A torsional vibration device for shear wave velocity measurement of coarse grained soils

Measurement 148 (2019) 106972

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A torsional vibration device for shear wave velocity measurement of coarse grained soils Degao Zou a,b, Xingyang Liu a,b,⇑, Jingmao Liu a,b, Hao Zhang a,b, Chenguang Zhou a,b, Huafu Pei a,b a b

The State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China School of Hydraulic Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China

a r t i c l e

i n f o

Article history: Received 27 January 2019 Received in revised form 16 August 2019 Accepted 19 August 2019 Available online 22 August 2019 Keywords: Shear wave velocity Testing device PMMA Fujian sand Gravel

a b s t r a c t A torsional vibration testing device was designed, fabricated and installed to measure the shear wave velocity of coarse grained soils in a large-scale triaxial testing apparatus. The reliability verification was carried out on a pair of polymethyl methacrylate (PMMA) specimens. The test results demonstrate that the designed testing system can produce torsional vibration and measure the shear wave velocity with high accuracy. In a different set of tests, the small strain modulus was measured for a type of clean sand (Fujian sand) and gravel at different effective confining pressures. The measured small strain modulus of the Fujian sand are in good agreement with existing studies. The measured small strain modulus of well-graded gravel is more sensitive to the variation of effective confining pressure. The results demonstrate that the testing device can be effectively use for shear wave measurement in coarse grained soils. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction The shear wave velocity, Vs, is an important mechanical parameter used to characterize the shear modulus of materials and has been widely used in earthquake ground response analysis [1], prediction of liquefaction potential [2] and soil stiffness assessment [3], etc. Ever since the piezoelectric bender element (BE) was first introduced by Shirley and Hampton [4], their technique has become the most widely used method for determining the Vs of soil in laboratory. Their technique has been incorporated in various soil test apparatuses due to low-cost and ease of implementation. Examples of these uses include consolidometers [5–7], triaxial apparatuses [8– 11], resonant columns [12–14], direct simple shear apparatuses [5,15,16] and centrifugal machines [17–19]. The BE method was also employed to test stiffer materials, including sandstone [20], basalt rock [21] and cement-treated clay [22,23]. As it is difficult to insert the bender element into stiffer materials, cavities of varying depths are typically pre-prepared on the top and bottom surfaces so that the bender element can be inserted more easily. Therefore, it is challenging to control the degree of coupling between the bender element and the specimen when testing stiffer materials. Gravel and rockfill materials are attractive for their good construction qualities such as high strength, low compressibility,

⇑ Corresponding author. E-mail address: [email protected] (X. Liu). https://doi.org/10.1016/j.measurement.2019.106972 0263-2241/Ó 2019 Elsevier Ltd. All rights reserved.

low cost etc., and have been widely used in the construction of large geotechnical structures such as the earth-rock dams, marine reclamation land, pavement base sections and high-speed railway roadbeds. However, the BE method is seldom used to measure the shear wave velocity of gravel and rockfill materials in large dimensions due to the large amount of energy needed for the artificially generated waveforms [24] and insufficient contact between the plates and coarse soil particles [25]. On the other hand, some researchers have adopted surface-only contact testing techniques for wave velocity measurement. Brignoli et al. [26] and Ismail and Rammah [27] used both bender and flat-plate ceramic elements to measure the small strain shear modulus. The results obtained through two methods were in close agreement. Their studies also revealed that it is not necessary to insert the flat-plate transducer in the soil specimen and thus minimizing modifications to specimen, but the flat-plate transducer requires a higher driving voltage. Suwal and Kuwano [28] utilized a disk shaped piezoceramic transducer for compression and shear wave measurement on an identical soil specimen. Gamal [29] developed the piezoelectric ring-actuator technique (P-RAT) and used it in a consolidometer. Karray et al. [30] proposed the systematic P-RAT interpretation method. In the P-RAT, the piezoelectric ring vibrates the porous stone (or porous metal) in radial direction to generate shear waves. The above measurement techniques greatly facilitate the measurement of stiff geotechnical materials in contrast to the more invasive BE method. However, these

