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Correlations between structural damage and ground motion parameters during the Ms8.0 Wenchuan Earthquake
Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
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Correlations between structural damage and ground motion parameters during the Ms8.0 Wenchuan Earthquake Zijun Wang, Boming Zhao n Beijing Jiaotong University, Beijing 100044, China
art ic l e i nf o
a b s t r a c t
Article history: Received 8 May 2013 Received in revised form 1 October 2014 Accepted 10 November 2014 Available online 7 March 2015
The Wenchuan Earthquake with a magnitude of Ms 8.0 struck the Sichuan province of China on May 12, 2008, where it mainly affected the area along the Longmenshan fault. In total, 420 three-component acceleration records were obtained by the China Strong Motion Networks Centre during this seismic event, among which over 50 records exceeded 100 gal. In the present study, we collected 48 near-fault acceleration records to derive strong ground motion parameters in terms of the peak ground acceleration, peak ground velocity, peak spectrum acceleration (5% of the damping ratio) and spectrum intensity (5% of damping ratio). We determined the building collapse ratios (CRs) for 20 targeted districts based on data acquired from both the China Earthquake Administration and the Chinese Academy of Sciences, where the CRs combined the data for all building types. Fragility curves were established between the CRs and the corresponding ground motion parameters, based on which the damage criteria were proposed. In particular, we derived the fragility curves for brick-concrete structures and frame-structures. These curves indicate how different structural types can determine the damage sustained. In addition, we developed a method for estimating building damage classifications. If we assume that buildings are built according to the improved Seismic Fortification Criterion in the revised “Code for Seismic Design of Buildings”, the predicted CRs for the 20 targeted districts would be significantly lower compared with the actual damage they sustained, which illustrates the validity of both the method and the revised code. & 2014 Elsevier Ltd. All rights reserved.
Keywords: collapse ratio seismic coefficient strong ground motion characteristics structural anti-seismic performance vulnerability Wenchuan earthquake
1. Introduction The Wenchuan Earthquake with a magnitude of Ms 8.0 that struck the Sichuan province of China on May 12, 2008 was a major tragedy for the Chinese people. There were severe losses of life and property damage in the earthquake-affected area, where numerous houses collapsed due to the shallow zone earthquake and high seismic intensity [1]. The degree of structural damage caused by earthquakes depends on both the strength of the ground motions and the anti-seismic performance of structures; thus, regression curves of the vulnerability functions between these factors have been derived based on damage statistics for previous destructive earthquakes worldwide [2–5]. Sakai et al. [6] and Rota et al. [7] studied the relationship between the damage index and peak ground acceleration (PGA) for the 1999 Chi-Chi earthquake and earthquakes in Italy, respectively, which indicated that the PGA can be used as an objective measure for characterizing the severity of ground motions in different areas. Miyakoshi et al.
n Correspondence to: School of Civil Engineering, Beijing Jiaotong University, Haidian District, Beijing, China. Tel.: þ86 13718875378, þ 86 1051684215. E-mail address: [email protected] (B. Zhao).
http://dx.doi.org/10.1016/j.soildyn.2014.11.005 0267-7261/& 2014 Elsevier Ltd. All rights reserved.
[8] proposed a fragility function between the damage ratio and peak ground velocity (PGV), with the aim of reinforcing concrete buildings and wooden buildings based on the 1995 Kobe earthquake. In addition, vulnerability functions have been established to describe ground motions related to the spectral acceleration and spectral displacement, which correspond to the natural structural vibration periods [9–11]. Furthermore, Wang et al. studied the vulnerability of buildings during the Wenchuan earthquake [12]. The primary aim of this study was to establish vulnerability functions for buildings affected by the Wenchuan earthquake and to deduce damage criteria from the structural damage classification based on these functions. First, we derived the strength of the ground motion parameters from the acceleration records for the Wenchuan earthquake, which included the PGA, PGV, peak spectrum acceleration (PSA) and spectrum intensity (SI). Next, we studied the relationships between these parameters and the corresponding building collapse ratios (CRs) based on the principles of structural dynamics and probability statistics in order to obtain fragility functions and the corresponding damage criteria. Finally, the CRs were predicted according to the fragility functions using the improved seismic coefficient provided in the revised “Code for Seismic Design of Buildings” [13]. The results showed that were significant
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Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
reductions in the predicted values compared with the actual CRs, thereby demonstrating the validity of the functions and the revised code.
2. Database A robust input database is essential for generating reliable regression vulnerability functions for buildings during an earthquake using a statistical approach. However, there are few opportunities to collect sound reliable data that encompass the acceleration records and the corresponding structural damage on a large scale. This makes it difficult to link input records directly to measures of damage. Thus, the 420 three-component acceleration records used in the present investigation highlight the consistency of the results presented below. Among the seismic records provided by the China Strong Motion Networks Centre (CSMNC), over 50 cases had peak accelerations that exceeded 100 gal along the Longmenshan mountain fault zone [14,15]. We also investigated damage information for buildings provided by both the China Earthquake Administration (CEA) and the Chinese Academy of Sciences (CAS) [16,17]. All of these data were used in this study. In order to derive the vulnerability functions, we selected 20 districts affected by the earthquake and their CRs were obtained. The targeted districts were within 102.59951 to 105.62941 E longitude and 30.74931 to 33.04411 N latitude. We selected 48 seismic stations within this range, which expanded outward by 0.51. Fig. 1 illustrates the distributions of surface ruptures, the 48 seismic stations (red triangles), and the 20 targeted districts (green circles). 2.1. Analysis of the strength of the ground motion data The strengths of critical ground motions can be defined by the shock wave, where its effects are measured based on the PGA and PGV. The PSA and SI can reflect the seismic duration and frequency
content of an event [18]. Therefore, we used the PGA, PGV, PSA and SI as parameters to assess the strengths of the ground motions during earthquake damage. In order to correct the baseline error, we used the threestep algorithm proposed by Chiu [19] to assess the strength of the ground motion data and the velocity waveform was obtained by integrating the filtered acceleration waveform. The spectral acceleration was derived from the acceleration waveform and the SI was calculated as the integral of the pseudo-spectral velocity of the ground motion, which ranged from 0.1 to 2.5 s (with a critical damping value of 5%). The maximum values of each parameter at the 48 stations are listed in Table 1. The following observations can be made based on the data provided in Table 1. At 39/48 stations, PGA exceeded 100 gal, where the highest PGA was 957.70 gal at the 051WCW station in the EW component. The largest PGV was 80.99 cm/s, which occurred at the 051SFB station in the NS component. In addition, the highest PSA and SI values were 3320.01 gal and 245.10 cm, respectively, which occurred at the 051WCW station in the EW component and the 051SFB station in the NS component.
2.2. Analysis of the structure CR The collapsed structures were defined as completely damaged or partially damaged structures that could not be repaired. Databases of the structure CRs were collected from two organizations: CEA and CAS [16,17]. The data from the CEA were based on field damage investigations gathered from a number of sources that addressed different building types. The CAS provided CRs of 101 larger residential areas, which were obtained by interpreting aerial images (with spatial resolutions of 0.5 m) taken along the source fault zone. The databases provided by these two organizations were combined and 20 districts were selected with their CRs. The locations of the 20 targeted districts are shown in Fig. 1 (green circles).
Fig. 1. Distributions of the surface ruptures during the Wenchuan earthquake and the 48 seismic stations (red triangles). The 20 targeted districts are shown by green circles.
Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
Table 1 Ground motion parameters of the 48 stations, i.e., PGA, PGV, PSA and SI. No.
Station
PGA/gal
PGV/cm/s
PSA/gal
SI/cm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 43 44 45 46 47 48
051AXT 051MXN 051MXT 051MZQ 051SFB 051WCW 051BXD 051BXY 051BXZ 051CDZ 051CXQ 051DXY 051DYB 051GYS 051GYZ 051HSD 051HSL 051JYC 051JYD 051JYH 051JZB 051JZG 051JZW 051JZY 051JZZ 051KDT 051LSF 051LSH 051LSJ 051LXM 051LXS 051LXT 051MED 051MEZ 051MXD 051PJD 051PJW 051PWM 051PXZ 051QLY 051SPC 051SPT 051XJB 051XJD 051XJL 051YAD 051YAM
289.54 421.28 306.57 824.12 581.59 957.70 77.54 190.23 153.25 79.80 184.83 135.11 136.33 320.49 424.48 102.49 142.56 297.19 511.33 519.49 112.20 241.45 173.72 100.04 299.48 34.18 124.14 91.49 118.15 357.81 261.76 379.58 29.60 57.64 246.49 195.81 101.17 287.37 142.20 199.85 40.86 40.15 73.79 132.09 107.64 153.58 175.37
38.97 34.30 20.25 80.99 61.05 47.91 3.56 7.54 6.65 13.19 27.10 21.50 31.61 20.13 29.29 5.51 7.84 30.46 35.93 30.88 6.13 9.50 7.70 5.97 6.07 2.39 6.44 5.66 7.47 21.45 8.39 16.13 2.64 2.63 28.80 15.49 17.13 17.64 19.67 10.34 6.01 6.53 4.86 5.89 13.18 5.11 8.87
1061.52 1380.08 1303.44 2356.05 3111.81 3320.01 333.47 658.12 567.54 196.00 674.05 589.40 472.02 1223.00 2393.09 409.04 872.38 1076.14 2456.49 2769.53 373.56 753.84 646.54 343.25 811.11 128.08 565.08 337.82 384.88 1409.04 1034.96 1625.69 103.18 203.61 1067.78 996.11 473.80 1248.83 468.19 904.93 174.85 126.62 307.25 492.42 344.07 535.62 694.79
113.81 113.98 94.32 193.52 245.10 211.05 14.44 26.35 22.86 40.98 59.10 59.42 72.57 62.29 126.98 19.32 25.52 145.48 123.88 87.16 15.55 29.54 25.92 17.84 16.27 6.36 25.31 25.66 30.46 83.94 28.39 65.73 4.69 6.22 153.52 64.60 50.63 54.48 75.27 46.84 17.07 19.69 13.15 23.52 49.16 23.30 35.47
In order to derive the corresponding strengths of the ground motions in the 20 targeted districts, we used the interpolation and attenuation curves, i.e., the former for their derivation and the latter to verify the consistency of the results. Two strategies were employed to interpolate the data. For the districts located within the area of influence of the stations, the effects of the local subsurface geology and morphology such as soil amplification were assumed to be the same. Thus, the strengths of the ground motion parameters for these districts were interpolated directly from the data for nearby stations, e.g., based on the inverse of the distance to a power. However, for the districts within non-homogeneous soil sites, interpolation was performed at the bedrock level. The ThomsonHaskell matrix was applied to derive the acceleration waves for the bedrock below the relevant stations, where the soil parameters were required to establish the dispersion equations, i.e., frequency, phase velocity, thickness, elastic characteristics and damping of the layers. Next, the waves were interpolated to the area below the targeted districts and the same method was used to obtain the waves for the corresponding districts at the surface [20,21].
