Earthquake Reaearch in China  2018, Vol. 32 Issue (4): 560-573
Experimental Research on Dynamic Shear Modular Ratio and Damping Ratio of Sandy Gravel Soil
Wang Xiaojun1, Zhao Fengxin2, You Hongbing2, Nie Dawei1
1. Shaanxi Earthquake Agency, Xi'an 710068, China;
2. China Earthquake Disaster Prevention Center, Beijing 100029, China
Abstract: The dynamic shear modulus ratio and damping ratio of sandy gravel are important parameters for the seismic response analysis of valley geomorphic sites, which have an important impact on the determination of design ground motion parameters. In this paper, the dynamic triaxial test of sandy gravels has been performed based on the project of the Shangluo Seismic Microzonation. Combined with the other results of sandy gravel, the recommended results of slightly dense, medium dense and dense sandy gravel were obtained. By building the typical site model, the influence of the dynamic shear modulus ratio and the damping ratio uncertainty on the seismic response of the site is studied. The results show that the uncertainty of the average of the dynamic shear modulus ratio and the damping ratio ±1 times the standard deviation has little effect on the peak acceleration of the sandy gravel site, and the rationality of the grouping and statistical results is explained. Under different probability levels, the change in the shear modulus ratio and damping ratio leads to a significant difference in the high frequency response spectrum. The response spectrum of 0.04-0.1s ranges from about 20%, but it has little effect on the long period spectrum of more than 1.0s. The study of dynamic shear modulus ratio and damping ratio of sandy gravel has the ability to improve the reliability of the designing ground motion parameters.
Key words: Sandy gravel     Dynamic shear modular ratio     Dynamic damping ratio     Uncertainty     Seismic response analysis of site

INTRODUCTION

In the seismic safety evaluation of various major engineering sites, the equivalent linearization method is generally used for site seismic response analysis (General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China et al., 2005). The dynamic shear modulus ratio and damping ratio of soil are very critical parameters and have important influence on the calculation results (Wang Shaobo et al., 2001; Sun Rui et al., 2010; He Weimin et al., 2016). The study of soil dynamics parameters has an important theoretical significance and engineering application value to reveal the dynamic characteristics of soil and reasonably determine the design ground motion parameters.

The dynamic shear modulus ratio and damping ratio of various types of soils are determined mainly by dynamic triaxial or resonant column tests. Many scholars conducted experimental research and achieved many valuable results (Sun Jing et al., 2003; He Weimin, et al., 2016). The most widely used in China is the dynamic shear modulus ratio and damping ratio of the 12 soils given by Liao Zhenpeng (1989) and was adopted as the original industry standard (China Earthquake Administration, 1994). Yuan Xiaoming et al. (2000) further provided recommended soil dynamic parameters for clay, silty clay, silt, sand, etc. with buried depths of ≤10m and 10m-20m. In addition, some scholars also targeted some typical soil dynamic characteristics in certain areas such as Bohai (Lü Yuejun et al., 2003), Nanjing (Chen Guoxing et al., 2004), Beijing (Shi Chunhua et al., 2009), Shanghai (Zhang Yajun et al., 2010), Xi'an (Chen Dangmin et al., 2012), Chengdu (Rong Mianshui et al., 2013; Shi Bingxin et al., 2015), Wuhan (Kong Yuyang et al., 2014) and Kunming, (Li Jianyou et al., 2015) analyzed the regional differences of the soil dynamic characteristics.

Sandy gravel is widely distributed in the landforms of river valleys. However, due to the difficulty in sampling and high test costs, there are few experimental studies on sandy gravel soil samples in the above studies. In practical engineering, the dynamic shear modulus ratio and damping ratio of gravels given by Liao Zhenpeng (1989) are generally used. In recent years, Zhang Xiaoping et al. (2011), Chen Dangmin et al. (2012), Rong Mianshui (2013) and others have calculated the dynamic parameters of gravel and sand gravel. Due to the small number of statistical samples, the above findings have certain limitations.

