Fig. 8. The differences due to three different aftershock mechanisms are minimal when the column is less damaged (see Fig. 9(b)), as compared to Fig. 9(a) and (c). 4.1.3. Summary of Kawashima et al.’s column In order to find trends in the seismic responses of Kawashima et al.’s column based on three different methods for representing aftershock ground motions, the maximum and 2nd residual displacements resulted from MS-AS, MS-MS, and MS-SM methods, and the predominant and mean periods (Td and Tm) of the corresponding ground motions are summarized in Tables 3 and 4. Fig. 10 shows that the maximum displacements during the aftershocks from the MS-MS method are much higher than those from the MS-AS and MS-SM methods, especially when the ratio of predominant periods of the main ⎛T ⎞ shock to aftershock motions ⎜ Td − AS ⎟ is less than 1.5 (Fig. 10(a)) and the ⎝ d − MS ⎠ ⎛T ⎞ ratio of mean periods ⎜ Tm − AS ⎟ is less than 0.9 (Fig. 10(b)). The average ⎝ m − MS ⎠ ratio of the maximum displacements due to MS-MS to MS-AS ( Max displ .MS − MS ) is found to be 153.08%. The ratios of maximum
Fig. 10. The ratio (%) of the absolute maximum displacements with respect to: (a) Td − AS /Td − MS , and (b)Tm − AS /Tm − MS .
Max displ .MS − AS
displacements from the MS-MS method to those from the MS-AS T T method tend to increase as Td − AS and m − AS decrease, which clearly d − MS
Tm − MS
indicates the effects of frequency contents in main shock and aftershock ground motions on structural responses. However, when the spectrally matched main shock ground motions are used for the aftershock ground motions (the MS-SM method), the maximum T displacement ratio does not vary with Td − AS and m − AS with approxiTd − MS
Tm − MS
mately 95.25% of an average ratio. This is because the frequency contents of the main shock ground motions are matched with those of actual aftershock ground motions during the spectral matching procedure. The relative residual displacements during the aftershock ground motions were investigated as well. The ratios of the relative residual displacements from the MS-MS and MS-SM with respect to the MS-AS method are shown in Fig. 11. A 100% ratio means that relative residual displacements due to either MS-MS or MS-SM is identical to the relative residual displacements observed under the actual aftershocks records (MS-AS). The figure indicates the results using the spectralmatch method are closer to the 100% line as compared with the results using MS-MS. More than 50% of the results based on MS-MS exhibits negative ratios, which indicates that the residual displacements using MS-MS for the aftershocks are shifted to the opposite direction of the 2nd residual displacements overserved using MS-AS. When Td − AS and Td − MS
Fig. 11. The relative residual displacement ratio (%) during the aftershocks: (a) with respect to Td − AS /Td − MS , and (b)Td − AS /Td − MS .
Tm − AS Tm − MS
are greater than 1.5 and 0.9, respectively, the simulation results
are similar among the three analysis methods.
clear difference in the results when the RC column was subjected to the actual main shock-after shock recordings (MS-AS) and the synthesized main shock-aftershock ground motion using the traditional method by repeating the main shock (MS-MS). However, the results based on the spectrally matched ground motions (MS-SM) are closer to those based on the actual main shock-after shock sequential records. This phenomenon becomes more pronounced when the RC column got more
4.2. Lehman and Moehle's column and Chai et al.’s column The main periods (T1) of Lehman and Moehle's column and Chair et al.’s column were found to be 0.25 s and 0.74 s, respectively. Each column was subjected to the six sequential ground motion sets for the 1994 Northridge earthquake (see Table 2) and each ground motion was scaled to 1 g of PGA. Fig. 12 shows the time history of the displacement 56
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Fig. 12. Time history displacements of the RC columns under the 1994 Northridge motions at the LA – Sepulveda VA Hospital station: (a) Lehman and Moehle's column and (b) Chai et al.’s column,.
Fig. 13. The ratio (%) of the absolute maximum displacements with respect to Tm − AS /Tm − MS : (a) Lehman and Moehle's column and (b) Chai et al.’s column.
Fig. 14. The relative residual displacement ratio (%) during the aftershocks with respect to Td − AS /Td − MS : (a) Lehman and Moehle's column and (b) Chai et al.’s column.
of each column under the main shock-aftershock ground motion set recorded at the LA – Sepulveda VA Hospital station. The maximum displacements during the aftershocks using MS-AS, MS-MS and MSSM were found to be: (1) 54.21, 88.81 and 50.68 mm, respectively for Lehman and Moehle's column, and (2) 40.63, 139.11, and 85.21 mm, for Chai et al.’s column. The ratios (%) of the absolute maximum displacements and the relative residual displacements of each column with respect to Tm − AS / Tm − MS are shown in Fig. 13 and Fig. 14, respectively. As discussed previously, using the ground motions based on the MS-MS method, the maximum displacements of the columns are overestimated as opposed to those using the actual main shock-aftershock records (MS-AS). The responses using the spectrally matched motions (MS-SM) are close to MS-AS. When investigating the relative residual displacements during the aftershocks, the responses obtained using MS-MS tend to shift the opposite direction to those using MS-AS, while MS-SM yields much closer responses to MS-AS (see Fig. 14).
