<figure><img src="image_1.png" /></figure>

HAL
open science

# Property estimation of free-field sand in 1-g shaking table tests

Chengshun Xu, Zhiwei Jiang, Xiuli Du, Lijun Deng, Zheng Li

<figure><img src="image_2.png" /></figure>

## To cite this version:

Chengshun Xu, Zhiwei Jiang, Xiuli Du, Lijun Deng, Zheng Li. Property estimation of free-field sand in 1-g shaking table tests. Earthquake Engineering and Engineering Vibration, 2022, 21 (3), pp.591-604. 10.1007/s11803-022-2105-4. hal-04391117

HAL Id: hal-04391117

https://univ-eiffel.hal.science/hal-04391117

Submitted on 12 Jan 2024

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<figure><img src="image_1.png" /></figure>

HAL
open science

# Property estimation of free-field sand in 1-g shaking table tests

Chengshun Xu, Zhiwei Jiang, Xiuli Du, Lijun Deng, Zheng Li

<figure><img src="image_2.png" /></figure>

## To cite this version:

Chengshun Xu, Zhiwei Jiang, Xiuli Du, Lijun Deng, Zheng Li. Property estimation of free-field sand in 1-g shaking table tests. Earthquake Engineering and Engineering Vibration, 2022, 21 (3), pp.591-604. 10.1007/s11803-022-2105-4. hal-04391117

HAL Id: hal-04391117

https://univ-eiffel.hal.science/hal-04391117v1

Submitted on 12 Jan 2024

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Public Domain
1

# Seismic Responses of Sand and Parameters Estimation Using 1-g Shaking Table

2

## Tests

3

4

Chengshun Xu¹, Zhiwei Jiang²,³, Xiuli Du⁴, Lijun Deng⁵, Zheng Li⁶

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6

## Corresponding Author:

7

Xiuli Du

8

College of Architecture and Civil Engineering

9

Beijing University of Technology

10

100 Ping Le Yuan, Chaoyang District, Beijing 100124, PR China

11

12

Phone: +86-13801139161

13

Email: duxiuli@bjut.edu.cn

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¹ Professor, College of Architecture and Civil Engineering, Beijing University of Technology, Beijing
100124, China, xuchengshun@bjut.edu.cn, 86-13401111718

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18

² -, College of Architecture and Civil Engineering, Beijing University of Technology, Beijing
100124, China, zhiweijiang163@163.com, 86-13391816693

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³ Postdoc, Department of Civil Engineering, Tsinghua University, Beijing 100124, China,
zhiweijiang163@163.com, 86-13391816693

21

22

⁴ Professor, College of Architecture and Civil Engineering, Beijing University of Technology, Beijing
100124, China, duxiuli@bjut.edu.cn, 86-13801139161

23

24

⁵ Associate Professor, Department of Civil Engineering and Environmental Engineering, University
of Alberta, Edmonton, Canada, T6G 1H9, ldeng@ualberta.ca, 1-780-492-6210

25

26

⁶ IFSTTAR, GERS, GMG, Allée des Ponts et Chaussées, Bouguenais cedex, France,
zheng.li@ifsttar.fr

27
1

# Seismic Responses of Sand and Parameters Estimation Using 1-g Shaking Table

2

## Tests

3

4

Chengshun Xu¹, Zhiwei Jiang²,³, Xiuli Du⁴, Lijun Deng⁵, Zheng Li⁶

5

6

## Corresponding Author:

7

Xiuli Du

8

College of Architecture and Civil Engineering

9

Beijing University of Technology

10

100 Ping Le Yuan, Chaoyang District, Beijing 100124, PR China

11

12

Phone: +86-13801139161

13

Email: duxiuli@bjut.edu.cn

14

15

16

¹ Professor, College of Architecture and Civil Engineering, Beijing University of Technology, Beijing
100124, China, xuchengshun@bjut.edu.cn, 86-13401111718

17

18

² -, College of Architecture and Civil Engineering, Beijing University of Technology, Beijing
100124, China, zhiweijiang163@163.com, 86-13391816693

19

20

³ Postdoc, Department of Civil Engineering, Tsinghua University, Beijing 100124, China,
zhiweijiang163@163.com, 86-13391816693

21

22

⁴ Professor, College of Architecture and Civil Engineering, Beijing University of Technology, Beijing
100124, China, duxiuli@bjut.edu.cn, 86-13801139161

23

24

⁵ Associate Professor, Department of Civil Engineering and Environmental Engineering, University
of Alberta, Edmonton, Canada, T6G 1H9, ldeng@ualberta.ca, 1-780-492-6210

25

26

⁶ IFSTTAR, GERS, GMG, Allée des Ponts et Chaussées, Bouguenais cedex, France,
zheng.li@ifsttar.fr

27
The seismic response of the free-field soil in the 1-g shaking table tests is crucial for the seismic response of buried structures in tests. But experimental data of 1-g shaking table tests of the free-field sand with a height greater than 1.5 m was very rare. There may be confusion when conducting the experimental design or analysis for the medium to large scale 1-g shaking table tests on buried structures. In the present paper, the 1-g shaking table tests of a 3-m-thick sand deposit were carried out, to provide the dynamic properties and deformation data of the soil for the researchers with the needs to conduct 1-g shaking table tests on buried structures. Typical experimental data were presented and dynamic soil properties were estimated using the white noise, pulse and earthquake motions. The shear strain distributions along the elevation were analysed and discussed. The 3-D finite element model of sand was calibrated using the test records and the model was then used to study the estimated properties and parameters. Results show that the frequencies, relative density and lateral deformation of the soil were notably varied during the tests. Despite of the variation, the parameters in the 3-D modelling could be approximately fitted using the experimental data throughout the entire tests to calibrate the numerical model. The large shear strain responses were observed in the middle region of the soil. The buried structures might have a large seismic response if it was buried in the region.

**Keywords:** 1-g shaking table test, seismic response of sand, dynamic soil properties, shear strain distribution, Davidenkov model
The seismic response of the free-field soil in the 1-g shaking table tests is crucial for the seismic response of buried structures in tests. But experimental data of 1-g shaking table tests of the free-field sand with a height greater than 1.5 m was very rare. There may be confusion when conducting the experimental design or analysis for the medium to large scale 1-g shaking table tests on buried structures. In the present paper, the 1-g shaking table tests of a 3-m-thick sand deposit were carried out, to provide the dynamic properties and deformation data of the soil for the researchers with the needs to conduct 1-g shaking table tests on buried structures. Typical experimental data were presented and dynamic soil properties were estimated using the white noise, pulse and earthquake motions. The shear strain distributions along the elevation were analysed and discussed. The 3-D finite element model of sand was calibrated using the test records and the model was then used to study the estimated properties and parameters. Results show that the frequencies, relative density and lateral deformation of the soil were notably varied during the tests. Despite of the variation, the parameters in the 3-D modelling could be approximately fitted using the experimental data throughout the entire tests to calibrate the numerical model. The large shear strain responses were observed in the middle region of the soil. The buried structures might have a large seismic response if it was buried in the region.

**Keywords:** 1-g shaking table test, seismic response of sand, dynamic soil properties, shear strain distribution, Davidenkov model
48

# 1. Introduction

49

50

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52

53

54

Compared with a geotechnical centrifuge test, a 1-g shaking table test enables large-scale soil-structure models and allows multi-point seismic motions to the models, and therefore in certain circumstances may be more favourable for the research in the seismic response of buried structures.

Researchers have conducted a number of 1-g shaking table tests on buried structures, e.g. subway stations [Kheradi et al. 2018], tunnels [Yu et al. 2018], and piles [Cengiz and Guler 2018], which examined the seismic behaviours of respective buried models buried in various soil types.

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Past 1-g shaking table tests suggested that the seismic response of underground structures was usually small or even remained elastic under extremely strong motions, in contrast to the observations from centrifuge tests or numerical analyses. The elastic response was often attributed to the scaling law and the limited geo-stress under the 1-g condition. There may be problems when analysing the tests results barely according to the scaling relationships. From another point of view, the seismic response of buried structures is primarily affected by the seismic deformation of the surrounding soil and relative stiffness between the soil and structure [Wang 1993]. Seismic responses of the underground structures in the 1-g shaking table tests can be estimated if the seismic deformation and stiffness of the corresponding free-field soil are understood.

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68

It should be noted that results of the 1-g shaking table tests cannot represent the seismic responses of the prototype underground structures. The seismic responses of the prototype are usually obtained using the complementary numerical analyses. As the underground structures sometimes have a complex geometry, the numerical model can be developed in three-dimension (3-D) and should be calibrated against experimental results. As the responses of the free-field soil is critical to the seismic
48

# 1. Introduction

49

50

51

52

53

54

Compared with a geotechnical centrifuge test, a 1-g shaking table test enables large-scale soil-structure models and allows multi-point seismic motions to the models, and therefore in certain circumstances may be more favourable for the research in the seismic response of buried structures.

Researchers have conducted a number of 1-g shaking table tests on buried structures, e.g. subway stations [Kheradi et al. 2018], tunnels [Yu et al. 2018], and piles [Cengiz and Guler 2018], which examined the seismic behaviours of respective buried models buried in various soil types.

55

56

57

58

59

60

61

62

63

Past 1-g shaking table tests suggested that the seismic response of underground structures was usually small or even remained elastic under extremely strong motions, in contrast to the observations from centrifuge tests or numerical analyses. The elastic response was often attributed to the scaling law and the limited geo-stress under the 1-g condition. There may be problems when analysing the tests results barely according to the scaling relationships. From another point of view, the seismic response of buried structures is primarily affected by the seismic deformation of the surrounding soil and relative stiffness between the soil and structure [Wang 1993]. Seismic responses of the underground structures in the 1-g shaking table tests can be estimated if the seismic deformation and stiffness of the corresponding free-field soil are understood.

64

65

66

67

68

It should be noted that results of the 1-g shaking table tests cannot represent the seismic responses of the prototype underground structures. The seismic responses of the prototype are usually obtained using the complementary numerical analyses. As the underground structures sometimes have a complex geometry, the numerical model can be developed in three-dimension (3-D) and should be calibrated against experimental results. As the responses of the free-field soil is critical to the seismic
69 responses of buried structures, the model calibration of the corresponding free-field soil is the most
70 important step toward the seismic simulation of the prototype underground structures. While the
71 calibration using the test results can be well performed on the condition that the properties of the free-
72 field soil are estimated.

73 Several researchers studied the seismic behaviour of free-field soil using the “free-field” motion
74 recorded at places far from the structures in the tests involving the soil-structure interaction [Borghei
75 and Ghayoomi 2019; Candia et al. 2016]. However, conducting free-field analyses in such a manner
76 may have been compromised because the structures may influence the soil nonlinearity during the tests
77 [Hashash et al. 2018; Chandra and Guéguen 2019]. Independent free-field tests are still needed in order
78 to further analyse the seismic responses of buried structures.

79 The dynamic experiments of free-field soil have been studied researchers prior to the tests on soil-
80 structure interaction. Moghadam and Baziar [2016] conducted free-field soil tests to check the
81 performance of the absorbing boundary of the box before performing shaking table tests of subway
82 stations. Chen et al. [2010] performed shaking table tests of the free-field soil to check how the
83 boundary effect of the wall of the container influence the tests results. Two groups of shaking table
84 tests on utility tunnels were then conducted after the check. Yan et al. [2015] carried out multi-points
85 shaking table tests of the free-field as the preliminary work for the subsequent multi-points shaking
86 table tests on long tunnels. Results show that the boundary effect of the box was very slight and did
87 not influence the responses of the synthetic soil in the container. These studies focused more on the
88 boundary condition provided by the container and the seismic soil deformation and stiffness were
89 rarely discussed.
69 responses of buried structures, the model calibration of the corresponding free-field soil is the most
70 important step toward the seismic simulation of the prototype underground structures. While the
71 calibration using the test results can be well performed on the condition that the properties of the free-
72 field soil are estimated.

73 Several researchers studied the seismic behaviour of free-field soil using the “free-field” motion
74 recorded at places far from the structures in the tests involving the soil-structure interaction [Borghei
75 and Ghayoomi 2019; Candia et al. 2016]. However, conducting free-field analyses in such a manner
76 may have been compromised because the structures may influence the soil nonlinearity during the tests
77 [Hashash et al. 2018; Chandra and Guéguen 2019]. Independent free-field tests are still needed in order
78 to further analyse the seismic responses of buried structures.

79 The dynamic experiments of free-field soil have been studied researchers prior to the tests on soil-
80 structure interaction. Moghadam and Baziar [2016] conducted free-field soil tests to check the
81 performance of the absorbing boundary of the box before performing shaking table tests of subway
82 stations. Chen et al. [2010] performed shaking table tests of the free-field soil to check how the
83 boundary effect of the wall of the container influence the tests results. Two groups of shaking table
84 tests on utility tunnels were then conducted after the check. Yan et al. [2015] carried out multi-points
85 shaking table tests of the free-field as the preliminary work for the subsequent multi-points shaking
86 table tests on long tunnels. Results show that the boundary effect of the box was very slight and did
87 not influence the responses of the synthetic soil in the container. These studies focused more on the
88 boundary condition provided by the container and the seismic soil deformation and stiffness were
89 rarely discussed.
90

Researchers also regarded the free-field soil as a large sand specimen and carried out the shaking table tests to identify the dynamic soil properties [Sadrekarimi 2013, Tsai et al. 2016; Dihoru et al. 2016] or to validate the design of the soil containers and the absorbing boundaries [Fishman et al. 1995; Dou and Byrne 1997; Lombardi et al. 2015]. The free-field soil was also seen as a site and the seismic site responses were studies [Rayhani and Nagger 2008; Hashash et al. 2015]. These studies on free-field soil did not aim to support a test on buried structures.

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The authors carried out three groups of shaking table tests to study the seismic responses of underground structures with complex geometry. The present study introduces a part of the them, i.e. the shaking table tests of the 3-m-thick free-field sand. The primary objective of the study is to provide seismic properties and deformation data of the sand column for the researchers with the needs to conduct 1-g shaking table tests on buried structures. A literature review suggests that experimental data of shaking table tests of the free-field soil with a height greater than 1.5 m are rare and the seismic behaviour of the free-field soil is unclear in the larger scale shaking table tests because the soil was pressure-depended material.