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Finally, the interpolated PGA and PGV were compared with the values derived from the attenuation curves provided by Si et al. [22] for the Wenchuan earthquake. The interpolation results showed that the original and predicted data were generally consistent. As mentioned above, the CRs used in this study were confirmed using comprehensive data, which represented the qualitative building damage at a large scale. Thus, the data derived from the interpolation and attenuation curves satisfied the required accuracy level. The derived values are listed in Table 2. Among the 20 targeted districts, the CRs exceeded 50% in eight districts, which accounted for 40% of the total districts, where Wolong was the worst affected area with a CR of 75%. By contrast, the CRs were relatively low for Anxian, Maoxian and Shigu, where all of the values were below 20%, which accounted for 15% of the group. The CRs of the remaining districts ranged from 20% to 50%. The damage levels in these 20 districts are illustrated in Fig. 2. An overview of the results is provided in Table 3, which show that the CRs exceeded 50% when PGA 4500 gal, PGV 4 45 cm/s, PSA41940 gal and SIs4 140 cm. In addition, the CRs that ranged
Table 2 Derived PGA, PGV, PSA, SI and corresponding CRs for the 20 targeted districts. No.
Affected Cities
PGA/gal
PGV/cm/s
PSA/gal
SI/cm
CRs/%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Tashui Nanxin Diban Qingping Bajiao Wolong Xiaoba Baishi Fuxin Xinshi Tumen Zundao Gongxing Hanwang Qinglian Xinchun Zagunao Shigu Xinqiao Junle
289.54 421.28 306.57 824.12 633.09 957.70 506.82 441.15 468.56 469.59 520.02 551.42 530.25 588.19 457.66 363.80 446.23 384.65 400.96 408.22
38.97 34.30 20.25 80.99 61.05 47.91 46.52 39.82 51.11 52.50 52.58 55.09 51.44 57.00 33.87 31.66 21.43 31.57 32.65 42.33
1061.52 1380.08 1303.44 2356.05 3111.81 3320.01 2022.52 1534.02 1746.77 1845.18 2083.24 2058.26 1947.36 2009.00 2192.43 1539.05 1708.55 1484.77 1894.86 1619.95
113.81 113.98 94.32 193.52 245.10 211.05 141.22 137.21 130.82 104.26 109.63 137.96 147.00 160.23 106.97 94.58 67.84 122.69 105.55 81.10
18.68 23.75 15.00 72.51 71.79 75.00 61.67 34.11 42.03 30.58 64.83 69.80 62.81 54.36 29.43 20.66 29.66 17.10 24.22 30.11
15%
CR<20% 20%50%
40%
45% Fig. 2. Distribution of the collapse ratios among the 20 targeted districts.
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Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
Table 3 Relationships between CR and PGA, PGV, PSA and SI. CRs
PGA (gal)
PGV (cm/s)
PSA (gal)
SI (cm)
o20% 20–50% 450%
o 385 360–470 4500
o 40 20–50 445
o 1485 1380–1900 4 1940
o 120 100–140 4140
between 20% and 50% roughly corresponded to PGA ¼360–470 gal, PGV ¼20–50 cm/s, PSA¼1380–1900 gal and SI ¼100–140 cm.
3. Analysis of the structural vulnerability 3.1. Structural vulnerability and the damage criteria For a given structural system, a seismic vulnerability function expresses the relationship between the intensity of earthquake excitation and the probable effects on the dynamic performance of that system [23]. Therefore, each vulnerability curve can describe the probability (P f ) of a specific level of damage (d) being equalled or exceeded (D Zd) for a given ground motion parameter (M), as specified in Eq. (1). P f ¼ P D ZdjM ð1Þ Thus seismic vulnerability functions are important for the assessment of seismic hazards, the management of earthquake disasters and anti-seismic structural design [24]. The fragility curve of CR with M can be established based on a standardized normal distribution function, as described in [23]: lnðM=cÞ CR ¼ ϕ ; ð2Þ
ζ
whereϕð U Þ¼ standardized normal distribution function, and the two parameters median (c) and log-standard deviation (ζ ) can be computed using the least squares method. In order to establish the damage criteria, we classified structural damage into three groups according to the results given above: CR o 20% ¼ “minor or moderate damage”, CR of 20–50% ¼“severe damage”, and CR 4 50% ¼“extremely severe damage”. The corresponding correlation coefficients for each level of damage are discussed below.
analysis, the fitted curve agreed well with the actual data when α ¼0.7. In Fig. 3, the dots denote the CRs that correspond to the PGA in targeted districts, the dashed line represents Eq. (3) and the solid line was obtained using Eq. (4). We found that the revised curve provided a better fit to the data when using the reduction coefficient α. The features of the CR distributions are discussed later. Similarly, the fragility curves of CRs that corresponded to PGV, PSA and SI can be established using Eqs. (5) to (7), respectively. lnðPGV=cv Þ CR ¼ ϕ α U
ð5Þ
lnðPSA=csa Þ CR ¼ ϕ α U
ð6Þ
lnðSI=csi Þ CR ¼ ϕ α U
ð7Þ
ζv
ζ sa
ζ si
The relevant median (c) and log-standard deviation (ζ ) parameters were computed for each curve and the results are shown in Table 4. When CR o50%, α ¼ 1. When PGV 446 cm/s, PSA42001 gal and SI4140 cm, CR 450% and α ¼ 0.7. The fragility curves between the CRs and PGV, PSA and SI are shown in Figs. 4–6. The conclusions obtained from the fragility curves are as follows. (1) The CRs were well correlated with the PGA and PGV to a certain extent, as indicated by the standard deviation, thereby demonstrating that there were correlations between the ground motion parameters and the collapse of structures. Reliable estimates of the structural vulnerability were obtained using the ground motion parameters inferred from the robust database. (2) The fitted curve for CR with PGA was better than that for CR with PGV, which may have two possible explanations. First, acceleration can directly reflect the seismic load imparted to buildings, thereby linking to structural damage. However, compared with acceleration, the velocity is affected more by the distribution of faults and the depth of layers. Second, the responses of buildings to the input parameters 100
The original curve The revised curve The actual data
90 80
Under the current lognormal assumption, the vulnerability function between PGA and CR takes the following analytical form: lnðPGA=ca Þ CR ¼ ϕ ; ð3Þ
ζa
70
CR (%)
3.2. Establishment of the relationship between CRs and ground motion parameters
60 50 40 30 20 10
where parameters ca and ζ a were computed using the least squares method as 525 gal and 0.4368, respectively. We estimated that CR would exceed 50% when PGA exceeds 525 gal, but the growth of CR slowed down when the value of PGA exceeded 525 gal, which indicates that the original curve was not entirely consistent with the assumed true relationship. Therefore, a reduction coefficient in terms of α was used to consider the reduction in the growth rate and the revised equation is as follows. lnðPGA=ca Þ ð4Þ CR ¼ ϕ α U
0
0
200
400
800
1000
1200
1400
1600
PGA (gal) Fig. 3. Fragility curve between CR and PGA. The dashed line represents the original curve and the solid line is the revised curve.
Table 4 Computed parameters for the fragility curves of PGV, PSA and SI.
ζa
Since ϕð0Þ ¼ 0:5, the curve remains continuous when the term within the brackets equals zero. According to the comparative
600
median c log-standard deviation ζ
PGV(cm/s)
PSA(gal)
SI(cm)
46.24 0.4599
2001.40 0.3793
135.90 0.3950
Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
ground motion parameters discussed above in order to estimate structural vulnerability.
100
The original curve The revised curve The actual data
90 80
CR (%)
70
Based on the four fragility curves, we determined damage criteria as follows. For PGA, CR exceeded 20% for PGA values4360 gal and it increased sharply to 50% for PGAs4525 gal. For PGV, CR was about 20% for PGVs432 cm/s and it reached 50% for PGVs of ca 46 cm/s. In addition, PSA waso1450 gal for CR valueso20% but42001 gal for CR values450%. SI waso97 cm for CRso20%, but4136 cm for CRs450%.
60 50 40 30 20 10 0
0
10
20
30
40
50
60
70
80
90
100
3.3. Fragility curves for brick-concrete and frame structures
PGV (cm/s) Fig. 4. Fragility curve between CR and PGV. The dashed line represents the original curve and the solid line is the revised curve. 100
The original curve The revised curve The actual data
90 80
CR (%)
70 60 50 40 30 20 10 0 0
500
1000
1500
2000
2500
3000
3500
4000
PSA (gal) Fig. 5. Fragility curve between CR and PSA. The dashed line represents the original curve and the solid line is the revised curve.
100
The original curve The revised curve The actual data
90 80
CR (%)
70 60 50 40
The fragility curves in section 3.2 were obtained by combining the data for all building types, so more detailed results were required to clarify the effects of different damage scenarios on various structural types to obtain a better understanding of the building types. It should be noted that the available data comprised structural damage information related to infrastructure in 10 cities from the 20 targeted areas. These data were processed in order to observe the structural damage sustained by different building types, including brick-concrete structures and frame structures [16]. We used “brick-concrete structure” to denote that brick or block walls and columns carried the vertical load of the building, while concrete was used for horizontal load-bearing beams and slabs. We used “frame-structure” to refer to reinforced concrete frame structures that comprised a frame or skeleton of reinforced concrete [16]. Columns are the primary load-carrying elements in the building and infill walls are used as partitions. Given the small amount of data related to wooden structures this sub-group was excluded from the present study. The CRs for the corresponding to brick-concrete and frame structures in the 10 cities are listed in Table 5. The lognormal form of Eq. (2) allows the vulnerability function between PGA, PSA and CR to be obtained based on the median (c) and the log-standard deviation (ζ ). The parameters c and ζ for each curve were inferred by least squares approximation. The results are shown in Table 6 and the fragility curves are presented in Fig. 7. Table 5 Derived PGA, PSA and corresponding CRs for brick-concrete and frame structures in the 10 cities.