5. Discussion The effects of the frequency contents of sequential ground motions on the responses of the RC columns with respect to the main period (T1) of columns were investigated. The main period of Kawashima et al.'s, Lehman and Moehle's and Chai et al.’s columns is 0.18, 0.25 and 0.78 s, respectively (see Fig. 15). As shown in the figure, the average maximum displacement ratio under all sequential ground motion sets of the 1994 Northridge earthquake based on MS-MS was higher than that based on MS-SM. Both ratios increase as T1 increases. However, the average maximum displacement ratio of MS-SM/MS-AS is close to 100% while that of MS-MS/MS-AS even reaches to approximately 350%. Using MS-MS estimated residual displacements in the opposite direction compared to the residual displacements using MS-AS when T1 is 0.18 s and 0.25 s (negative sign in Fig. 15b). However, when T1 is 0.78 s, the residual displacements for MS-MS become in the same 57
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(MS-AS); 2) repeating/scaling main shock ground motions with frequency-invariant scaling factors (MS-MS); and 3) spectrally matching main shock ground motions to corresponding aftershock ground motions (MS-SM). Nonlinear time history analyses were conducted on three RC columns using these actual and synthesized sequential ground motions sets. The results clearly demonstrated that the frequency contents of the ground motions played significant role on the responses of the RC columns. When using the traditional method (MS-MS), the maximum displacements tend to be overestimated as compared to those due to the actual recorded sequential ground motions (MS-AS). In addition, the residual displacements using MS-MS were estimated to be in the opposite direction to those using MS-AS when the columns’ main period (T1) is shorter than mean periods of main shock motions (Tm). These differences became pronounced when the predominant and mean period of the aftershock ground motions are less than those of the main shock ground motions. When main shock ground motions spectrally matched to aftershock motions were used (MS-SM), the responses of the RC column were much closer to those using actual ground motion records (MS-AS) even though the time series of spectrally match motions still resemble those of main shock motions. Therefore, the period-dependent scaling is recommended to obtain aftershock motions for main shock-aftershock sequential analyses, especially when shorter predominant and mean periods are expected for aftershock ground motions compared to those for main shock T T motions (specifically when Td − AS <1.5 or Tm − AS <1.0 ). d − MS
m − MS
References Fig. 15. Average maximum displacement ratio (a) and relative residual displacement ratio (b) with respect to the main period (T1) of the RC columns.
[1] Elnashai AS, Gencturk B, Kwon O-S, AlQadi IL, Hashash Y, Rosesler JR, Kim SJ, Jeon S-H, Dukes J, Valdivia A. The Maule (Chile) Earthquake of February 27, 2010 - Consequence Assessment and Case Studies, MAE Center Report No. 10-04, Urbana, IL, 2010. [2] U.S. Geological Survey (USGS), Magnitude 8.8—offshore Bio-bio, Chile, in, 2010. [3] U.S. Geological Survey (USGS), Magnitude 9.0—near the east coast of Honshu, Japan, in, h 2011. [4] Kam WY, Pampanin S. The seismic performance of RC buildings in the 22 February 2011 Christchurch earthquake. Struct Concr 2011;12:223–33. [5] Chouw N, Hao H. Pounding damage to buildings and bridges in the 22 February 2011 Christchurch Earthquake. Int J Prot Struct 2012;3:123–40. [6] Ruiz-García J. Mainshock-aftershock ground motion features and their influence in building's seismic response. J Earthq Eng 2012;16:719–37. [7] Hatzigeorgiou GD, Liolios AA. Nonlinear behaviour of RC frames under repeated strong ground motions. Soil Dyn Earthq Eng 2010;30:1010–25. [8] Zhang S, Wang G, Sa W. Damage evaluation of concrete gravity dams under mainshock–aftershock seismic sequences. Soil Dyn Earthq Eng 2013;50:16–27. [9] Faisal A, Majid TA, Hatzigeorgiou GD. Investigation of story ductility demands of inelastic concrete frames subjected to repeated earthquakes. Soil Dyn Earthq Eng 2013;44:42–53. [10] Hatzivassiliou M, Hatzigeorgiou GD. Seismic sequence effects on three-dimensional reinforced concrete buildings. Soil Dyn Earthq Eng 2015;72:77–88. [11] Takewaki I, Murakami S, Fujita K, Yoshitomi S, Tsuji M. The 2011 off the Pacific coast of Tohoku earthquake and response of high-rise buildings under long-period ground motions. Soil Dyn Earthq Eng 2011;31:1511–28. [12] Fragiacomo M, Amadio C, Macorini L. Seismic response of steel frames under repeated earthquake ground motions. Eng Struct 2004;26:2021–35. [13] Li Q, Ellingwood BR. Performance evaluation and damage assessment of steel frame buildings under main shock–aftershock earthquake sequences. Earthq Eng Struct Dyn 2007;36:405–27. [14] Luco N, Bazzurro P, Cornell A. Dynamic versus static computation of the residual capacity of a mainshock-damged building to withstand an aftershock, in: Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada; 2004. [15] Conte JP. Effects of earthquake frequency nonstationarity on inelastic structural response. In: Proceedings of the 10th World Conference on Earthq. Eng., Rotterdam, A.A. Balkema; 1992. [16] Conte JP, Peng BF. Fully nonstationary analytical earthquake ground motion model. J Eng Mech 1997;123:15–24. [17] Moustafa A, Ueno K, Takewaki I. Critical earthquake loads for SDOF inelastic structures considering evolution of seismic waves. Earthq Struct 2010;1:147–62. [18] Moustafa A, Takewaki I. Response of nonlinear single-degree-of-freedom structures to random acceleration sequences. Eng Struct 2011;33:1251–8. [19] Moustafa A, Takewaki I. Characterization of earthquake ground motion of multiple sequences. Earthq Struct 2012;3:629–47. [20] Atkinson GM. Earthquake source spectra in eastern North America. Bull Seismol Soc Am 1993;83:1778–98. [21] Mazzoni S, McKenna F, Scott MH, Fenves GL, et al. OpenSees command language
