Earthquake Reaearch in China  2017, Vol. 31 Issue (1): 12-24
Development and Prospect of Study on Soil Nonlinear Dynamic Characteristics under Strong-Motion
Wang Yushi1, Li Xiaojun1,2, Lan Riqing1, Wang Ning1, Chen Hongjuan1     
1 Institute of Geophysics, China Earthquake Administration, Beijing 100081, China;
2 College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China
Abstract: Ground motions are significantly influenced by dynamic characteristics of overburden soil layers near ground surface, as thick and soft soil layers would obviously amplify the ground motion strength. The conventional research method on soil nonlinear dynamic characteristics under strong motions is based on experiments in laboratories for the deficiency of observation data, but it is difficult to reliably simulate the complex factors of soils in actual earthquake durations, including loading paths, boundary conditions, and drainage conditions. The incremental data of the vertical downhole observation array, which is comprised of at least one observation point on ground surface and one observation point in a downhole rock base, makes it possible to study soil nonlinear dynamics according to in situ observation data, and provides new basic data and development opportunities to soil nonlinear dynamics studies.
Key words: Strong-motion     Soil dynamics     Local site effect     Strong-motion observation     Vertical array record    

INTRODUCTION

Historical earthquake damage and strong motion observation data show that ground motions are significantly influenced by dynamic characteristics of overburden soil layers near the ground surface (site effect), which is the main factor causing different degrees of building damage and hence should be considered in anti-seismic design for building engineering (Seed et al., 1969; Aki, 1993; Chin et al., 1991; Beresnev et al., 1994; Hu Yuxian, 2006). For general engineering structures, the empirical method currently is used for modification (Li Xiaojun et al., 2001; Gao Mengtan et al., 2015; Stewart et al., 2013; Li Xiaojun, 2013); but for significant engineering structures, the influence degree of dynamic characteristics of overburden soil layers near the ground surface on ground motions should be considered. This provides site-related ground motion input for the analysis of seismic response of engineering structures (Hu Yuxian et al., 2005). When ground motion intensity reaches a certain scale (for example, when peak ground motion acceleration PGA is over 75cm/s2), nonlinearity of soil dynamic parameters should be considered (Régnier et al., 2013).

1 SITE AMPLIFICATION PHENOMENA AND SOIL NONLINEAR DYNAMIC CHARACTERISTICS

The attention given to the site seismic amplification effect can be traced back to at least the year 1898 (Milne, 1898), but observational evidences back then stemmed mainly from artificial seismic explosion rather than natural earthquakes. Since the 1906 San Francisco earthquake, the fact that soft soil sites aggravate earthquake damage has gradually aroused attention (Richter, 1958; Borcherdt et al., 1976). For example, after the Venezuela MS 6.5 earthquake in 1967, 10 to 24-storey buildings seismically designed in Caracas city in the Caracas valley were severely damaged, and the damage rate was closely related to the thickness of overburden soil layers: the damage rate of buildings on 230m-300m overburden soil layers was as high as 80%, the damage rate of buildings on 160m-230m overburden soil layers 75%, while buildings on shallow soil layers suffered almost no damage (Seed et al., 1972; Drake, 1993). In the Michoacan MS 8.1 earthquake in Mexico in 1985, the epicentral distance from Mexico City, located in the Mexico basin, was about 400km, but 35% buildings in the lacustrine region in the city were subjected to different degrees of damage. 5 to 15-storey mid-high buildings were particularly seriously damaged, meanwhile buildings lower than 5 storeys and higher than 23 storeys were slightly damaged (Seed et al., 1988; Esteva, 1988; Drake, 1993). In the Loma Prieta earthquake in 1989, the San Francisco Bay area and Santa Cruz, located on a thick soft soil site, suffered from significantly heavier damage (Seed et al., 1990, 1991). In the 2008 Wenchuan MS 8.0 earthquake and 2014 Ludian MS 6.5 earthquake, the old town of Hanyuan and Longquan village of Longtoushan, located on loose landslide deposit, also suffered more severe damage than that in the surrounding hard site areas (Li Ping et al., 2012; Ye Liaoyuan et al., 2014).