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In the present study, a series of shaking table tests of sand deposit and 3-D finite element modelling were carried out. The dimensions of the sand deposit were 3.2 m × 2.4 m × 3 m (length×width×height). Clean sand used in this study had a largest grain size of 2 cm. In total, 25 input motions were imposed in the test sequence, aiming to represent the seismic deformations for buried structures in the non-free-field tests. Dynamic soil properties were estimated using the white noise, pulse and earthquake motions. The seismic deformation of soil along the elevation were analysed and discussed. The 3-D finite element modelling of the sand deposit was calibrated using the time histories

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Researchers also regarded the free-field soil as a large sand specimen and carried out the shaking table tests to identify the dynamic soil properties [Sadrekarimi 2013, Tsai et al. 2016; Dihoru et al. 2016] or to validate the design of the soil containers and the absorbing boundaries [Fishman et al. 1995; Dou and Byrne 1997; Lombardi et al. 2015]. The free-field soil was also seen as a site and the seismic site responses were studies [Rayhani and Nagger 2008; Hashash et al. 2015]. These studies on free-field soil did not aim to support a test on buried structures.

96

97

98

99

100

101

102

103

The authors carried out three groups of shaking table tests to study the seismic responses of underground structures with complex geometry. The present study introduces a part of the them, i.e. the shaking table tests of the 3-m-thick free-field sand. The primary objective of the study is to provide seismic properties and deformation data of the sand column for the researchers with the needs to conduct 1-g shaking table tests on buried structures. A literature review suggests that experimental data of shaking table tests of the free-field soil with a height greater than 1.5 m are rare and the seismic behaviour of the free-field soil is unclear in the larger scale shaking table tests because the soil was pressure-depended material.

104

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110

In the present study, a series of shaking table tests of sand deposit and 3-D finite element modelling were carried out. The dimensions of the sand deposit were 3.2 m × 2.4 m × 3 m (length×width×height). Clean sand used in this study had a largest grain size of 2 cm. In total, 25 input motions were imposed in the test sequence, aiming to represent the seismic deformations for buried structures in the non-free-field tests. Dynamic soil properties were estimated using the white noise, pulse and earthquake motions. The seismic deformation of soil along the elevation were analysed and discussed. The 3-D finite element modelling of the sand deposit was calibrated using the time histories
recorded in tests, which would be further applied in the 3-D analysis of buried structures. Numerical
analyses were also conducted to study the estimated properties and parameters.

## 2. Experimental programs

A series of shaking table tests (STT) were conducted to study the seismic deformation of the 3-m
thick sand deposit. The following subsections describe the geotechnical properties of the soil,
experimental setup, instrumentation and input motions.

### 2.1. Properties of sand

The sand was collected at a site of Beijing Subway Line 6, Shijingshan District, Beijing, China.
Fig. 1 shows the grain size distribution and basic properties of the sand used in the shaking table test.
The values of the coefficient of uniformity ($C_u$), coefficient of curvature ($C_c$) and median grain
diameter ($D_{50}$) were 8.3, 0.75 and 0.82 mm, respectively. With a fines content less than 2%, the soil
was classified as poorly-graded sand (SP) according to Unified Soil Classification System. The
initial water content ($w$) was 6.3%. The initial total unit weight ($\gamma_t$) of the soil built in the shaking
table container was 17.6 kN/m$^3$. The values of the maximum and minimum void ratio ($e_{max}$ and $e_{min}$)
were 0.92 and 0.43, respectively.

<figure><img src="image_3.png" /></figure>

126

Figure 1. Physical properties of the sand and grain size distribution in the shaking table test.
111

recorded in tests, which would be further applied in the 3-D analysis of buried structures. Numerical
analyses were also conducted to study the estimated properties and parameters.

112

113

**2. Experimental programs**

114

A series of shaking table tests (STT) were conducted to study the seismic deformation of the 3-m
thick sand deposit. The following subsections describe the geotechnical properties of the soil,
experimental setup, instrumentation and input motions.

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116

117

**2.1. Properties of sand**

118

The sand was collected at a site of Beijing Subway Line 6, Shijingshan District, Beijing, China.

119

Fig. 1 shows the grain size distribution and basic properties of the sand used in the shaking table test.

120

The values of the coefficient of uniformity ($C_u$), coefficient of curvature ($C_c$) and median grain
diameter ($D_{50}$) were 8.3, 0.75 and 0.82 mm, respectively. With a fines content less than 2%, the soil
was classified as poorly-graded sand (SP) according to Unified Soil Classification System. The
initial water content ($w$) was 6.3%. The initial total unit weight ($\gamma_t$) of the soil built in the shaking
table container was 17.6 kN/m$^3$. The values of the maximum and minimum void ratio ($e_{max}$ and $e_{min}$)
were 0.92 and 0.43, respectively.

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<figure><img src="image_3.png" /></figure>

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<caption>**Figure 1.** Physical properties of the sand and grain size distribution in the shaking table test.</caption>
The maximum shear modulus ($G_{max}$) of soil at the initial state in the shaking table tests was roughly estimated and understood using the torsion shear tests (TST). It was also used to avoid qualitative mistakes when estimating $G_{max}$ using the pulse motions, which will be introduced in the subsequent sections. The largest grain diameter of sand allowed in the TST was only 1 mm and the sand grain with diameter greater than 1 mm was sieved out to make the scalped specimen. Therefore, the modulus of the specimen may be larger than the sand in STT [Wichtmann and Triantafyllidis 2009].

The specimen was a hollow cylinder with a size of 10 cm×6 cm×15 cm (outer diameter × inner diameter × height). The values of $C_u$, $C_c$ and $D_{50}$ of the remolded sand specimen were 4.9, 2.0 and 0.4 mm, respectively. The soil specimen was constructed with $\gamma_t$ of 16.9 kN/m³ and water content of 6.3%. To approximate the stress state of the soil at a depth of 2.1 m in the STT, an empirical value of 0.4 for the soil lateral pressure coefficient ($K_0$) was applied and the TST was performed under a vertical pressure of 37.5 kPa and a lateral pressure of 15 kPa. Results showed that the value of $G_{max}$ at small shear strain amplitude was 43 MPa.

## 2.2. Model soil construction

The STT was carried out at China Academy of Building Research, Beijing, China. The operating frequency of the shaking table in the range of 0.1~50 Hz. The soil container was a 3.2 m × 2.4 m × 3 m (length × width × height) unconstrained laminar shear box with a 1 cm thick inner rubber membrane. Fig. 2 (a) shows the shaking table and laminar shear box. Each frame making up the box had a height of 12 cm and the frames were supported with rollers. The input base motions were excited at the bottom of the box in the longitudinal direction.
128

The maximum shear modulus ($G_{max}$) of soil at the initial state in the shaking table tests was roughly estimated and understood using the torsion shear tests (TST). It was also used to avoid qualitative mistakes when estimating $G_{max}$ using the pulse motions, which will be introduced in the subsequent sections. The largest grain diameter of sand allowed in the TST was only 1 mm and the sand grain with diameter greater than 1 mm was sieved out to make the scalped specimen. Therefore, the modulus of the specimen may be larger than the sand in STT [Wichtmann and Triantafyllidis 2009].

129

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The specimen was a hollow cylinder with a size of 10 cm×6 cm×15 cm (outer diameter × inner diameter × height). The values of $C_u$, $C_c$ and $D_{50}$ of the remolded sand specimen were 4.9, 2.0 and 0.4 mm, respectively. The soil specimen was constructed with $\gamma_t$ of 16.9 kN/m³ and water content of 6.3%. To approximate the stress state of the soil at a depth of 2.1 m in the STT, an empirical value of 0.4 for the soil lateral pressure coefficient ($K_0$) was applied and the TST was performed under a vertical pressure of 37.5 kPa and a lateral pressure of 15 kPa. Results showed that the value of $G_{max}$ at small shear strain amplitude was 43 MPa.

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## 2.2. Model soil construction

142

The STT was carried out at China Academy of Building Research, Beijing, China. The operating frequency of the shaking table in the range of 0.1~50 Hz. The soil container was a 3.2 m × 2.4 m × 3 m (length × width × height) unconstrained laminar shear box with a 1 cm thick inner rubber membrane. Fig. 2 (a) shows the shaking table and laminar shear box. Each frame making up the box had a height of 12 cm and the frames were supported with rollers. The input base motions were excited at the bottom of the box in the longitudinal direction.

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Usually a pluviator would be used to prepare a small specimen in centrifuge tests to keep the uniformity of the soil. However, limited by the experimental condition of the lab, no pluviator was used for the 3-m thick sand specimen. The sand was manually filled and carefully compacted about every 10 cm lift until the box was full. The uniformity of the soil was indirectly checked using the dynamic records, which will be introduced in the subsequent section. The sensors were buried at designated locations in the soil during the processes of filling and compaction.

## 2.3. Instrumentation

A total of 35 accelerometers (ACC), 3 laser displacement sensors (LDS) and a shape acceleration array (SAA) are shown in Fig. 2 (b). The ACC were named as Channel *n*, i.e. CHn ($n$=01, 02, ..., 35). CH01 was placed on the table to record input motions imposed by the shaker. CH02~CH29 were buried in the box to record the soil response and CH30~CH35 were used to record motions of the box. The sampling frequency of accelerometers was 256 Hz. For the ACC buried in the box, CH02~CH15 were placed at the central position of the box and comprised of a dense vertical ACC array. The distance between the array and box wall was 1.6 m. The array could measure the 1-D shear wave propagation effectively as noted by Tsai et al. [2016]. The LDS were hung over the ground surface to record the settlement of the sand.
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Usually a pluviator would be used to prepare a small specimen in centrifuge tests to keep the uniformity of the soil. However, limited by the experimental condition of the lab, no pluviator was used for the 3-m thick sand specimen. The sand was manually filled and carefully compacted about every 10 cm lift until the box was full. The uniformity of the soil was indirectly checked using the dynamic records, which will be introduced in the subsequent section. The sensors were buried at designated locations in the soil during the processes of filling and compaction.

## 2.3. Instrumentation

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163

A total of 35 accelerometers (ACC), 3 laser displacement sensors (LDS) and a shape acceleration array (SAA) are shown in Fig. 2 (b). The ACC were named as Channel *n*, i.e. CHn ($n$=01, 02, ..., 35). CH01 was placed on the table to record input motions imposed by the shaker. CH02~CH29 were buried in the box to record the soil response and CH30~CH35 were used to record motions of the box. The sampling frequency of accelerometers was 256 Hz. For the ACC buried in the box, CH02~CH15 were placed at the central position of the box and comprised of a dense vertical ACC array. The distance between the array and box wall was 1.6 m. The array could measure the 1-D shear wave propagation effectively as noted by Tsai et al. [2016]. The LDS were hung over the ground surface to record the settlement of the sand.
<figure><img src="image_4.png" /><figcaption>165 **Figure 2.** Test setup: (a) shaking table and laminar box; (b) schematic diagram of sensor arrangement.</figcaption></figure>

167 The flexible SAA was effective to monitor the lateral deformation of the soil in the field
168 [Abdoun et al. 2013] or in the laboratory tests [Lin et al. 2015] suggested by the literature review.
169 The SAA was also used in the present STT to measure the accumulated shear deformation of the soil
170 within the depth of 0~2.4 m, limited by the length of the SAA (Fig. 2b).

171 **2.4. Input motions**

172 The present free-field soil tests were a part of the tests on buried structures. In the non-free-field
173 tests, the input motions with different amplitude and spectrum contents were usually used to study
174 the seismic performance of buried structures [Abuhajar et al. 2016; Chen et al. 2015a]. The seismic
175 responses and properties of the corresponding free-field soil were closely connected with the seismic
176 responses of buried structures. Therefore, similar earthquake motions and input sequence was
177 applied in the present study.
164

<figure><img src="image_4.png" /><figcaption>Figure 2. Test setup: (a) shaking table and laminar box; (b) schematic diagram of sensor arrangement.</figcaption></figure>

167
The flexible SAA was effective to monitor the lateral deformation of the soil in the field
168
[Abdoun et al. 2013] or in the laboratory tests [Lin et al. 2015] suggested by the literature review.

169
The SAA was also used in the present STT to measure the accumulated shear deformation of the soil
170
within the depth of 0~2.4 m, limited by the length of the SAA (Fig. 2b).

171 **2.4. Input motions**

172
The present free-field soil tests were a part of the tests on buried structures. In the non-free-field
173
tests, the input motions with different amplitude and spectrum contents were usually used to study
174
the seismic performance of buried structures [Abuhajar et al. 2016; Chen et al. 2015a]. The seismic
175
responses and properties of the corresponding free-field soil were closely connected with the seismic
176
responses of buried structures. Therefore, similar earthquake motions and input sequence was
177
applied in the present study.
A white noise, a pulse motion and four earthquake motions were selected as input motions for the STT. Figs. 3 (a) and (b) show time histories of the white noise and pulse motion recorded at the base. The white noise was a wide band excitation and generated based on the stationary Gaussian white noise theory [Clough 1975] which was used to determine the predominant frequencies of the soil-box system. The pulse motion was to create a shear wave transmitting through the soil to obtain the average shear wave velocity of the soil. The pulse was used to determine the small-strain damping ratio by the free-vibration of the soil. In total, the white noise and pulse motions were input 5 times during the STT, respectively. Fig. 4 shows the input seismic motions recorded on the surface of the shaking table and their normalized Fourier amplitude. The input earthquake motions consisted of three natural and one artificial motions. The natural motions were selected from the Loma Prieta earthquake (Gilroy Array #3 station H2*, USA, 1989), Kobe earthquake (KJMA station H1*, Japan, 1995) and Sichuan earthquake (20~40 s, 51WCW station EW, China, 2008). As the soil was collected at Beijing, the artificial motion was fitted according to the native site design parameters and spectra [MOHURD 2010; GAQSIQ 2015].

<figure><img src="image_5.png" /></figure>

192

<caption>193 **Figure 3.** Input dynamic motions: (a) white noise and (b) pulse motion.</caption>

<footnote>* Downloaded from PEER Ground Motion Database, Pacific Earthquake Engineering Center:
https://ngawest2.berkeley.edu</footnote>
A white noise, a pulse motion and four earthquake motions were selected as input motions for the STT. Figs. 3 (a) and (b) show time histories of the white noise and pulse motion recorded at the base. The white noise was a wide band excitation and generated based on the stationary Gaussian white noise theory [Clough 1975] which was used to determine the predominant frequencies of the soil-box system. The pulse motion was to create a shear wave transmitting through the soil to obtain the average shear wave velocity of the soil. The pulse was used to determine the small-strain damping ratio by the free-vibration of the soil. In total, the white noise and pulse motions were input 5 times during the STT, respectively. Fig. 4 shows the input seismic motions recorded on the surface of the shaking table and their normalized Fourier amplitude. The input earthquake motions consisted of three natural and one artificial motions. The natural motions were selected from the Loma Prieta earthquake (Gilroy Array #3 station H2*, USA, 1989), Kobe earthquake (KJMA station H1*, Japan, 1995) and Sichuan earthquake (20~40 s, 51WCW station EW, China, 2008). As the soil was collected at Beijing, the artificial motion was fitted according to the native site design parameters and spectra [MOHURD 2010; GAQSIQ 2015].