direction as those obtained from MS-AS. This difference might attribute to differences in T1 relative to the range of mean periods (Tm) of main shock motions (0.46 – 0.77 s). The residual displacements using MS-SM are in the same direction with those using MS-AS for all three columns. These observations of the results demonstrate the importance of properly characterizing the frequency contents of aftershock ground motion when conducting structural analyses and analyzing the responses of structures under main shock-aftershock sequential loadings. When ground motions are not available for the forward prediction, main shock ground motions can be obtained based on spectral accelerations estimated by many existing ground motion prediction equations (GMPEs) developed by many researchers [31–35] with certain conditions including: source parameters (e.g., fault mechanism and earthquake magnitude); path parameters (e.g., distance from the source); and site condition parameters (e.g., shear-wave velocity profile). Recently, Kim and Shin [36] proposed a model to predict period-dependent scaling factors for aftershock ground motions. This method can be used to properly obtain aftershock ground motions for the forward prediction. 6. Conclusions To obtain realistic sequential earthquake ground motions is of great concern in the earthquake engineering practice, in order to ensure the integrity of infrastructure and accurately estimate structural responses. Up to date, researchers have synthesized aftershock motions based on main shock ground motions using frequency-invariant scaling factors or randomly choosing different main shocks. However, recent studies have demonstrated that aftershock ground motions should be differentiated from main shock ground motions due to their different mechanisms. This research focused on investigating the effects of the frequency contents of aftershock ground motions on responses of RC columns. Three different methods were used to generate/obtain aftershock ground motions: 1) actual aftershock ground motion records 58
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earthquake ground motions. J Geotech Geoenviron Eng 1998;124:150–9. [30] Seimosft. SeismoMatch, V2.1.2, < 〈http://www.seismosoft.com/〉 > 2015. [31] Abrahamson NA, Silva WJ, Kamai R. Summary of the ASK14 ground motion relation for active crustal regions. Earthq Spectra 2014;30:1025–55. [32] Boore DM, Stewart JP, Seyhan E, Atkinson GA. NGA-West2 Equations for predicting response spectral accelerations for shallow crustal earthquakes, in: PEER Report No. 2013/05, Pacific Earthquake Engineering Research Center, Berkeley, CA, 2013:134. [33] Campbell KW, Bozorgnia Y. NGA-West2 ground motion model for the average horizontal components of PGA, PGV, and 5% damped linear acceleration response spectra. Earthq Spectra 2014;30:1087–115. [34] Chiou BS-J, Youngs RR. Update of the Chiou and Youngs NGA model for the average horizontal component of peak ground motion and response spectra. Earthq Spectra 2014;30:1117–53. [35] Idriss IM. An NGA-West2 empirical model for estimating the horizontal spectral values generated by shallow crustal earthquakes. Earthq Spectra 2014;30:1155–77. [36] Kim B, Shin M. A model for estimating horizontal aftershock ground motions for active crustal regions. Soil Dyn Earthq Eng 2017;92:165–75.
manual. Open Syst Earthqauke Eng Simluations 2009. [22] Kawashima K, Hosotani M, Yondea K. Carbon fiber sheet retrofit of reinforced concrete bridge piers toward new generation seismic design methodology of bridges. Tokyo, Japan: Tokyo Institute of Technology; 2001. [23] Lehman DE, Moehle JP. Seismic performance of well-confined concrete bridge columns. Pacific Earthquake Engineering Research Center; 2000. p. 295. [24] Chai YH, Priestley MJN, Seible F. Seismic retrofit of circular bridge columns for enhanced flexural performance. Acids Struct J 1991;88:572–84. [25] Mander JB, Priestley MJN, Park R. Theoretical stress‐strain model for confined concrete. J Struct Eng 1988;114:1804–26. [26] Andrawes B, Shin M, Wierschem N. Active confinement of reinforced concrete bridge columns using shape memory alloys. J Bridge Eng ASCE 2010;15:81–9. [27] GeorgeE Brown, Jr., Network for Earthquake Engineering Simulation, NEEShub, 〈https://nees.org/resources/databases〉 [accessed 16.04.05]; 2009. [28] Ancheta TD, Darragh RB, Stewart JP, Seyhan E, Silva WJ, Chiou BS-J, Wooddell KE, Graves RW, Kottke AR, Boore DM, Kishida T, Donahue JL. NGA-West2 Database. Earthquake Spectra 2014;30:989–1005. [29] Rathje EM, Abrahamson NA, Bray JD. Simplified frequency content estimates of
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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Effects of frequency contents of aftershock ground motions on reinforced concrete (RC) bridge columns Moochul Shina, Byungmin Kimb,
MARK
⁎
a
Department of Civil and Environmental Engineering, Western New England University, 1215 Wilbraham Rd.,Springfield, MA 01119, USA School of Urban and Environmental Engineering, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Eonyang-eup, Ulju-gun, Ulsan 44919, Korea b
A R T I C L E I N F O
A BS T RAC T
Keywords: Aftershock Bridge RC Column Time history analysis Nonlinear analysis Spectral match
This study focuses on exploring effects of frequency contents of aftershock ground motions on seismic responses of reinforced concrete (RC) bridge columns. It has been well recognized that RC columns damaged by a sizeable main shock event become more vulnerable to following aftershocks. Therefore, it is essential to use proper main shock-aftershock sequential ground motions in seismic analyses to ensure the safety and integrity of infrastructure. Using frequency –invariant scaling factors, conventional methods were developed in the past. These methods combine sequential ground motions when performing a time history nonlinear analysis. However, these conventional methods neglect frequency contents of aftershock ground motions, which are usually different from those of main shock ground motions. This research demonstrates the importance of properly representing aftershock ground motions in estimating seismic responses of RC columns, and presents the differences in frequency contents between aftershock ground motions and the corresponding main shock ground motions. Time history seismic analyses using a finite element analysis program OpenSees are carried out. First, main shock motions recorded during the 1994 Northridge, California, the United States of America, the 1997 Umbria-Mache, Italy and the 1999 ChiChi, Taiwan earthquakes are used in this study. Then, the corresponding aftershock motions are selected or obtained: (1) from recordings during the seismic events, (2) by scaling main shock (which represents a traditional method), or (3) by spectrally matching main shock motions to the aftershock motions. The peak displacements and residual displacements of the RC columns using the spectrally matched motions are closer to those results using real aftershock motion records, as opposed to using the scaled motions. This demonstrates that the frequency contents of aftershock ground motions have significant impacts on the seismic responses of RC columns.