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surface-only contact techniques have not yet been used in largescale triaxial tests since specimen compaction poses a great challenge in maintaining the integrity of the transducer. The brittle piezoelectric materials comprising the transducer can be damaged when employing manual compaction techniques for coarser soils with high dry density. The large particle size of gravel and rockfill materials makes them suitable candidates for testing of mechanical properties in large-scale triaxial tests, as the large-scale triaxial apparatus can accommodate large-sized specimens. Compared to soils with low stiffness, the measurement of the small strain modulus of gravel by wave propagation testing techniques in large-scale triaxial tests is rare. The shear waves can be generated by using a hammer to tap the top cap [31] or the steel plate projecting out from the loading piston [32]. In both cases, the shear waves were recorded by two accelerometers attached to the side of the specimen. While the tapping method is easy to implement, it is difficult to maintain repeatability through manual tapping to conduct tests across different specimens. Modoni et al. [33] utilized an electromagnetic actuator and geophones as the signal trigger and receiver, respectively. With this method, the uncertainty caused by human factors is eliminated and the test repeatability is guaranteed; however, due to the difficult coupling between the geophone and the soil specimen, disturbance is generated at the top of the specimen. AnhDan et al. [34] put forward the Trigger-Accelerometer (TA) method. The wave source was composed of a piezoelectric stack, a steel bar and a steel plate. In their

method, the generation of stress waves can be controlled precisely, and the trigger and receiver can be installed in a convenient and flexible manner. Wicaksono et al. [35] conducted a comparative study by measuring the small strain shear modulus of Toyoura

Fig. 3. Schematic of Part A and the piezoelectric stack before and after assembly.

Fig. 1. The customized top cap, which is composed of Part A and Part B, modeled as a torsional vibration system.

Fig. 2. Schematic of Part A and Part B and their sub components.

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sand with both the TA and the BE method, and showed that the shear modulus estimated with the TA method is 30% higher than that estimated from the BE method. However, the specific causes of this discrepancy are still unknown. Therefore, further studies are needed for understanding the applications of the TA method. Flora and Lirer [24] performed further studies on undisturbed gravel soil by triggering the steel plate with an electromagnetic actuator; however, the steel plate needs be inserted 15 mm deep into the soil specimen thus creating a certain disturbance within the range of insertion depth. It can be seen that there are usually challenges in the wave velocity test of gravel, such as poor repeatability, large disturbance or controversial results. The above discussions indicate that many researchers have made significant contributions to the study on the small strain shear modulus of soils, but for coarse grained soils, in particular

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for gravel and rockfill materials, further developments are required for the proper application of wave propagation based measurement of small strain shear modulus. This study is novel in the following aspects: First, in this study a new shear wave velocity measuring device was developed specifically for large-scale triaxial tests. The device makes possible the investigation of small modulus of gravel and rockfill materials. Second, the study used the device to conduct a series of measurements of the polymethyl methacrylate (PMMA) specimen to demonstrate the feasibility of the developed device. Third, a type of clean sand and a type of gravel were tested at different effective pressures and compared with existing results from literature. The findings of this study may further improve the understanding of the small strain dynamic properties of coarse grained soils and provide a reference for future studies with similar goals.

Fig. 4. Schematic of the top cap before and after assembly.

Fig. 5. Photograph of complete assembly of the customized top cap.

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2. Laboratory testing equipment 2.1. Top cap design The top cap of a large-scale static and dynamic hydraulic servo triaxial apparatus [36] was designed based on the principles of a torsional vibration system and fabricated at the Earthquake Engineering Research Institute at Dalian University of Technology. The maximum axial force of the triaxial apparatus is 150 kN (compression)/100 kN (tension).

The top cap is the combination of Part A and Part B shown in Fig. 1. Part A is designed as the fixed end and it is fastened with the axial loading system to provide the reaction force. Part B is in contact with the top of the specimen and helps deliver the torsional vibration controlled by a piezoelectric stack. The testing device can be simplified as the torsional vibration system shown in Fig. 1. The kinetic equation of the top cap system driven by the external voltage and without considering the system damping is as follows:

I€h þ kt h ¼ F pzt R0

ð1Þ

where h is the angular rotation; kt is the torsional stiffness of the axis; I is the moment of inertia of the inertial plate to the axis; R0 is the distance from the center to the output force vector of the piezoelectric stack; Fpzt is the output force generated by the piezoelectric stack driven by an external voltage. When the hysteresis of the piezoelectric stack is not taken into account, Fpzt can be simplified to [37]:

F pzt ¼ kpzt ½aU ðt Þ  D

ð2Þ

where kpzt is the equivalent stiffness of piezoelectric stack; a is the proportion coefficient; U(t) is the external input voltage; D is the output displacement of the piezoelectric stack. Therefore, the kinetic equation of the top cap system can be further simplified as follows: 0 0 €h þ kt þ kpzt R h ¼ aU ðt Þkpzt R I I 2

Fig. 6. Diagram of shear wave measurement by designed top cap and accelerometers.

ð3Þ

The schematic of Part A, Part B and the piezoelectric stack before and after assembly are as shown in Figs. 2–4. Part A consists of Part A1 and Part A2 and Part B consists of Part B1 and Part B2 (Fig. 2). Before the test, the piezoelectric stack (AE0505D08F, Thorlabs, Inc) with a fixed hemispheric end cap is embedded inside a designated cavity within A2 (Fig. 3). The hemispheric end cap

Fig. 7. Schematic of the entire apparatus before and during the shear wave velocity test.