<figure><img src="image_5.png" /></figure>

192

<caption>193 **Figure 3.** Input dynamic motions: (a) white noise and (b) pulse motion.</caption>

<footnote>* Downloaded from PEER Ground Motion Database, Pacific Earthquake Engineering Center:
https://ngawest2.berkeley.edu</footnote>
The predominant frequencies of motions were scaled for the STT in an attempt to saddle the estimated predominant frequency of the sand specimen to obtain the strongest responses. However, as the laminar box was unconstrained in the shaking direction, the response of the soil-box system was limited to ensure the safety of equipment and personnel. The scaling factors (prototype/model) for frequencies of the Loma Prieta earthquake (LP), Kobe earthquake, Sichuan earthquake (Sc) and Beijing artificial earthquake (BJ) were finally taken as 1/3, 1/4, 1/3 and 1/2, respectively. However, since the actual predominant frequency of the sand specimen was notably changed by the input sequence, predominant frequencies of scaled input motions may not be consistent with predominant frequencies of the sand specimen during the course of the test.

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Input seismic acceleration and normalized Fourier amplitude, with peak amplitude ($Am_{pk}$): (a) Loma Prieta, (b) Kobe, (c) Sichuan and (d) Beijing. These motions are at the 0.4 g $a_{pk}$ stage, recorded at the base.</figcaption></figure>

Table 1 shows the sequence of input motions (IM), which were divided into four stages, i.e. 0.2 g, 0.4 g, 0.62 g and 1.0 g stage, differentiated by $a_{pk}$ of input motions. The white noise and pulse motion were both input at the beginning and end of each stage, with a small $a_{pk}$ of 0.05 g. After each
The predominant frequencies of motions were scaled for the STT in an attempt to saddle the estimated predominant frequency of the sand specimen to obtain the strongest responses. However, as the laminar box was unconstrained in the shaking direction, the response of the soil-box system was limited to ensure the safety of equipment and personnel. The scaling factors (prototype/model) for frequencies of the Loma Prieta earthquake (LP), Kobe earthquake, Sichuan earthquake (Sc) and Beijing artificial earthquake (BJ) were finally taken as 1/3, 1/4, 1/3 and 1/2, respectively. However, since the actual predominant frequency of the sand specimen was notably changed by the input sequence, predominant frequencies of scaled input motions may not be consistent with predominant frequencies of the sand specimen during the course of the test.

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Input seismic acceleration and normalized Fourier amplitude, with peak amplitude ($Am_{pk}$): (a) Loma Prieta, (b) Kobe, (c) Sichuan and (d) Beijing. These motions are at the 0.4 g $a_{pk}$ stage, recorded at the base.</figcaption></figure>

Table 1 shows the sequence of input motions (IM), which were divided into four stages, i.e. 0.2 g, 0.4 g, 0.62 g and 1.0 g stage, differentiated by $a_{pk}$ of input motions. The white noise and pulse motion were both input at the beginning and end of each stage, with a small $a_{pk}$ of 0.05 g. After each
motion was loaded, waiting time was applied to observe the experimental phenomena. Because large residual displacements of several laminar rings at the top of the box were considerably large (about 0.2 m) at the end of IM-23, the seismic input were terminated after IM-23 for safety concerns.

<table><caption>Table 1. Input motion sequence.</caption><thead><tr><th>No.</th><th>Input motion</th><th>Station</th><th>a<sub>pk</sub> (g)*</th><th>a<sub>pk</sub>-stage</th></tr></thead><tbody><tr><td>IM-1</td><td>1st white noise</td><td>N.A.</td><td>0.05</td><td></td></tr><tr><td>IM-2</td><td>1st pulse</td><td>N.A.</td><td>0.05</td><td></td></tr><tr><td>IM-3</td><td>Loma Prieta</td><td>Gilroy Array #3</td><td>0.2</td><td></td></tr><tr><td>IM-4</td><td>Kobe</td><td>KJMA</td><td>0.2</td><td rowspan="2">0.2 g</td></tr><tr><td>IM-5</td><td>Sichuan</td><td>51WCW</td><td>0.2</td></tr><tr><td>IM-6</td><td>Beijing artificial earthquake</td><td>N.A.</td><td>0.2</td><td></td></tr><tr><td>IM-7</td><td>2nd white noise</td><td>N.A.</td><td>0.05</td><td></td></tr><tr><td>IM-8</td><td>2nd pulse</td><td>N.A.</td><td>0.05</td><td></td></tr><tr><td>IM-9</td><td>Loma Prieta</td><td>Gilroy Array #3</td><td>0.4</td><td></td></tr><tr><td>IM-10</td><td>Kobe</td><td>KJMA</td><td>0.4</td><td rowspan="2">0.4 g</td></tr><tr><td>IM-11</td><td>Sichuan</td><td>51WCW</td><td>0.4</td></tr><tr><td>IM-12</td><td>Beijing artificial earthquake</td><td>N.A.</td><td>0.4</td><td></td></tr><tr><td>IM-13</td><td>3rd white noise</td><td>N.A.</td><td>0.05</td><td></td></tr><tr><td>IM-14</td><td>3rd pulse</td><td>N.A.</td><td>0.05</td><td></td></tr><tr><td>IM-15</td><td>Loma Prieta</td><td>Gilroy Array #3</td><td>0.62</td><td>0.62 g</td></tr></tbody></table>
motion was loaded, waiting time was applied to observe the experimental phenomena. Because large residual displacements of several laminar rings at the top of the box were considerably large (about 0.2 m) at the end of IM-23, the seismic input were terminated after IM-23 for safety concerns.

<table><caption>**Table 1.** Input motion sequence.</caption><thead><tr><th>No.</th><th>Input motion</th><th>Station</th><th>a<sub>pk</sub> (g)*</th><th>a<sub>pk</sub>-stage</th></tr></thead><tbody><tr><td>IM-1</td><td>1st white noise</td><td>N.A.</td><td>0.05</td><td></td></tr><tr><td>IM-2</td><td>1st pulse</td><td>N.A.</td><td>0.05</td><td></td></tr><tr><td>IM-3</td><td>Loma Prieta</td><td>Gilroy Array #3</td><td>0.2</td><td></td></tr><tr><td>IM-4</td><td>Kobe</td><td>KJMA</td><td>0.2</td><td rowspan="2">0.2 g</td></tr><tr><td>IM-5</td><td>Sichuan</td><td>51WCW</td><td>0.2</td></tr><tr><td>IM-6</td><td>Beijing artificial earthquake</td><td>N.A.</td><td>0.2</td><td></td></tr><tr><td>IM-7</td><td>2nd white noise</td><td>N.A.</td><td>0.05</td><td></td></tr><tr><td>IM-8</td><td>2nd pulse</td><td>N.A.</td><td>0.05</td><td></td></tr><tr><td>IM-9</td><td>Loma Prieta</td><td>Gilroy Array #3</td><td>0.4</td><td></td></tr><tr><td>IM-10</td><td>Kobe</td><td>KJMA</td><td>0.4</td><td rowspan="2">0.4 g</td></tr><tr><td>IM-11</td><td>Sichuan</td><td>51WCW</td><td>0.4</td></tr><tr><td>IM-12</td><td>Beijing artificial earthquake</td><td>N.A.</td><td>0.4</td><td></td></tr><tr><td>IM-13</td><td>3rd white noise</td><td>N.A.</td><td>0.05</td><td></td></tr><tr><td>IM-14</td><td>3rd pulse</td><td>N.A.</td><td>0.05</td><td></td></tr><tr><td>IM-15</td><td>Loma Prieta</td><td>Gilroy Array #3</td><td>0.62</td><td>0.62 g</td></tr></tbody></table>
<table><tr><td>IM-16</td><td>Kobe</td><td>KJMA</td><td>0.62</td></tr><tr><td>IM-17</td><td>Sichuan</td><td>51WCW</td><td>0.62</td></tr><tr><td>IM-18</td><td>Beijing artificial earthquake</td><td>N.A.</td><td>0.62</td></tr><tr><td>IM-19</td><td>4th white noise</td><td>N.A.</td><td>0.05</td></tr><tr><td>IM-20</td><td>4th pulse</td><td>N.A.</td><td>0.05</td></tr><tr><td>IM-21</td><td>Loma Prieta</td><td>Gilroy Array #3</td><td>1.0</td></tr><tr><td>IM-22</td><td>Kobe</td><td>KJMA</td><td>1.0</td></tr><tr><td>IM-23</td><td>Sichuan</td><td>51WCW</td><td>1.0</td></tr><tr><td>IM-24</td><td>5th white noise</td><td>N.A.</td><td>0.05</td></tr><tr><td>IM-25</td><td>5th pulse</td><td>N.A.</td><td>0.05</td></tr></table>

*Note: $a_{pk}$=peak acceleration

## 3. Tests results

In this section, dynamic soil properties were introduced using the results of white noises, pulse motions and seismic motions. The seismic deformation and shear strain distribution of the soil were then analyzed.

### 3.1. Validity of 1-D condition

The laminar shear box was used to mimic the one-dimensional (1-D) condition for the soil. The deformation mode of the 1-D soil column would follow the shear deformation mode with the equal displacement at an elevation. The boundary effects of the box with the rubber membrane were then checked using the peak horizontal displacement ($d_{pk}$) responses at the elevations of CH05, CH07 and CH15. The displacement was acquired via the double-integration for time-histories of acceleration
<table><tr><td>IM-16</td><td>Kobe</td><td>KJMA</td><td>0.62</td></tr><tr><td>IM-17</td><td>Sichuan</td><td>51WCW</td><td>0.62</td></tr><tr><td>IM-18</td><td>Beijing artificial earthquake</td><td>N.A.</td><td>0.62</td></tr><tr><td>IM-19</td><td>4th white noise</td><td>N.A.</td><td>0.05</td></tr><tr><td>IM-20</td><td>4th pulse</td><td>N.A.</td><td>0.05</td></tr><tr><td>IM-21</td><td>Loma Prieta</td><td>Gilroy Array #3</td><td>1.0</td></tr><tr><td>IM-22</td><td>Kobe</td><td>KJMA</td><td>1.0</td></tr><tr><td>IM-23</td><td>Sichuan</td><td>51WCW</td><td>1.0</td></tr><tr><td>IM-24</td><td>5th white noise</td><td>N.A.</td><td>0.05</td></tr><tr><td>IM-25</td><td>5th pulse</td><td>N.A.</td><td>0.05</td></tr></table>

*Note: $a_{pk}$=peak acceleration

## 3. Tests results

In this section, dynamic soil properties were introduced using the results of white noises, pulse motions and seismic motions. The seismic deformation and shear strain distribution of the soil were then analyzed.

### 3.1. Validity of 1-D condition

The laminar shear box was used to mimic the one-dimensional (1-D) condition for the soil. The deformation mode of the 1-D soil column would follow the shear deformation mode with the equal displacement at an elevation. The boundary effects of the box with the rubber membrane were then checked using the peak horizontal displacement ($d_{pk}$) responses at the elevations of CH05, CH07 and CH15. The displacement was acquired via the double-integration for time-histories of acceleration
225 hearafter and when executing the double-integration, band pass filter was applied with the frequency
226 ranging from 0.5 to 40 Hz [Li et al. 2013]. As the Sichuan motion had the largest peak Fourier
227 amplitude, the horizontal $d_{pk}$ under Sichuan motion was selected to make the comparison, as depicted
228 in Table 2.

229 The discrepancy of the horizontal $d_{pk}$ at the three elevations were very slight during the four $a_{pk}$
230 stages. The largest relative difference was observed between CH15 and CH29 at the 1.0 g stage and
231 the value was only about 5%. The slight difference may be because of the large inertia effect of the
232 laminar rings under the 1.0 g seismic effects, but the affected region was very limited within 0.4 m. It
233 implied that the soil in the box followed the simple shear deformation during the whole tests,
234 especially at the central line, where the CH02~CH15 were placed. The good boundary condition of
235 the box with the rubber membrane also implied that the filling and compaction of the soil were good
236 and had very slight influence on the seismic responses of the 3-m-thick sand deposit. Similar
237 carefully manual filling and compaction processes can be further used in the subsequent tests.

<table><caption>238 **Table. 2** Comparison of peak horizontal displacement at three elevations under Wenchuan motions
239 (Unit: cm)</caption><thead><tr><th>Stage</th><th>CH05</th><th>CH18</th><th>CH25</th><th>CH07</th><th>CH19</th><th>CH26</th><th>CH15</th><th>CH22</th><th>CH29</th></tr></thead><tbody><tr><td>0.2 g</td><td>0.74</td><td>0.74</td><td>0.74</td><td>0.75</td><td>0.76</td><td>0.77</td><td>0.82</td><td>0.83</td><td>0.82</td></tr><tr><td>0.4 g</td><td>1.71</td><td>1.71</td><td>1.72</td><td>1.81</td><td>1.83</td><td>1.85</td><td>2.10</td><td>2.13</td><td>2.14</td></tr><tr><td>0.62 g</td><td>2.40</td><td>2.43</td><td>2.46</td><td>2.68</td><td>2.72</td><td>2.80</td><td>3.81</td><td>3.82</td><td>3.91</td></tr><tr><td>1.0 g</td><td>3.72</td><td>3.74</td><td>3.76</td><td>4.02</td><td>4.14</td><td>4.23</td><td>6.68</td><td>6.69</td><td>7.05</td></tr></tbody></table>

240 **3.2. Dynamic properties of soil column**
225 hearafter and when executing the double-integration, band pass filter was applied with the frequency ranging from 0.5 to 40 Hz [Li et al. 2013]. As the Sichuan motion had the largest peak Fourier amplitude, the horizontal $d_{pk}$ under Sichuan motion was selected to make the comparison, as depicted in Table 2.