30 20 10 0
133
0
30
60
90
120
150
180
210
240
270
300
SI (cm) Fig. 6. Fragility curve between CR and SI. The dashed line represents the original curve and the solid line is the revised curve.
may differ depending on their age, structural type and seismic design level. (3) The CRs were correlated with the PSA and SI within certain limits, as indicated by the corresponding variances. The statistical deviations in these two parameter correlations were lower than those between CR and PGA, thereby indicating that the PSA and SI may better reflect the relationship between the frequency content of ground motion and the dominant period of buildings, and thus the behaviour of buildings subjected to earthquakes. In addition, because the SI was obtained by numerical integration, it may have been affected by the spread of the site conditions for stations by modifying the spectral amplitudes in each frequency band [25,26]. This demonstrates the feasibility of using the four
No. Affected Cities
PGA/gal
PSA/gal
Brick-Concrete CRs/%
Frame Structure CRs/%
1 2 3 4 5 6 7 8 9 10
289.54 633.09 468.56 469.59 520.02 530.25 588.19 457.66 363.80 400.96
1061.52 3111.81 1746.77 1845.18 2083.24 1947.36 2009.00 2192.43 1539.05 1894.86
20 70 46 36 64 65 64 – – 25
– 23 – – 18 24 25 13 13 7
Tashui Bajiao Fuxin Xinshi Tumen Gongxing Hanwang Qinglian Xinchun Xinqiao
Table 6 Computed parameters for the fragility curves of PGV and SI.
median c log-standard deviation ζ
Brick-Concrete
Frame Structure
PGA(gal)
PSA(gal)
PGA(gal)
PSA(gal)
484.64 0.4265
1927.35 0.4222
852.35 0.5731
2745.72 0.2930
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Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
100
100
Brick-Concrete curve Frame-Structure curve Comprehensive curve data of Brick-Concrete data of Frame-Structure
90 80
80 70
60
CR (%)
CR (%)
70
Brick-Concrete curve Frame-Structure curve Comprehensive curve data of Brick-Concrete data of Frame-Structure
90
50 40
60 50 40
30
30
20
20
10
10 0
0
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
0
500
1000
1500
2000
2500
3000
3500
4000
PSA (gal)
PGA (gal)
Fig. 7. Fragility curves between CR with PGA (a) and CR with PSA (b). The blue line represents the curve for brick-concrete structures and the green line denotes the curve of frame structures. The red line is the comprehensive curve derived in section 3.2.
The following conclusions can be made based on the results given above. (1) In general, the damage situation for buildings in the affected area was valid for brick-concrete and frame structure systems. However, because brick-concrete buildings were the main structural type in the area, the vulnerability curves for brickconcrete structures tended to map the results of the comprehensive curves more closely. (2) As the PGA increased, the growth rate of CRs was slower for frame structures than brick-concrete structures. This suggests that brick-concrete systems are highly brittle, thereby allowing them to be compromised more readily when the maximum strength is exceeded. By contrast, the frame structures provide higher ductility levels and there is little increase in stress beyond the yield strength when they are subjected to nonlinear deformations. (3) When the PSA increased, both the brick-concrete and frame structures tended to be damaged, thereby indicating that the spectrum acceleration provided a closer approximation of the behaviours of buildings during earthquakes than the PGA.
4. Structural damage estimation based on the current code
For “small earthquakes”, the response spectrum is based on the seismic design according to the code. When checking the structural resistance, the “ultimate limit state design” (which is based on the characteristic values inferred by probability theory) is used for the main members. The ground motion design acceleration required for the structure to remain in the elastic stage is determined as the characteristic value of the earthquake action under the seismic fortification condition. Thus, because the necessary structural strength can be reached by withstanding the first level, the goal required to reach the second level (structures can be repaired in a medium earthquake) will also be satisfied, and the seismic requirement can be fulfilled in the third level by the concept design. In general, the design calculation in the first stage can meet the demands of seismic resistance for most structures. 4.2. Estimation of structural damage Based on the code, the horizontal earthquake action F with a single-degree-of-freedom (SDOF) system is determined as, F ¼ m USa ðTÞ;
where m is the mass of the SDOF system and Sa represents the maximum absolute value of acceleration. Eq. (8) can be rewritten as
4.1. Seismic design method The aims of the “Code for Seismic Design of Buildings” [13] (referred to as the code) can be classified in terms of three earthquake performance levels: “minimal damage under a small earthquake, repairable damage under a medium earthquake and non-collapse under a severe earthquake”. The return periods defined for small, moderate and severe earthquake are 50 years, 475 years and 4 2000 years, respectively. The intensity of a moderate earthquake is defined as the basic seismic fortification intensity with a 4 10% probability in 50 years. The specific seismic design can be divided into two stages. The first allows ordinary buildings to resist “small earthquakes”, which is achieved by computing and checking the structural strength and deformation to ensure that the buildings’ main members will not fail under the action of frequent earthquakes, which have a probability of 4 63% in 50 years. The second stage checks the elastioplastic deformation of the main structure in order to prevent global structural collapse during infrequent earthquakes. The seismic fortification criterion of an infrequent earthquake is generally one degree larger than the basic seismic criterion and its probability is 4 2–3%, depending on the risk potential within the region.
ð8Þ
F ¼ mg U
amax Sa ðTÞ U ¼ G U k U βðTÞ; amax g
ð9Þ
where amax is the PGA, G ¼ mg is the weight of the SDOF system, k ¼ amax =g is the seismic coefficient, g is the acceleration due to gravity, and β ðTÞ is the dynamic coefficient. The seismic coefficient k is a key parameter for seismic design, which can be obtained based on observational data. Many previous studies have indicated that if the seismic intensity is doubled, the value of k will also roughly double. The current code employs the seismic fortification intensity and seismic coefficient simultaneously. The value of the seismic coefficient k1 is equal to k/3 for the first stage, and it is 1.5–2.0 times larger than k for the second stage; thus, k2 was determined as 2k in our study. Although earthquakes exhibit some regularities in their frequency and magnitude of damage in a given area over a certain time, earthquakes are complex natural phenomena that can occur randomly, where they may exceed the level of seismic fortification intensity predicted by the seismic zonation maps. Some typical examples of historical highly destructive earthquakes are listed in Table 7 [27–29]. In fact, the seismic fortification intensities in the targeted districts were 2–3 degrees lower than the intensities that they actually experienced during the Wenchuan earthquake.
Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
In order to make structures more resilient during destructive earthquakes, the basic seismic intensity should be determined with a lower exceedance probability limit. Thus, active faults must be investigated and studied to obtain better predictions of the probability and magnitude of future earthquakes. It is also necessary to establish the statistical relationships between the ground motion records and earthquake characteristics, including the source and path features, soil effects, and site conditions.
4.3. Structural damage estimation based on the damage criteria To estimate the damage incurred by the targeted structures when subjected to higher seismic intensities compared with the designed intensities, ranging from 6–8 degrees, the design forces of these structures should be estimated accurately. Thus, the critical seismic fortification acceleration aF should be calculated first by the following equation: aF ¼ k2 U g ¼ 2k U g;
ð10Þ
where g is the acceleration due to gravity and k2 can be determined as k2 ¼ 2k, where k is related directly to the basic
135
seismic intensity. The values of k and the results of PGA=aF for the 20 targeted districts are listed in Table 8. The fragility function of CR with PGA=aF as the argument can be established as follows, lnðPGA=aF =cF Þ CR ¼ ϕ α U ; ð11Þ
ζF
where the parameters cF and ζ F were computed using least squares method as 2.60 and 0.5123, respectively. When PGA=aF o2.60, α ¼1. CR 450% for PGA=aF 42.60 and α ¼ 0.7. As shown in Fig. 8, the fragility curve agreed well with the relationship between PGA=aF and CR. Thus, further conclusions can be made based on these results. The targeted districts may sustain “severe damage” (CRs of 20% to 50%) if PGA=aF ¼ 1.7–2.60. Districts where the PGA=aF 4 2.60 may sustain “extremely severe damage” with CRs of 4 50%. However, Xinqiao town (with red circle) is a special case, where PGA=aF was about 4.1 but the corresponding CR was only 24%. It is possible that the site conditions at Xinqiao town make the general earthquake-resistant capacity of this area better than that in other districts. 4.4. Structural damage prediction based on the revised code
No. Time
Place
Magnitude Fortification Intensity
Epicentral Intensity
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Xingtai Xingtai Yangjiang Liyang Liyang Haicheng Tangshan Fengzhen Buerjin Yangjiang Longzhen Beian Jiujiang Yutian Wenchuan
6.5 7.2 6.4 5.4 6 7.3 7.8 5.8 5.2 5 5 5.3 5.7 7.3 8
VIII IX-X VIII VII VIII IX XI VII strong VIII weak IX weak VII VII VII VII XI
1966.3.8 1966.3.22 1969.7.26 1974.4.22 1979.7.9 1975.2.4 1976.7.28 1981.8.13 1982.3.20 1986.1.28 1986.2.9 1986.3.1 2005.11.26 2008.3.21 2008.5.12
VII(0.1g) VII(0.1g) VII(0.1g) VII(0.1g) VII(0.1g) VII(0.15g) VIII(0.2g) VII(0.1g) VI(0.05g) VII(0.1g) VI(0.05g) VI(0.05g) VI(0.05g) VI(0.05g) VII(0.1g)
The Wenchuan earthquake occurred along the Longmenshan fault [1], which is a thrust fault running through the base of the Longmen Mountains in Sichuan province, but the basic seismic index had been underestimated in this area prior to the occurrence of the earthquake. In order to revise the Chinese Code for Seismic Design of Buildings (GB 50011–2010), studies have focused on the deformation feature of the Quaternary period of the 100
The original curve The revised curve The actual data
90 80 70
CR (%)
Table 7 Comparison of the actual intensity and design intensity of strong earthquakes throughout history.
60 50 40 30 20 10 0 0
1
2
3
4
Table 8 Seismic coefficients and corresponding CRs.