1. Introduction Aftershock ground motions can cause substantial harm to already damaged structures by a main shock [e.g, 1–4]. When the Christchurch earthquake in New Zealand occurred in 2011, the aftershocks caused severe damages in the area structurally and economically [4,5]. In order to ensure safety and integrity of infrastructure, precisely characterizing and obtaining sequential ground motions (i.e. main shockaftershocks) is of great concern in the earthquake engineering field. However, there have been only a few limited approaches to estimate aftershock ground motions for main shock-aftershock sequential analyses of structures. First approach is to use sequential ground motions recorded at same stations. Some studies have tried to explore the influence of the aftershocks on seismic responses of structures or
⁎
structural components such as buildings, dam, frames, etc. using sequential ground motions [6–11]. Ruiz-García [6] conducted numerical analyses on structures using recorded main shock and aftershock motions in Mexico, and reported that the structural responses would change due to the different predominant periods in aftershock ground motions. A study by Hatzigeorgiou and Liolios [7] used sequential seismic ground motions recorded in the U.S. to examine the seismic performances of reinforced concrete (RC) frame structures. However, actual aftershock records are not always available for use, especially for the forward prediction. Second approach to acquire aftershock ground motions is to scale main shock ground motions using frequencyinvariant scaling factors [12,13]. Some researchers generated sequential ground motions by randomly selecting them among a set of traditional main shock records and scaling them up/down for their
Corresponding author. E-mail address: [email protected] (B. Kim).
http://dx.doi.org/10.1016/j.soildyn.2017.02.012 Received 15 April 2016; Received in revised form 25 February 2017; Accepted 26 February 2017 0267-7261/ © 2017 Elsevier Ltd. All rights reserved.
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Fig. 1. Schematics of the tested columns: (a) Kawashima et al. [22], (b) Lehman and Moehle [23], (c) Chai et al. [24], and (d) schematic of the numerical column model of Kawashima et al.’s column and (e) fiber section of the numerical column models.
analyses. [7,13,14]. Researchers are aware of the limitations of these conventional approaches using main shocks to obtain aftershocks for seismic analyses, since the frequency contents of aftershock ground motions are usually different from those of main shock ground motions. Conte 1992 [15] and Conte and Peng, 1997 [16] demonstrated that the nonstationary frequency contents of earthquake motions could make significant impacts on responses of inelastic structures using a time-varying stochastic earthquake model. A group of researchers studied the effects of different characteristics earthquake ground motions, which inherently include different waves, on steel frame (bi-linear) structures [17]. In their studies, they took into accounts the nonstationary nature of the frequencies of different seismic waves. Then, Moustafa and Takewaki [18,19] continually investigated structural responses of inelastic structures when they are subjected to random sequential motions using a simple stochastic model for the repeated motions, and the characteristics of sequential ground motions. It is well known that long period components of the ground motions from smaller magnitude earthquakes are generally smaller than those from larger earthquakes. Therefore, the ground motions from the aftershocks (whose magnitudes are usually smaller than main shocks)
Table 1 The geometrical and mechanical properties of the tested columns. Kawashima et al.
Lehman and Moehle
Chai et al.
Diameter of the cross section (mm)
400
609.6
609.6
Effective height (mm) Slenderness ratio Vertical force (kN)
1350
2438.4
3657.6
3.4: 1 185
4:1 653
6:1 1778
Yielding strength of longitudinal reinforcement (MPa)
374
483
315
Yielding strength of transverse reinforcement (MPa)
363
666
352
Compressive strength of concrete (MPa)
30
30
33
49
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Fig. 2. Comparison of the force-displacement relationships of: (a.1) Kawashima et al.; (b) Lehman and Moehle; (c) Chai et al.; and (a.2) the strain of one of the longitudinal reinforcement of Kawashima et al. Table 2 Selected sequential main shock-aftershock pairs with record sequence numbers (RSN) of the NGA-West2 database. Earthquake Name
Main shock Magnitude
Main shock RSN
Aftershock Magnitude
Aftershock RSN
Station Name
1994 1994 1994 1994 1994 1994 1997 1997 1997 1997 1999 1999 1999 1999 1999 1999
6.7 6.7 6.7 6.7 6.7 6.7 6.0 6.0 6.0 6.0 7.6 7.6 7.6 7.6 7.6 7.6
1004 1039 1044 1052 1085 1086 4349 4349 4345 4352 1507 1512 1512 1513 1513 1549
5.3 6.0 5.2 5.2 5.3 5.3 5.5 5.6 5.5 5.5 6.2 6.2 6.3 5.9 6.3 6.2
3771 1681 1670 1671 1737 3767 4364 4385 4362 4367 2622 2628 3473 2391 3474 2658
LA - Sepulveda VA Hospital Moorpark - Fire Sta Newhall - Fire Sta Pacoima Kagel Canyon Sylmar - Converter Sta East Sylmar - Olive View Med FF Colfiorito Colfiorito Assisi-Stallone Nocera Umbra TCU071 TCU078 TCU078 TCU079 TCU079 TCU129
Northridge Northridge Northridge Northridge Northridge Northridge Umbria Marche, Umbria Marche, Umbria Marche, Umbria Marche, Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan
Italy Italy Italy Italy
bridge columns under main shock-aftershock sequential loading conditions. In addition, the study investigates the feasibility of the use of main shock ground motions to generate subsequent motions by spectrally matching the frequency contents of main shocks to those of aftershock motions for sequential seismic analyses. Main shock and aftershock earthquake ground motion pairs recorded during the 1994 Northridge, California, the United States of America, the 1997 UmbriaMache, Italy and the 1999 Chi-Chi, Taiwan earthquakes are selected for the seismic structural analyses using the program OpenSees [21]. To
are weak at long periods, which results in difference in frequency contents in ground motions for main shocks and aftershocks. Given the same magnitudes between main shocks and aftershocks, Atkinson [20] reported that the short-period spectral accelerations from aftershock earthquakes are smaller than those from main shocks using the Eastern North America earthquake records. A RC column is one of the important components of a lifeline structure. This study focuses on the effects of frequency contents of aftershock motions on seismic responses of reinforced concrete (RC)
50
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summarized in Table 1. More details of the tested columns can be found in their studies [22–24]. For developing numerical columns, total four nonlinear displacement-based beam-column elements were used, while nonlinear constitutive material models were assigned to each fiber: core concrete (Concrete01 or Concrete 04), cover concrete (Concrete01 or Concrete04) and longitudinal reinforcement (Steel 02), respectively. Mander et al.’s concrete model [25] was used for the constitutive model of concrete for the columns tested by Lehman and Moehle and Chai et al., while the concrete model developed by Kawashima et al. was used to describe the constitutive behavior of concrete of Kawashima et al.’s column. Five elements and six nodes were used to build the corresponding numerical column models. Four of them were inelastic beam-column elements while an elastic beamcolumn element was selected for the top portion of the columns. Fig. 1.d shows the schematic of the numerical column model of Kawashima et al.’s column as an example. A lumped mass was assigned to the top node of each column, which represents the weight of a superstructure. More details of one numerical column model can be found in a study by Andrawes et al. [26]. The numerical column models were subjected to the same cyclic loading protocols that were adopted during each experimental test. Fig. 2 compares the force-displacement relationships between the experiment and the numerical analysis of each column. Especially local strain results were compared with the strain values obtained from one strain gage placed on the longitudinal reinforcement at the height of 525 mm from the top of the footing for Kawashima et al.’s column (see Fig. 1(a)). The results of the numerical columns agreed well with the experimental results of all three numerical columns including the strain from the Kawashima et al.’s column. The maximum lateral force of the numerical models was 104.0%, 104.2% and 100.6% to that of the tested Kawashima et al., Lehman and Moehle, and Chai et al.’s columns, respectively. The George E. Brown, Jr. Network for Earthquake Engineering Simulation's data bases available the NEEShub [27] is used to collect the digitalized test data for the Lehman and Moehle and Cahit et al.'s columns.