D. Zou et al. / Measurement 148 (2019) 106972

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Fig. 8. Instruments used for reliability verification.

Fig. 9. The arrangement of accelerometers used to verify torsional vibration.

protects the stack and will ensure that the force applied on the piezoelectric stack is uniform. A preload is be applied on the piezoelectric stack by the preload bolt installed in Part B1 so that compression and extension range of the piezoelectric stack can be

controlled by increasing or decreasing the input voltage (Fig. 4). Part B2 is a porous stone placed in a circular depression at the bottom of Part B1. The photograph and specific dimensions of the complete assembly are shown in Fig. 5.

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The piezoelectric stack inside Part A will generate longitudinal vibration that causes Part B to experience torsional vibration when the external voltage is applied. The vibration from Part B is trans-

mitted to the specimen, and two accelerometers attached to the side of the specimen convert the vibration received into measurable electrical signals (Fig. 6). Fig. 7 shows the schematic of the

Fig. 10. Torsional vibration test for (a) Part B of the top cap and (b) the PMMA specimen.

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entire apparatus before and during shear wave velocity test. A compensatory force is applied when isotropic confining pressure is high. The travel time Dt of the shear wave can be determined by comparing two received signals. Since the distance L between the accelerometers is known, the shear wave velocity Vs can be calculated by:

Vs ¼

L Dt

ð4Þ

There are multiple methods to estimate the travel time. The point of first arrival and the peak-to-peak are two commonly used techniques to determine travel time. According to the results of international tests [38] conducted jointly by 23 labs around the world, the results obtained by the point of first arrival are more consistent. In cases where it is difficult to determine the point of first arrival, the peak-to-peak method is preferred. For consistency and brevity, this study used the point of first arrival to calculate the shear wave velocity. The design of the device is based on the classical torsional vibration system. In order to avoid direct contact between the piezoelectric transducer and the soil during specimen compaction, the piezoelectric stack is sealed within the top cap. Thus, firm contact between the surface of the top cap and the tested specimen can be guaranteed without concern for damage to the transducer. Therefore, the device in this study can meet the shear wave velocity test of compacted soils in a large triaxial test, and enrich the testing methods of small strain shear modulus for different types of soils.

Fig. 11. Effect of the applied voltage on acceleration signals at the measuring position.

2.2. Reliability verification In order to verify the reliability of the new top cap, a series of tests were carried out using a pair of polymethyl methacrylate (PMMA) specimens consisting of a larger specimen measuring 200-mm-diameter  500-mm-height and a small specimen with 100-mm-diameter  200-mm-height. Both were cut from the same PMMA specimen that had a diameter of 500 mm and a height of 1000 mm. The 200-mm-diameter specimen was used for the verification of torsional vibration measurement. The 200-mmdiameter and 100-mm-diameter specimens were both used for the verification of wave velocity measurement. The associated electronics equipment include accelerometers (LC0119T, Lance, Inc), a signal generator card (PXIe-6738, National Instruments), a piezoelectric linear power amplifier (EPA-104-203, PiezoSystem, Inc) and a high precision dynamic data acquisition card (PXIe4480, National Instruments). Data was acquired at a sampling rate of 200 kHz per channel. A custom LabVIEW Signal Express program was developed for data acquisition and processing. The instruments used for reliability verification are shown in Fig. 8. As shown in Fig. 9, four accelerometers were fixed along the circumference of Part B of the top cap and the 200-mm-diameter PMMA specimen to acquire the acceleration signals in the tangential direction (X-direction) of the measuring positions. A single sinusoidal wave with an amplitude of 0–10 V at 1000 Hz was generated to excite the top cap. It can be seen from Fig. 10 that the motion in the horizontal plane (X-Z Plane) of Part B caused by the piezoelectric stack is torsional. In order to verify the effect of the applied voltage on the top cap, sinusoidal waves at 1000 Hz with amplitude of 0–20 V and 0–30 V were also applied. As can be seen from Fig. 11, the output acceleration of the measuring position is almost proportional to the applied voltage, which also verifies the applicability of Eq. (3). In addition, the accelerations in the Y and Z directions of Position A and Position A’ were also tested. It is fair to state that the motion of Part B driven by the piezoelectric stack is not pure torsional vibration, and the acceleration components in the Y and Z directions still exist as shown in Fig. 12. However, the acceleration

Fig. 12. Acceleration signals at Position A and A’ in three directions.

signals in the Y and Z directions are much smaller than that of the tangential direction (X direction). Therefore, the data indicates that the acceleration components in the Y and Z directions do not affect the measurement of shear wave velocity. The 200-mm-diameter and 100-mm-diameter specimens were both used for verifying the wave velocity measurement (Fig. 13). Two ultrasonic transducers (PZT-8, Beijing Ultrasonic) were used to measure the compression wave velocities of these two PMMA specimens. The tests were carried out in two new test systems

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Fig. 15. Compression wave test results of PMMA specimens in different sizes.

