Characteristics of ground motion parameters in the 2008 Ms 8.0 Wenchuan earthquake

J.J. Hu & L.L. Xie Key Laboratory of Earthquake Engineering and Engineering Vibration，Institute of Engineering Mechanics, CEA

SUMMARY: The near field earthquake ground motions and engineering damage distribution caused by the great 2008 Ms 8.0 Wenchuan earthquake was investigated to identify the rupture directivity effect. Statistical result indicates that this thrust faulting earthquake, dominated by the unilateral rupture propagation, caused a distinct rupture directivity effect on the ground motion recordings. Specifically, acceleration in forward direction is larger than that of the backward direction, and the difference depends on the rupture distance to the fault; response spectra in the forward direction is higher than that of the backward direction, especially for longer natural period; the difference between the forward and backward direction may reach 2~4 times on average.

Keywords: Wenchuan earthquake, ground motion parameter, directivity, engineering damage

1. THE GREAT WENCHUAN EARTHQUAKE

On May 12, 2008, a great earthquake of magnitude Ms 8.0 occurred in Sichuan province, . The epicenter located (N31.0N, 103.4E) in , which is only 21 km to Dujingyan city and 75 km to the provincial capital Chendu. This earthquake caused severe engineering damage with huge economic loss and death toll. The earthquake affected an extensive area of places, including Sichuan, Gansu, Shanxi, , Yunnan and Ningxia. It also caused a large number of land slids and quake-lakes. The seismic intensity in the epicenter region reaches XI degree. Inversion of fault mechanics and field survey show that the rupture nucleated in town, then propagated to the north east direction. The whole fault is about 300 km from south west to north east, which is predominately a unilateral rupture thus it may cause a directivity effect both in the ground motion distribution and engineering damage (Hu, 2009). Directivity caused by the rupture propagation effect is an important factor which both affects the distribution and attenuation of near-field ground motions and the low frequency wave forms (Somerville and Seism, 1996; Somerville, et al., 1997; Somerville, 2002; Abrahamson and Silva, 1996). This kind of effect is becoming more and more obvious in the near-field ground motions from the recent large earthquakes. The first study on ground motion directivity was carried out by Benioff in 1955, who studied the long period displacement ground motions in the Mw 7.5 Kern County earthquake. While the directivity effect in short period ground motions was not proved until 1978 by Bakun who studied two small earthquakes in middle California, this is more interesting to engineers. After that, with the development of strong motion observation technology, more and more near-field ground motion are provided for studying the directivity effect (Boatwright and Boore, 1982; Archuleta, 1982).

2. GROUND MOTION DATABASE

The 2008 Ms 8.0 great earthquake caused huge damage, it is one of the most destructive earthquakes in China. Strong motion instruments installed in the earthquake fault region recorded amount of near-field ground motions during the main shock. The China Strong Ground Motion Network Center acquired 420 sets of three-component acceleration recordings, which include free field, topographical and structural array stations. Thus it provides a good chance to study the characteristics of the ground motion distributions in the near-field region (Hu, 2009; Li, et al., 2008; Yu, et al., 2009).

We selected 198 sets of near-field acceleration ground motions from the released database. In order to analysis the directivity effect, we avoid the low signal-noise ratio or component-lost or too large rupture distanced recordings. And all the selected stations are on the similar soil site conditions. Figure 1 shows the ground motion stations and fault model. To compare the ground motions in different directions, we classify the stations into two types: stations which located in the forward direction is defined as the Forward Direction (FD) stations (shown as triangular in Figure 1); stations which located in the backward direction is defined as the Backward Direction (BD) stations (shown as circle in Figure 1). So there are 105 stations in FD and 93 stations in BD. Also, to analysis the directivity effect, the original orientated recordings were rotated to Fault Normal (FN) and Fault Parallel (FP) directions.

37 Tong Xin Xi Ning Hai Yuan Huan Xian 36 Gu Yuan XiJi Peng Yang ZhenXi Yuan Feng Ping Liang Huan Ting 35 Long Xian Wu GanShan Gu Qing Shui Li Xian Xi'an 34 Xi He Liang Dang Zhouqu Cheng Huan Xian Xian NanpingWudu Kang Lue Xian Yang 33 Mian Xian Wen Xian Ning Qiang Songpan Qing Chuan Pingwu Guang Yuan 32 Heishui Jian Ge BeichuanJiangyou Garzê Mao XianAn Xian Zitong Zhaggo Jinchuan Li XianWenchuan Ting Latitude 31 Xiaojin Pi XianXindu Gong Zhai Gong Zhai Kang DingTianMing Quan ShanPengshan 30 Tang Litang Lu DingYa'an Hong Ya E MeishanLe Shan Chongqing Han Yuan 29 Dao Cheng Xiang Cheng MianYue Ning Xi 28