5
6
7
8
9
10
PGA/aF
Location
k
kR
PGA=aF
PGA=aR
CRð%Þ
CRR ð%Þ
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Tashui Nanxin Diban Qingping Bajiao Wolong Xiaoba Baishi Fuxin Xinshi Tumen Zundao Gongxing Hanwang Qinglian Xinchun Zagunao Shigu Xinqiao Junle
0.10 0.15 0.15 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.15 0.05 0.10
0.15 0.20 0.20 0.15 0.15 0.20 0.15 0.20 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.20 0.10 0.15
1.45 1.40 1.02 4.12 3.17 4.79 2.53 2.21 2.34 2.35 2.60 2.76 2.65 2.94 2.29 1.82 2.23 1.28 4.01 2.04
0.97 1.05 0.77 2.75 2.11 2.39 1.69 1.10 1.56 1.57 1.73 1.84 1.77 1.96 1.53 1.21 1.49 0.96 2.00 1.36
18.68 23.75 15.00 72.51 71.79 75.00 61.67 34.11 42.03 30.58 64.83 69.80 62.81 54.36 29.43 20.66 29.66 17.10 24.22 30.11
2.65 3.88 0.85 54.25 34.16 43.58 19.98 4.70 15.97 16.08 21.41 24.90 22.54 29.06 14.88 6.82 13.77 2.61 30.57 10.30
Fig. 8. Fragility curve between CR and PGA=aF . The dashed line represents the original curve and the solid line is the revised curve. The special case of Xinqiao town is indicated by the red circle.
100
The fitted curve The predicated CRs
90 80 70
CR R(%)
No.
60 50 40 30 20 10 0
0
1
2
3
4
5
6
7
8
PGA/aR Fig. 9. Fragility curve between the predicted CRR and PGA=aR .
9
10
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Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
Longmenshan fault and its corresponding characteristics in terms of activity, surface ruptures, aftershock distributions, slip rates, recurrence periods and the potential for extremely strong earthquakes [30,31]. Ultimately, the basic seismic intensities in the revised code were increased by 0.5, 1.0 or 2.0 degrees, respectively. The revised seismic coefficients kR for the 20 targeted districts are listed in Table 8. The revised aR can be calculated by substituting the revised seismic coefficients kR into Eq. (10), i.e.,aR ¼ kR2 Ug ¼ 2kR Ug. Next, the predicted CRR for PGA during the Wenchuan earthquake were estimated based on the revised aR . The computed values of PGA=aR and CRR are also given in Table 8. The fragility curves for both are presented in Fig. 9. As shown in Fig. 9, most of the predicted CRR s in the targeted districts were below 30%, except for Bajiao, Qingping and Wolong, with 34%, 54% and 43%, respectively. These results indicate that the structural anti-seismic capacity can be increased according to the revised code.
5. Discussion (1) The Wenchuan earthquake caused structural damage on a large scale. Based on data related to damage information around the cities and seismic records, we established how the ground motion parameters were associated with structural damage and the laws that govern these relationships. Clearly, severe ground shaking is the direct cause of building damage during earthquakes, but the factors involved in the damage process are highly complicated and thus a detailed seismic response analysis of different types of structures when subjected to earthquake loads is necessary to understand the mechanisms and processes that lead to structural failure. Furthermore, the use of different ground motion parameters to estimate damage requires a sound theoretical basis to design a seismic fortification criterion. (2) Our approach can be extended to other earthquakes. However, the results obtained for the Wenchuan earthquake show that the level of structural damage and CR were higher than those in the 1995 Kobe earthquake and the 1999 Chi-Chi earthquake [32,33]. This was because the affected districts were less developed rural areas in Sichuan province and thus the earthquake-resistant capacities of the structures were poor in these areas. Brickconcrete buildings were the most common construction type, where most of these buildings had a similar number of stories and structural form. We focused on building collapse in a wider sense, but the comprehensive curves that we obtained may reflect the general damage situation for brick-concrete buildings as well as the specific damage characteristics in the region. In addition, because there were far fewer frame structures than brick-concrete structures, the fragility curves for the former suggest that the damage features do not consider factors such as age, the number of stories and the local geology. (3) The basic seismic fortification standard specified in the “Code for Seismic Design of Buildings” is the acceleration index under the condition that the soil site is category II. In practice, the ground motion parameters and CRs are obtained based on the actual site conditions, but it is not difficult to compare the two directly when establishing the relationship. Strictly speaking, when comparing the PGA with the critical seismic fortification acceleration, adjustments in the PGA should be made according to the actual site conditions using the coefficient specified in the Seismic Ground Motion Parameter Zonation Map of China. For the magnitude of the
ground motion in the present study, the difference in the peak accelerations was about 10% when the site category differed by one level among the four levels. (4) We established the fragility curves of the CRs with the ground motion parameters based on standardized normal distribution functions. However, as the values of the parameters increased, the growth of the CR decreased, thereby indicating that the original curve (Eq. (3)) was not entirely consistent with their relationship. Therefore, we used a reduction coefficient in terms of α to describe the relationship (Eq. (4)). The exact cause of the reduction in the growth rate is still unclear, but the following factors may be considered. a) Due to the uncertainty of the construction levels, material qualities, structural forms, site conditions and the diversity of the natural structural vibration periods, it may have been difficult for the CRs of structures to reach 100% within the meizoseismal area. b) According to the local seismic fortification levels, most of the structures would be damaged with a PGA of 500– 600 gal, but the actual changes in the CRs were small when the PGA exceeded 600 gal, possibly because the targeted districts are located in mountainous areas where the PGA was high for a short duration of time, thereby resulting in a relatively low level of actual structural damage to some extent. In addition, the earthquake-resistance capacity of structures built on rocks is greater.
6. Summary In this study, we obtained observation-based data related to the Wenchuan earthquake and we determined the corresponding ground motion parameters for 20 targeted districts using interpolation methods and attenuation curves. We generalized the vulnerability curves between the CRs and ground motion parameters. If the buildings had been built according to the improved Seismic Fortification Criterion of the revised “Code for Seismic Design of Buildings”, the predicted CRs for the 20 targeted districts would have been reduced significantly compared with the actual damage that they sustained. The main conclusions of this study are as follows. (1) In total, we processed 144 three-component observed records from 48 stations in the targeted districts and the strength of their ground motion parameters, i.e., the PGA, PGV, PSA (5% of damping ratio) and SI (5% of damping ratio). (2) We derived the relationships between the CRs and the ground motion parameters, and we generated their fragility curves based on the standard normal distribution function. The damage criteria were determined as follows. CR4 20% for PGA 4360 gal and CR increased sharply to 50% for PGA 4 525 gal. For PGV, CR was about 20% for PGV 4 32 cm/s and CR ¼50% for PGV of about 46 cm/s. In addition, PSAo1450 gal for CR o20%, and PSA42001 gal for CR 450%. SIo97 cm for CR 420%, and SI 4136 cm for CR 450%. (3) Among the two types of the buildings, brick-concrete structures are highly brittle and readily compromised when the maximum strength is exceeded. By contrast, frame structures have higher ductility levels and thus they exhibit little increases in stress beyond the yield strength when subjected to nonlinear deformations. We found that the fragility curves based on the PSA provided a more accurate approximation of the behaviours of buildings during earthquakes compared with those based on the PGA. (4) We established an effective method for estimating the structural damage levels by using the fragility curve between CR and
Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
PGA=aF to eliminate the deviation in the design forces for these structures. The targeted districts could sustain “severe damage” (CR¼20–50%) when PGA=aF of 1.7–2.60. Districts where PGA=aF 4 2.60 could sustain “extremely severe damage”, i.e., CR450%. However, Xinqiao town was a special case, where PGA=aF was about 4.1 but the corresponding CR was only 24%, possibly because the site conditions in Xinqiao town meant that the general earthquake-resistant capacity was better than that in other districts. (5) The predicted CRR that corresponded to the PGA for Wenchuan earthquake can be computed based on the revised seismic coefficient kR , which was used to construct the fragility curve for CRR and PGA=aR . Most of the predicted CRR s in the targeted districts were below 30%, except for Bajiao, Qingping and Wolong, with 34%, 54% and 43%, respectively. These results indicate that the structural anti-seismic capacity can be increased based on the revised code.
Acknowledgements We would like to thank the China Strong Motion Networks Centre for providing the observation-based data and Professor Lei Liping for sharing remote sensing data related to the damage conditions during the Wenchuan earthquake. We would also like to express our deep gratitude to Prof. Elgamal and three anonymous reviewers for many valuable comments. The authors are indebted to Dr. Pedro MartinezVazquez of the University of Birmingham for his useful critiques of this research. This research has been supported by the National Natural Science Foundation of China (No. U1434210 and No. 51278045) and the National Key Technologies Research & Development Program of China (No. 2015BAK19B02). References [1] Xu XW, Wen XZ, Yu GH, et al. Co-seismic reverse- and oblique-slip surface faulting generated by the 2008 Mw 7.9 Wenchuan earthquake, China. Geology 2009;37:515–8. [2] Wood HO, Neumann F. Modified Mercalli intensity scale of 1931. Bulletin of the Seismological Society of America 1931;21:277–83. [3] Furukawa A, Spence R, Ohta Y, et al. Analytical study on vulnerability functions for casualty estimation in the collapse of adobe buildings induced by earthquake. Bull Earthquake Eng 2010;8:451–79. [4] Barbat AH, Pujades LG, Lantada N. Seismic damage evaluation in urban areas using the capacity spectrum method: Application to Barcelona. Soil Dynamics and Earthquake Engineering 2008;28:851–65. [5] Jaiswal K, Wald D, D’Ayala D. Developing empirical collapse fragility functions for global building types. Earthquake Spectra 2011;27:775–95. [6] Sakai Y, Yoshioka S, Koketsu K, et al. Investigation on indices of representing destructive power of strong ground motions to estimate damage to buildings based on the 1999 Chi-Chi earthquake, Taiwan. Journal of Structural and Construction Engineering 2001;549:43–50. [7] Rota M, Penna A, Strobbia CL. Processing Italian damage data to derive typological fragility curves. Soil Dynamics and Earthquake Engineering 2008;28:933–47. [8] Miyakoshi J, Kambara H, Ishii D, et al. Vulnerability function based on earthquake response analysis with dispersion of structural strength and ductility capacity. Journal of Structural Engineering 2005;51B:105–10.