Fig. 13. PMMA specimens in different sizes.

(large top cap with end platen and small top cap with end platen used for 200-mm-diameter and 100-mm-diameter specimens, respectively), where the ultrasonic transducers can be embedded. A single sinusoidal wave with amplitude of ±60 V at 10 kHz was generated. The details and results of the compression wave test are illustrated in Figs. 14 and 15. The compression wave velocities Vp of the 200-mm-diameter and the 100-mm-diameter PMMA specimens are 2500.0 m/s and

2352.0 m/s, respectively. The velocities are close, which demonstrates that the compression wave velocity test is almost independent of the test system. As the 200-mm-diameter PMMA specimen is close to the actual size of the soil specimen in this paper, the value of compression wave velocity is hereafter assumed to be 2500.0 m/s. Assuming the PMMA is an ideal linear elastic body (i.e. the elastic modulus is independent of the confining pressures), then according to the elastic wave theory [39], the relationship between shear wave velocity and compression wave velocity is as follows:

Fig. 14. The test setup of compression wave measurement for PMMA specimens.

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sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1  2m Vs ¼ Vp 2ð1  mÞ

ð5Þ

According to literature [40], the Poisson’s ratio of PMMA is

m ¼ 0:34. Thus from Eq. (5), the theoretical value of the shear wave velocity of the PMMA specimen is 1230.9 m/s, based on the published value of the Poisson’s ratio and the measured Vp. As a comparison, the shear wave velocity of the same PMMA specimen was directly measured with the customized top cap (Fig. 16). Based on the measurements enabled by the top cap, the shear wave velocity of PMMA specimen is estimated to be 1285.7 m/s, which was

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slightly larger than theoretical value (relative error of 4.5%). Thus, the measured value obtained with newly developed top cap matches well with the theoretical value. The soil specimen is usually covered with a rubber membrane in geotechnical triaxial tests to prevent the pressurized water in the pressure chamber from entering the specimen, or to prevent the water content in the specimen from changing in undrained tests [41]. Due to the uniqueness of each specimen of granular materials, it is difficult to make a direct comparison to determine the influence of the rubber membrane on the shear wave velocity of the soil specimen. However, for the PMMA specimen, it is easier

Fig. 16. The result of the shear wave velocity test for the PMMA specimen.

Fig. 17. The influence of the rubber membrane and vacuum pressures on the shear wave velocity of the PMMA specimen.

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Fig.19. Grain size distribution curves of tested geo-materials. Fig. 18. Shear wave velocities of PMMA specimen under different vacuum pressures. Table 1 Main physical properties of tested geomaterials.

to study the the influence of the rubber membrane on the shear wave velocity. Therefore, shear wave velocity measurements were made for a PMMA specimen enclosed by a rubber membrane to determine the influence of the rubber membrane. The PMMA specimen was first covered with a 1.5 mm thick rubber membrane, and then the shear wave velocity was measured as the confining pressure increased from 10 kPa to 100 kPa in increments of 10 kPa. Fig. 17 shows the testing setup and the acquired shear wave signals under confining pressures of 30 kPa and 80 kPa. Fig. 18 compares the shear wave velocities under different confining pressures with the previously obtained theoretical value (1230.9 m/s). As can be observed, within the confining pressure range of 10 kPa100 kPa, the measured shear wave velocities are slightly less than the theoretical values and stay within an error range of 1.17.8%. With the increase of the contact degree between the rubber membrane and the PMMA specimen due to increasing pressure, the measured shear wave velocities gradually stabilized and converged towards the theoretical value. The highest errors occurred when the confining pressures were 10 kPa and 20 kPa. The data therefore suggests that the relative error of the shear wave velocity caused by the rubber membrane is <5% when the confining pressure exceeds 20 kPa.