For the deficiency of strong motion records, the research of site effect based on strong motion observation data started rather late. Gutenberg (1957) first studied the effects of local site conditions on ground motions from the perspective of seismology using observation data obtained from the Anderson-Wood torsion seismometer. Earlier evidences of site effects were recorded for the 1985 Mexico MS 8.1 earthquake, showing that the peak ground acceleration obtained at the Ministry of Transportation and Communication of Mexico, which lies on a soft clay site, was about 5 times of that for hard soil site in nearby mountainous area (Drake, 1993). Records from the Treasure Island station on a soft soil site and Yerba Buena Island station on a nearby bedrock site for the 1989 Loma Prieta earthquake and its following aftershocks (Darragh et al., 1991; Seed et al., 1991; Borcherdt et al., 1992), records from TAP056A station on soft soil layers and TAP056 station on a hard soil site which is only 20m away for multiple earthquakes that occurred in Taiwan during April and May 2004 (Wen et al., 2008), and records from 0514Z0 station on soft soil layers and 0514Z1 station on bedrock site which only 50m away among the Zigong Topography Observation Array for the Wenchuan MS 8.0 earthquake, all showed that soil layer sites significantly amplify intensities of ground motions (Wang Haiyun et al., 2010; Yang Yu et al., 2011; Tang Hui et al., 2012). A large number of strong motion records for the 1994 Northridge earthquake (Trifunac et al., 1996), the 1995 Niigata earthquake in Japan (Pavlenko et al., 2003) and the 1999 Chi-chi earthquake in Taiwan (Pavlenko et al., 2008) also showed the existence of significant site effect. In the 2014 Ludian MS 6.5 earthquake, records of strong motion acceleration obtained at 53LLT station which lies on a loose landslide deposit showed significant amplitude anomalies, especially showing that response spectra with periods of 0.2-1s had abundant components (Cui Jianwen et al., 2014; Ji Kun et al., 2014), which may also have been influenced by soft site conditions. Observation data from vertical arrays such as KiK-net etc indicate that the site amplification effect for ground motions is not exceptional, but a common phenomenon.

Fig. 1 Comparison of spectral accelerations at 0514Z0 station on soil site and 0514Z1 station on the rock base in the Zigong Topography Observation Array, which shows the significant influence of seismic site effect on ground motion

With the accumulation of strong ground motion observation data, influences of soil nonlinear dynamic characteristics on site effect have gradually become a research focus (Liang Jianwen et al., 2013). Under the effect of strong motions, strain of soil medium can reach a magnitude of 10-2, and soil will show significant nonlinear viscoelasticity or even elastic-plastic characteristics (Ishihara, 1996), which has been confirmed in strong motion observations. For example, Tokimatsu et al. (1981), found that soil dynamic stiffness decreased with the increase of strain by analyzing ground acceleration records obtained at four site points for different earthquakes. Records at Treasure Island station and other stations on soft soil sites for the 1989 Loma Prieta earthquake and its aftershocks also show obvious nonlinear characteristics (Darragh et al., 1991; Bersenev et al., 1996; Rubinstein et al., 2004). Strong motion records for the 1994 Northridge earthquake (Trifunac et al., 1996; Field et al., 1997; Hartzell, 1998; Cultrera et al., 1999), the 1999 Chi-Chi earthquake in Taiwan (Pavlenko et al., 2008) and the 2011 east Japan earthquake (Bonilla et al., 2011a, 2011b) all showed that site soil presented obvious dynamic nonlinearity (Fig. 2). Records acquired by strong motion observation arrays in Taiwan such as SMART1, SMART2 and LSST more conclusively revealed that under the effect of strong motion, site soil showed obvious dynamic nonlinearity (Wen, 1994; Beresnev et al., 1995a, 1995b; Borja et al., 1999; Huang et al., 2001; Wen et al., 1994, 2008). Régnier et al. (2013), based on analysis of a large amount of recorded data from KiK-net, semi-quantitatively and semi-qualitatively evaluated site soil nonlinear dynamic characteristics and its influencing parameters, and found that when PGA>75cm/s2, site soil nonlinearity should be taken into account. Because of the influence of soil nonlinear characteristics, under the effect of ground motions of different intensities, the amplification effects of soil layers at the same site also show significant differences, which should be taken into consideration when determining ground motion input for the seismic design of engineering structures.

Fig. 2 Borehole transfer functions computed at KiK-net station TTRH02 in Japan The orange shaded area represents the 95% confident limits of the transfer function using weak-motion events (PGA < 10cm/s2). The solid line is the transfer function computed using the October 2000 Tottori main shock data (From Bonilla et al., 2011a)
2 THEORETICAL AND EXPERIMENTAL STUDY OF SOIL NONLINEAR DYNAMIC CHARACTERISTICS

As soil is a typical type of nonlinear medium, its stress-strain constitutive relation models can be mainly categorized as a nonlinear elastic model and elastic-plastic model, such as the Mohr-Coulomb model, Druker-Prager model, Duncan-Zhang's EB and Eμ model, Cambridge model, Lade-Duncan model, Tsinghua elastic-plastic model, Shen Zhujiang's Double-yield Surface model and other improved models. Soil elastic-plastic constitutive models focus on problems such as plastic behaviors and strength of soil body under slow loading-unloading conditions. Except for overlaying soil layers, sand liquefaction and soft soil seismic subsidence on fault dislocations, it is difficult for a soil body to attain a plastic state under strong motions. Therefore, under the effect of strong motions, a simplified nonlinear elastic model is generally used for the study of soil nonlinear dynamic characteristics.