27 26 98 100 102 104 106 108 110 Longitude

Figure 1. Strong ground motion stations in Wenchuan Earthquake

3. CHARACTERISTICS OF AMPLITUDE, SPECTRA AND DURATION

3.1. Peak Ground Acceleration Field

The Peak Ground Acceleration (PGA) is one of the most important parameters in characterizing a ground motion. We compare the contour maps and attenuation relations to see how the rupture directivity affects the amplitude distribution and the difference between the FD and FD. Based on the PGAs in all the selected locations, the PGA contour maps were obtained through a two dimensional interpolation method (see Fig. 2). Figure 2 (a), (b) and (c) show the PGA contour maps of FN, FP and vertical component, respectively. Also, in the figures we draw a simple inverted finite fault model. From the contour map we can see that there exists a distinct difference between the FD and BD directions. In other word, the distribution of ground motion amplitude is affected by the rupture propagation direction. Results indicate that: on the one hand, for the similar rupture distance, the amplitude value in the rupture propagation direction (FD) is larger than that of the opposite direction (BD); on the other hand, the attenuation in the FD is slower than that of the BD, which is indicated from the contour intervals.

3.2. Peak Ground Acceleration Attenuation Relations

The quantitative analysis of FD and BD PGA attenuation relations is done through a simple amplitude-distance regression model (see Eqn. 3.1). In Eqn. 3.1, the distance is defined as the closest distance to the fault. Table. 1 is the three regression parameters a, b and c.

log (PGA ) a b *log ( D  c ) (3.1) 10 10 rup

Figure 3 shows the comparison of PGA attenuation relations in FD and BD. Where (a), (b) and (c) is the FN, FP and Vertical component, respectively. We give the FD, BD and all station regression model parameters and the attenuation relations. In Fig. 3, the blue solid line represents the FD attenuation relation; the red dash line represents the BD attenuation relation; the pink dot dash line represents the attenuation relation from all the FD and BD station data.

Table 3.1. PGA attenuation relation model parameters Component a b c FN 15.4193 4.9712 406.6065 FP 13.7855 4.4684 338.7368 Vertical 6.0348 -1.9848 59.6074

From the comparison of the attenuation relation in FD and BD we can see that: on the one hand, for the same rupture distance, the PGA value in FD is larger than that of the BD; on the other hand, with the increasing of the rupture distance, the difference between the FD and BD is decreasing.

37 2 Comparison of FD and BD PGA (FN Comp.) (cm/s ) Xi Ning Hai Yuan Huan Xian 3 700 10 Lanzhou 20 Gu20 Yuan 36 XiJi Peng Yang Forward Direction 50 ZhenXi Yuan Feng 600 Ping Liang Backward Direction 20 Huan Ting FD 0 1 35 20 0 Long Xian Wu GanShan Gu Qing 0Shui 0 8 2 2 2 0 0 0 0 0 500 20 5 20 5 Li Xian Xi'an 0 Xi He 0 34 LiangFeng Dang Xian 5 50 80 Zhouqu Cheng Huan 8Xian Xian 2 0 0 400 10 20 0 2 1Wudu2 Kang LueXian Yang 1 0 0 BD 0 Nanping100 2 00 Mian Xian0 2 12 33 200 Wen Xian 1 10 5 0 Ning Qiang 2 Songpan8 0 300 Qing Chuan 8 0 1 Pingwu Guang Yuan )