In this paper, the dynamic triaxial test of sandy cobbles and the dynamic triaxial test results of collecting and sorting other sandy gravel rocks are used to perform group statistics to obtain the recommended triaxial recommendations for slightly dense, medium dense and dense sandy gravel. A typical site model is established to study the influence of the dynamic shear modulus ratio and the uncertainty of the damping ratio on the seismic response of the site, and to provide reference for improving the reliability of the seismic safety evaluation results of the engineering site.

1 SANDY GRAVEL SAMPLE MAKING

Due to the inability in obtaining an active triaxial test specimen of sandy gravel in the field, the common practice is to remodel in the room according to the actual measured density, the number of shots, and wave speed, and to make its dynamic triaxial sample.The vast majority of sites in the Shangluo earthquake area are located on river valley terraces. The gravel layer is widely distributed in the floodplain and first-order terraces with a maximum thickness of up to 10m. It is the main lithology of the site of the Shangluo community, and its gravel framework is made of long quartz with sub-circular or angular general grounding, and general grading with a particle size of 1.5cm-3cm, gravel sand and a small amount of cohesive soil fill. The Institute of Engineering Seismic Investigation of Shaanxi Province conducted a dynamic triaxial test of sandy gravel in the Shangluo Earthquake Zoning Project of Shangluo city(Shaanxi Engineering Seismic Investigation Institute, 2016).

The team drilled six groups of sand gravel (Fig. 1) using mechanical and manual methods next to the boreholes SLZK7, SLZK27, SLZK20, SLZK3, SLZK43, and SLZK33 on the floodplain. Each group weighed at least 50kg. The density of sand gravel was measured on-site using the water-filling method, and they were 1.98, 2.05, 1.93, 2.10, 2.32 and 1.99g/cm3, respectively. When the indoor dynamic triaxial test was conducted, the sand gravel sample was mainly produced based on the compaction and remodeling of the sand gravel taken. Sample size: Φ150mm×300mm

 Fig. 1 Sandy gravel sampling and the water-filling method
2 TEST INSTRUMENTS, METHODS AND PRINCIPLES

Since the particle size of sandy gravel is larger than 5mm, the general equipment can't complete the dynamic triaxial test. Therefore, Heilongjiang Seismic Technology Co., Ltd. was commissioned to use the most advanced GDS-DYNTTS dynamic triaxial test system (Fig. 2) to perform the sand gravel triaxial test. The consolidation stress ratio is 1.0, and the consolidation pressure is determined according to the self-gravity stress of the soil. When the self-gravity stress of the soil is less than 100kPa, it is consolidated at 100kPa. When the soil's own weight pressure is greater than 600kPa, it is consolidated at 600kPa. All specimens have an axial deformation increment of less than 0.01mm per hour as the consolidation stability criterion. The dynamic triaxial test is to close the drain switch after the sample has been pressure-consolidated and then increasing dynamic stress is applied progressively to each sample. Each stage is shaken 10 times and the corresponding dynamic stress and dynamic strain are collected. The test standard is "Standard for Geotechnical Test Methods" (GB/T50123-1999) (The State Bureau of Quality and Technical Supervision et al., 1999).

 Fig. 2 The GDS-DYNTTS dynamic triaxial testing equipment

A large number of experimental studies have shown that the dynamic constitutive relation of the soil (Liao Zhenpeng, 1989) can be expressed in the following hyperbolic form:

 $\tau = \frac{\gamma }{{a + b\gamma }}$ (1)

In formula(1), τ is the shear stress, γ is the shear strain; a and b are the experimental parameters, which are related to the soil properties. From this we can get the expression of the dynamic shear modulus:

 ${G_{\rm{d}}} = \frac{1}{{a + b\gamma }}$ (2)

Among them, a=1/Gdmax, Gdmax is the maximum dynamic shear modulus that can be considered as the shear modulus b=1/τmax corresponding to the shear strain of 10-6. τmax is the maximum shear stress when the shear strain tends to infinity. The expression of the normalized dimensionless dynamic modulus ratio is:

 $\frac{{{G_{\rm{d}}}}}{{{G_{{\rm{dmax}}}}}} = \frac{1}{{1 + \gamma /{\gamma _{\rm{r}}}}}$ (3)

Where γr is the reference strain and its expression is γr=a/b.