Material

Gs

D50 (mm)

Cu

emax

emin

Fujian sand Gravel

2.640 2.729

0.55 9.80

2.42 82.95

0.830 0.339

0.508 0.162

(LC0120T, Lance, Inc) were then installed on the side of the specimen. Afterwards, isotropic confining pressures of 100–500 kPa were applied to S1, S2 and S3 in steps of 100 kPa. For the gravel test, the ratio of the specimen diameter D to the maximum grain size Dmax was equal to 5, which just satisfies the requirement established by SL 237-001-1999, Specification of Soil Test [42]. The initial void ratio of the gravel specimen is 0.193. Isotropic confining pressures of 50, 100, 200, 300, 400, 500 and 600 kPa were applied to gravel specimen. The axial strain was measured by a built-in, high precision linear variable differential transducer (LVDT), and the isotropic strain is assumed when calculating the void ratio after consolidation [43]. The distance between accelerometers was measured by a vertical local deformation transducer (LDT) [44] and the measured distance is used for calculating the shear wave velocity.

4. Results and discussions 3. Testing materials and procedure The sand used in the test is Fujian sand, which is widely used for testing in China. The gravel used in the test was retrieved from a construction site in Xinjiang, China. The gravel-sized grains are smooth, less angular, and not easy to break. The grain-size distribution curves are shown in Fig. 19. The main physical properties of the tested geomaterials are listed in Table 1. All tested specimens were 200 mm in diameter and 500 mm in height. They were tested under air-dry conditions and prepared in five layers with a compacted thickness of 10 cm per layer by employing manual compaction technique using a steel tamper having a mass of 5.2 kg to obtain specified dry densities. During the preparation of the specimens, each layer was scarified to shallow depth before the next layer was deposited in order to ensure interlock between successive layers. A vacuum pressure of 30 kPa was applied to hold the specimen in place and the split mold was then disassembled. The initial void ratios of the sand are 0.618, 0.575 and 0.533, respectively for specimens S1, S2 and S3. After the specimen was prepared, a vacuum pressure of 30 kPa was applied to the specimen, and two piezoelectric accelerometers

For all tested sands, four different input single sinusoidal waves at 1500, 2000, 2500 and 3000 Hz were employed individually in the shear wave velocity test. The test results of Specimen S2 at a confining pressure of 200 kPa are shown in Fig. 20. When the input frequency is between 1500 Hz and 3000 Hz, the input frequency has little influence on the shear wave velocity of the Fujian sand. Therefore, the proceeding analysis for Fujian sand is based on the results of input frequency f = 2000 Hz. Figs. 21 and 22 display the measured shear wave velocities as a function of confining pressure and as a function of void ratio, respectively. The figures show that the shear wave velocity increases with the effective confining pressure but decreases as the void ratio increases. When the soil density q is known, the small strain shear modulus G0 can be determined by the following formula:

G0 ¼ qV 2s

ð6Þ

G0 is influenced by many factors, such as grain shape, grain size distribution, void ratio, stress level, stress history and chemical changes. The following empirical equation proposed by Hardin

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Fig. 20. Received signal on Specimen S2 under 200 kPa isotropic stress.

et al. [12] is based on experimental data from Ottawa sand and crushed quartz sand, and is widely used to determine the small strain shear modulus:

 G0 ¼ A

Fig. 21. Shear wave velocity vs confining pressure levels (sand).

Fig. 22. Shear wave velocity vs void ratio at different confining pressure levels (sand).

ae 1þe

 0 n

r

Pa

¼ AF ðeÞ

 0 n

r

Pa

ð7Þ

where material constant A = 6.9, a = 2.17, and n = 0.5 for round grains and A = 3.2, a = 2.97, and n = 0.5 for angular grains [45]; Pa is the reference pressure (taken as 100 kPa). To remove the influence of the void ratio, the void ratio function F(e) = [(2.973-e)2/ (1 + e)] is used to normalize G0 values. The normalized G0 values are plotted against the normalized confining pressure in Fig. 23 for comparison with Zhou [46] and Cai et al. [47], where the small strain modulus of Fujian sand were tested using the BE method and were also plotted alongside those predicted by Hardin’s empirical equation. The test results in this paper are closer to those of Cai et al. (maximum relative error <18%) when the confining pressures are 100 kPa and 200 kPa. On the other hand, the test results in this paper are closer to those of Zhou (maximum relative error <12%) when the confining pressures are 300 kPa and 400 kPa. Moreover, the test results are in good agreement with Hardin’s empirical equation (maximum relative error <10%). Compared with relatively uniform sands, the propagation of shear waves in gravel is more complex due to high heterogeneity of gravel. The dynamic modulus measured by wave propagation techniques is often significantly higher than the static modulus determined by small unload/reload cycles. The difference between the dynamic and static modulus is related to many factors such as wavelength, mean grain size and stress level, etc. [25,48]. Therefore, the proper selection of the input frequency for the measurement of shear wave velocity in gravel remains to be further investigated. In this study, the input frequency for gravel test is selected to ensure that not only can clear signals be collected, but also that k is at least greater than 20D50 (k is the wavelength in the dynamic measurement and can be referred to literature [32]) to reduce the influence of the high heterogeneity of gravel on test results. For gravel specimen, the results from different excitation frequencies at a confining pressure of 200 kPa are shown in Figs. 24 and 25. The figures indicate that the change of wave velocity is relatively small when the excitation frequency falls within

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Fig. 23. Comparison of measured G0 with existing research of sand.