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Contents lists available at ScienceDirect
Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Correlations between structural damage and ground motion parameters during the Ms8.0 Wenchuan Earthquake Zijun Wang, Boming Zhao n Beijing Jiaotong University, Beijing 100044, China
art ic l e i nf o
a b s t r a c t
Article history: Received 8 May 2013 Received in revised form 1 October 2014 Accepted 10 November 2014 Available online 7 March 2015
The Wenchuan Earthquake with a magnitude of Ms 8.0 struck the Sichuan province of China on May 12, 2008, where it mainly affected the area along the Longmenshan fault. In total, 420 three-component acceleration records were obtained by the China Strong Motion Networks Centre during this seismic event, among which over 50 records exceeded 100 gal. In the present study, we collected 48 near-fault acceleration records to derive strong ground motion parameters in terms of the peak ground acceleration, peak ground velocity, peak spectrum acceleration (5% of the damping ratio) and spectrum intensity (5% of damping ratio). We determined the building collapse ratios (CRs) for 20 targeted districts based on data acquired from both the China Earthquake Administration and the Chinese Academy of Sciences, where the CRs combined the data for all building types. Fragility curves were established between the CRs and the corresponding ground motion parameters, based on which the damage criteria were proposed. In particular, we derived the fragility curves for brick-concrete structures and frame-structures. These curves indicate how different structural types can determine the damage sustained. In addition, we developed a method for estimating building damage classifications. If we assume that buildings are built according to the improved Seismic Fortification Criterion in the revised “Code for Seismic Design of Buildings”, the predicted CRs for the 20 targeted districts would be significantly lower compared with the actual damage they sustained, which illustrates the validity of both the method and the revised code. & 2014 Elsevier Ltd. All rights reserved.
Keywords: collapse ratio seismic coefficient strong ground motion characteristics structural anti-seismic performance vulnerability Wenchuan earthquake
1. Introduction The Wenchuan Earthquake with a magnitude of Ms 8.0 that struck the Sichuan province of China on May 12, 2008 was a major tragedy for the Chinese people. There were severe losses of life and property damage in the earthquake-affected area, where numerous houses collapsed due to the shallow zone earthquake and high seismic intensity [1]. The degree of structural damage caused by earthquakes depends on both the strength of the ground motions and the anti-seismic performance of structures; thus, regression curves of the vulnerability functions between these factors have been derived based on damage statistics for previous destructive earthquakes worldwide [2–5]. Sakai et al. [6] and Rota et al. [7] studied the relationship between the damage index and peak ground acceleration (PGA) for the 1999 Chi-Chi earthquake and earthquakes in Italy, respectively, which indicated that the PGA can be used as an objective measure for characterizing the severity of ground motions in different areas. Miyakoshi et al.
n Correspondence to: School of Civil Engineering, Beijing Jiaotong University, Haidian District, Beijing, China. Tel.: þ86 13718875378, þ 86 1051684215. E-mail address: [email protected] (B. Zhao).
http://dx.doi.org/10.1016/j.soildyn.2014.11.005 0267-7261/& 2014 Elsevier Ltd. All rights reserved.
[8] proposed a fragility function between the damage ratio and peak ground velocity (PGV), with the aim of reinforcing concrete buildings and wooden buildings based on the 1995 Kobe earthquake. In addition, vulnerability functions have been established to describe ground motions related to the spectral acceleration and spectral displacement, which correspond to the natural structural vibration periods [9–11]. Furthermore, Wang et al. studied the vulnerability of buildings during the Wenchuan earthquake [12]. The primary aim of this study was to establish vulnerability functions for buildings affected by the Wenchuan earthquake and to deduce damage criteria from the structural damage classification based on these functions. First, we derived the strength of the ground motion parameters from the acceleration records for the Wenchuan earthquake, which included the PGA, PGV, peak spectrum acceleration (PSA) and spectrum intensity (SI). Next, we studied the relationships between these parameters and the corresponding building collapse ratios (CRs) based on the principles of structural dynamics and probability statistics in order to obtain fragility functions and the corresponding damage criteria. Finally, the CRs were predicted according to the fragility functions using the improved seismic coefficient provided in the revised “Code for Seismic Design of Buildings” [13]. The results showed that were significant
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Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
reductions in the predicted values compared with the actual CRs, thereby demonstrating the validity of the functions and the revised code.
2. Database A robust input database is essential for generating reliable regression vulnerability functions for buildings during an earthquake using a statistical approach. However, there are few opportunities to collect sound reliable data that encompass the acceleration records and the corresponding structural damage on a large scale. This makes it difficult to link input records directly to measures of damage. Thus, the 420 three-component acceleration records used in the present investigation highlight the consistency of the results presented below. Among the seismic records provided by the China Strong Motion Networks Centre (CSMNC), over 50 cases had peak accelerations that exceeded 100 gal along the Longmenshan mountain fault zone [14,15]. We also investigated damage information for buildings provided by both the China Earthquake Administration (CEA) and the Chinese Academy of Sciences (CAS) [16,17]. All of these data were used in this study. In order to derive the vulnerability functions, we selected 20 districts affected by the earthquake and their CRs were obtained. The targeted districts were within 102.59951 to 105.62941 E longitude and 30.74931 to 33.04411 N latitude. We selected 48 seismic stations within this range, which expanded outward by 0.51. Fig. 1 illustrates the distributions of surface ruptures, the 48 seismic stations (red triangles), and the 20 targeted districts (green circles). 2.1. Analysis of the strength of the ground motion data The strengths of critical ground motions can be defined by the shock wave, where its effects are measured based on the PGA and PGV. The PSA and SI can reflect the seismic duration and frequency
content of an event [18]. Therefore, we used the PGA, PGV, PSA and SI as parameters to assess the strengths of the ground motions during earthquake damage. In order to correct the baseline error, we used the threestep algorithm proposed by Chiu [19] to assess the strength of the ground motion data and the velocity waveform was obtained by integrating the filtered acceleration waveform. The spectral acceleration was derived from the acceleration waveform and the SI was calculated as the integral of the pseudo-spectral velocity of the ground motion, which ranged from 0.1 to 2.5 s (with a critical damping value of 5%). The maximum values of each parameter at the 48 stations are listed in Table 1. The following observations can be made based on the data provided in Table 1. At 39/48 stations, PGA exceeded 100 gal, where the highest PGA was 957.70 gal at the 051WCW station in the EW component. The largest PGV was 80.99 cm/s, which occurred at the 051SFB station in the NS component. In addition, the highest PSA and SI values were 3320.01 gal and 245.10 cm, respectively, which occurred at the 051WCW station in the EW component and the 051SFB station in the NS component.
2.2. Analysis of the structure CR The collapsed structures were defined as completely damaged or partially damaged structures that could not be repaired. Databases of the structure CRs were collected from two organizations: CEA and CAS [16,17]. The data from the CEA were based on field damage investigations gathered from a number of sources that addressed different building types. The CAS provided CRs of 101 larger residential areas, which were obtained by interpreting aerial images (with spatial resolutions of 0.5 m) taken along the source fault zone. The databases provided by these two organizations were combined and 20 districts were selected with their CRs. The locations of the 20 targeted districts are shown in Fig. 1 (green circles).
Fig. 1. Distributions of the surface ruptures during the Wenchuan earthquake and the 48 seismic stations (red triangles). The 20 targeted districts are shown by green circles.
Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
Table 1 Ground motion parameters of the 48 stations, i.e., PGA, PGV, PSA and SI. No.
Station
PGA/gal
PGV/cm/s
PSA/gal
SI/cm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 42 43 44 45 46 47 48
051AXT 051MXN 051MXT 051MZQ 051SFB 051WCW 051BXD 051BXY 051BXZ 051CDZ 051CXQ 051DXY 051DYB 051GYS 051GYZ 051HSD 051HSL 051JYC 051JYD 051JYH 051JZB 051JZG 051JZW 051JZY 051JZZ 051KDT 051LSF 051LSH 051LSJ 051LXM 051LXS 051LXT 051MED 051MEZ 051MXD 051PJD 051PJW 051PWM 051PXZ 051QLY 051SPC 051SPT 051XJB 051XJD 051XJL 051YAD 051YAM
289.54 421.28 306.57 824.12 581.59 957.70 77.54 190.23 153.25 79.80 184.83 135.11 136.33 320.49 424.48 102.49 142.56 297.19 511.33 519.49 112.20 241.45 173.72 100.04 299.48 34.18 124.14 91.49 118.15 357.81 261.76 379.58 29.60 57.64 246.49 195.81 101.17 287.37 142.20 199.85 40.86 40.15 73.79 132.09 107.64 153.58 175.37
38.97 34.30 20.25 80.99 61.05 47.91 3.56 7.54 6.65 13.19 27.10 21.50 31.61 20.13 29.29 5.51 7.84 30.46 35.93 30.88 6.13 9.50 7.70 5.97 6.07 2.39 6.44 5.66 7.47 21.45 8.39 16.13 2.64 2.63 28.80 15.49 17.13 17.64 19.67 10.34 6.01 6.53 4.86 5.89 13.18 5.11 8.87
1061.52 1380.08 1303.44 2356.05 3111.81 3320.01 333.47 658.12 567.54 196.00 674.05 589.40 472.02 1223.00 2393.09 409.04 872.38 1076.14 2456.49 2769.53 373.56 753.84 646.54 343.25 811.11 128.08 565.08 337.82 384.88 1409.04 1034.96 1625.69 103.18 203.61 1067.78 996.11 473.80 1248.83 468.19 904.93 174.85 126.62 307.25 492.42 344.07 535.62 694.79
113.81 113.98 94.32 193.52 245.10 211.05 14.44 26.35 22.86 40.98 59.10 59.42 72.57 62.29 126.98 19.32 25.52 145.48 123.88 87.16 15.55 29.54 25.92 17.84 16.27 6.36 25.31 25.66 30.46 83.94 28.39 65.73 4.69 6.22 153.52 64.60 50.63 54.48 75.27 46.84 17.07 19.69 13.15 23.52 49.16 23.30 35.47
In order to derive the corresponding strengths of the ground motions in the 20 targeted districts, we used the interpolation and attenuation curves, i.e., the former for their derivation and the latter to verify the consistency of the results. Two strategies were employed to interpolate the data. For the districts located within the area of influence of the stations, the effects of the local subsurface geology and morphology such as soil amplification were assumed to be the same. Thus, the strengths of the ground motion parameters for these districts were interpolated directly from the data for nearby stations, e.g., based on the inverse of the distance to a power. However, for the districts within non-homogeneous soil sites, interpolation was performed at the bedrock level. The ThomsonHaskell matrix was applied to derive the acceleration waves for the bedrock below the relevant stations, where the soil parameters were required to establish the dispersion equations, i.e., frequency, phase velocity, thickness, elastic characteristics and damping of the layers. Next, the waves were interpolated to the area below the targeted districts and the same method was used to obtain the waves for the corresponding districts at the surface [20,21].