Researchers have provided different models describing soil nonlinear dynamic characteristics. Kanai (1952) firstly analyzed site response using a linear viscoelastic constitutive model, then Seed and Idriss et al. explored soil nonlinear characteristics under strong motions using the method of equivalent linearization (Idriss et al., 1968a, 1968b; Seed et al., 1969), followed by more complex nonlinear constitutive models which are also applied in the analysis of seismic responses of soil layers (Iwan, 1967; Hardin et al., 1972; Joyner et al., 1975; Pyke, 1979; Lee et al., 2009). At present, equivalent linearization method (Li Xiaojun, 1989, 1992a, 1992b, 1992c; Li Xiaojun et al., 1994; Qi Wenhao et al., 2007; Ding Haiping et al., 2014) and its frequency-dependent modified method are still widely used in China (Sugito et al., 1994; Yoshida et al., 2002; Assimaki et al., 2002; Meng, 2007; Jiang Tong et al., 2007; Wang Wei et al., 2010; Wang et al., 2014), but the methods have inherent defects (Krarner, 1996; Pender, 1997).

For a sufficiently long time, research of soil nonlinear dynamic characteristics has been mainly based on experiments in laboratories (Chen Guoxing et al., 1995; Field et al., 1998; Yuan Xiaoming et al., 2000; Zhao Chenggang, 2006; Xie Dingyi, 2007; Du Xiuli et al., 2011; Liu Hanlong, 2012), however, loading paths that soil bears in indoor experiments and in actual the earthquake process are obviously different (Krarner, 1996), and factors such as drainage conditions and boundary conditions cannot be simulated accurately. Also, when soil strain is relatively larger, using experimental results of different soil dynamic characteristics will cause significant differences in the calculation of site seismic response (Lv Yuejun et al., 2003; Chen Guoxing et al., 2004, 2007; Lan Jingyan et al., 2012; Jiang Qifeng et al., 2014). Therefore, it is necessary to use strong motion records from in situ measurement to evaluate discreteness and reliability of soil dynamic nonlinear parameters.

3 STUDY OF SOIL NONLINEAR DYNAMIC CHARACTERISTICS BASED ON GROUND SURFACE STRONG-MOTION OBSERVATION DATA

Before the advent of recorded data from vertical arrays, the methods used for the study of soil nonlinear dynamic characteristics based on ground surface strong-motion observation data mainly included the standard spectral ratio method and generalized inversion method.

The standard spectral ratio method, also known as the reference site method and traditional spectral ratio method, is the earliest and the most intuitive quantitative method for the study of local site effect. This method usually chooses a station on bedrock site, which is very close to the station on soil layer site, as a reference station, and in this way, we believe that ground motions at both site stations will not be affected by source characteristics and transmission routes, and by comparing spectral ratios of strong motion records at station on the soil site and reference station on a bedrock site, we can quantitatively analyze the influences of local site conditions on ground motions (Borcherdt, 1970; King et al., 1984; Darragh et al., 1991; Gagnepain-Beyneix et al., 1995; Frankel et al., 2002; Schlindwein et al., 2003; Wen et al., 2008). The disadvantage of this method is that except for limited special observatory arrays.It is not easy to find reliable reference stations on bedrock sites near stations on soil-layer sites.

In the method of standard spectral ratio, the reference station on a bedrock site must be close enough to the station on a soil-layer site, thus a suitable reference station cannot always be found. To deal with this problem, Andrews (1986) and Moya et al. (2003) put forward and developed the generalized inversion method. This method uses at the same time acceleration records obtained from multiple stations on bedrock site (not necessarily very close to the station on a soil-layer site) for multiple strong earthquakes, and by linear inversion, isolated the effects of source items, transmission routes and site response. Although the generalized inversion method to a certain extent solves the problem of reference station selection in the standard spectral ratio method, as research is usually done in the frequency domain, it cannot to take into account the influence of source characteristics and transmission routes. Theoretically, it is only applicable to small-moderate earthquakes that caused by a small area of fault rupture. Compared with the standard spectral ratio method, the precision of the generalized inversion method is obviously lower. For stations on bedrock sites involved in inversions, there are significant errors between inversion results and observation records (Roumelioti et al., 2003), and results also have great differences from observed ground surface/downhole spectral ratios (Tsuda et al., 2006, 2010), therefore, it can be concluded that the method of generalized inversion is only applied for semi-qualitative and semi-quantitative evaluation of site effects. One possible improvement is to use the empirical Green's function method for more accurate inversion of the rupture process (Hartzell et al., 2011).