Fig. 3. Ratios of spectral accelerations of aftershocks (SaAS) to those of main shocks (SaMS) after normalizing them by PGA values. The blue line represents a mean ratio.
generate sequential motions, structural responses are evaluated using three different methods: 1) using the synthetic aftershock ground motions obtained by repeating/scaling main shock motions (a traditional method), 2) using spectrally matching main shock motions, and 3) by using actual aftershock ground motion recordings. Those responses are compared to one another to investigate the frequency effects of sequential motions on RC structures. 2. Modeling and validation 2.1. Modeling The finite element program OpenSees was used to develop numerical models of three reinforced concrete (RC) bridge columns: (1) a RC column performed by Kawashima et al. [22], (2) a RC column by Lehman and Moehle [23], and (3) a RC column tested by Chai et al. [24]. A quasi-static cyclic testing was carried out for each column. Fig. 1 shows schematics of the tested bridge columns. The diameters of the tested circular columns by Kawashima et al., Lehman and Moehle and Chai et al. were 400 mm, 609.6 mm and 609.6 mm, respectively. The effective heights of each column where the lateral cyclic force was applied were 1350 mm, 2438.4 mm and 3657.6 mm, respectively. Approximate 5~18% of the RC crosssections were applied as vertical forces. Since applying a high vertical force is practically challenging, this range was considered from tests conducted in the past. The geometrical and mechanical properties of each tested column are
3. Selected main shock-aftershock ground motions A number of ground motions recorded during the M6.7 1994 Northridge, California, the United States of America, the M6.0 1997 Umbria-Mache, Italy, and the M7.6 1999 Chi-Chi, Taiwan earthquakes were selected from the Next Generation Attenuation relationships for Western U.S. (NGA-West2) database [28]. These earthquakes have abundant recordings of aftershock earthquakes. We chose aftershock
Fig. 4. (a) Comparisons of predominant periods (Td) of the selected main shock (MS) and aftershock (AS) ground motions, and (b) mean periods (Tm) of MS and AS ground motions.
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Fig. 5. (a) Main shock and aftershock spectral accelerations, and (b) acceleration time series of the M6.7 Northridge, California, earthquake recorded at the LA-Sepulveda VA Hospital station, as well as those of the main shock motion spectral matched to the aftershock motion.
Fig. 6. Seismic responses of the RC column (Kawashima et al.) under the M6.7 1994 Northridge main shock and aftershock ground motions recorded at the LA – Sepulveda VA Hospital station: (a) time histories of the top displacement, (b) lateral force and displacement relationships, and (c) time histories of a strain of a longitudinal rebar.
and record sequence number (RSN) of the selected main shockaftershock pairs. Fig. 3 shows ratios of spectral accelerations (Sa) of the selected
ground motions recorded at the stations at which the selected main shock motions were recorded. Total 16 main shock-aftershock ground motion sets were selected herein. Table 2 summarizes the magnitudes 52
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Table 3 The maximum displacements during the aftershock ground motions for Kawashima et al.’s column. 1 g of PGA
1 g of Sa at T1
Sequential motion sets (MS. RSN-AS. RSN)
Td-MS (sec)
Td-AS (sec)
Max.disp MS-AS (mm)
Max.disp MS-MS (mm)
Max.disp MS-SM (mm)
Max.disp MS-AS (mm)
Max.disp MS-MS (mm)
Max.disp MS-SM (mm)
1004–3771 1039–1681 1044–1670 1052–1671 1085–1737 1086–3767 4349–4364 4349–4385 4345–4362 4352–4367 1507–2622 1512–2628 1512–3743 1513–2391 1513–3474 1549–2658
0.28 0.26 0.32 0.5 0.38 0.36 0.08 0.08 0.32 0.16 0.26 0.16 0.16 0.2 0.2 0.24
0.22 0.3 0.38 0.38 0.12 0.28 0.24 0.32 0.28 0.18 0.14 0.3 0.16 0.2 0.26 0.18
56.80 100.53 69.44 101.84 70.61 54.11 145.87 127.73 61.82 32.12 18.59 138.07 177.42 54.60 88.80 44.06
80.82 68.19 101.66 119.48 105.77 139.68 94.01 94.01 54.05 55.89 71.19 111.10 111.11 192.98 192.98 71.45
52.41 100.15 67.82 113.46 67.76 74.46 130.60 95.10 43.51 28.36 17.56 113.21 128.53 70.93 107.18 43.29
16.95 65.06 44.12 72.15 23.12 33.17 18.84 19.57 23.47 9.74 13.38 18.07 24.68 25.16 37.51 25.31
29.30 30.64 37.32 132.36 48.50 125.70 10.89 10.89 22.69 11.84 20.18 16.79 16.79 58.39 58.39 44.12
16.97 54.44 42.54 83.86 29.17 41.45 20.63 16.62 16.95 8.33 10.81 16.07 15.55 15.17 34.23 29.19
Table 4 The 2nd Residual displacements during the aftershock ground motions for Kawashima et al.’s column. 1 g of PGA Sequential motion sets (MS. RSN-AS. RSN)
Tm-MS
Tm-AS
(sec)
1004–3771 1039–1681 1044–1670 1052–1671 1085–1737 1086–3767 4349–4364 4349–4385 4345–4362 4352–4367 1507–2622 1512–2628 1512–3743 1513–2391 1513–3474 1549–2658