229 The discrepancy of the horizontal $d_{pk}$ at the three elevations were very slight during the four $a_{pk}$ stages. The largest relative difference was observed between CH15 and CH29 at the 1.0 g stage and the value was only about 5%. The slight difference may be because of the large inertia effect of the laminar rings under the 1.0 g seismic effects, but the affected region was very limited within 0.4 m. It implied that the soil in the box followed the simple shear deformation during the whole tests, especially at the central line, where the CH02~CH15 were placed. The good boundary condition of the box with the rubber membrane also implied that the filling and compaction of the soil were good and had very slight influence on the seismic responses of the 3-m-thick sand deposit. Similar carefully manual filling and compaction processes can be further used in the subsequent tests.

<table><caption>238 **Table. 2** Comparison of peak horizontal displacement at three elevations under Wenchuan motions (Unit: cm)</caption><thead><tr><th>Stage</th><th>CH05</th><th>CH18</th><th>CH25</th><th>CH07</th><th>CH19</th><th>CH26</th><th>CH15</th><th>CH22</th><th>CH29</th></tr></thead><tbody><tr><td>0.2 g</td><td>0.74</td><td>0.74</td><td>0.74</td><td>0.75</td><td>0.76</td><td>0.77</td><td>0.82</td><td>0.83</td><td>0.82</td></tr><tr><td>0.4 g</td><td>1.71</td><td>1.71</td><td>1.72</td><td>1.81</td><td>1.83</td><td>1.85</td><td>2.10</td><td>2.13</td><td>2.14</td></tr><tr><td>0.62 g</td><td>2.40</td><td>2.43</td><td>2.46</td><td>2.68</td><td>2.72</td><td>2.80</td><td>3.81</td><td>3.82</td><td>3.91</td></tr><tr><td>1.0 g</td><td>3.72</td><td>3.74</td><td>3.76</td><td>4.02</td><td>4.14</td><td>4.23</td><td>6.68</td><td>6.69</td><td>7.05</td></tr></tbody></table>

240 **3.2. Dynamic properties of soil column**
Because the white noise was a wide band excitation, the deposit would develop resonance at the predominant frequencies. Fig. 5 (a) shows the transfer functions under white noises at CH15 and CH07. The 1st and 2nd mode frequencies ($f_1$ and $f_2$) were about 9.08 Hz and 28.78 Hz at IM-1, according to peaks of the transfer functions and their phase angles [Li et al. 2013]. The same method was used to obtain the predominant frequencies at subsequent white noise motions and the values of $f_1$ and $f_2$ are summarized in Table 3.

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Responses of soil under white noise and pulse motions: (a) transfer functions under white noise at IM-1; (b) time-history of acceleration at CH15, IM-2; (c) time lags of soil under pulse motions.</figcaption></figure>

The damping ratios can be obtained using the responses under pulse motions. After a pulse motion was loaded, the response of the deposit was damped off under the free vibration. The acceleration response of CH15 due to IM-2 is shown in Fig. 5 (b). The logarithm decrement method [Chopra 2007] was used to calculate the viscous damping ratio ($\xi$) of the soil-box system subjected to pulse motions. As observed in Table 3, $\xi$ increased with $a_{pk}$ possibly because the deposit experienced greater shear strain.

<table><caption>**Table 3.** Frequencies and damping ratio of the soil column</caption><thead><tr><th>Motion</th><th>IM-1</th><th>IM-7</th><th>IM-13</th><th>IM-19</th><th>IM-24</th><th>Estimation approach</th></tr></thead></table>
Because the white noise was a wide band excitation, the deposit would develop resonance at the predominant frequencies. Fig. 5 (a) shows the transfer functions under white noises at CH15 and CH07. The 1st and 2nd mode frequencies ($f_1$ and $f_2$) were about 9.08 Hz and 28.78 Hz at IM-1, according to peaks of the transfer functions and their phase angles [Li et al. 2013]. The same method was used to obtain the predominant frequencies at subsequent white noise motions and the values of $f_1$ and $f_2$ are summarized in Table 3.

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Responses of soil under white noise and pulse motions: (a) transfer functions under white noise at IM-1; (b) time-history of acceleration at CH15, IM-2; (c) time lags of soil under pulse motions.</figcaption></figure>

The damping ratios can be obtained using the responses under pulse motions. After a pulse motion was loaded, the response of the deposit was damped off under the free vibration. The acceleration response of CH15 due to IM-2 is shown in Fig. 5 (b). The logarithm decrement method [Chopra 2007] was used to calculate the viscous damping ratio ($\xi$) of the soil-box system subjected to pulse motions. As observed in Table 3, $\xi$ increased with $a_{pk}$ possibly because the deposit experienced greater shear strain.

<table><caption>**Table 3.** Frequencies and damping ratio of the soil column</caption><thead><tr><th>Motion</th><th>IM-1</th><th>IM-7</th><th>IM-13</th><th>IM-19</th><th>IM-24</th><th>Estimation approach</th></tr></thead></table>
<table><tr><td>f<sub>1</sub> (Hz)</td><td>9.08</td><td>7.19</td><td>6.24</td><td>6.31</td><td>6.39</td><td rowspan="2">White noise</td></tr><tr><td>f<sub>2</sub> (Hz)</td><td>28.78</td><td>24.84</td><td>21.94</td><td>22.71</td><td>21.53</td></tr><tr><td>Avg. ξ (%)</td><td>3.58</td><td>5.39</td><td>5.75</td><td>7.07</td><td>7.86</td><td>Pulse motion</td></tr></table>

### 3.3. Properties variation of soil among $a_{pk}$ stages

The settlement of sand was observed during the course of the shaking. The average accumulated settlement recorded by the laser sensors (LA00, LA02 and LA03 in Fig. 2b) is shown in Table 4. The accumulated settlement was up to 103.35 mm at the end of the tests. Fig. 6 (a) shows the settlement of sand at the end of the test. Because of the settlement, the volume of the soil decreased at each $a_{pk}$ stage. $\gamma_t$ was also various and ranged from 17.6 kN/m³ to 18.2 kN/m³ at different $a_{pk}$ stages. The soil was densified and the corresponding average relative density ($D_r$) of sand ranged from 68.6% to 78.9%. Table 4 summarizes the average settlement, $\gamma_t$ and $D_r$ at $a_{pk}$ stages.

<table><caption>**Table 4.** Properties of soil measured among stages.</caption><thead><tr><th>Motion</th><th>IM-2</th><th>IM-8</th><th>IM-14</th><th>IM-20</th><th>IM-25</th><th>Estimation approach</th></tr></thead><tbody><tr><td>Avg. accumulated settlement (mm)</td><td>0</td><td>3.19</td><td>5.00</td><td>55.14</td><td>103.35</td><td>Laser disp. sensor</td></tr><tr><td>γ<sub>t</sub> (kN/m<sup>3</sup>)</td><td>17.6</td><td>17.7</td><td>17.7</td><td>18.0</td><td>18.2</td><td></td></tr><tr><td>Avg. relative density, D<sub>r</sub> (%)</td><td>68.6</td><td>69.1</td><td>69.3</td><td>74.6</td><td>79.5</td><td></td></tr><tr><td>Avg. void ratio, e</td><td>0.59</td><td>0.58</td><td>0.58</td><td>0.56</td><td>0.53</td><td></td></tr></tbody></table>
<table><tr><td>f<sub>1</sub> (Hz)</td><td>9.08</td><td>7.19</td><td>6.24</td><td>6.31</td><td>6.39</td><td rowspan="2">White noise</td></tr><tr><td>f<sub>2</sub> (Hz)</td><td>28.78</td><td>24.84</td><td>21.94</td><td>22.71</td><td>21.53</td></tr><tr><td>Avg. ξ (%)</td><td>3.58</td><td>5.39</td><td>5.75</td><td>7.07</td><td>7.86</td><td>Pulse motion</td></tr></table>

### 3.3. Properties variation of soil among $a_{pk}$ stages

The settlement of sand was observed during the course of the shaking. The average accumulated settlement recorded by the laser sensors (LA00, LA02 and LA03 in Fig. 2b) is shown in Table 4. The accumulated settlement was up to 103.35 mm at the end of the tests. Fig. 6 (a) shows the settlement of sand at the end of the test. Because of the settlement, the volume of the soil decreased at each $a_{pk}$ stage. $γ_t$ was also various and ranged from 17.6 kN/m³ to 18.2 kN/m³ at different $a_{pk}$ stages. The soil was densified and the corresponding average relative density ($D_r$) of sand ranged from 68.6% to 78.9%. Table 4 summarizes the average settlement, $γ_t$ and $D_r$ at $a_{pk}$ stages.

<table><caption>**Table 4.** Properties of soil measured among stages.</caption><thead><tr><th>Motion</th><th>IM-2</th><th>IM-8</th><th>IM-14</th><th>IM-20</th><th>IM-25</th><th>Estimation approach</th></tr></thead><tbody><tr><td>Avg. accumulated settlement (mm)</td><td>0</td><td>3.19</td><td>5.00</td><td>55.14</td><td>103.35</td><td>Laser disp. sensor</td></tr><tr><td>γ<sub>t</sub> (kN/m<sup>3</sup>)</td><td>17.6</td><td>17.7</td><td>17.7</td><td>18.0</td><td>18.2</td><td></td></tr><tr><td>Avg. relative density, D<sub>r</sub> (%)</td><td>68.6</td><td>69.1</td><td>69.3</td><td>74.6</td><td>79.5</td><td></td></tr><tr><td>Avg. void ratio, e</td><td>0.59</td><td>0.58</td><td>0.58</td><td>0.56</td><td>0.53</td><td></td></tr></tbody></table>
<table><tr><td>Accumulated lateral displacement at soil surface (mm)</td><td>0</td><td>0.67</td><td>1.87</td><td>11.0</td><td>106.2</td><td>Shape Acceleration Array (SAA)</td></tr></table>

267

<figure><img src="image_8.png" /></figure>

268

269

270

**Figure 6.** Final state of soil and box: (a) top view; (b) overview. ALSD means accumulated lateral shear deformation and LRD is large residual displacement.

271

272

273

274

275

276

277

278

Sometimes the residual displacement may be eliminated from the integration displacement during the filter process. The SAA could follow the deformation of the soil and record the residual displacement within the soil. The results could be a supplement as the typical experimental data for the integral displacement. Fig. 7 shows the accumulated lateral shear deformation of the soil. The accumulated deformation of the soil was increased with $a_{pk}$ stages, especially for the soil at the elevation range of 2~3 m when $a_{pk}$ was greater than 0.62 g. The residual displacement of the soil at an $a_{pk}$ stage did not follow a regular deformation pattern along the elevation, which might be due to the complex loading history of seismic motions.
<table><tr><td>Accumulated lateral displacement at soil surface (mm)</td><td>0</td><td>0.67</td><td>1.87</td><td>11.0</td><td>106.2</td><td>Shape Acceleration Array (SAA)</td></tr></table>

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Final state of soil and box: (a) top view; (b) overview. ALSD means accumulated lateral shear deformation and LRD is large residual displacement.</figcaption></figure>

Sometimes the residual displacement may be eliminated from the integration displacement during the filter process. The SAA could follow the deformation of the soil and record the residual displacement within the soil. The results could be a supplement as the typical experimental data for the integral displacement. Fig. 7 shows the accumulated lateral shear deformation of the soil. The accumulated deformation of the soil was increased with $a_{pk}$ stages, especially for the soil at the elevation range of 2~3 m when $a_{pk}$ was greater than 0.62 g. The residual displacement of the soil at an $a_{pk}$ stage did not follow a regular deformation pattern along the elevation, which might be due to the complex loading history of seismic motions.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Accumulated lateral shear deformation of soil at the depth from 0 to 2.4 m.</figcaption></figure>

Table 4 summarizes the values of accumulated lateral shear deformation (ALSD) at the soil surface. According to the measured decreasing $f_1$ and $f_2$, the sand specimen was softened during the course of the test, despite of the densification of the sand specimen. The ALSD implied that the sand specimen was partly failed. Fig. 6 shows the final state of the soil and box. The large residual displacement (LRD) about 20 cm was observed at the top rings using the unconstrained laminar shear box. The soil could not constrain the lateral movement of the rings because the settlement of the soil was large up to 103.35 mm, while the height of a ring was only 120 mm. The seismic tests were then terminated at IM-23 for the safety concern.

**3.4.** *G*<sub>max</sub> of sand via back analysis

When a pulse motion was excited, a shear wave was transmitted from the bottom to the top of the soil. The average transition time could be attained by counting the time lag of the first peak from CH01 to CH15. Fig. 8 shows the time lag of pulses. The average shear wave velocity ($V_{sp}$) of the soil could then be computed by $H/t$, where $H$ was the height of the entire soil and $t$ was the transmission time lag between the first peaks of CH01 and CH15. Table 5 shows the values of $V_{sp}$.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Accumulated lateral shear deformation of soil at the depth from 0 to 2.4 m.</figcaption></figure>

Table 4 summarizes the values of accumulated lateral shear deformation (ALSD) at the soil surface. According to the measured decreasing $f_1$ and $f_2$, the sand specimen was softened during the course of the test, despite of the densification of the sand specimen. The ALSD implied that the sand specimen was partly failed. Fig. 6 show the final state of the soil and box. The large residual displacement (LRD) about 20 cm was observed at the top rings using the unconstrained laminar shear box. The soil could not constrain the lateral movement of the rings because the settlement of the soil was large up to 103.35 mm, while the height of a ring was only 120 mm. The seismic tests were then terminated at IM-23 for the safety concern.

**3.4.** *G*<sub>max</sub> of sand via back analysis

When a pulse motion was excited, a shear wave was transmitted from the bottom to the top of the soil. The average transition time could be attained by counting the time lag of the first peak from CH01 to CH15. Fig. 8 shows the time lag of pulses. The average shear wave velocity ($V_{sp}$) of the soil could then be computed by $H/t$, where $H$ was the height of the entire soil and $t$ was the transmission time lag between the first peaks of CH01 and CH15. Table 5 shows the values of $V_{sp}$.
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Time lag under pulse motions and their fitted results: (a) IM-2; (b) IM-14; (c) IM-25</figcaption></figure>

The average shear wave velocity of the soil can also be estimated via:

$$V_{sf} = 4 \cdot f_1 \cdot h_s \quad (1)$$

where $V_{sf}$ was the average shear wave velocity estimated using frequency and $h_s$ was the height of the sand deposit. The values of $V_{sf}$ were summarized in Table 5. There was slight discrepancy between the estimated $V_{sf}$ and $V_{sp}$. It may be because of the slight nonlinearity of the soil caused by the white noise and pulse motions.