4 EMPIRICAL STUDY OF SOIL NONLINEAR DYNAMIC CHARACTERISTICS BASED ON OBSERVATION DATA FROM VERTICAL ARRAYS

Recorded data by vertical arrays is the most direct and strongest evidence reflecting soil nonlinear dynamic characteristics (Pender, 1997), and an increase in the amount of recorded data makes possible the empirical research of soil nonlinear dynamic characteristics based on strong motion observations. Earlier records of strong motions were obtained by the Garner Valley and Hollister vertical earthquake observation array in California, USA (Steidl et al., 1996, 1998; Archuleta, 2000) and the Luodong vertical array in Yilan, Taiwan (Wen, 1994; Beresnev et al., 1995a, 1995b; Zeghal et al., 1995; Borja et al., 1999; Huang et al., 2001; Wen et al., 1994, 2008) for some moderate to strong earthquakes, and multiple vertical arrays in Sendai, Shizuoka and Kushiro in Japan (Sato et al., 1996; Satoh et al., 1995, 1997; Iai et al., 1995; Pavlenko et al., 2003) for several great earthquakes such as the 1995 Hanshin earthquake, leading the empirical research of soil nonlinear dynamic characteristics based on in situ measured data from vertical arrays. However, due to limited data, these early studies are mostly case studies of forward modeling of site seismic response, rarely involving researches of soil dynamic parameter inversions and characteristics under the effect of strong motions.

After the 1995 Hanshin earthquake, the vertical array observation network KiK-net, evenly distributed in Japan was set up, and currently, the number of vertical arrays has increased to 696. Since October 1997, KiK-net has acquired enormous records of ground surface three-component and downhole bedrock three-component accelerations, and till March 2015, has obtained 1700 sets of strong motion records with PGA>200gal and more than 110 sets of strong motion records with PGA>500gal, among which, the 2008 Iwate-Miyagi inland MS 7.2 earthquake has the greatest PGA, which is 4, 022.1gal recorded at IWTH25 station. Six MS ≥6.8 earthquakes were recorded with more than 300 sets of records, among which, the greatest earthquake was the east Japan MW 9.0 earthquake on March 11, 2011 (525 sets of records). Such an abundance of vertical array records provides basic data for the study of soil nonlinear dynamic characteristics under the effect of strong motions.

Using vertical array records, the frequency domain method (Elgamal et al., 2001; Harichance et al., 2005), time main method (Glaser et al., 2000) and combination method (Assimaki et al., 2007) are all used in inversions of soil dynamic parameters. However, the frequency domain method cannot express time-varying features of parameters, the time domain method cannot be directly applied and the combination method is only for equivalent linearity parameter inversions (Hashash et al., 2010). In recent years, inversion techniques such as self-learning simulation (Tsai et al., 2008, 2009; Groholski, 2012; Groholski et al., 2014) and the square optimization algorithm (Mercado et al., 2015) have been introduced into the inversions of soil dynamic parameters, and has been preliminarily applied in numerical simulation tests and liquefaction analysis of Wildlife vertical array records in California. Good results have been achieved.

5 THE CURRENT STATUS OF VERTICAL ARRAYS FOR STRONG MOTION OBSERVATIONS IN MAINLAND OF CHINA

The #2 Xiangtang vertical array, covering 3 observation points which are located on the earth's surface, 16m underground and 32m underground respectively, was set up in Luanxian County, Tangshan, China in 1994 (Xie Lili et al., 1999), and #3 Xiangtang vertical array, covering 2 observation points which are located on the earth's surface and 47m underground, was added in 2001 (Zhou Yongnian et al., 2005), by which, a batch of acceleration records of strong motions with relatively lower intensities were acquired (Zhou Zhenghua et al., 2004), providing basic data for research of site seismic amplification effect and soil nonlinear dynamic characteristics for engineering sites in Chinese mainland (Chen Xueliang et al., 2007; Lu Tao et al., 2008). The Tonghai site effect array set up in 2007 includes #3 and #4 vertical arrays, of which #3 vertical array contains 3 observation points which are located on the earth's surface, 30m and 60m underground respectively, and #4 vertical array contains 3 observation points which are located on the earth's surface, 45m and 90m underground respectively. Since built, Tonghai site effect station has also acquired observation data for moderate to strong earthquakes with relatively larger epicentral distances, but has not yet obtained strong motion acceleration records with greater intensities.