The following relationship exists between the hysteretic damping ratio and the dynamic shear modulus:

 $\lambda = {\lambda _{\max }}{\left({1 - \frac{{{G_d}}}{{{G_{{\rm{dmax}}}}}}} \right)^\alpha }$ (4)

In formula(4), λmax is the maximum hysteretic damping ratio when the dynamic shear modulus tends to zero. α is the empirical coefficient, which is often set to 1.

3 TEST RESULTS AND COMPARATIVE ANALYSIS 3.1 Test Results

Fig. 3 is the curve of dynamic shear modulus ratio and damping ratio with dynamic shear strain obtained from the results of dynamic triaxial tests. For the sake of comparison, the gravel results given by Liao Zhenpeng (1989) are also given in the figure.

 Fig. 3 Dynamic triaxial test results of the sandy gravels

It can be seen from Fig. 3 that there are large differences betweon the dynamic shear modulus ratio and the damping ratio with different sand gravels, which are related to the shear wave speed, density, gradation, and other parameters of the sample. Liao Zhenpeng's sandy gravel results (1989) are widely used in site safety evaluation of different projects. The dynamic shear modulus ratio decays faster with shear strain, and the damping ratio is relatively small, compared with the results of 6 groups of samples. Compared with the large differences, it is shown that the results given by Liao Zhenpeng (1989) have certain limitations.

3.2 Other Literature Results

Due to the high cost of moving triaxial tests for sandy gravel and gravel samples, the number of samples for this test is relatively small. Therefore, indoor blinding and reshaping samples based on on-site standard shots, wave speeds, etc. were further collected with reference to the dynamic parameters of gravel, sand gravel soil samples from other documents with consistent principles and methods. These soil samples all contain a large proportion of gravel, some of the coarse sand, and some contain a small amount of clay, with similar dynamic characteristics.

Zhang Xiaoping et al. (2011) collected dynamic triaxial test data of sandy gravel in Dalian and gave the average results (Fig. 4). Chen Dangmin et al. (2012) combined the Xi'an earthquake zoning project and conducted four sets of dynamic triaxial tests on sand gravel samples. The results are shown in Fig. 4. Rong Mianshui et al. (2013) collected dynamic triaxial test data for slightly dense, medium dense and dense sand gravel in the Chengdu Basin. The average results are shown in Fig. 5. For the sake of comparison, the results of sandy gravel given by Liao Zhenpeng (1989) are given in the figure.

 Fig. 4 Dynamic triaxial test results from Zhang Xiaoping et al. (2011) and Chen Dangmin et al. (2012)

 Fig. 5 Dynamic triaxial test results of sandy gravel from Rong Mianshui et al.(2013)

In addition, we also collected the dynamic triaxial results of sand-bearing gravel in seismic zone from the Urban Earthquake Zoning of Hotan City completed by the Institute of Natural Disaster Prevention of Xinjiang Uygur Autonomous Regine (2015a), the Earthquake Planning of Hutubi County (Institute of Natural Disaster Prevention of Xinjiang Uygur Autonomous Regine, 2015b), and the Earthquake Zoning of Kashga Ecomoc Zone completed by China Earthquake Disaster Prevention Center, and active fault detection (earthquake zoning section) (China Earthquake Disaster Prevention Center, 2015) (Fig. 6).

 Fig. 6 Other dynamic triaxial test results of gravel from seismic microzonation

As can be seen from these figures, the results generally reflect the changing rule of the dynamic triaxial test of sandy gravel soil samples, but there are also certain differences, which are related to the parameters such as density and particle size distribution of different samples.

3.3 Recommended Results

Based on the dynamic triaxial test results of the seven groups of sandy gravel soil specimens given by Rong Mianshui et al. (2013), Chen Dangmin et al. (2012), and the earthquake subdivision report, we divide 17 samples into 3 groups according to the degree of compaction of the samples, namely:

(1) Slight sandy gravel: mainly distributed in the upper part and middle part of the gravel layer, the gravel content is 45%-60%, and most of them are not in contact. The N120 hammering number is 4-7 hits/10cm, and the density is approximately 1.90 g/cm3. Shear wave speed is about 200-300m/s in altogether 6 groups, as shown in Fig. 7(a).