<table><caption>**Table 5.** Estimated shear moduli (unit: MPa) and shear wave (unit: m/s) of sand</caption><thead><tr><th></th><th>IM-2</th><th>IM-8</th><th>IM-14</th><th>IM-20</th><th>IM-25</th><th>Average value</th><th>Estimation method</th></tr></thead><tbody><tr><td>G<sub>1</sub></td><td>5.0</td><td>4.0</td><td>3.4</td><td>3.4</td><td>3.0</td><td>3.8</td><td rowspan="3">Fitting time lag under pulse motions</td></tr><tr><td>G<sub>2</sub></td><td>21.7</td><td>12.0</td><td>7.8</td><td>11.5</td><td>11.5</td><td>12.9</td></tr><tr><td>G<sub>3</sub></td><td>55.4</td><td>32.4</td><td>27.1</td><td>32.2</td><td>33.4</td><td>36.1</td></tr><tr><td>V<sub>sG</sub></td><td>114</td><td>88.4</td><td>78.0</td><td>85.5</td><td>85.6</td><td>91.3</td><td>Estimated G<sub>1</sub>, G<sub>2</sub> and G<sub>3</sub></td></tr><tr><td>V<sub>sp</sub></td><td>128</td><td>85.3</td><td>76.8</td><td>85.3</td><td>85.3</td><td>92.1</td><td>Pulse motions</td></tr><tr><td>V<sub>sf</sub></td><td>109</td><td>86.3</td><td>74.9</td><td>75.7</td><td>76.7</td><td>84.5</td><td>Frequency using Eq. (1)</td></tr></tbody></table>

* G<sub>1</sub>, G<sub>2</sub> and G<sub>3</sub> were the average shear moduli between CH15 and CH10, C10 and CH06, CH06 and CH01, respectively.
<figure><img src="image_10.png" /><figcaption>Figure 8. Time lag under pulse motions and their fitted results: (a) IM-2; (b) IM-14; (c) IM-25</figcaption></figure>

The average shear wave velocity of the soil can also be estimated via:

$$V_{sf} = 4 \cdot f_1 \cdot h_s \qquad (1)$$

where $V_{sf}$ was the average shear wave velocity estimated using frequency and $h_s$ was the height of the sand deposit. The values of $V_{sf}$ were summarized in Table 5. There was slight discrepancy between the estimated $V_{sf}$ and $V_{sp}$. It may be because of the slight nonlinearity of the soil caused by the white noise and pulse motions.

<table><caption>Table 5. Estimated shear moduli (unit: MPa) and shear wave (unit: m/s) of sand</caption><thead><tr><th></th><th>IM-2</th><th>IM-8</th><th>IM-14</th><th>IM-20</th><th>IM-25</th><th>Average value</th><th>Estimation method</th></tr></thead><tbody><tr><td>G<sub>1</sub></td><td>5.0</td><td>4.0</td><td>3.4</td><td>3.4</td><td>3.0</td><td>3.8</td><td rowspan="3">Fitting time lag under pulse motions</td></tr><tr><td>G<sub>2</sub></td><td>21.7</td><td>12.0</td><td>7.8</td><td>11.5</td><td>11.5</td><td>12.9</td></tr><tr><td>G<sub>3</sub></td><td>55.4</td><td>32.4</td><td>27.1</td><td>32.2</td><td>33.4</td><td>36.1</td></tr><tr><td>V<sub>sG</sub></td><td>114</td><td>88.4</td><td>78.0</td><td>85.5</td><td>85.6</td><td>91.3</td><td>Estimated G<sub>1</sub>, G<sub>2</sub> and G<sub>3</sub></td></tr><tr><td>V<sub>sp</sub></td><td>128</td><td>85.3</td><td>76.8</td><td>85.3</td><td>85.3</td><td>92.1</td><td>Pulse motions</td></tr><tr><td>V<sub>sf</sub></td><td>109</td><td>86.3</td><td>74.9</td><td>75.7</td><td>76.7</td><td>84.5</td><td>Frequency using Eq. (1)</td></tr></tbody></table>

* G<sub>1</sub>, G<sub>2</sub> and G<sub>3</sub> were the average shear moduli between CH15 and CH10, C10 and CH06, CH06 and CH01, respectively.
The values of $V_s$ at every elevation should have been well calculated by counting the time lag of soil under pulse motions with a high-performance data acquisition system in centrifuge tests [Brennan et al. 2005; Li et al. 2013]. However, the sampling frequency of accelerometers in the 1-g shaking table tests was usually much lower than those in centrifuge tests and the sampling frequency were only 256 Hz in the present tests. Other researchers also encountered similar problems and estimated the values of $V_s$ or $G_{max}$ using other methods. Tsai et al. [2016] estimated $G_{max}$ by matching the shear modulus reduction results obtained from STT with the curves derived by Seed and Idriss [1970]. Dihoru et al. [2016] estimated $G_{max}$ using the aliasing frequencies and critical shear wavelength. Sadrekarimi [2013] and Anjali et al. [2015] calculated $G_{max}$ via empirical equations and empirical parameters. The literature review suggested that there were difficulties to estimate the values of $G_{max}$ with a very good precision in the 1-g shaking table tests.

For the present tests, the values of $V_s$ were estimated in three layers via the back-analysis method. The three-layers $V_s$ might be more helpful for analysing the seismic responses or performing numerical analysis of the free-field soil, compared with the bare average values. When conducting the back-analysis, $V_s$ of a layer was estimated by considering following criterions: (1) fitting the time-lag of the pulses along the elevation to acquire the three-layer $V_s$. The average values of the fitted three-layer shear wave velocity ($V_{sG}$) was then checked by comparing with the values of $V_{sp}$ and $V_{sf}$. (2) referencing the degradation relationships of the results from the published literature, which will be introduced in Section 3.4; (3) the application of $\gamma - G/G_{max}$ curve in the finite element modelling of the sand to indirectly verify the $\gamma - G/G_{max}$ relationship, which will be introduced in Section 4.
The values of $V_s$ at every elevation should have been well calculated by counting the time lag of soil under pulse motions with a high-performance data acquisition system in centrifuge tests [Brennan et al. 2005; Li et al. 2013]. However, the sampling frequency of accelerometers in the 1-g shaking table tests was usually much lower than those in centrifuge tests and the sampling frequency were only 256 Hz in the present tests. Other researchers also encountered similar problems and estimated the values of $V_s$ or $G_{max}$ using other methods. Tsai et al. [2016] estimated $G_{max}$ by matching the shear modulus reduction results obtained from STT with the curves derived by Seed and Idriss [1970]. Dihoru et al. [2016] estimated $G_{max}$ using the aliasing frequencies and critical shear wavelength. Sadrekarimi [2013] and Anjali et al. [2015] calculated $G_{max}$ via empirical equations and empirical parameters. The literature review suggested that there were difficulties to estimate the values of $G_{max}$ with a very good precision in the 1-g shaking table tests.

For the present tests, the values of $V_s$ were estimated in three layers via the back-analysis method. The three-layers $V_s$ might be more helpful for analysing the seismic responses or performing numerical analysis of the free-field soil, compared with the bare average values. When conducting the back-analysis, $V_s$ of a layer was estimated by considering following criterions: (1) fitting the time-lag of the pulses along the elevation to acquire the three-layer $V_s$. The average values of the fitted three-layer shear wave velocity ($V_{sG}$) was then checked by comparing with the values of $V_{sp}$ and $V_{sf}$. (2) referencing the degradation relationships of the results from the published literature, which will be introduced in Section 3.4; (3) the application of $\gamma -G/G_{max}$ curve in the finite element modelling of the sand to indirectly verify the $\gamma -G/G_{max}$ relationship, which will be introduced in Section 4.
Fig. 8 shows the fitted three-layer time lag under the pulse motions. The thicknesses of the layers from the bottom to the top were 1.1 m, 1.04 m and 0.79 m, respectively. At the initial condition, there might be a little discrepancy when conducting the fitting at IM-2. It was limited by the sampling frequency of the accelerometers and the stiffer medium had the lower precision. The larger modulus of the soil at the initial state may be due to the suction effect of the wet sand. In the later $a_{pk}$ stages, the time lag was long enough caused by the softened soil and the fitting was good. The estimated $V_{sG}$ was acquired via the fitted results and it was compared with the values of $V_{sp}$ and $V_{sf}$. Table 5 shows the comparison among $V_{sG}$, $V_{sp}$ and $V_{sf}$. The comparison implied that the estimation of the shear wave velocity was good. The average shear moduli of the three layers ($G_1$, $G_2$ and $G_3$) was then computed using the corresponding shear wave velocity and the various density of the soil at $a_{pk}$ stages (Table 4). Table 5 shows the values of $G_1$, $G_2$ and $G_3$, which were the maximum shear moduli could be approximately used in the subsequent analyses.

### 3.5. Soil dynamic properties using earthquake motions

The time histories of shear strain at CHi ($i=2, 3, ..., 14$) can be estimated using Eq. 2 [Zeghal and Elgamal 1994; Li et al. 2013] under earthquake motions:

$$ \gamma_i = \frac{u_{i+1} - u_{i-1}}{2h} \quad (i=2, 3, ..., 14) \qquad (2) $$

where $\gamma_i$ is the time-history of shear strain at the CHi elevation; $u_i$ is the time-history of displacement at the CHi elevation and $h$ is the distance between CHi+1 and CHi in Fig. 2 (b).

The shear stress at an elevation can be estimated using Eq. 3 [Zeghal and Elgamal 1994; Li et al. 2013]:

$$ \tau_i(z) = \int_0^{z_i} \rho \ddot{u}_i dz \quad (i=2, ..., 14) \qquad (3) $$
Fig. 8 shows the fitted three-layer time lag under the pulse motions. The thicknesses of the layers from the bottom to the top were 1.1 m, 1.04 m and 0.79 m, respectively. At the initial condition, there might be a little discrepancy when conducting the fitting at IM-2. It was limited by the sampling frequency of the accelerometers and the stiffer medium had the lower precision. The larger modulus of the soil at the initial state may be due to the suction effect of the wet sand. In the later $a_{pk}$ stages, the time lag was long enough caused by the softened soil and the fitting was good. The estimated $V_{sG}$ was acquired via the fitted results and it was compared with the values of $V_{sp}$ and $V_{sf}$. Table 5 shows the comparison among $V_{sG}$, $V_{sp}$ and $V_{sf}$. The comparison implied that the estimation of the shear wave velocity was good. The average shear moduli of the three layers ($G_1$, $G_2$ and $G_3$) was then computed using the corresponding shear wave velocity and the various density of the soil at $a_{pk}$ stages (Table 4). Table 5 shows the values of $G_1$, $G_2$ and $G_3$, which were the maximum shear moduli could be approximately used in the subsequent analyses.

### 3.5. Soil dynamic properties using earthquake motions

The time histories of shear strain at CHi ($i=2, 3, ..., 14$) can be estimated using Eq. 2 [Zeghal and Elgamal 1994; Li et al. 2013] under earthquake motions:

$$ \gamma_i = \frac{u_{i+1} - u_{i-1}}{2h} \quad (i=2, 3, ..., 14) \qquad (2) $$

where $\gamma_i$ is the time-history of shear strain at the CHi elevation; $u_i$ is the time-history of displacement at the CHi elevation and $h$ is the distance between CHi+1 and CHi in Fig. 2 (b).

The shear stress at an elevation can be estimated using Eq. 3 [Zeghal and Elgamal 1994; Li et al. 2013]:

$$ \tau_i(z) = \int_0^{z_i} \rho \ddot{u}_i dz \quad (i=2, ..., 14) \qquad (3) $$
where $\tau_i$ is the shear stress at the CHi elevation; $\ddot{u}_i$ is the acceleration at the CHi elevation; $z_i$ is the distance from the soil surface to CHi; and $\rho$ is the soil density, i.e. $\gamma_i$ in Table 4. Then the shear stress-shear strain relationships of the soil at an elevation could be obtained using Eqs. 2 and 3.

Fig. 9 (a) shows the typical shear stress-shear strain hysteresis measured at the CH04, CH08 and CH13 of IM-11. The shear modulus ($G_i$) and damping ratio ($D_i$) of the soil material could be calculated from each hysteresis. Fig. 9 (b) shows the methods of calculating $G_i$ and $D_i$. For the ith hysteresis loop, the minimum/maximum strain ($\gamma_{min}, \gamma_{max}$) and stress ($\tau_{min}, \tau_{max}$) could be located and then $G_i$ could be calculated using Eq. 4 [Brennan et al. 2005]:

$$G_i = \frac{\tau_{i,max} - \tau_{i,min}}{\gamma_{i,max} - \gamma_{i,min}} \qquad (4)$$

where $G_i$ is the shear modulus calculated using the ith hysteresis loop; $\gamma_{i,max}$ and $\gamma_{i,min}$ are the maximum and minimum strain of the ith hysteresis loop; and $\tau_{i,max}$ and $\tau_{i,min}$ are the maximum and minimum shear stress of the ith loop.

<figure><img src="image_11.png" /><figcaption>**Figure 9.** Shear stress-strain loops at IM-11 and the method of calculating dynamic soil properties: (a) hysteresis and $G_{max}$ derived from records at CH04, CH08 and CH13; (b) schematic of the method of estimating the shear modulus and damping ratio.</figcaption></figure>
where $\tau_i$ is the shear stress at the CHi elevation; $\ddot{u}_i$ is the acceleration at the CHi elevation; $z_i$ is the distance from the soil surface to CHi; and $\rho$ is the soil density, i.e. $\gamma_i$ in Table 4. Then the shear stress-shear strain relationships of the soil at an elevation could be obtained using Eqs. 2 and 3.

Fig. 9 (a) shows the typical shear stress-shear strain hysteresis measured at the CH04, CH08 and CH13 of IM-11. The shear modulus ($G_i$) and damping ratio ($D_i$) of the soil material could be calculated from each hysteresis. Fig. 9 (b) shows the methods of calculating $G_i$ and $D_i$. For the ith hysteresis loop, the minimum/maximum strain ($\gamma_{min}, \gamma_{max}$) and stress ($\tau_{min}, \tau_{max}$) could be located and then $G_i$ could be calculated using Eq. 4 [Brennan et al. 2005]:

$$G_i = \frac{\tau_{i,max} - \tau_{i,min}}{\gamma_{i,max} - \gamma_{i,min}} \qquad (4)$$

where $G_i$ is the shear modulus calculated using the ith hysteresis loop; $\gamma_{i,max}$ and $\gamma_{i,min}$ are the maximum and minimum strain of the ith hysteresis loop; and $\tau_{i,max}$ and $\tau_{i,min}$ are the maximum and minimum shear stress of the ith loop.