Although observation data from KiK-net vertical array are available for public download, it's difficult to get soil samples from corresponding station sites, restricting the development of comparative study between field observation and indoor experimental results. So far, there are only a total of four vertical arrays in the Chinese mainland as mentioned above. Compared to the number of strong motion observation stations in the Chinese mainland, or the vertical array scale in Japan, the number of vertical arrays for observations of seismic responses at soil-layer sites needs to be increased.

6 PROSPECT

Vertical array observation records provided sufficient and reliable basic data for the study of soil nonlinear dynamic characteristics under effect of strong motions, and new opportunities for empirical research of soil nonlinear dynamics based on in situ observation. The following may become subjects of intense interest:

(1) Test and improvement of soil nonlinear dynamic models based on observation data. Soil nonlinear dynamic models commonly used are currently obtained based on indoor experimental data, reflecting that the effectiveness and applicability of soil nonlinear dynamic behavior in the process of actual strong motions still need to be tested and improved by observation data of strong motions.

(2) Inversions of soil nonlinear dynamic parameters based on observation data. At present, soil nonlinear dynamic parameters are also achieved based on indoor experimental data, and high discreteness and uncertainty often exist in the indoor experimental results. Soil nonlinear dynamic parameters need to be inverted with strong motion records, and further be compared with indoor experimental results, for the purpose of testing and improvement of indoor experiment methods.

(3) Test and improvement of indoor experimental methods for soil nonlinear dynamic parameters. As observation points for strong motions are scattered, for engineering sites located outside the range of observation points, soil nonlinear dynamic parameters still need to be obtained by indoor experimental methods. Deficiencies of current indoor experimental methods can be explored by comparing inversion results of soil nonlinear dynamic parameters based on strong motion observation data from vertical arrays with indoor experimental results, so its precision can be improved.

(4) Improvement of soil nonlinear dynamic response algorithm and engineering application. Current soil nonlinear dynamic response algorithm also needs inspection and improvement. In practical engineering applications, the method of equivalent linearization is still the most commonly used. However, the equivalent linearization method cannot reflect changes of soil properties within the duration of shaking, which can easily cause the phenomenon of false resonance. When using the equivalent linearization method, in each step of iteration process within the duration of shaking, dynamic shear modulus and dynamic damping ratio are constants, therefore, the natural vibration characteristics of the system remain the same. However, in the actual process of earthquakes, as soil is nonlinear, natural vibration characteristics change frequently. When frequency components of the input earthquake energy consist with a certain order of natural vibration frequency of equivalent linearization site model, the frequency component will be significantly amplified, especially when there are weak and soft intercalated layers in site models, and resonance may cause the calculated value of strain of weak intercalated layers to be far greater than the actual strain value. Therefore, it is necessary to improve the reliability of equivalent linearization method for site seismic response calculation by comparison with field measured data, comprehensive consideration of factors such as ground motion levels and weakness of site soil, improving the key parameter taking value method for equivalent strain reduction coefficient, in the method of equivalent linearity or taking into account the frequency dependency of soil dynamic parameters.

ACKNOWLEDGEMENTS

We extend heartfelt thanks to anonymous reviewers for their pertinent opinions and suggestions, and thank KiK-net and CSMNC for the download service they provided for access to strong motion observation data.

This paper has been published in Chinese in the journal of Technology for Earthquake Disaster Prevention, Volume 11, Number 3, 2016.

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强震动作用下土体非线性动力特征研究发展与展望
王玉石1, 李小军1,2, 兰日清1, 王宁1, 陈红娟1     
1 中国地震局地球物理研究所, 北京 100081;
2 北京工业大学建筑工程学院, 北京 100124
摘要:浅地表覆盖土层动力特性对地震动影响显著, 软厚土层会明显改变地震动强度及频谱特性。由于观测数据匮乏, 强震动作用下土体非线性动力特征研究长期以来均以室内试验为主, 但在实验室中难以可靠地模拟实际地震历程中土体承受的加载路径、边界条件、排水条件等复杂因素。近二十年来竖向台阵(至少包含一个地表测点和一个井下基岩测点)记录数据大量增加, 为土体非线性动力学研究提供了新的基础数据与发展机遇, 使基于现场观测的土体非线性动力特征实证研究成为可能。
关键词强震动    土动力学    局部场地效应    强震动观测    竖向台阵记录