1500 Hz3500 Hz. When the excitation frequency increases from 2500 Hz to 3000 Hz, the ratio between k and D50 decreases from 21.3 to 19.8. The following analyses for gravel specimen is based on the results of input frequency f = 2500 Hz. As shown in Fig. 26, the relationship between the small strain shear modulus and the confining pressures for gravel specimen also follows a similar form as Eq. (7). Compared with Fujian sand, the small strain shear modulus of gravel is more sensitive to changes in the confining pressure. The reason for the sensitivity is the large uniformity coefficient of gravel specimen. The large uniformity coefficient indicates that the contact surface area among grains increases significantly as confining pressure increases. However, there is still no consensus on the existence of void ratio function that can be used to normalize the small strain shear modulus for both sand and gravel. The mineral composition, grain shape, grain-size distribution, and initial stress anisotropy may be contributing factors that should be accounted for in the void ratio function. Therefore, the small strain shear modulus of two types of materials cannot be compared directly. At the current stage, further study is needed to fully develop the void ratio function for gravel. While not completely verified, certain research results have suggested that the small strain shear modulus of soil with high gravel content may be influenced significantly by the mean grain size D50. However, for sand, the relationship between the small strain shear modulus and the mean grain size is drastically different. Because of the size limitation of the resonant column test apparatus, and the aforementioned obstacles in the application of the BE method for gravel or rockfill materials, the maximum grain size in the test is generally limited to below 20 mm or less. The grain size limitation limits the scope of the presented results. Because the piezoelectric stack inside the top cap will not be damaged during specimen compaction, the testing device in this paper is flexible in application, and can be used for measuring shear wave velocity of coarse-grained soil in large-scale triaxial tests, especially for gravel and rockfill materials at a wide range of densities. The top cap does not need to be inserted into the specimen and is thus also suitable for cemented or undisturbed materials. More indepth research to investigate coarse grained soils can be further explored in the future.

5. Conclusion In this study, a top cap designed as a torsional vibration system was fabricated and installed in a large-scale triaxial apparatus for shear wave velocity measurement. Firstly, a series of tests were carried out using a pair of polymethyl methacrylate (PMMA) specimens to verify the reliability of the new testing device. The test results from the 200-mm-diameter PMMA specimen indicate that the motion of the designed top cap is torsional. Furthermore, the test results from the 200-mm-diameter and 100-mm-diameter PMMA specimens indicate that measured shear wave velocity is 4.5% larger than the value predicted by theory. A rubber membrane was coated over the 200-mm-diameter specimen to investigate the influence of the rubber membrane on shear wave velocity. Tests were furthermore performed within confining pressures between 10 kPa and 100 kPa. The results show that the measured shear wave velocities of PMMA specimen with the rubber membrane are slightly less than theoretical values (error within 1.1%7.8%). The maximum errors occurred when the confining pressures were 10 kPa and 20 kPa. Subsequently, the testing device was also applied to measure the small strain shear modulus, G0, of sand and gravel. The measured G0 of Fujian sand agreed well with the existing research results. The G0 of gravel is found to be more sensitive to the level of confining pressure. The customized testing device in this study can effectively measure the shear wave velocity of coarse grained soils (especially for gravel and rockfill materials with large particle sizes, for which it is difficult to apply the BE and resonant column method) in large-scale triaxial tests. The piezoelectric transducer inside the top cap does not need to be inserted into the specimen and so does not cause any disturbance to the specimen. Additionally, the bottom surface of the developed top cap is in full contact with the specimen, and the friction coefficient of the bottom surface can be adjusted to enhance the propagation of stress waves for accommodating different kinds of soil. The components of the top cap are independent from each other, easy to assemble, water-tight, and the modular, which makes it convenient for replacing components. Finally, the testing device described in this manuscript can enable a wide range of test conditions for future studies to explore the relationship between the mean grain size D50 and G0 of coarser soil.

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Fig. 24. Received shear wave signal in gravel specimen under 200 kPa isotropic stress. Results from excitation frequencies at 1500 Hz, 2500 Hz, and 3500 Hz are shown.

Fig. 25. Relationship between shear wave velocity and input frequency for gravel specimen under 200 kPa isotropic stress.

Fig. 26. Shear modulus (G0) vs normalized confining pressure (r’/Pa) for gravel and Fujian sand.