<figure><img src="image_11.png" /><figcaption>**Figure 9.** Shear stress-strain loops at IM-11 and the method of calculating dynamic soil properties: (a) hysteresis and $G_{max}$ derived from records at CH04, CH08 and CH13; (b) schematic of the method of estimating the shear modulus and damping ratio.</figcaption></figure>
As each of the hysteresis loop in Fig. 9 (a) can be transferred to a point of $G_i$ and a point of $D_i$, a group of points of $G_i$ and $D_i$ can be obtained from the seismic hysteresis loops in Fig. 10. The shear strain-dependent $G_i$ and $D_i$ of CH08 at IM-11 were then obtained. The $G$ and $D$ at the 0.4 g stage under the other three earthquake motions could also be calculated using the same method. The values of $G$ and $D$ at the 0.4 g stage were then normalized using $G_{max}$ at IM-8, i.e. $G_2$ in Table 5.
Fig. 10 shows the shear modulus degradation and damping relationships CH08 at the 0.4 g stage.

<figure><img src="image_12.png" /><figcaption>**Figure 10.** Shear modulus degradation and damping relationships: shaking table test (STT, CH08, 0.4 g stage), D & Q model [Darendeli 2001; Menq 2003], and fitted Davidenkov [Martin 1975] model used in Layer 2 of the FE modeling.</figcaption></figure>

370

371

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The soil dynamic properties from the STT were compared with those from the $\gamma$-$G/G_{max}$ and $\gamma$-$D$ equation proposed by Darendeli [2001] and Menq [2003] (D & M model). The lower and upper limits of $\gamma$-$G/G_{max}$ and $\gamma$-$D$ could be computed according to the values of confining pressure ($\sigma'_o$), 0.014% standard deviation of the reference strain and 0.09 standard deviation of the curvature coefficient [Menq 2003]. The value of $\sigma'_o$ at the position of CH08 can be estimated using the lateral earth pressure coefficient $K_0$ and vertical effective stress $\sigma'_v$. $K_0$ can be expressed by Eq. 5 [Gaudin 1999]:
As each of the hysteresis loop in Fig. 9 (a) can be transferred to a point of $G_i$ and a point of $D_i$, a group of points of $G_i$ and $D_i$ can be obtained from the seismic hysteresis loops in Fig. 10. The shear strain-dependent $G_i$ and $D_i$ of CH08 at IM-11 were then obtained. The $G$ and $D$ at the 0.4 g stage under the other three earthquake motions could also be calculated using the same method. The values of $G$ and $D$ at the 0.4 g stage were then normalized using $G_{max}$ at IM-8, i.e. $G_2$ in Table 5.
Fig. 10 shows the shear modulus degradation and damping relationships CH08 at the 0.4 g stage.

<figure><img src="image_12.png" /><figcaption>**Figure 10.** Shear modulus degradation and damping relationships: shaking table test (STT, CH08, 0.4 g stage), D & Q model [Darendeli 2001; Menq 2003], and fitted Davidenkov [Martin 1975] model used in Layer 2 of the FE modeling.</figcaption></figure>

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The soil dynamic properties from the STT were compared with those from the $\gamma$-$G/G_{max}$ and $\gamma$-$D$ equation proposed by Darendeli [2001] and Menq [2003] (D & M model). The lower and upper limits of $\gamma$-$G/G_{max}$ and $\gamma$-$D$ could be computed according to the values of confining pressure ($\sigma'_o$), 0.014% standard deviation of the reference strain and 0.09 standard deviation of the curvature coefficient [Menq 2003]. The value of $\sigma'_o$ at the position of CH08 can be estimated using the lateral earth pressure coefficient $K_0$ and vertical effective stress $\sigma'_v$. $K_0$ can be expressed by Eq. 5 [Gaudin 1999]:
$$381 \qquad K_0 = -\frac{1}{2.9} D_r + 0.63 \qquad (5)$$

As $\sigma'_v$ was about 24.2 kPa at the CH08 elevation, $\sigma'_o=14.3$ kPa was applied to the D & M model.

Fig. 10 shows the ranges of $\gamma - G/G_{max}$ and $\gamma - D$.

As shown in Fig. 10 (a), for the $G/G_{max}$ relationships, the results of the STT and D & M generally matched well, which suggests that the $G_{max}$ parameters and $G/G_{max}$ relationship were properly estimated. The scattered relationships of $D$ were observed for the results of STT. Similar scattering was also reported in the results of field tests [Zeghal et al. 1995], centrifuge tests [Li et al. 2013; Brennan et al. 2005] and shaking table tests [Sadrekarimi 2013]. The damping ratio might depend on $\sigma'_o$ and $e$ of the soil. According to the D & Q model, $D$ was more sensitive than the $G/G_{max}$ to the change in $\sigma'_o$ and $e$. The change in $\sigma'_o$ and $e$ during the shaking could have led to the scattered damping relationships.

The results of STT were set as a target to fit the Davidenkov model [Martin 1975]. The fitted parameters were applied in the numerical modelling, which would be introduced in the subsequent sections.

## 3.6. Seismic deformation and shear strain distribution

The seismic deformation of soil was usually simplified as the shear deformation mode with the shear strain gradually decreasing from the bottom to the top of the soil when performing seismic design or analyses of buried structures [Wang 1993], as shown in Fig. 11 (a). The time instant of $t_1$ was the moment when the relative displacement between CH15 and CH01 reached the maximum value (Fig. 11 c). Fig. 11 (a) also show the typical deformation of the sand at time $t_1$ in the present shaking table tests. As shown in Fig. 11 (a), the deformation of sand in shaking table tests did not
$$381 \qquad K_0 = -\frac{1}{2.9} D_r + 0.63 \qquad (5)$$

As $\sigma'_v$ was about 24.2 kPa at the CH08 elevation, $\sigma'_o=14.3$ kPa was applied to the D & M model.

Fig. 10 shows the ranges of $\gamma - G/G_{max}$ and $\gamma - D$.

As shown in Fig. 10 (a), for the $G/G_{max}$ relationships, the results of the STT and D & M generally matched well, which suggests that the $G_{max}$ parameters and $G/G_{max}$ relationship were properly estimated. The scattered relationships of $D$ were observed for the results of STT. Similar scattering was also reported in the results of field tests [Zeghal et al. 1995], centrifuge tests [Li et al. 2013; Brennan et al. 2005] and shaking table tests [Sadrekarimi 2013]. The damping ratio might depend on $\sigma'_o$ and $e$ of the soil. According to the D & Q model, $D$ was more sensitive than the $G/G_{max}$ to the change in $\sigma'_o$ and $e$. The change in $\sigma'_o$ and $e$ during the shaking could have led to the scattered damping relationships.

The results of STT were set as a target to fit the Davidenkov model [Martin 1975]. The fitted parameters were applied in the numerical modelling, which would be introduced in the subsequent sections.

## 3.6. Seismic deformation and shear strain distribution

The seismic deformation of soil was usually simplified as the shear deformation mode with the shear strain gradually decreasing from the bottom to the top of the soil when performing seismic design or analyses of buried structures [Wang 1993], as shown in Fig. 11 (a). The time instant of $t_1$ was the moment when the relative displacement between CH15 and CH01 reached the maximum value (Fig. 11 c). Fig. 11 (a) also show the typical deformation of the sand at time $t_1$ in the present shaking table tests. As shown in Fig. 11 (a), the deformation of sand in shaking table tests did not
follow the simplified shear deformation mode, especially in the elevation region of 0~1.2 m. Because
the shear modulus of soil was greatly shifted within the depth of 0~3 m, the shear stiffness in the
elevation region of 0~1.2 m was much larger than that in the upper region (IM-11), e.g. Gmax at
CH04 was about 32.4 MPa but only 4 MP at CH13 (Table 5). The shear deformation of soil may not
be compatible under seismic effects. When analysing the seismic deformation of soil within the
depth of 0~3 m under the 1-g condition, the soil properties variation with the depth should be
thoroughly considered.

Furthermore, the displacement directions of the upper and lower parts of the sand were opposite
at t₁, because the cyclic displacement at the soil surface reached the maximum value (Fig. 11a) and
the bottom of the soil started to move in the opposite direction at the time instant. The direction of
the displacement at the top was positive, but negative at the bottom. This might lead to larger shear
responses at the middle region.

<figure><img src="image_13.png" /><figcaption>**Figure 11.** Seismic sand responses at IM-11: (a) typical deformation at t₁ and simplified shear
deformation mode; (b) vertical distributions of shear strain at t₁, t₂ and t₃; (c), (d) and (e) time instant
of t₁, t₂ and t₃.</figcaption></figure>
follow the simplified shear deformation mode, especially in the elevation region of 0~1.2 m. Because the shear modulus of soil was greatly shifted within the depth of 0~3 m, the shear stiffness in the elevation region of 0~1.2 m was much larger than that in the upper region (IM-11), e.g. $G_{max}$ at CH04 was about 32.4 MPa but only 4 MP at CH13 (Table 5). The shear deformation of soil may not be compatible under seismic effects. When analysing the seismic deformation of soil within the depth of 0~3 m under the 1-g condition, the soil properties variation with the depth should be thoroughly considered.

Furthermore, the displacement directions of the upper and lower parts of the sand were opposite at $t_1$, because the cyclic displacement at the soil surface reached the maximum value (Fig. 11a) and the bottom of the soil started to move in the opposite direction at the time instant. The direction of the displacement at the top was positive, but negative at the bottom. This might lead to larger shear responses at the middle region.

<figure><img src="image_13.png" /><figcaption>**Figure 11.** Seismic sand responses at IM-11: (a) typical deformation at $t_1$ and simplified shear deformation mode; (b) vertical distributions of shear strain at $t_1$, $t_2$ and $t_3$; (c), (d) and (e) time instant of $t_1$, $t_2$ and $t_3$.</figcaption></figure>
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Time histories of $\gamma$ at CH02~CH14 can be estimated using Eq. (2). Fig. 11 (b) show the vertical distributions of $\gamma$ at $t_1$, $t_2$ and $t_3$. $t_2$ and $t_3$ were the time instants when the relative acceleration (CH15 and CH01) and base acceleration reached the maximum values. As shown in Fig. 11 (b), the largest $\gamma$ distribution was observed at $t_1$. The values of $\gamma$ were large at the middle region, i.e. the elevation range from 1.2~1.9 m, but small in the top and bottom regions. The $\gamma$ distribution of the soil was different from the simplified shear strain distribution in the 3 m-height 1-g shaking table tests.

<figure><img src="image_14.png" /></figure>

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**Figure 12.** Vertical distributions of shear strain ($\gamma$) at the instant of peak relative displacement: (a) distributions at IM-10 and IM-11; (b) distributions at IM-9 and IM-12; (c) distributions at IM-16 and IM-17; (d) distributions at IM-15 and IM-18; (e) $\gamma$ distribution when maximum $\gamma$ occurred at CH07 and max $\gamma$ distribution.

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Figs. 12 (a)~(d) show the $\gamma$ distribution of the sand in 0.4 g and 0.62 g stages at $t_1$. Responses of $\gamma$ were gradually increased from the 0~1.2 m, and large values were always observed in the elevation range from 1.2 m to 1.9 m under different motions. The values of $\gamma$ at the elevation range of 1.9~3.0 m was also large at some positions, but the values or positions were unstable, which might be because of the low vertical stress of the soil and slight inertial effects of laminar rings.
Time histories of $\gamma$ at CH02~CH14 can be estimated using Eq. (2). Fig. 11 (b) shows the vertical distributions of $\gamma$ at $t_1$, $t_2$ and $t_3$. $t_2$ and $t_3$ were the time instants when the relative acceleration (CH15 and CH01) and base acceleration reached the maximum values. As shown in Fig. 11 (b), the largest $\gamma$ distribution was observed at $t_1$. The values of $\gamma$ were large at the middle region, i.e. the elevation range from 1.2~1.9 m, but small in the top and bottom regions. The $\gamma$ distribution of the soil was different from the simplified shear strain distribution in the 3 m-height 1-g shaking table tests.

<figure><img src="image_14.png" /></figure>

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**Figure 12.** Vertical distributions of shear strain ($\gamma$) at the instant of peak relative displacement: (a) distributions at IM-10 and IM-11; (b) distributions at IM-9 and IM-12; (c) distributions at IM-16 and IM-17; (d) distributions at IM-15 and IM-18; (e) $\gamma$ distribution when maximum $\gamma$ occurred at CH07 and max $\gamma$ distribution.

Figs. 12 (a)–(d) show the $\gamma$ distribution of the sand in 0.4 g and 0.62 g stages at $t_1$. Responses of $\gamma$ were gradually increased from the 0~1.2 m, and large values were always observed in the elevation range from 1.2 m to 1.9 m under different motions. The values of $\gamma$ at the elevation range of 1.9~3.0 m was also large at some positions, but the values or positions were unstable, which might be because of the low vertical stress of the soil and slight inertial effects of laminar rings.

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elevation range from 1.2 m to 1.9 m under different motions. The values of $\gamma$ at the elevation range of 1.9~3.0 m was also large at some positions, but the values or positions were unstable, which might be because of the low vertical stress of the soil and slight inertial effects of laminar rings.

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The $\gamma$ distributions of soil were meaningful for the studies of buried structures, because the seismic responses of buried structures might be notably influenced by $\gamma$ of the soil along the elevation [Wang 1993]. Because the greatest $\gamma$ responses of the 3-m thick sand were within the elevation range of 1.2~1.9 m, the seismic responses of buried structures would follow the trend and the large responses might also be acquired within the region. However, the present seismic responses of free-field soil were just a sole case and the position of the region may vary with the type of the soil, soil container and input motions. The $\gamma$ distributions of free-field soil should be further studied to support the seismic design and analysis of shaking table tests on buried structures.

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The maximum $\gamma$ of soil at an elevation may be interested for the studies of buried structures.
Fig. 12 (e) show the maximum shear strain of soil at CH02~CH14 (LP-max) along the elevation,
which was independent with time. For example, if the CH07 was interested, $\gamma$ distribution would
be obtained at the time instant when $\gamma$ at CH07 reached the maximum value (LP-CH07 in Fig. 12
e).

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# 4. Parameter study via numerical modelling

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The 3-D finite element modelling was calibrated using the time histories of the test results. The calibrated numerical model of the sand would be further extended to the seismic 3-D simulation of buried structure with complex geometry. The estimated parameters in the previous sections were studied during the calibration process.