131
Finally, the interpolated PGA and PGV were compared with the values derived from the attenuation curves provided by Si et al. [22] for the Wenchuan earthquake. The interpolation results showed that the original and predicted data were generally consistent. As mentioned above, the CRs used in this study were confirmed using comprehensive data, which represented the qualitative building damage at a large scale. Thus, the data derived from the interpolation and attenuation curves satisfied the required accuracy level. The derived values are listed in Table 2. Among the 20 targeted districts, the CRs exceeded 50% in eight districts, which accounted for 40% of the total districts, where Wolong was the worst affected area with a CR of 75%. By contrast, the CRs were relatively low for Anxian, Maoxian and Shigu, where all of the values were below 20%, which accounted for 15% of the group. The CRs of the remaining districts ranged from 20% to 50%. The damage levels in these 20 districts are illustrated in Fig. 2. An overview of the results is provided in Table 3, which show that the CRs exceeded 50% when PGA 4500 gal, PGV 4 45 cm/s, PSA41940 gal and SIs4 140 cm. In addition, the CRs that ranged
Table 2 Derived PGA, PGV, PSA, SI and corresponding CRs for the 20 targeted districts. No.
Affected Cities
PGA/gal
PGV/cm/s
PSA/gal
SI/cm
CRs/%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Tashui Nanxin Diban Qingping Bajiao Wolong Xiaoba Baishi Fuxin Xinshi Tumen Zundao Gongxing Hanwang Qinglian Xinchun Zagunao Shigu Xinqiao Junle
289.54 421.28 306.57 824.12 633.09 957.70 506.82 441.15 468.56 469.59 520.02 551.42 530.25 588.19 457.66 363.80 446.23 384.65 400.96 408.22
38.97 34.30 20.25 80.99 61.05 47.91 46.52 39.82 51.11 52.50 52.58 55.09 51.44 57.00 33.87 31.66 21.43 31.57 32.65 42.33
1061.52 1380.08 1303.44 2356.05 3111.81 3320.01 2022.52 1534.02 1746.77 1845.18 2083.24 2058.26 1947.36 2009.00 2192.43 1539.05 1708.55 1484.77 1894.86 1619.95
113.81 113.98 94.32 193.52 245.10 211.05 141.22 137.21 130.82 104.26 109.63 137.96 147.00 160.23 106.97 94.58 67.84 122.69 105.55 81.10
18.68 23.75 15.00 72.51 71.79 75.00 61.67 34.11 42.03 30.58 64.83 69.80 62.81 54.36 29.43 20.66 29.66 17.10 24.22 30.11
15%
CR<20% 20%
40%
45% Fig. 2. Distribution of the collapse ratios among the 20 targeted districts.
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Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
Table 3 Relationships between CR and PGA, PGV, PSA and SI. CRs
PGA (gal)
PGV (cm/s)
PSA (gal)
SI (cm)
o20% 20–50% 450%
o 385 360–470 4500
o 40 20–50 445
o 1485 1380–1900 4 1940
o 120 100–140 4140
between 20% and 50% roughly corresponded to PGA ¼360–470 gal, PGV ¼20–50 cm/s, PSA¼1380–1900 gal and SI ¼100–140 cm.
3. Analysis of the structural vulnerability 3.1. Structural vulnerability and the damage criteria For a given structural system, a seismic vulnerability function expresses the relationship between the intensity of earthquake excitation and the probable effects on the dynamic performance of that system [23]. Therefore, each vulnerability curve can describe the probability (P f ) of a specific level of damage (d) being equalled or exceeded (D Zd) for a given ground motion parameter (M), as specified in Eq. (1). P f ¼ P D ZdjM ð1Þ Thus seismic vulnerability functions are important for the assessment of seismic hazards, the management of earthquake disasters and anti-seismic structural design [24]. The fragility curve of CR with M can be established based on a standardized normal distribution function, as described in [23]: lnðM=cÞ CR ¼ ϕ ; ð2Þ
ζ
whereϕð U Þ¼ standardized normal distribution function, and the two parameters median (c) and log-standard deviation (ζ ) can be computed using the least squares method. In order to establish the damage criteria, we classified structural damage into three groups according to the results given above: CR o 20% ¼ “minor or moderate damage”, CR of 20–50% ¼“severe damage”, and CR 4 50% ¼“extremely severe damage”. The corresponding correlation coefficients for each level of damage are discussed below.
analysis, the fitted curve agreed well with the actual data when α ¼0.7. In Fig. 3, the dots denote the CRs that correspond to the PGA in targeted districts, the dashed line represents Eq. (3) and the solid line was obtained using Eq. (4). We found that the revised curve provided a better fit to the data when using the reduction coefficient α. The features of the CR distributions are discussed later. Similarly, the fragility curves of CRs that corresponded to PGV, PSA and SI can be established using Eqs. (5) to (7), respectively. lnðPGV=cv Þ CR ¼ ϕ α U
ð5Þ
lnðPSA=csa Þ CR ¼ ϕ α U
ð6Þ
lnðSI=csi Þ CR ¼ ϕ α U
ð7Þ
ζv
ζ sa
ζ si
The relevant median (c) and log-standard deviation (ζ ) parameters were computed for each curve and the results are shown in Table 4. When CR o50%, α ¼ 1. When PGV 446 cm/s, PSA42001 gal and SI4140 cm, CR 450% and α ¼ 0.7. The fragility curves between the CRs and PGV, PSA and SI are shown in Figs. 4–6. The conclusions obtained from the fragility curves are as follows. (1) The CRs were well correlated with the PGA and PGV to a certain extent, as indicated by the standard deviation, thereby demonstrating that there were correlations between the ground motion parameters and the collapse of structures. Reliable estimates of the structural vulnerability were obtained using the ground motion parameters inferred from the robust database. (2) The fitted curve for CR with PGA was better than that for CR with PGV, which may have two possible explanations. First, acceleration can directly reflect the seismic load imparted to buildings, thereby linking to structural damage. However, compared with acceleration, the velocity is affected more by the distribution of faults and the depth of layers. Second, the responses of buildings to the input parameters 100
The original curve The revised curve The actual data
90 80
Under the current lognormal assumption, the vulnerability function between PGA and CR takes the following analytical form: lnðPGA=ca Þ CR ¼ ϕ ; ð3Þ
ζa
70
CR (%)
3.2. Establishment of the relationship between CRs and ground motion parameters
60 50 40 30 20 10
where parameters ca and ζ a were computed using the least squares method as 525 gal and 0.4368, respectively. We estimated that CR would exceed 50% when PGA exceeds 525 gal, but the growth of CR slowed down when the value of PGA exceeded 525 gal, which indicates that the original curve was not entirely consistent with the assumed true relationship. Therefore, a reduction coefficient in terms of α was used to consider the reduction in the growth rate and the revised equation is as follows. lnðPGA=ca Þ ð4Þ CR ¼ ϕ α U
0
0
200
400
800
1000
1200
1400
1600
PGA (gal) Fig. 3. Fragility curve between CR and PGA. The dashed line represents the original curve and the solid line is the revised curve.
Table 4 Computed parameters for the fragility curves of PGV, PSA and SI.
ζa
Since ϕð0Þ ¼ 0:5, the curve remains continuous when the term within the brackets equals zero. According to the comparative
600
median c log-standard deviation ζ
PGV(cm/s)
PSA(gal)
SI(cm)
46.24 0.4599
2001.40 0.3793
135.90 0.3950
Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
ground motion parameters discussed above in order to estimate structural vulnerability.
100
The original curve The revised curve The actual data
90 80
CR (%)
70
Based on the four fragility curves, we determined damage criteria as follows. For PGA, CR exceeded 20% for PGA values4360 gal and it increased sharply to 50% for PGAs4525 gal. For PGV, CR was about 20% for PGVs432 cm/s and it reached 50% for PGVs of ca 46 cm/s. In addition, PSA waso1450 gal for CR valueso20% but42001 gal for CR values450%. SI waso97 cm for CRso20%, but4136 cm for CRs450%.
60 50 40 30 20 10 0
0
10
20
30
40
50
60
70
80
90
100
3.3. Fragility curves for brick-concrete and frame structures
PGV (cm/s) Fig. 4. Fragility curve between CR and PGV. The dashed line represents the original curve and the solid line is the revised curve. 100
The original curve The revised curve The actual data
90 80
CR (%)
70 60 50 40 30 20 10 0 0
500
1000
1500
2000
2500
3000
3500
4000
PSA (gal) Fig. 5. Fragility curve between CR and PSA. The dashed line represents the original curve and the solid line is the revised curve.
100
The original curve The revised curve The actual data
90 80
CR (%)
70 60 50 40
The fragility curves in section 3.2 were obtained by combining the data for all building types, so more detailed results were required to clarify the effects of different damage scenarios on various structural types to obtain a better understanding of the building types. It should be noted that the available data comprised structural damage information related to infrastructure in 10 cities from the 20 targeted areas. These data were processed in order to observe the structural damage sustained by different building types, including brick-concrete structures and frame structures [16]. We used “brick-concrete structure” to denote that brick or block walls and columns carried the vertical load of the building, while concrete was used for horizontal load-bearing beams and slabs. We used “frame-structure” to refer to reinforced concrete frame structures that comprised a frame or skeleton of reinforced concrete [16]. Columns are the primary load-carrying elements in the building and infill walls are used as partitions. Given the small amount of data related to wooden structures this sub-group was excluded from the present study. The CRs for the corresponding to brick-concrete and frame structures in the 10 cities are listed in Table 5. The lognormal form of Eq. (2) allows the vulnerability function between PGA, PSA and CR to be obtained based on the median (c) and the log-standard deviation (ζ ). The parameters c and ζ for each curve were inferred by least squares approximation. The results are shown in Table 6 and the fragility curves are presented in Fig. 7. Table 5 Derived PGA, PSA and corresponding CRs for brick-concrete and frame structures in the 10 cities.