0.46 0.47 0.53 0.66 0.76 0.76 0.54 0.54 0.34 0.24 0.33 0.43 0.43 0.49 0.49 0.35
1 g of Sa at T1
(sec)
2nd Residual disp. MS-AS (mm)
2nd Residual disp. MS-MS (mm)
2nd Residual disp. MS-SM (mm)
2nd Residual disp. MS-AS (mm)
2nd Residual disp. MS-MS (mm)
2nd Residual disp. MS-SM (mm)
0.28 0.55 0.44 0.53 0.34 0.31 0.60 0.64 0.32 0.19 0.20 0.44 0.56 0.28 0.38 0.39
8.80 15.95 −5.88 12.25 18.92 11.91 0.09 1.94 12.06 8.25 −0.93 4.71 14.82 24.50 22.48 11.52
13.69 13.03 1.13 4.67 1.60 −3.38 7.06 7.06 8.65 1.35 1.74 3.30 3.30 36.96 36.96 13.46
10.57 18.10 1.77 3.23 10.91 15.56 −0.79 1.21 4.65 7.87 −1.56 0.38 1.52 33.32 34.84 12.06
−1.51 9.61 4.03 17.93 6.61 25.99 0.18 −1.39 −1.57 0.15 −2.21 −0.15 1.10 −5.75 −5.83 3.05
0.49 2.55 4.51 14.63 11.40 16.08 −0.44 −0.44 −1.32 0.17 −2.45 −0.33 −0.33 −8.76 −8.76 7.78
−1.28 9.46 4.74 14.26 8.62 22.46 −1.68 −0.11 −1.31 0.15 −2.44 −0.44 −0.46 −6.60 −5.65 4.99
Fig. 7. Time history displacements of the RC column (Kawashima et al.) under: (a) the 1997 Umbria-Marche earthquake motions measured at the Nocera Umbra station, and (b) the 1999 Chichi earthquake motions measured at the TCU 129 station.
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Fig. 8. Time history displacements of the RC column under: (a) the 1994 Northridge motions at the LA–Sepulveda VA Hospital station, (b) 1997 Umbria-Marche motions at the Nocera Umbra station, and (c) 1999 Chichi motions at the TCU129 station.
column, (2) Lehman and Moehle's column and (3) Chai et al.’s column. The numerical columns were subjected to three different sequential ground motions: (1) actual main shock and after shock ground motions recorded at same stations (MS-AS), (2) repeating/scaling main shocks to represent aftershocks (MS-MS), or (3) spectrally matching main shock motions to the aftershock motions (MS-SM). The maximum displacement and the relative residual displacement (i.e. the final (2nd) residual displacement –1st residual displacement) during these three sequential ground motions were considered as seismic responses. The main shock ground motions were spectrally matched to the aftershock ground motions by using a program SeismoMatch v2.1.2 [30] over a period range of 0.02 s through 2.00 s Fig. 5 shows main shock and aftershock motions of the M6.7 Northridge, California, earthquake recorded at the LA-Sepulveda VA Hospital station, as well as those of the main shock motion spectral matched to the aftershock motion. The spectral shape of the aftershock motion is quite different from that of the main shock motion as shown in Fig. 5(a). The spectrally matched main shock motion is similar to the aftershock motion over an entire period range. The acceleration time series of the main shock motion spectrally matched to the aftershock motion still resemble those of the main shock motion as shown in Fig. 5(b).
aftershocks to those of the corresponding main shocks. The spectral accelerations were normalized by peak ground accelerations (PGA) to evaluate the variation of spectral accelerations at different periods. It is worth noting that Sa of aftershocks (SaAS) is generally smaller than those of main shocks (SaMS) at periods longer than approximately 2.0 s Fig. 4 shows predominant periods (Td) and mean periods (Tm) of the selected main shock and aftershock ground motions. The predominant period is the period at which the maximum spectral acceleration occurs in an acceleration response spectrum calculated at 5% damping. Rathje et al. [29] proposed the mean period which can be estimated by:
Tm =
∑ Ci2 / fi ∑ Ci2
,
(1)
where Ci is the Fourier amplitude, and fi represents the discrete Fourier transform frequencies between 0.25 and 20 Hz. The predominant periods for main shock and aftershock motions are different, but do not show a clear trend (Fig. 4a). However, 10 out of 16 aftershock motions have shorter mean periods than those for main shock motions (Fig. 4b), which is consistent with the observation in Fig. 3. The average mean period of the aftershock motions is approximately 0.40 s, while that of the main shock motions is about 0.49 s.
4.1. Kawashima et al. Column 4.1.1. Scaled to 1 g of PGA The main period (T1) of Kawashima et al.'s column was found to be 0.18 s, and the 10% of the compressive strength of the cross section was assigned to the top node representing the weight of the super-
4. Main shock-aftershock sequential analysis A series of nonlinear time history analyses were conducted on the three validated numerical RC column models: (1) Kawashima et al.’s 54
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Fig. 9. Lateral force-displacement relationships of the RC column (Kawashima et al.) under: (a) the 1994 Northridge motions at the LA – Sepulveda VA Hospital station, (b) 1997 Umbria-Marche motions at the Nocera Umbra station, and (c) 1999 Chichi motions at the TCU129 station.