 Fig. 7 The statistical results of the sandy gravel dynamic triaxial test

(2) Medium-density sandy gravel: mainly distributed in the lower part and middle part of the gravel layer, the content of gravels is 60%-70%, staggered in continuous contact. The N120 hammering number 7-10 blows/10cm, and the density is about 2.00g/cm3. Shear wave speed is about 300-400m/s in a total of 5 groups, as shown in Fig. 7(b) below.

(3) Dense sandy gravel, with gravel content greater than 70%, staggered, in continuous contact. The N120 hammering count is greater than 10 strokes/10cm, and the density is approximately 2.20g/cm3. Shear wave velocity is approximately 400-500m/s in a total of 6 groups, as shown in Fig. 7(c).

The average ratio of dynamic shear modulus and damping ratio of each group of sand gravel under eight typical strains are obtained, as shown in Fig. 7(d) and Table 1, and the dynamic shearing modeling ratio G/Gmax and the standard deviation of the damping ratio λ are also given in the table.

Table 1 The average and standard deviation of the dynamic shear modulus ratio and the damping ratio of sandy gravel

As can be seen from the figure, the results given by Liao Zhenpeng (1989) and Zhang Xiaoping et al.(2011) are basically consistent with the results obtained by statistical analysis of the slightly sand gravel, and the dynamic shear modulus ratio is significantly lower than those of medially dense and dense sand gravel.

4 EXAMPLE ANALYSIS

Because there are certain differences between different groups of samples, in order to study the impact of the dynamic shear modulus ratio and the uncertainty of the damping ratio on the seismic response of the site, a typical site model consisting of sand gravel is established. The parameters such as shear wave velocity and thickness are as follows in Table 2.

Table 2 Calculation model of the site

The dynamic triaxial numbers 1, 4, and 7 represent the average values of slightly dense, medium dense, and dense sandy gravel (Table 1); the numbers 2, 5, and 8 represent slightly dense, medium dense, dense sand gravel, and the dynamic shear modulus of the gravel stone is +1 times the standard deviation from the mean, and the standard deviation of the damping ratio is -1 times the standard deviation; and the numbers 3, 6, and 9 represent the movements of the slightly dense, medium dense and dense sand gravel. The shear modulus is ±1 standard deviation from the mean and the damping ratio is + 1 standard deviation. The maximum value of the grouping is taken when the dynamic shear modulus ratio is greater than 1.0; the grouping minimum value is taken when the damping ratio is less than zero. According to Chen Guoxing et al. (2007), the impact of these two combinations on the peak surface acceleration is most significant.

The input ground motion is based on the unrelated three different sample time histories synthesized based on the bedrock response spectrum in the seismic safety evaluation of a project site, as shown in Fig. 8 and Fig. 9. The peak accelerations with a probability of surpassing 63%, 10%, and 2% for 50 years were 72.1gal, 202.8gal, and 358.8gal, respectively. The calculated peak acceleration and surface acceleration response spectra are shown in Table 3 and Fig. 10(a)-(i).

 Fig. 8 The input acceleration time history

 Fig. 9 Accelerated response spectrum of bedrock

Table 3 Horizontal peak acceleration at different levels of exceeding probability (unit: gal)

 Fig. 10 Surface acceleration response spectrum

(1) Effect on Peak Acceleration

From Table 3 and Fig. 10(a)-(i), we can see that under the action of input ground motion at different levels of probability, when the dynamic shear modulus is more than the mean value of +1 times the standard deviation and the damping ratio is equal to -1 standard deviation, the acceleration is maximum. The peak value of the ground acceleration is the minimum when corresponding to the mean -1 standard deviation of the dynamic shear modulus and the +1 standard deviation of the average damping ratio.

The results of the working condition 1 of the slightly dense (average) are between the those of the other two working conditions, reflecting the influence of the dynamic shear modulus ratio and the damping ratio on the ground surface peak acceleration.