30 20 10 0
133
0
30
60
90
120
150
180
210
240
270
300
SI (cm) Fig. 6. Fragility curve between CR and SI. The dashed line represents the original curve and the solid line is the revised curve.
may differ depending on their age, structural type and seismic design level. (3) The CRs were correlated with the PSA and SI within certain limits, as indicated by the corresponding variances. The statistical deviations in these two parameter correlations were lower than those between CR and PGA, thereby indicating that the PSA and SI may better reflect the relationship between the frequency content of ground motion and the dominant period of buildings, and thus the behaviour of buildings subjected to earthquakes. In addition, because the SI was obtained by numerical integration, it may have been affected by the spread of the site conditions for stations by modifying the spectral amplitudes in each frequency band [25,26]. This demonstrates the feasibility of using the four
No. Affected Cities
PGA/gal
PSA/gal
Brick-Concrete CRs/%
Frame Structure CRs/%
1 2 3 4 5 6 7 8 9 10
289.54 633.09 468.56 469.59 520.02 530.25 588.19 457.66 363.80 400.96
1061.52 3111.81 1746.77 1845.18 2083.24 1947.36 2009.00 2192.43 1539.05 1894.86
20 70 46 36 64 65 64 – – 25
– 23 – – 18 24 25 13 13 7
Tashui Bajiao Fuxin Xinshi Tumen Gongxing Hanwang Qinglian Xinchun Xinqiao
Table 6 Computed parameters for the fragility curves of PGV and SI.
median c log-standard deviation ζ
Brick-Concrete
Frame Structure
PGA(gal)
PSA(gal)
PGA(gal)
PSA(gal)
484.64 0.4265
1927.35 0.4222
852.35 0.5731
2745.72 0.2930
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Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
100
100
Brick-Concrete curve Frame-Structure curve Comprehensive curve data of Brick-Concrete data of Frame-Structure
90 80
80 70
60
CR (%)
CR (%)
70
Brick-Concrete curve Frame-Structure curve Comprehensive curve data of Brick-Concrete data of Frame-Structure
90
50 40
60 50 40
30
30
20
20
10
10 0
0
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
0
500
1000
1500
2000
2500
3000
3500
4000
PSA (gal)
PGA (gal)
Fig. 7. Fragility curves between CR with PGA (a) and CR with PSA (b). The blue line represents the curve for brick-concrete structures and the green line denotes the curve of frame structures. The red line is the comprehensive curve derived in section 3.2.
The following conclusions can be made based on the results given above. (1) In general, the damage situation for buildings in the affected area was valid for brick-concrete and frame structure systems. However, because brick-concrete buildings were the main structural type in the area, the vulnerability curves for brickconcrete structures tended to map the results of the comprehensive curves more closely. (2) As the PGA increased, the growth rate of CRs was slower for frame structures than brick-concrete structures. This suggests that brick-concrete systems are highly brittle, thereby allowing them to be compromised more readily when the maximum strength is exceeded. By contrast, the frame structures provide higher ductility levels and there is little increase in stress beyond the yield strength when they are subjected to nonlinear deformations. (3) When the PSA increased, both the brick-concrete and frame structures tended to be damaged, thereby indicating that the spectrum acceleration provided a closer approximation of the behaviours of buildings during earthquakes than the PGA.
4. Structural damage estimation based on the current code
For “small earthquakes”, the response spectrum is based on the seismic design according to the code. When checking the structural resistance, the “ultimate limit state design” (which is based on the characteristic values inferred by probability theory) is used for the main members. The ground motion design acceleration required for the structure to remain in the elastic stage is determined as the characteristic value of the earthquake action under the seismic fortification condition. Thus, because the necessary structural strength can be reached by withstanding the first level, the goal required to reach the second level (structures can be repaired in a medium earthquake) will also be satisfied, and the seismic requirement can be fulfilled in the third level by the concept design. In general, the design calculation in the first stage can meet the demands of seismic resistance for most structures. 4.2. Estimation of structural damage Based on the code, the horizontal earthquake action F with a single-degree-of-freedom (SDOF) system is determined as, F ¼ m USa ðTÞ;
where m is the mass of the SDOF system and Sa represents the maximum absolute value of acceleration. Eq. (8) can be rewritten as
4.1. Seismic design method The aims of the “Code for Seismic Design of Buildings” [13] (referred to as the code) can be classified in terms of three earthquake performance levels: “minimal damage under a small earthquake, repairable damage under a medium earthquake and non-collapse under a severe earthquake”. The return periods defined for small, moderate and severe earthquake are 50 years, 475 years and 4 2000 years, respectively. The intensity of a moderate earthquake is defined as the basic seismic fortification intensity with a 4 10% probability in 50 years. The specific seismic design can be divided into two stages. The first allows ordinary buildings to resist “small earthquakes”, which is achieved by computing and checking the structural strength and deformation to ensure that the buildings’ main members will not fail under the action of frequent earthquakes, which have a probability of 4 63% in 50 years. The second stage checks the elastioplastic deformation of the main structure in order to prevent global structural collapse during infrequent earthquakes. The seismic fortification criterion of an infrequent earthquake is generally one degree larger than the basic seismic criterion and its probability is 4 2–3%, depending on the risk potential within the region.
ð8Þ
F ¼ mg U
amax Sa ðTÞ U ¼ G U k U βðTÞ; amax g
ð9Þ
where amax is the PGA, G ¼ mg is the weight of the SDOF system, k ¼ amax =g is the seismic coefficient, g is the acceleration due to gravity, and β ðTÞ is the dynamic coefficient. The seismic coefficient k is a key parameter for seismic design, which can be obtained based on observational data. Many previous studies have indicated that if the seismic intensity is doubled, the value of k will also roughly double. The current code employs the seismic fortification intensity and seismic coefficient simultaneously. The value of the seismic coefficient k1 is equal to k/3 for the first stage, and it is 1.5–2.0 times larger than k for the second stage; thus, k2 was determined as 2k in our study. Although earthquakes exhibit some regularities in their frequency and magnitude of damage in a given area over a certain time, earthquakes are complex natural phenomena that can occur randomly, where they may exceed the level of seismic fortification intensity predicted by the seismic zonation maps. Some typical examples of historical highly destructive earthquakes are listed in Table 7 [27–29]. In fact, the seismic fortification intensities in the targeted districts were 2–3 degrees lower than the intensities that they actually experienced during the Wenchuan earthquake.
Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
In order to make structures more resilient during destructive earthquakes, the basic seismic intensity should be determined with a lower exceedance probability limit. Thus, active faults must be investigated and studied to obtain better predictions of the probability and magnitude of future earthquakes. It is also necessary to establish the statistical relationships between the ground motion records and earthquake characteristics, including the source and path features, soil effects, and site conditions.
4.3. Structural damage estimation based on the damage criteria To estimate the damage incurred by the targeted structures when subjected to higher seismic intensities compared with the designed intensities, ranging from 6–8 degrees, the design forces of these structures should be estimated accurately. Thus, the critical seismic fortification acceleration aF should be calculated first by the following equation: aF ¼ k2 U g ¼ 2k U g;
ð10Þ
where g is the acceleration due to gravity and k2 can be determined as k2 ¼ 2k, where k is related directly to the basic
135
seismic intensity. The values of k and the results of PGA=aF for the 20 targeted districts are listed in Table 8. The fragility function of CR with PGA=aF as the argument can be established as follows, lnðPGA=aF =cF Þ CR ¼ ϕ α U ; ð11Þ
ζF
where the parameters cF and ζ F were computed using least squares method as 2.60 and 0.5123, respectively. When PGA=aF o2.60, α ¼1. CR 450% for PGA=aF 42.60 and α ¼ 0.7. As shown in Fig. 8, the fragility curve agreed well with the relationship between PGA=aF and CR. Thus, further conclusions can be made based on these results. The targeted districts may sustain “severe damage” (CRs of 20% to 50%) if PGA=aF ¼ 1.7–2.60. Districts where the PGA=aF 4 2.60 may sustain “extremely severe damage” with CRs of 4 50%. However, Xinqiao town (with red circle) is a special case, where PGA=aF was about 4.1 but the corresponding CR was only 24%. It is possible that the site conditions at Xinqiao town make the general earthquake-resistant capacity of this area better than that in other districts. 4.4. Structural damage prediction based on the revised code
No. Time
Place
Magnitude Fortification Intensity
Epicentral Intensity
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Xingtai Xingtai Yangjiang Liyang Liyang Haicheng Tangshan Fengzhen Buerjin Yangjiang Longzhen Beian Jiujiang Yutian Wenchuan
6.5 7.2 6.4 5.4 6 7.3 7.8 5.8 5.2 5 5 5.3 5.7 7.3 8
VIII IX-X VIII VII VIII IX XI VII strong VIII weak IX weak VII VII VII VII XI
1966.3.8 1966.3.22 1969.7.26 1974.4.22 1979.7.9 1975.2.4 1976.7.28 1981.8.13 1982.3.20 1986.1.28 1986.2.9 1986.3.1 2005.11.26 2008.3.21 2008.5.12
VII(0.1g) VII(0.1g) VII(0.1g) VII(0.1g) VII(0.1g) VII(0.15g) VIII(0.2g) VII(0.1g) VI(0.05g) VII(0.1g) VI(0.05g) VI(0.05g) VI(0.05g) VI(0.05g) VII(0.1g)
The Wenchuan earthquake occurred along the Longmenshan fault [1], which is a thrust fault running through the base of the Longmen Mountains in Sichuan province, but the basic seismic index had been underestimated in this area prior to the occurrence of the earthquake. In order to revise the Chinese Code for Seismic Design of Buildings (GB 50011–2010), studies have focused on the deformation feature of the Quaternary period of the 100
The original curve The revised curve The actual data
90 80 70
CR (%)
Table 7 Comparison of the actual intensity and design intensity of strong earthquakes throughout history.
60 50 40 30 20 10 0 0
1
2
3
4
Table 8 Seismic coefficients and corresponding CRs.