0 2 0 5 0 Heishui 0 2 Jian Ge 0 32 0Barkam1 40 0 0Beichuan1 2 2 0 0Jiangyou 2 5 0 8 Garzê Mao XianAn Xian0 0 Zitong 0 0 0 0 200 Jinchuan0 5 Li XianWenchuan 0 Mianyang 2 5 2 Zhaggo 0 6 Mianzhu1 2 Yan Ting1 0 0 Deyang2 20 8 50 Xiaojin 30Pi XianGuanghan 0 Latitude 31 2 0 100 0 0 0 0 Chengdu8 8 2 0 100 0 5 0 8 12Gong0 Zhai 0 10 50 5 0Pengshan 5 PGA (cm/s Kang Ding8 2 0 MeishanZiyang 0 30 Ba Tang Litang 20Lu Ding0Ya'an Hong Ya 20 1 0 0 00 Le Shan Chongqing 8 Han1 Yuan 10 50 E5 Meishan 29 Dao Cheng20 0 0 2 2 2 Xiang Cheng 0 0 Mian Ning 2 0 28 20 (a) FD: log10(PGA)=17.8527+−5.7214*log10(Drup+471.2265) 27 (a) BD: log10(PGA)=229.2775+−58.7403*log10(Drup+7336.3135) Guiyang 0 26 10 1 2 98 100 102 104 106 108 110 10 10 Longitude Rupture Distance (km) 37 2 (cm/s ) Xi Ning Hai Yuan Huan Xian Comparison of FD and BD PGA (FP Comp.) 700 20 20 3 Lanzhou 10 36 20 XiJi Gu Yuan Peng YangXi Feng 2 Zhen Yuan Forward Direction 600 Ping0 Liang Huan Ting FD 0 0 Backward Direction 35 5 2 80Long Xian0 20 Wu GanShan Gu Qing Shui 2 500 5 50 0 0 0 80 Li Xian8 5 Xi'an 0 Xi He 80 0 34 2 Liang Dang 2 Zhouqu0 Cheng80 Xian 0 2 0 2 0 5 2 0 0 5 400 1 WuduKang LueXian Yang 1 2 0 1 0 Nanping 0 20 0 Mian Xian 33 1 0 5Wen Xian 0 2 00 8 4 1 BD 8 0 Ning Qiang2 00 0 10 0 Songpan 3 0 8 1 Qing Chuan 2 0 0 0 300 0 2 12 0 2 Pingwu800 0 1 Guang Yuan 5 0 5200 3 80 ) 1Heishui 02 2 000 Jian Ge 2 32 Barkam0 0 0 2 2 000 2 0 8 1 0 Garzê 1 Mao1 Xian0 Zitong 0 0 5 020 200 8 0 045 Jinchuan0 0 0 Zhaggo Li Xian0 0 5 000Mianyang 0 2 Mianzhu 8 0 3 1 Yan Ting 0 0 1 0 Deyang 2 2 Xiaojin0 Guanghan0 0 Latitude 31 5 1 1 0 400 0 2 Xindu

5 1 0 Chengdu 100 1200 0 2 1 5 0 0 0 0 8 8 0Ziyang Kang Ding Meishan2 20 PGA (cm/s 30 Ba Tang Litang Lu80 DingYa'an 0 1 100 2 0 0

0 2 1 0 05 E MeishanLe Shan Chongqing 1 5 20 8 5 0 Han Yuan 0 0 10 8 2 50 Dao Cheng 0 0 29 Xiang Cheng 5 20 Yue0 Xi Mian2 Ning 0 (b) 2 28 0 (b) 50 FD: log10(PGA)=16.6402+−5.3685*log10(Drup+410.0657) 27 BD: log10(PGA)=240.4647+−61.2371*log10(Drup+7776.167) Guiyang 0 26 10 98 100 102 104 106 108 110 1 2 10 10 Longitude Rupture Distance (km) 37 2 (cm/s ) Xi Ning Hai Yuan Huan Xian Comparison of FD and BD PGA (UP Comp.) 700 3 Lanzhou Gu Yuan 10 36 XiJi Peng Yang ZhenXi YuanFeng Ping Liang Forward Direction 600 Huan Ting Backward Direction 35 Long Xian Wu GanShan Gu Qing Shui 2 0 0 20 2 500 Li Xian Xi'an 2 Xi He 34 0 Liang Dang20 Zhouqu Cheng Xian 801 20 0 400 0 WuduKang LueXian Yang Nanping 80 Mian Xian 0 33 20 Wen Xian 0 2 0 5 120 5 0 0 1 0 Ning Qiang 0 5 8 1 10 0 5 2 00 Qing Chuan 300 2 50 Pingwu1 Guang Yuan 0 1

8 ) Heishui0 0 Jian Ge 2 32 Barkam 0 120 2 1 00 2 3 12 Mao2 00Xian Garzê 0 5 0 Zitong 0 Jinchuan Li Xian0 0 0 Mianyang0 200 Zhaggo 0 40Mianzhu 0 Yan8 Ting 0 5 Deyang 5 5 Xiaojin0 Latitude 31 3 00Pi Xian0 2 10 Chengdu 0 0 120 5 80Gong Zhai 100 2 0 2 Pengshan 0 Kang Ding 0 Ziyang PGA (cm/s 30 Ba Tang Litang Lu DingYa'an Meishan

2 Le Shan Chongqing 0 1 0 0 2 Han2 Yuan 10 0 29 XiangDao Cheng Cheng Yue Xi Mian Ning 0 2 28 (c) (c) 27 FD: log10(PGA)=6.7346+−2.2198*log10(Drup+71.4937) Guiyang BD: log10(PGA)=217.2237+−55.7344*log10(Drup+7296.6677) 0 26 10 1 2 98 100 102 104 106 108 110 10 10 Longitude Rupture Distance (km) Figure 2. PGA contour map. (a) FN Figure 3. PGA attenuation relation in FD and BD. component;(b) FP component; (c) Vertical (a) FN component; (b) FP component; (c) Vertical component component

3.3. Spectral Ordinate

The influence of directivity effect on spectral ordinate of ground motion is analyzed through the comparing the mean spectra of rupture forward and backward sites. Spectrum and mean spectrum of forward and backward sites and their ratio (FD-BD Ratio) are shown in Figure 4. It is observed that , for period shorter than 2sec, the mean spectra of forward sites (blue solid line) is about twice as large as that of backward (black dot and dash line); at long period (T>2sec), directivity effect is more significant and the spectral ratio can reach up to 4. This means the impact of directivity effect on structure with long natural period will be even more significant.