Take the example of the slightly dense sand gravel with 2% surpassing probability in 50 years (Fig. 10(c)). The ratio of the dynamic shear modulus of each soil layer in working condition after iteration in the slightly dense 1 had an average of 0.844, and the damping ratio of 0.039. The ratio of dynamic shear modulus of each soil layer in working condition 3 in the slightly dense had an average of 0.671, and the damping ratio of 0.115. The ratio of dynamic shear modulus of each soil layer in working condition 1 in the slightly dense had an average of 0.759, and a damping ratio of 0.076. The higher the ratio of the dynamic shear modulus and the smaller the damping ratio after iteration, the greater the peak acceleration obtained; the smaller the dynamic shear modulus ratio and the greater the damping ratio, the smaller the obtained peak acceleration is.

Table 3 also gives the ratio of the average value of different working conditions, which are the ratio of slightly dense 2, slightly dense 3 and slightly dense 1; the ratio of medium dense 5, medium dense 6 and medium dense 4; dense 8, dense 9 and dense 7 ratio. For the sandy gravel site, compared with the slightly dense 1, medium dense 4, and compact 7 operating conditions, the dynamic shear modulus ratio and damping ratio increase or decrease caused the ground surface peak acceleration to increase by 1.06—1.14 times and decrease by 0.91—0.95 times, about 10% or so.

Due to the harder sand and gravel site, the shear strain under medium and strong earthquakes is smaller, and the impact on peak acceleration is less than that of soft soil sites (Chen Guoxing et al., 2007; Shi Chunhua et al., 2009), but the impact laws are basically the same. In addition, although there is a certain degree of dispersion in the experimental results of each group, the uncertainty of the dynamic shear modulus ratio and the standard deviation of ±1 standard deviation of the damping ratio has little influence on the peak acceleration, which also indicates the rationality of the grouping and statistical results.

(2) Effect on Surface Response Spectrum

Fig. 11(a) gives the ratios of the response spectra of slightly dense 2, slightly dense 3, and slightly dense 1 with different probability levels. Fig. 11(b) gives the ratio of the lower response spectrum of the working conditions of density 8, dense 9 and dense 7. It can be seen from Fig. 10 and Fig. 11 that under different levels of probability, the changes of the dynamic shear modulus ratio and the damping ratio led to significant differences in the high-frequency partial response spectrum, and the 0.04s-0.1s response spectrum changes around 20%, with the highest value up to 25%, but it has little effect on the long-term response spectrum greater than 1.0s. The main reason is that the sand gravel site is hard, and is sensitive to the response of the high frequency. The change of the dynamic shear modulus ratio and the damping ratio leads to the obvious amplification or reduction of the high frequency partial response spectrum.

 Fig. 11 Influences on the surface acceleration response spectrum
5 CONCLUSION

This paper makes use of dynamic triaxial test results of sandy gravel carried out by the Shangluo Earthquake Zoning Project, combined with dynamic triaxial test results and empirical values of other gravel soil samples collected and arranged, and through grouping statistical analysis, obtains the recommended triaxial test results for slightly dense, medium dense and dense sand gravel. A typical site model is established to study the earthquake response of the uncertainty of the dynamic shear modulus ratio and the uncertainty of the damping ratio of sand gravel to the site. The research shows:

(1) The recommended results of the dynamic triaxial tests for slightly dense, medium dense, and dense sandy gravel obtained from statistical analysis of groups reflect the effect of compactness on the dynamic modulus ratio and damping ratio. Although there is some dispersion in the experimental results of each group, the uncertainty of the dynamic shear modulus ratio and the standard deviation of ±1 standard deviation of the damping ratio has little effect on the peak acceleration, which also explains the rationality of grouping and statistical results.

(2) The site of sandy gravel is relatively hard, and the shear strain under medium and strong earthquakes is small, and the impact on the peak acceleration is less than that of soft soil, but the influences are basically the same.

(3) At different levels of probability, the dynamic shear modulus ratio and the damping ratio result in significant differences in the high-frequency partial response spectra. The 0.04-0.1s response spectrum varies around 20%, but it responds to long-periods greater than 1.0s. The spectrum has little effect.

This paper has been published in Chinese in the journal of Technology for Earthquake Disaster Prevention, Volume 13, Number 1, 2018.

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1. 陕西省地震局，西安 710068;
2. 中国地震灾害防御中心，北京 100029