5
6
7
8
9
10
PGA/aF
Location
k
kR
PGA=aF
PGA=aR
CRð%Þ
CRR ð%Þ
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Tashui Nanxin Diban Qingping Bajiao Wolong Xiaoba Baishi Fuxin Xinshi Tumen Zundao Gongxing Hanwang Qinglian Xinchun Zagunao Shigu Xinqiao Junle
0.10 0.15 0.15 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.15 0.05 0.10
0.15 0.20 0.20 0.15 0.15 0.20 0.15 0.20 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.20 0.10 0.15
1.45 1.40 1.02 4.12 3.17 4.79 2.53 2.21 2.34 2.35 2.60 2.76 2.65 2.94 2.29 1.82 2.23 1.28 4.01 2.04
0.97 1.05 0.77 2.75 2.11 2.39 1.69 1.10 1.56 1.57 1.73 1.84 1.77 1.96 1.53 1.21 1.49 0.96 2.00 1.36
18.68 23.75 15.00 72.51 71.79 75.00 61.67 34.11 42.03 30.58 64.83 69.80 62.81 54.36 29.43 20.66 29.66 17.10 24.22 30.11
2.65 3.88 0.85 54.25 34.16 43.58 19.98 4.70 15.97 16.08 21.41 24.90 22.54 29.06 14.88 6.82 13.77 2.61 30.57 10.30
Fig. 8. Fragility curve between CR and PGA=aF . The dashed line represents the original curve and the solid line is the revised curve. The special case of Xinqiao town is indicated by the red circle.
100
The fitted curve The predicated CRs
90 80 70
CR R(%)
No.
60 50 40 30 20 10 0
0
1
2
3
4
5
6
7
8
PGA/aR Fig. 9. Fragility curve between the predicted CRR and PGA=aR .
9
10
136
Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
Longmenshan fault and its corresponding characteristics in terms of activity, surface ruptures, aftershock distributions, slip rates, recurrence periods and the potential for extremely strong earthquakes [30,31]. Ultimately, the basic seismic intensities in the revised code were increased by 0.5, 1.0 or 2.0 degrees, respectively. The revised seismic coefficients kR for the 20 targeted districts are listed in Table 8. The revised aR can be calculated by substituting the revised seismic coefficients kR into Eq. (10), i.e.,aR ¼ kR2 Ug ¼ 2kR Ug. Next, the predicted CRR for PGA during the Wenchuan earthquake were estimated based on the revised aR . The computed values of PGA=aR and CRR are also given in Table 8. The fragility curves for both are presented in Fig. 9. As shown in Fig. 9, most of the predicted CRR s in the targeted districts were below 30%, except for Bajiao, Qingping and Wolong, with 34%, 54% and 43%, respectively. These results indicate that the structural anti-seismic capacity can be increased according to the revised code.
5. Discussion (1) The Wenchuan earthquake caused structural damage on a large scale. Based on data related to damage information around the cities and seismic records, we established how the ground motion parameters were associated with structural damage and the laws that govern these relationships. Clearly, severe ground shaking is the direct cause of building damage during earthquakes, but the factors involved in the damage process are highly complicated and thus a detailed seismic response analysis of different types of structures when subjected to earthquake loads is necessary to understand the mechanisms and processes that lead to structural failure. Furthermore, the use of different ground motion parameters to estimate damage requires a sound theoretical basis to design a seismic fortification criterion. (2) Our approach can be extended to other earthquakes. However, the results obtained for the Wenchuan earthquake show that the level of structural damage and CR were higher than those in the 1995 Kobe earthquake and the 1999 Chi-Chi earthquake [32,33]. This was because the affected districts were less developed rural areas in Sichuan province and thus the earthquake-resistant capacities of the structures were poor in these areas. Brickconcrete buildings were the most common construction type, where most of these buildings had a similar number of stories and structural form. We focused on building collapse in a wider sense, but the comprehensive curves that we obtained may reflect the general damage situation for brick-concrete buildings as well as the specific damage characteristics in the region. In addition, because there were far fewer frame structures than brick-concrete structures, the fragility curves for the former suggest that the damage features do not consider factors such as age, the number of stories and the local geology. (3) The basic seismic fortification standard specified in the “Code for Seismic Design of Buildings” is the acceleration index under the condition that the soil site is category II. In practice, the ground motion parameters and CRs are obtained based on the actual site conditions, but it is not difficult to compare the two directly when establishing the relationship. Strictly speaking, when comparing the PGA with the critical seismic fortification acceleration, adjustments in the PGA should be made according to the actual site conditions using the coefficient specified in the Seismic Ground Motion Parameter Zonation Map of China. For the magnitude of the
ground motion in the present study, the difference in the peak accelerations was about 10% when the site category differed by one level among the four levels. (4) We established the fragility curves of the CRs with the ground motion parameters based on standardized normal distribution functions. However, as the values of the parameters increased, the growth of the CR decreased, thereby indicating that the original curve (Eq. (3)) was not entirely consistent with their relationship. Therefore, we used a reduction coefficient in terms of α to describe the relationship (Eq. (4)). The exact cause of the reduction in the growth rate is still unclear, but the following factors may be considered. a) Due to the uncertainty of the construction levels, material qualities, structural forms, site conditions and the diversity of the natural structural vibration periods, it may have been difficult for the CRs of structures to reach 100% within the meizoseismal area. b) According to the local seismic fortification levels, most of the structures would be damaged with a PGA of 500– 600 gal, but the actual changes in the CRs were small when the PGA exceeded 600 gal, possibly because the targeted districts are located in mountainous areas where the PGA was high for a short duration of time, thereby resulting in a relatively low level of actual structural damage to some extent. In addition, the earthquake-resistance capacity of structures built on rocks is greater.
6. Summary In this study, we obtained observation-based data related to the Wenchuan earthquake and we determined the corresponding ground motion parameters for 20 targeted districts using interpolation methods and attenuation curves. We generalized the vulnerability curves between the CRs and ground motion parameters. If the buildings had been built according to the improved Seismic Fortification Criterion of the revised “Code for Seismic Design of Buildings”, the predicted CRs for the 20 targeted districts would have been reduced significantly compared with the actual damage that they sustained. The main conclusions of this study are as follows. (1) In total, we processed 144 three-component observed records from 48 stations in the targeted districts and the strength of their ground motion parameters, i.e., the PGA, PGV, PSA (5% of damping ratio) and SI (5% of damping ratio). (2) We derived the relationships between the CRs and the ground motion parameters, and we generated their fragility curves based on the standard normal distribution function. The damage criteria were determined as follows. CR4 20% for PGA 4360 gal and CR increased sharply to 50% for PGA 4 525 gal. For PGV, CR was about 20% for PGV 4 32 cm/s and CR ¼50% for PGV of about 46 cm/s. In addition, PSAo1450 gal for CR o20%, and PSA42001 gal for CR 450%. SIo97 cm for CR 420%, and SI 4136 cm for CR 450%. (3) Among the two types of the buildings, brick-concrete structures are highly brittle and readily compromised when the maximum strength is exceeded. By contrast, frame structures have higher ductility levels and thus they exhibit little increases in stress beyond the yield strength when subjected to nonlinear deformations. We found that the fragility curves based on the PSA provided a more accurate approximation of the behaviours of buildings during earthquakes compared with those based on the PGA. (4) We established an effective method for estimating the structural damage levels by using the fragility curve between CR and
Z. Wang, B. Zhao / Soil Dynamics and Earthquake Engineering 72 (2015) 129–137
PGA=aF to eliminate the deviation in the design forces for these structures. The targeted districts could sustain “severe damage” (CR¼20–50%) when PGA=aF of 1.7–2.60. Districts where PGA=aF 4 2.60 could sustain “extremely severe damage”, i.e., CR450%. However, Xinqiao town was a special case, where PGA=aF was about 4.1 but the corresponding CR was only 24%, possibly because the site conditions in Xinqiao town meant that the general earthquake-resistant capacity was better than that in other districts. (5) The predicted CRR that corresponded to the PGA for Wenchuan earthquake can be computed based on the revised seismic coefficient kR , which was used to construct the fragility curve for CRR and PGA=aR . Most of the predicted CRR s in the targeted districts were below 30%, except for Bajiao, Qingping and Wolong, with 34%, 54% and 43%, respectively. These results indicate that the structural anti-seismic capacity can be increased based on the revised code.
Acknowledgements We would like to thank the China Strong Motion Networks Centre for providing the observation-based data and Professor Lei Liping for sharing remote sensing data related to the damage conditions during the Wenchuan earthquake. We would also like to express our deep gratitude to Prof. Elgamal and three anonymous reviewers for many valuable comments. The authors are indebted to Dr. Pedro MartinezVazquez of the University of Birmingham for his useful critiques of this research. This research has been supported by the National Natural Science Foundation of China (No. U1434210 and No. 51278045) and the National Key Technologies Research & Development Program of China (No. 2015BAK19B02). References [1] Xu XW, Wen XZ, Yu GH, et al. Co-seismic reverse- and oblique-slip surface faulting generated by the 2008 Mw 7.9 Wenchuan earthquake, China. Geology 2009;37:515–8. [2] Wood HO, Neumann F. Modified Mercalli intensity scale of 1931. Bulletin of the Seismological Society of America 1931;21:277–83. [3] Furukawa A, Spence R, Ohta Y, et al. Analytical study on vulnerability functions for casualty estimation in the collapse of adobe buildings induced by earthquake. Bull Earthquake Eng 2010;8:451–79. [4] Barbat AH, Pujades LG, Lantada N. Seismic damage evaluation in urban areas using the capacity spectrum method: Application to Barcelona. Soil Dynamics and Earthquake Engineering 2008;28:851–65. [5] Jaiswal K, Wald D, D’Ayala D. Developing empirical collapse fragility functions for global building types. Earthquake Spectra 2011;27:775–95. [6] Sakai Y, Yoshioka S, Koketsu K, et al. Investigation on indices of representing destructive power of strong ground motions to estimate damage to buildings based on the 1999 Chi-Chi earthquake, Taiwan. Journal of Structural and Construction Engineering 2001;549:43–50. [7] Rota M, Penna A, Strobbia CL. Processing Italian damage data to derive typological fragility curves. Soil Dynamics and Earthquake Engineering 2008;28:933–47. [8] Miyakoshi J, Kambara H, Ishii D, et al. Vulnerability function based on earthquake response analysis with dispersion of structural strength and ductility capacity. Journal of Structural Engineering 2005;51B:105–10.
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