Response Spectra of FN component for 5% Damping Ratio 4 10 Forward Direction Backward Direction 3 10

) 2

2 10

1

Sa (cm/s 10

0 10

−1 10 4 −1 0 10 10 3

2

FD−BD Ratio 1 −1 0 1 10 10 10 T (s)

Figure 4. Mean spectra and its ration in forward and back word direction (FN component)

3.4. Energy Duration

The influence of directivity effect on the relative energy duration is present in this section. To compare the distance dependence of the duration for the backward and forward ground motion, a simple duration-distance attenuation relationship is chosen, described by Equation 3.2. The duration-distance distribution for the forward and backward is shown in Figure 5, along with duration-distance distribution based on the model obtained by Equation 3.2 at all sites including backward and forward. The regressed line for forward is represented with blue solid line, the one for backward and all sites are shown with red dotted line and pink dot dash line respectively, triangle and circle are the indicator for sites of the forward and backward .According to the figure, the duration for backward is markedly larger than forward, and the duration becomes longer with increasing distance. TabD 0.9 rup (3.2)

Forward and Backword Durations of FN Components

Forward Direction Backward Direction

BD 2 10

FD Duration (s)

FD: T =63.2708+0.087505*D 90 rup BD: T =88.9427+0.089724*D 90 rup

1 10 1 2 10 10 Rupture Distance (km)

Figure 5. Relations between duration and distance

4. CONCLUSION

Through the selected 198 sets of three-component strong ground motions, we investigated the amplitude contour maps and attenuation relations of PGA, as well as the spectral ordinate and energy duration in the great Wenchuan earthquake to investigate parameters of ground motion between FD and BD. Results indicate that PGA is affected by the rupture directivity, both the ground motion field and attenuation relation show distinct difference between FD and BD: the amplitude is larger in the FD direction than that of the BD within the same rupture distance; and the difference decreases with the increasing of the rupture distance. Response spectra in the forward direction are higher than that of the backward direction, especially for longer natural period; the difference between the forward and backward direction may reach 2~4 times on average; the duration for backward is markedly larger than forward, and the duration becomes longer with increasing distance.

AKCNOWLEDGEMENT This work was financially supported by Basic Science Research Foundation of Institute of Engineering Mechanics, China Earthquake Administration under Grant 2011B02, and 973 Program under Grant 2011CB013601. Thanks for the China Strong Ground Motion Network Center for providing the strong ground motion data.

REFERENCES

Somerville, P.G. and Smith, N.F.(1996). Forward rupture directivity in the Kobe and Northridge earthquakes, and implications for structural engineering. Seismological Research Letters 67:22,55. Somerville, P.G., Smith, N.F., Graves, R.W., et al.(1997). Modification of empirical strong ground motion attenuation relations to include the amplitude and duration effects of rupture directivity. Seismological Research Letters 68:1, 199-222. Somerville, P.G.(2002). Characterizing near fault ground motion for the design and evaluation of bridges. Proceedings of the Third National Seismic Conference and Workshop on Bridges and Highways. held in Portland, Oregon. Abrahamson, N.A., and Silva, W.J.(1996). Empirical Ground Motion Models, Report to Brookhaven National Laboratory. Boatwright, J. and Boore, D. M. (1982). Analysis of the Ground Accelerations radiated by the 1980 Livermore Valley Earthquakes for Directivity and Dynamic Source Characteristics, Bull. Seism. Soc. Am., 72,1843-1865. Archuleta R.J. (1984). A faulting model for the 1979 Imperial Valley earthquake. Journal of Geophysical Research, 89,4559-4585 Hu, J. J. (2009). Rupture directivity and supershear rupture, Doctoral Dissertation of Institute of Engineering Mechanics, CEA, Li, X.J. Zhou, Z.H. Yu H.Y. and Wen, R. Z. (2008). Investigation and report of seismic damage and reconstruction after Wenchuan earthquake, China architectural press, . Yu, H.Y. Wang, D. and Yang, Y.Q. (2009). Primilnary analysis of strong ground motion acceleration in Ms 8.0 Wenchuan earthquake. Earthquake Engineering and Engineering Vibration 29:1,1-13.