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## 4.1. Configuration of the finite element model

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The sand deposit for the shaking table tests was modelled using the finite element software ABAQUS with the Explicit solver. The size of the numerical model was 3.2 m × 2.4 m × 3 m
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The $\gamma$ distributions of soil were meaningful for the studies of buried structures, because the seismic responses of buried structures might be notably influenced by $\gamma$ of the soil along the elevation [Wang 1993]. Because the greatest $\gamma$ responses of the 3-m thick sand were within the elevation range of 1.2~1.9 m, the seismic responses of buried structures would follow the trend and the large responses might also be acquired within the region. However, the present seismic responses of free-field soil were just a sole case and the position of the region may vary with the type of the soil, soil container and input motions. The $\gamma$ distributions of free-field soil should be further studied to support the seismic design and analysis of shaking table tests on buried structures.

The maximum $\gamma$ of soil at an elevation may be interested for the studies of buried structures.
Fig. 12 (e) show the maximum shear strain of soil at CH02~CH14 (LP-max) along the elevation, which was independent with time. For example, if the CH07 was interested, $\gamma$ distribution would be obtained at the time instant when $\gamma$ at CH07 reached the maximum value (LP-CH07 in Fig. 12 e).

# 4. Parameter study via numerical modelling

The 3-D finite element modelling was calibrated using the time histories of the test results. The calibrated numerical model of the sand would be further extended to the seismic 3-D simulation of buried structure with complex geometry. The estimated parameters in the previous sections were studied during the calibration process.

## 4.1. Configuration of the finite element model

The sand deposit for the shaking table tests was modelled using the finite element software ABAQUS with the Explicit solver. The size of the numerical model was 3.2 m x 2.4 m x 3 m
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(length×width×height). The soil model was divided into 3 layers (Fig. 13), i.e. Layer 1 (L1), Layer 2

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(L2) and Layer 3 (L3), according to the $V_s$ estimation process. The thicknesses of L1, L2 and L3

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were 1.1 m, 1.04 m and 0.79 m, respectively.

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The soil was meshed with the 8-node linear brick, reduced integration element (C3D8R). For the convenience, each laminar ring of the box was simplified as a continuous beam (Stringer in ABAQUS). The beam elements were composed by the exterior nodes of the soil at the same elevation, with the box type transversal section of 0.12 m × 0.06 m × 0.004 m (height × width × thickness). The beam elements made the exterior nodes of the soil at the same elevation have the same degrees of freedom, so they would move following the same manner.

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<figure><img src="image_15.png" /></figure>

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<caption>**Figure 13.** Configuration of the finite element model.</caption>

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Zero displacement boundary conditions, i.e. $u_y=0$ and $u_z=0$ (Fig. 13), were applied to the numerical model in the FEM, because there was no transverse (Z axis) input motions. The accelerations recorded at the shaking table were excited in the X direction at the bottom of the model. Before the acceleration was loaded, the 1-g initial geo-stress was applied.

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**4.2. Soil constitutive model**
(length×width×height). The soil model was divided into 3 layers (Fig. 13), i.e. Layer 1 (L1), Layer 2
(L2) and Layer 3 (L3), according to the $V_s$ estimation process. The thicknesses of L1, L2 and L3
were 1.1 m, 1.04 m and 0.79 m, respectively.

The soil was meshed with the 8-node linear brick, reduced integration element (C3D8R). For
the convenience, each laminar ring of the box was simplified as a continuous beam (Stringer in
ABAQUS). The beam elements were composed by the exterior nodes of the soil at the same
elevation, with the box type transversal section of 0.12 m × 0.06 m × 0.004 m (height × width ×
thickness). The beam elements made the exterior nodes of the soil at the same elevation have the
same degrees of freedom, so they would move following the same manner.

<figure><img src="image_15.png" /></figure>

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<caption>466 **Figure 13.** Configuration of the finite element model.</caption>

Zero displacement boundary conditions, i.e. $u_y=0$ and $u_z=0$ (Fig. 13), were applied to the
numerical model in the FEM, because there was no transverse (Z axis) input motions. The
accelerations recorded at the shaking table were excited in the X direction at the bottom of the
model. Before the acceleration was loaded, the 1-g initial geo-stress was applied.

471 **4.2. Soil constitutive model**
The Davidenkov constitutive model [Martin 1975] is a viscoelastic hyperbolic model for the soil dynamic behavior. The simple model has shown to be effective in the time history analyses of ground response and dynamic soil-structure interactions [Martin and Seed 1982; Chen et al. 2015a; Chen et al. 2015b]. The backbone curve of model can be expressed as:

$$ \tau(\gamma) = G \cdot \gamma = G_{\max} \cdot \gamma \cdot [1 - H(\gamma)] \quad (5) $$

$$ H(\gamma) = \left\{ \frac{(\gamma / \gamma_0)^{2B}}{1 + (\gamma / \gamma_0)^{2B}} \right\}^A \quad (6) $$

where H is a function of $\gamma$; A and B are fitting coefficients and $\gamma_0$ is the reference strain [Hardin and Drnevich 1972].

Fig. 9 (b) shows the stress-strain loops of the Davidenkov model. The loops were constituted using the Masing rules [Martin and Seed 1978]. The loops were composed of uploading and unloading sections, which can be described as Eqs. 7 and 8, respectively:

$$ \text{uploading: } \tau = G_{\max}(\gamma - \gamma_{\min})[1 - H(\frac{\gamma - \gamma_{\min}}{2})] + \tau_{\min} \quad (7) $$

$$ \text{unloading: } \tau = -G_{\max}(\gamma_{\max} - \gamma)[1 - H(\frac{\gamma_{\max} - \gamma}{2})] + \tau_{\max} \quad (8) $$

where $\tau_{\min}$ and $\tau_{\max}$ are minimum and maximum stress shown in Fig. 9 (b).

The damping ratio was then identified by the strain-dependent loops, using the method shown in Fig. 9 (b). The Davidenkov model was compiled as a VUMAT user subroutine for ABAQUS.

## 4.3. Parameters for simulation

As the properties of the soil could hardly be identified at any input motion during the 1-g shaking table tests, there might be problems when calibrating the numerical model using the corresponding motions. However, the simulation was not to study the soil dynamics or seismic site
The Davidenkov constitutive model [Martin 1975] is a viscoelastic hyperbolic model for the soil dynamic behavior. The simple model has shown to be effective in the time history analyses of ground response and dynamic soil-structure interactions [Martin and Seed 1982; Chen et al. 2015a; Chen et al. 2015b]. The backbone curve of model can be expressed as:

$$ \tau(\gamma) = G \cdot \gamma = G_{\max} \cdot \gamma \cdot [1 - H(\gamma)] \qquad (5) $$

$$ H(\gamma) = \left\{ \frac{(\gamma / \gamma_0)^{2B}}{1 + (\gamma / \gamma_0)^{2B}} \right\}^A \qquad (6) $$

where H is a function of $\gamma$; A and B are fitting coefficients and $\gamma_0$ is the reference strain [Hardin and Drnevich 1972].

Fig. 9 (b) shows the stress-strain loops of the Davidenkov model. The loops were constituted using the Masing rules [Martin and Seed 1978]. The loops were composed of uploading and unloading sections, which can be described as Eqs. 7 and 8, respectively:

$$ \text{uploading: } \tau = G_{\max}(\gamma - \gamma_{\min})[1 - H(\frac{\gamma - \gamma_{\min}}{2})] + \tau_{\min} \qquad (7) $$

$$ \text{unloading: } \tau = -G_{\max}(\gamma_{\max} - \gamma)[1 - H(\frac{\gamma_{\max} - \gamma}{2})] + \tau_{\max} \qquad (8) $$

where $\tau_{\min}$ and $\tau_{\max}$ are minimum and maximum stress shown in Fig. 9 (b).

The damping ratio was then identified by the strain-dependent loops, using the method shown in Fig. 9 (b). The Davidenkov model was compiled as a VUMAT user subroutine for ABAQUS.

## 4.3. Parameters for simulation

As the properties of the soil could hardly be identified at any input motion during the 1-g shaking table tests, there might be problems when calibrating the numerical model using the corresponding motions. However, the simulation was not to study the soil dynamics or seismic site
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responses, but to calibrate the numerical model which would be further extended to the simulation of
buried structures.

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Therefore, the simulation was conducted using two groups of parameters to compare the results
of calibration. The first group was the parameters fitted using the dynamic soil properties estimated
at an $a_{pk}$ stage, e. g. shear modulus degradation fitting at the 0.4 g stage in Fig. 10. The fitted
parameters of the Davidenkov model at 0.2 g stage, 0.4 g stage, 0.62 g stage and 1.0 g stage were
named as S2, S4, S6 and S10, respectively. The values of $G_{max}$ used in S2, S4, S6 and S10 were the
shear modulus estimated at the beginning of the stages (Table 5). As the properties of the soil was
various during the tests, according to the results of frequencies, settlement and accumulated lateral
displacement, the parameters of S2, S4, S6 and S10 could incorporate the variation to some extent.

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The second group was the parameters fitted using the shear modulus degradation data acquired
under all the seismic motions. The fitted parameters were named as SA. The values of $G_{max}$ used in
SA were the average maximum shear modulus during the entire tests (Table 5). Figs. 14, 15 and 16
show the fitted Davidenkov model at CH13, CH08 and CH04 using all the shear modulus
degradation data acquired via the shaking table tests, respectively. When acquiring the parameters of
SA, the experimental data was much more abundant and only the main trend of $\gamma - G/G_{max}$ should be
set as the target to fit. Therefore, the parameters of SA could be easier to acquire, compared with S2,
S4, S6 and S10, especially when there were difficulties to identify the dynamic soil properties at any
input motion.

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responses, but to calibrate the numerical model which would be further extended to the simulation of
buried structures.

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Therefore, the simulation was conducted using two groups of parameters to compare the results
of calibration. The first group was the parameters fitted using the dynamic soil properties estimated
at an $a_{pk}$ stage, e. g. shear modulus degradation fitting at the 0.4 g stage in Fig. 10. The fitted
parameters of the Davidenkov model at 0.2 g stage, 0.4 g stage, 0.62 g stage and 1.0 g stage were
named as S2, S4, S6 and S10, respectively. The values of $G_{max}$ used in S2, S4, S6 and S10 were the
shear modulus estimated at the beginning of the stages (Table 5). As the properties of the soil was
various during the tests, according to the results of frequencies, settlement and accumulated lateral
displacement, the parameters of S2, S4, S6 and S10 could incorporate the variation to some extent.

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The second group was the parameters fitted using the shear modulus degradation data acquired
under all the seismic motions. The fitted parameters were named as SA. The values of $G_{max}$ used in
SA were the average maximum shear modulus during the entire tests (Table 5). Figs. 14, 15 and 16
show the fitted Davidenkov model at CH13, CH08 and CH04 using all the shear modulus
degradation data acquired via the shaking table tests, respectively. When acquiring the parameters of
SA, the experimental data was much more abundant and only the main trend of $\gamma - G/G_{max}$ should be
set as the target to fit. Therefore, the parameters of SA could be easier to acquire, compared with S2,
S4, S6 and S10, especially when there were difficulties to identify the dynamic soil properties at any
input motion.

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<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /><figcaption>**Figure 14.** Shear modulus degradation and damping relationships: shaking table test with all data at CH13, D & Q model [Darendeli 2001; Menq 2003], and fitted Davidenkov [Martin 1975] model used in Layer 1 of the FE modeling.</figcaption></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>**Figure 15.** Shear modulus degradation and damping relationships: shaking table test with all data at CH08, D & Q model [Darendeli 2001; Menq 2003], and fitted Davidenkov [Martin 1975] model used in Layer 2 of the FE modeling.</figcaption></figure>
<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /><figcaption>**Figure 14.** Shear modulus degradation and damping relationships: shaking table test with all data at CH13, D & Q model [Darendeli 2001; Menq 2003], and fitted Davidenkov [Martin 1975] model used in Layer 1 of the FE modeling.</figcaption></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>**Figure 15.** Shear modulus degradation and damping relationships: shaking table test with all data at CH08, D & Q model [Darendeli 2001; Menq 2003], and fitted Davidenkov [Martin 1975] model used in Layer 2 of the FE modeling.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Figure 16.** Shear modulus degradation and damping relationships: shaking table test with all data at CH04, D & Q model [Darendeli 2001; Menq 2003], and fitted Davidenkov [Martin 1975] model used in Layer 3 of the FE modeling.</figcaption></figure>

The $G/G_{max}$ curves of the Davidenkov model matched well with the test results in the figures, but *D* results were still scattered throughout the motions due to the inherent nature of damping ratios. Nevertheless, the Davidenkov curves for damping ratios were adopted for the present numerical simulations. Table 6 summarizes the parameters of the Davidenkov model. The Rayleigh damping was also incorporated in the numerical simulations to supply the small strain damping. The coefficients $\alpha$ and $\beta$ were computed using $f_1, f_2$ and $\xi$ in Table 3 via the method introduced by Chopra [2007].

<table><caption>**Table 6.** Fitted parameters used in the finite element modelling.</caption><thead><tr><th></th><th>G<sub>max</sub> (MPa)</th><th>A</th><th>B</th><th>γ<sub>0</sub> (10<sup>-2%</sup>)</th><th>Rayleigh damping α</th><th>Rayleigh damping β</th></tr></thead><tbody><tr><td></td><td>L1</td><td>5.0</td><td>0.8</td><td>0.32</td><td>0.5</td><td></td></tr><tr><td rowspan="2">0.2 g stage (S2)</td><td>L2</td><td>21.7</td><td>0.9</td><td>0.3</td><td>0.74</td><td>0.484</td><td>0.0019</td></tr><tr><td>L3</td><td>55.4</td><td>0.8</td><td>0.32</td><td>0.8</td><td></td><td></td></tr></tbody></table>
<figure><img src="image_20.png" /><figcaption>**Figure 16.** Shear modulus degradation and damping relationships: shaking table test with all data at CH04, D & Q model [Darendeli 2001; Menq 2003], and fitted Davidenkov [Martin 1975] model used in Layer 3 of the FE modeling.</figcaption></figure>

The $G/G_{max}$ curves of the Davidenkov model matched well with the test results in the figures, but *D* results were still scattered throughout the motions due to the inherent nature of damping ratios. Nevertheless, the Davidenkov curves for damping ratios were adopted for the present numerical simulations. Table 6 summarizes the parameters of the Davidenkov model. The Rayleigh damping was also incorporated in the numerical simulations to supply the small strain damping. The coefficients $\alpha$ and $\beta$ were computed using $f_1, f_2$ and $\xi$ in Table 3 via the method introduced by Chopra [2007].