than using MS-MS. Similar observations are found in the lateral force and displacement relationships (Fig. 6b) and time histories of a strain of a longitudinal rebar (Fig. 6c). The detailed responses of the simulations were summarized in Tables 3 and 4. These results clearly demonstrate the importance of properly characterizing the frequency contents of aftershock ground motions for main shock-aftershock sequential analyses. Fig. 7(a) and (b) show the time history displacements of the RC column under two sequential ground motions sets; one is from the 1996 Umbria-Marche, Italy earthquake and another one is from the 1999 Chi-Chi, Taiwan earthquake. The seismic responses of the RC column are different between MS-AS and MS-MS analyses, while the responses under the spectrally matched aftershocks (MS-SM) are closer to those under the actual ground motions records (MS-AS). All the simulation results based on 16 different main shock-aftershock sequential ground motion sets show similar trends. More details are discussed in the next section.
structure. All of the selected main shock and aftershock ground motions were scaled to have the peak ground acceleration (PGA) of 1g. Fig. 6 shows seismic responses of the RC column model subjected to three sets of main shock-aftershock ground motions: MS-AS; MSMS; and MS-SM for the 1944 Northridge earthquake. The RSN for main shock and aftershock ground motions are 1004 and 3771, respectively. The main shock ground motions are identical for the three sets of the sequential ground motions, and followed by three different aftershock ground motions. Fig. 6 clearly shows the differences between the seismic responses of the RC column when it was subjected to the actual sequential ground motions (MS-AS) and the main shock ground motion followed by the synthetic aftershock ground motion generated by repeating the main shock motion (MS-MS). The seismic responses of the column are overestimated when it was subjected to a sequential ground motion set using a traditional method as compared to that under the actual main shock-aftershock ground motion. This was due to the fact that the RC column's main period changed when subject to a main shock ground motion and the frequency contents of aftershock ground motions affected the response of the RC column. When the main shock motion is spectrally matched to the aftershock motion, the frequency contents of spectrally matched motion become similar to those of the aftershock motion. The 2nd residual displacement under MS-AS is shifted toward the original position while the 2nd residual displacement under MS-MS is shifted to the opposite direction. The maximum and final residual displacements recorded under MS-SM are closer to those using MS-AS rather
4.1.2. Scaled to the spectral acceleration of 1 g The ground motions were scaled to match the spectral acceleration of 1g at the main period of the original column (T1=0.18 s) in order to further examine the effects of the frequency contents on the seismic responses of the RC column. Fig. 8 shows the time history displacements of the RC column under three sets of earthquake sequential ground motions: the 1994 Northridge, USA; 1997 Umbria-Marche, Italy; and 1999 Chi-Chi, Taiwan earthquakes. All three cases show the 55
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damaged by the main shocks. When the damage is minor, the differences among MS-AS, MS-MS and MS-SM responses are minimal, since the structure still behaves elastically, and the change of the main period of the structure is insignificant. Fig. 8(b) shows a case of the RC column with little damage under the main shock. The residual displacement after the main shock, for instance, is 0.17 mm, while those due to the 1994 Northridge main shock motion at the LA – Sepulveda VA Hospital station and the 1999 Chi-Chi main shock motion at the TCU129 station are −1.29 mm 5.20 mm, respectively (see Fig. 8(a) and (c)). Fig. 9 shows the corresponding force-displacement relationships of the RC column under the same sequential ground motion sets used in Fig. 8. The differences due to three different aftershock mechanisms are minimal when the column is less damaged (see Fig. 9(b)), as compared to Fig. 9(a) and (c). 4.1.3. Summary of Kawashima et al.’s column In order to find trends in the seismic responses of Kawashima et al.’s column based on three different methods for representing aftershock ground motions, the maximum and 2nd residual displacements resulted from MS-AS, MS-MS, and MS-SM methods, and the predominant and mean periods (Td and Tm) of the corresponding ground motions are summarized in Tables 3 and 4. Fig. 10 shows that the maximum displacements during the aftershocks from the MS-MS method are much higher than those from the MS-AS and MS-SM methods, especially when the ratio of predominant periods of the main ⎛T ⎞ shock to aftershock motions ⎜ Td − AS ⎟ is less than 1.5 (Fig. 10(a)) and the ⎝ d − MS ⎠ ⎛T ⎞ ratio of mean periods ⎜ Tm − AS ⎟ is less than 0.9 (Fig. 10(b)). The average ⎝ m − MS ⎠ ratio of the maximum displacements due to MS-MS to MS-AS ( Max displ .MS − MS ) is found to be 153.08%. The ratios of maximum
Fig. 10. The ratio (%) of the absolute maximum displacements with respect to: (a) Td − AS /Td − MS , and (b)Tm − AS /Tm − MS .
Max displ .MS − AS
displacements from the MS-MS method to those from the MS-AS T T method tend to increase as Td − AS and m − AS decrease, which clearly d − MS
Tm − MS
indicates the effects of frequency contents in main shock and aftershock ground motions on structural responses. However, when the spectrally matched main shock ground motions are used for the aftershock ground motions (the MS-SM method), the maximum T displacement ratio does not vary with Td − AS and m − AS with approxiTd − MS
Tm − MS
mately 95.25% of an average ratio. This is because the frequency contents of the main shock ground motions are matched with those of actual aftershock ground motions during the spectral matching procedure. The relative residual displacements during the aftershock ground motions were investigated as well. The ratios of the relative residual displacements from the MS-MS and MS-SM with respect to the MS-AS method are shown in Fig. 11. A 100% ratio means that relative residual displacements due to either MS-MS or MS-SM is identical to the relative residual displacements observed under the actual aftershocks records (MS-AS). The figure indicates the results using the spectralmatch method are closer to the 100% line as compared with the results using MS-MS. More than 50% of the results based on MS-MS exhibits negative ratios, which indicates that the residual displacements using MS-MS for the aftershocks are shifted to the opposite direction of the 2nd residual displacements overserved using MS-AS. When Td − AS and Td − MS
Fig. 11. The relative residual displacement ratio (%) during the aftershocks: (a) with respect to Td − AS /Td − MS , and (b)Td − AS /Td − MS .