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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors acknowledge the financial support from the National Key R&D Program of China (Grant No. 2017YFC0404902), the National Natural Science Foundation of China (Grant No. 51779034, 51608095) and the Fundamental Research Funds for Central Universities (Grant No. DUT19ZD216, DUT18RC(3)046). References [1] S.L. Kramer, Geotechnical Earthquake Engineering, Prentice-Hall Inc., New Jersey, 1996. [2] T.L. Youd, I.M. Idriss, Liquefaction resistance of soils: summary report from the 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils, J. Geotech. Geoenviron. 127 (10) (2001) 817–833. [3] A.M. Tang, M.N. Vu, Y.J. Cui, Effects of the maximum soil aggregates size and cyclic wetting-drying on the stiffness of a lime-treated clayey soil, Géotechnique 61 (5) (2011) 421–429. [4] D.J. Shirley, L.D. Hampton, Shear-wave measurements in laboratory sediments, J. Acoust. Soc. Am. 63 (2) (1978) 607–613. [5] R. Dyvik, T.S. Olsen, Gmax measured in oedometer and DSS tests using bender elements, Proc. 12th Int Conf. Soil Mech. Found. Engng, Rio de Janeiro 1 (1989) 39–42. [6] M.A. Fam, G. Cascante, M.B. Dusseault, Large and small strain properties of sands subjected to local void increase, J. Geotech. Geoenviron. 128 (12) (2002) 1018–1025. [7] J.L. Ayala, F.A. Villalobos, G. Alvarado, Study of the elastic shear modulus of Bío Bío sand using bender elements in an oedometer, Geotech. Test. J. 40 (4) (2017) 673–682. [8] C.R. Bates, Dynamic soil property measurements during triaxial testing, Géotechnique 39 (4) (1989) 721–726. [9] A. Gajo, A. Fedel, L. Mongiovì, Experimental analysis of the effects of fluid-solid coupling on the velocity of elastic waves in saturated porous media, Géotechnique 47 (5) (1997) 993–1008. [10] E.C. Leong, J. Cahyadi, H. Rahardjo, Measuring shear and compression wave velocities of soil using bender–extender elements, Can. Geotech. J. 46 (7) (2009) 792–812. [11] G. Alvarado, M.R. Coop, On the performance of bender elements in triaxial tests, Géotechnique 62 (1) (2011) 1–17. [12] B.O. Hardin, F.E. Richart, Elastic wave velocities in granular soils, J. Soil Mech. Found. Eng. Div. 89 (1) (1963) 39–56. [13] X. Gu, J. Yang, M. Huang, Laboratory measurements of small strain properties of dry sands by bender element, Soils Found. 53 (5) (2013) 735–745. [14] J. Yang, X. Liu, Shear wave velocity and stiffness of sand: the role of non-plastic fines, Géotechnique 66 (6) (2016) 500–514. [15] D. Zekkos, A. Athanasopoulos-Zekkos, J. Hubler, et al., Development of a largesize cyclic direct simple shear device for characterization of ground materials with oversized particles, Geotech. Test. J. 41 (2) (2018) 263–279. [16] A. Zamani, B.M. Montoya, Undrained monotonic shear response of MICPtreated silty sands, J. Geotech. Geoenviron. 144 (6) (2018) 1–12. [17] W.B. Gohl, W. D. L. Finn, Use of piezoceramic bender elements in soil dynamics testing, Recent Advances in Instrumentation, Data Acquisition and Testing in Soil Dynamics. ASCE (1991) 118–133. [18] L. Fu, X. Zeng, J. Ludwig Figueroa, Shear wave velocity measurement in centrifuge using bender elements, Int. J. Phys. Model. Geotech. 4 (2) (2004) 01– 11. [19] Y. Zhou, Z. Sun, Y. Chen, Zhejiang University benchmark centrifuge test for LEAP-GWU-2015 and liquefaction responses of a sloping ground, Soil Dyn. Earthq. Eng. 113 (2018) 698–713. [20] G. Alvarado, Influence of Late Cementation on the Behaviour of Reservoir Sands (Ph.D. thesis), Imperial College London, London, 2007.