<table><caption>**Table 6.** Fitted parameters used in the finite element modelling.</caption><thead><tr><th></th><th>G<sub>max</sub> (MPa)</th><th>A</th><th>B</th><th>γ<sub>0</sub> (10<sup>-2%</sup>)</th><th>Rayleigh damping α</th><th>Rayleigh damping β</th></tr></thead><tbody><tr><td></td><td>L1</td><td>5.0</td><td>0.8</td><td>0.32</td><td>0.5</td><td></td></tr><tr><td rowspan="2">0.2 g stage (S2)</td><td>L2</td><td>21.7</td><td>0.9</td><td>0.3</td><td>0.74</td><td>0.484</td><td>0.0019</td></tr><tr><td>L3</td><td>55.4</td><td>0.8</td><td>0.32</td><td>0.8</td><td></td><td></td></tr></tbody></table>
<table><tbody><tr><td></td><td>L1</td><td>4.0</td><td>1.1</td><td>0.32</td><td>1</td><td></td><td></td></tr><tr><td rowspan="2">0.4 g stage (S4)</td><td>L2</td><td>12.0</td><td>1.1</td><td>0.37</td><td>2</td><td>0.607</td><td>0.0034</td></tr><tr><td>L3</td><td>32.4</td><td>0.9</td><td>0.32</td><td>0.9</td><td></td><td></td></tr><tr><td></td><td>L1</td><td>3.4</td><td>1.1</td><td>0.32</td><td>1</td><td></td><td></td></tr><tr><td rowspan="2">0.62 g stage (S6)</td><td>L2</td><td>7.8</td><td>1.0</td><td>0.32</td><td>2.5</td><td>0.667</td><td>0.0039</td></tr><tr><td>L3</td><td>27.1</td><td>1</td><td>0.32</td><td>0.9</td><td></td><td></td></tr><tr><td></td><td>L1</td><td>3.4</td><td>1.1</td><td>0.32</td><td>1.1</td><td></td><td></td></tr><tr><td rowspan="2">1.0 g stage (S10)</td><td>L2</td><td>11.5</td><td>1.0</td><td>0.32</td><td>1.3</td><td>0.720</td><td>0.0048</td></tr><tr><td>L3</td><td>32.2</td><td>0.9</td><td>0.32</td><td>0.8</td><td></td><td></td></tr><tr><td rowspan="3">All stages<br/>incorporated (SA)</td><td>L1</td><td>3.8</td><td>1.1</td><td>0.34</td><td>1.2</td><td></td><td></td></tr><tr><td>L2</td><td>12.9</td><td>1.1</td><td>0.34</td><td>1.2</td><td>0.6195</td><td>0.0035</td></tr><tr><td>L3</td><td>36.1</td><td>1.0</td><td>0.34</td><td>0.8</td><td></td><td></td></tr></tbody></table>

## 4.4. Results

The time histories of displacement and their Fourier spectra were presented because the results of displacement may be more interested in when performing the analyses of buried structures. Figs. 17~22 show the numerical results of displacement and their spectra computed using the parameters of S2, S4 and S6. The amplitudes and frequencies of the displacement matched very well with the tests results. The good agreement of results of displacement indirectly verified that the soil material properties acquired through the back analysis were good. It was also implied that the numerical model was good and the method of the simulation on the free-field soil could be extended to the simulation on buried structures.
<table><tbody><tr><td></td><td>L1</td><td>4.0</td><td>1.1</td><td>0.32</td><td>1</td><td></td><td></td></tr><tr><td rowspan="2">0.4 g stage (S4)</td><td>L2</td><td>12.0</td><td>1.1</td><td>0.37</td><td>2</td><td>0.607</td><td>0.0034</td></tr><tr><td>L3</td><td>32.4</td><td>0.9</td><td>0.32</td><td>0.9</td><td></td><td></td></tr><tr><td></td><td>L1</td><td>3.4</td><td>1.1</td><td>0.32</td><td>1</td><td></td><td></td></tr><tr><td rowspan="2">0.62 g stage (S6)</td><td>L2</td><td>7.8</td><td>1.0</td><td>0.32</td><td>2.5</td><td>0.667</td><td>0.0039</td></tr><tr><td>L3</td><td>27.1</td><td>1</td><td>0.32</td><td>0.9</td><td></td><td></td></tr><tr><td></td><td>L1</td><td>3.4</td><td>1.1</td><td>0.32</td><td>1.1</td><td></td><td></td></tr><tr><td rowspan="2">1.0 g stage (S10)</td><td>L2</td><td>11.5</td><td>1.0</td><td>0.32</td><td>1.3</td><td>0.720</td><td>0.0048</td></tr><tr><td>L3</td><td>32.2</td><td>0.9</td><td>0.32</td><td>0.8</td><td></td><td></td></tr><tr><td rowspan="3">All stages<br>incorporated (SA)</td><td>L1</td><td>3.8</td><td>1.1</td><td>0.34</td><td>1.2</td><td></td><td></td></tr><tr><td>L2</td><td>12.9</td><td>1.1</td><td>0.34</td><td>1.2</td><td>0.6195</td><td>0.0035</td></tr><tr><td>L3</td><td>36.1</td><td>1.0</td><td>0.34</td><td>0.8</td><td></td><td></td></tr></tbody></table>

## 4.4. Results

The time histories of displacement and their Fourier spectra were presented because the results of displacement may be more interested in when performing the analyses of buried structures. Figs. 17~22 show the numerical results of displacement and their spectra computed using the parameters of S2, S4 and S6. The amplitudes and frequencies of the displacement matched very well with the tests results. The good agreement of results of displacement indirectly verified that the soil material properties acquired through the back analysis were good. It was also implied that the numerical model was good and the method of the simulation on the free-field soil could be extended to the simulation on buried structures.
<figure><img src="image_21.png" /><figcaption>**Figure 17.** Comparison between displacement results of STT and FEM subjected to IM-3 (LP motion-0.2 g) at CH13, CH08 and CH04.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Figure 18.** Comparison between displacement results of STT and FEM subjected to IM-6 (Beijing motion-0.2 g) at CH13, CH08 and CH04.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>**Figure 17.** Comparison between displacement results of STT and FEM subjected to IM-3 (LP motion-0.2 g) at CH13, CH08 and CH04.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Figure 18.** Comparison between displacement results of STT and FEM subjected to IM-6 (Beijing motion-0.2 g) at CH13, CH08 and CH04.</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>**Figure 19.** Comparison between displacement results of STT and FEM subjected to IM-9 (LP motion-0.4 g) at CH13, CH08 and CH04.</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>**Figure 20.** Comparison between acceleration results of STT and FEM subjected to IM-12 (Beijing motion-0.4 g) at CH13, CH08 and CH04.</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>**Figure 19.** Comparison between displacement results of STT and FEM subjected to IM-9 (LP motion-0.4 g) at CH13, CH08 and CH04.</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>**Figure 20.** Comparison between acceleration results of STT and FEM subjected to IM-12 (Beijing motion-0.4 g) at CH13, CH08 and CH04.</figcaption></figure>
<figure><img src="image_25.png" /><figcaption>**Figure 21.** Comparison between displacement results of STT and FEM subjected to IM-15 (LP motion-0.62 g) at CH13, CH08 and CH04.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>**Figure 22.** Comparison between displacement results of STT and FEM subjected to IM-18 (Beijing motion-0.62 g) at CH13, CH08 and CH04.</figcaption></figure>

Figs. 17~22 also show numerical result comparisons using the parameters between SA and $Sn$ ($n=2$, 4 or 6). The discrepancies between the results computed using SA and $Sn$ ($n=2$, 4 or 6) were slight, especially at the 0.2 g and 0.4 g stage. It was may be because the effective confining pressure
<figure><img src="image_25.png" /><figcaption>**Figure 21.** Comparison between displacement results of STT and FEM subjected to IM-15 (LP motion-0.62 g) at CH13, CH08 and CH04.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>**Figure 22.** Comparison between displacement results of STT and FEM subjected to IM-18 (Beijing motion-0.62 g) at CH13, CH08 and CH04.</figcaption></figure>

Figs. 17~22 also show numerical result comparisons using the parameters between SA and $Sn$ ($n=2$, 4 or 6). The discrepancies between the results computed using SA and $Sn$ ($n=2$, 4 or 6) were slight, especially at the 0.2 g and 0.4 g stage. It was may be because the effective confining pressure
563

of the soil at an elevation was not notably changed throughout the tests, which might be the most

564

influential factor contribute to the seismic responses of the sand. The frequencies, settlement and lateral

565

shear deformation of the soil were more variable in from the 0.62 g stage and even the accelerometers

566

vertically moved following the settlement of the soil. Therefore, the modelling results were no better

567

than those in the previous $a_{pk}$ stages, because the numerical and constitutive model of the soil could

568

not incorporate the accumulated effects such as settlement and lateral deformation in the tests.

569

However, the calibration was still accepted because the numerical results using SA only had slight

570

discrepancy with the tests results. It suggested that the parameters of SA could also obtain the

571

approximately good results when conducting the calibration under the small and strong motions, but

572

the results should be carefully checked under the severe seismic conditions. The parameters of SA

573

could be used when there were difficulties to acquire the parameters of the soil.

574

## 5. Conclusions

575

The seismic responses of a 3-m-thick sand deposit were studied using the 1-g shaking table tests.

576

Dynamic properties of soil were analyzed using white noises, pulse motions and earthquake motions.

577

Seismic soil deformation and shear strain distribution of sand was discussed. The 3-D finite element

578

analyses of the sand were conducted using the Davidenkov model to supply a calibrated numerical

579

model for potential seismic analyses on buried structures. Following conclusions may be drawn:

580

1. Dynamic sand properties of the sand column with largest sand grain up to 2 cm were notably

581

vaired due to the seismic effects during the tests. The ranges of 1st and 2nd predominant frequencies

582

of the sand acquired by white noise motions were 6.39~9.08 Hz and 21.53~28.78 Hz, respectively.
of the soil at an elevation was not notably changed throughout the tests, which might be the most influential factor contribute to the seismic responses of the sand. The frequencies, settlement and lateral shear deformation of the soil were more variable in from the 0.62 g stage and even the accelerometers vertically moved following the settlement of the soil. Therefore, the modelling results were no better than those in the previous $a_{pk}$ stages, because the numerical and constitutive model of the soil could not incorporate the accumulated effects such as settlement and lateral deformation in the tests. However, the calibration was still accepted because the numerical results using SA only had slight discrepancy with the tests results. It suggested that the parameters of SA could also obtain the approximately good results when conducting the calibration under the small and strong motions, but the results should be carefully checked under the severe seismic conditions. The parameters of SA could be used when there were difficulties to acquire the parameters of the soil.

## 5. Conclusions

The seismic responses of a 3-m-thick sand deposit were studied using the 1-g shaking table tests.

Dynamic properties of soil were analyzed using white noises, pulse motions and earthquake motions.

Seismic soil deformation and shear strain distribution of sand was discussed. The 3-D finite element analyses of the sand were conducted using the Davidenkov model to supply a calibrated numerical model for potential seismic analyses on buried structures. Following conclusions may be drawn:

1. Dynamic sand properties of the sand column with largest sand grain up to 2 cm were notably vailed due to the seismic effects during the tests. The ranges of 1st and 2nd predominant frequencies of the sand acquired by white noise motions were 6.39~9.08 Hz and 21.53~28.78 Hz, respectively.
Meanwhile, the relative density of the soil increased from 68.6% to 79.5%, with accumulated lateral shear displacement at the soil surface up to 106.2 mm using the unconstrained laminar shear box.

2. The buried structure could have the strongest seismic responses in middle region if it was buried in the 3-m thick free-field soil in the 1-g shaking table tests. The largest shear strain of the soil under earthquake motions was within the elevation range from 1.2 m to 1.9 m.

3. The parameters of soil for the simulation could be approximately fitted using all the experimental data throughout the tests to calibrate the numerical model of the free-field soil under small and strong motions, if there were difficulties to identify the dynamic soil properties in 1-g shaking table tests with very good precision.
Meanwhile, the relative density of the soil increased from 68.6% to 79.5%, with accumulated lateral shear displacement at the soil surface up to 106.2 mm using the unconstrained laminar shear box.

2. The buried structure could have the strongest seismic responses in middle region if it was buried in the 3-m thick free-field soil in the 1-g shaking table tests. The largest shear strain of the soil under earthquake motions was within the elevation range from 1.2 m to 1.9 m.

3. The parameters of soil for the simulation could be approximately fitted using all the experimental data throughout the tests to calibrate the numerical model of the free-field soil under small and strong motions, if there were difficulties to identify the dynamic soil properties in 1-g shaking table tests with very good precision.
592

**Acknowledgements** This research was funded by the Innovative Research Groups of the National Natural

593

Science Foundation of China (Grant No. 51421005), National Natural Science Foundation of China (Grant

594

No. 51578026 and 51708009) and National Key Research and Development Program of China

595

(No.2018YFC1504305). The authors would like to thank China Railway Six Group Co., Ltd. for collecting

596

soil samples. We are thankful to Institute of Foundation Engineering, China Academy of Building Research,

597

for the support of laminar shear box. We are thankful to Prof. Guoxing Chen at Nanjing University of

598

Technology for the support of ABAQUS. We are thankful to Yiyao Shen, Yanmei Li, Chenglong Jiang,

599

students at Beijing University of Technology, for their assistance in the shaking table tests and laboratory

600

tests. We are also thankful to Keshab Sharma and Austin Hong, students at the University of Alberta, for

601

technical editing.

602
592

**Acknowledgements** This research was funded by the Innovative Research Groups of the National Natural

593

Science Foundation of China (Grant No. 51421005), National Natural Science Foundation of China (Grant

594

No. 51578026 and 51708009) and National Key Research and Development Program of China

595

(No.2018YFC1504305). The authors would like to thank China Railway Six Group Co., Ltd. for collecting

596

soil samples. We are thankful to Institute of Foundation Engineering, China Academy of Building Research,

597

for the support of laminar shear box. We are thankful to Prof. Guoxing Chen at Nanjing University of

598

Technology for the support of ABAQUS. We are thankful to Yiyao Shen, Yanmei Li, Chenglong Jiang,

599

students at Beijing University of Technology, for their assistance in the shaking table tests and laboratory

600

tests. We are also thankful to Keshab Sharma and Austin Hong, students at the University of Alberta, for

601

technical editing.

602
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