Tm − AS Tm − MS
are greater than 1.5 and 0.9, respectively, the simulation results
are similar among the three analysis methods.
clear difference in the results when the RC column was subjected to the actual main shock-after shock recordings (MS-AS) and the synthesized main shock-aftershock ground motion using the traditional method by repeating the main shock (MS-MS). However, the results based on the spectrally matched ground motions (MS-SM) are closer to those based on the actual main shock-after shock sequential records. This phenomenon becomes more pronounced when the RC column got more
4.2. Lehman and Moehle's column and Chai et al.’s column The main periods (T1) of Lehman and Moehle's column and Chair et al.’s column were found to be 0.25 s and 0.74 s, respectively. Each column was subjected to the six sequential ground motion sets for the 1994 Northridge earthquake (see Table 2) and each ground motion was scaled to 1 g of PGA. Fig. 12 shows the time history of the displacement 56
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Fig. 12. Time history displacements of the RC columns under the 1994 Northridge motions at the LA – Sepulveda VA Hospital station: (a) Lehman and Moehle's column and (b) Chai et al.’s column,.
Fig. 13. The ratio (%) of the absolute maximum displacements with respect to Tm − AS /Tm − MS : (a) Lehman and Moehle's column and (b) Chai et al.’s column.
Fig. 14. The relative residual displacement ratio (%) during the aftershocks with respect to Td − AS /Td − MS : (a) Lehman and Moehle's column and (b) Chai et al.’s column.
of each column under the main shock-aftershock ground motion set recorded at the LA – Sepulveda VA Hospital station. The maximum displacements during the aftershocks using MS-AS, MS-MS and MSSM were found to be: (1) 54.21, 88.81 and 50.68 mm, respectively for Lehman and Moehle's column, and (2) 40.63, 139.11, and 85.21 mm, for Chai et al.’s column. The ratios (%) of the absolute maximum displacements and the relative residual displacements of each column with respect to Tm − AS / Tm − MS are shown in Fig. 13 and Fig. 14, respectively. As discussed previously, using the ground motions based on the MS-MS method, the maximum displacements of the columns are overestimated as opposed to those using the actual main shock-aftershock records (MS-AS). The responses using the spectrally matched motions (MS-SM) are close to MS-AS. When investigating the relative residual displacements during the aftershocks, the responses obtained using MS-MS tend to shift the opposite direction to those using MS-AS, while MS-SM yields much closer responses to MS-AS (see Fig. 14).
5. Discussion The effects of the frequency contents of sequential ground motions on the responses of the RC columns with respect to the main period (T1) of columns were investigated. The main period of Kawashima et al.'s, Lehman and Moehle's and Chai et al.’s columns is 0.18, 0.25 and 0.78 s, respectively (see Fig. 15). As shown in the figure, the average maximum displacement ratio under all sequential ground motion sets of the 1994 Northridge earthquake based on MS-MS was higher than that based on MS-SM. Both ratios increase as T1 increases. However, the average maximum displacement ratio of MS-SM/MS-AS is close to 100% while that of MS-MS/MS-AS even reaches to approximately 350%. Using MS-MS estimated residual displacements in the opposite direction compared to the residual displacements using MS-AS when T1 is 0.18 s and 0.25 s (negative sign in Fig. 15b). However, when T1 is 0.78 s, the residual displacements for MS-MS become in the same 57
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(MS-AS); 2) repeating/scaling main shock ground motions with frequency-invariant scaling factors (MS-MS); and 3) spectrally matching main shock ground motions to corresponding aftershock ground motions (MS-SM). Nonlinear time history analyses were conducted on three RC columns using these actual and synthesized sequential ground motions sets. The results clearly demonstrated that the frequency contents of the ground motions played significant role on the responses of the RC columns. When using the traditional method (MS-MS), the maximum displacements tend to be overestimated as compared to those due to the actual recorded sequential ground motions (MS-AS). In addition, the residual displacements using MS-MS were estimated to be in the opposite direction to those using MS-AS when the columns’ main period (T1) is shorter than mean periods of main shock motions (Tm). These differences became pronounced when the predominant and mean period of the aftershock ground motions are less than those of the main shock ground motions. When main shock ground motions spectrally matched to aftershock motions were used (MS-SM), the responses of the RC column were much closer to those using actual ground motion records (MS-AS) even though the time series of spectrally match motions still resemble those of main shock motions. Therefore, the period-dependent scaling is recommended to obtain aftershock motions for main shock-aftershock sequential analyses, especially when shorter predominant and mean periods are expected for aftershock ground motions compared to those for main shock T T motions (specifically when Td − AS <1.5 or Tm − AS <1.0 ). d − MS
m − MS
References Fig. 15. Average maximum displacement ratio (a) and relative residual displacement ratio (b) with respect to the main period (T1) of the RC columns.
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direction as those obtained from MS-AS. This difference might attribute to differences in T1 relative to the range of mean periods (Tm) of main shock motions (0.46 – 0.77 s). The residual displacements using MS-SM are in the same direction with those using MS-AS for all three columns. These observations of the results demonstrate the importance of properly characterizing the frequency contents of aftershock ground motion when conducting structural analyses and analyzing the responses of structures under main shock-aftershock sequential loadings. When ground motions are not available for the forward prediction, main shock ground motions can be obtained based on spectral accelerations estimated by many existing ground motion prediction equations (GMPEs) developed by many researchers [31–35] with certain conditions including: source parameters (e.g., fault mechanism and earthquake magnitude); path parameters (e.g., distance from the source); and site condition parameters (e.g., shear-wave velocity profile). Recently, Kim and Shin [36] proposed a model to predict period-dependent scaling factors for aftershock ground motions. This method can be used to properly obtain aftershock ground motions for the forward prediction. 6. Conclusions To obtain realistic sequential earthquake ground motions is of great concern in the earthquake engineering practice, in order to ensure the integrity of infrastructure and accurately estimate structural responses. Up to date, researchers have synthesized aftershock motions based on main shock ground motions using frequency-invariant scaling factors or randomly choosing different main shocks. However, recent studies have demonstrated that aftershock ground motions should be differentiated from main shock ground motions due to their different mechanisms. This research focused on investigating the effects of the frequency contents of aftershock ground motions on responses of RC columns. Three different methods were used to generate/obtain aftershock ground motions: 1) actual aftershock ground motion records 58
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