[21] A. Juneja, M. Endait, Laboratory measurement of elastic waves in basalt rock, Measurement 103 (2017) 217–226. [22] H. Xiao, K. Yao, Y. Liu, et al., Bender element measurement of small strain shear modulus of cement-treated marine clay-Effect of test setup and methodology, Constr. Build. Mater. 172 (2018) 433–447. [23] Q. Khan, S. Subramanian, D.Y.C. Wong, et al., Bender elements in stiff cemented clay: shear wave velocity (Vs) correction by applying wavelength considerations, Can. Geotech. J. 1041 (2018) 1–8. [24] A. Flora, S. Lirer, Small strain shear modulus of undisturbed gravelly soils during undrained cyclic triaxial tests, Geotech. Geol. Eng. 31 (4) (2013) 1107– 1122. [25] S. Maqbool, R. Kuwano, J. Koseki, Improvement and application of a P-wave measurement system for laboratory specimens of sand and gravel, Soils Found. 51 (1) (2011) 41–52. [26] E.G.M. Brignoli, M. Gotti, K.H. Stokoe, Measurement of shear waves in laboratory specimens by means of piezoelectric transducers, Geotech. Test. J. 19 (4) (1996) 384–397. [27] M.A. Ismail, K.I. Rammah, Shear-plate transducers as a possible alternative to bender elements for measuring Gmax, Géotechnique 55 (5) (2005) 403–407. [28] L.P. Suwal, R. Kuwano, Disk shaped piezo-ceramic transducer for P and S wave measurement in a laboratory soil specimen, Soils Found. 53 (4) (2013) 510– 524. [29] D. Gamal EL Dean, Development of a New Piezoelectric Pulse Testing Device and Soil Characterization using Shear Waves (Ph.D. thesis), Université de Sherbrooke, Québec, 2007. [30] M. Karray, M. Ben Romdhan, M.N. Hussien, et al., Measuring shear wave velocity of granular material using the piezoelectric ring-actuator technique (P-RAT), Can. Geotech. J. 52 (9) (2015) 1302–1317. [31] S. Nishio, K. Tamaoki, Measurement of shear wave velocities in diluvial gravel samples under triaxial conditions, Soils Found. 28 (2) (1988) 35–48. [32] Y. Tanaka, K. Kudo, K. Nishi, et al., Small strain characteristics of soils in Hualien, Taiwan, Soils Found. 40 (3) (2000) 111–125. [33] G. Modoni, A. Flora, C. Mancuso, et al., Evaluation of gravel stiffness by pulse wave transmission tests, Geotech. Test. J. 23 (4) (2000) 506–521. [34] L.Q. AnhDan, J. Koseki, T. Sato, Comparison of Young’s moduli of dense sand and gravel measured by dynamic and static methods, Geotech. Test. J. 25 (4) (2002) 1–20. [35] R.I. Wicaksono, R. Kuwano, Small strain shear stiffness of Toyoura sand obtained from various wave measurement techniques, Bull. ERS 42 (42) (2009) 107–120. [36] X. Kong, J. Liu, D. Zou, et al., Stress-dilatancy relationship of Zipingpu gravel under cyclic loading in triaxial stress states, Int. J. Geomech. 16 (4) (2016) 1– 13. [37] I. Chopra, J. Sirohi, Smart Structures Theory, Cambridge University Press, New York, 2013. [38] S. Yamashita, T. Kawaguchi, Y. Nakata, et al., Interpretation of International parallel test on the measurement of Gmax using bender elements, Soils Found. 49 (4) (2009) 631–650. [39] J. Achenbach, Wave Propagation in Elastic Solids, Elsevier, Amsterdam, 2012. [40] The Acoustic Institute of Tongji University, Measuring technique in ultrasonic engineering, Shanghai People0 s Publishing House, Shanghai, 1977 (in Chinese). [41] D. Fang, H. Xia, Influence of piston friction and rubber membrane in triaxial tests, Hydropower Pumped Storage 5 (1989) 27–36 (in Chinese). [42] Specification of Soil Test (SL 237-001-1999), China Water Conservancy and Hydropower Press, Beijing, 1999 (in Chinese). [43] X. Gu, J. Yang, M. Huang, et al., Measurement of elastic parameters of dry sand using bender-extender element, Rock. Soil. Mech 36 (2015) 220–224 (in Chinese). [44] S. Goto, F. Tatsuoka, S. Shibuya, et al., A simple gauge for local small strain measurements in the laboratory, Soils Found. 31 (1) (1991) 169–180. [45] B.O. Hardin, W.L. Black, Sand stiffness under various triaxial stresses, J. Soil Mech. Found. Div. ASCE 92 (1966) 27–42. [46] Y. Zhou, Shear Wave Velocity-based Characterization of Soil Structure and its Effects on Dynamic Behavior (Ph.D. thesis), Zhejiang University, Hang Zhou, 2007 (in Chinese). [47] Y. Cai, Q. Dong, J. Wang, et al., Measurement of small strain shear modulus of clean and natural sands in saturated condition using bender element test, Soil Dyn. Earthq. Eng. 76 (2015) 100–110. [48] T. Enomoto, O.H. Qureshi, T. Sato, J. Koseki, Strength and deformation characteristics and small strain properties of undisturbed gravelly soils, Soils Found. 53 (6) (2013) 951–965.