Advertisement

Granular Matter

, 21:92 | Cite as

Acoustic emission generated by glass beads in compression and shearing

  • Alister SmithEmail author
  • Neil Dixon
Open Access
Original Paper
  • 178 Downloads

Abstract

Acoustic emission (AE) monitoring offers the potential to sense particle-scale interactions that lead to macro-scale responses of granular materials. This paper presents results from a programme of drained triaxial tests performed on densely packed glass beads to establish quantitative interpretation of AE during isotropic compression, shearing and associated stick–slip events. Relationships have been quantified between: AE and boundary work (i.e. AE generated per Joule) for a unit volume of glass beads under isotropic compression and shear; AE and shear displacement rate; and the amplitude of deviator stress cycles and AE activity during stick–slip events. In shear, AE generation increased with shear strain and reached peak values that were maintained from volume minimum (i.e. the transition from contractive to dilative behaviour) to peak dilatancy, whereupon AE generation gradually reduced and then remained around a constant mean value with further increments of shear strain. In each stick–slip event, AE activity increased during shear strength mobilisation, particle climbing and dilation, and then reduced with the subsequent deviator stress drop during particle sliding and contraction. The amplitude of these cycles in AE activity were governed by the amplitude of deviator stress cycles during stick–slip events, which were also proportional to the imposed stress level and inversely proportional to particle size.

Keywords

Acoustic emission Deformation Friction Granular media Monitoring Stick–slip 

List of symbols

A

AE waveform amplitude

B

Skempton’s pore pressure parameter

b-value

Measure of the proportion of low and high magnitude events in an AE waveform

\( C_{\text{c}} \)

Coefficient of curvature

\( C_{\text{u}} \)

Coefficient of uniformity

\( D_{r} \)

Relative density (%)

d50

Mean particle size

\( e_{\hbox{max} } \)

Maximum void ratio

\( e_{\hbox{min} } \)

Minimum void ratio

M

Frictional constant defining the slope of the critical state line in q–p′ space (\( 6\sin \phi '_{{\text{cv}}} / 3 - \sin \phi '_{{\text{cv}}} \))

m

Log-scale measure of AE magnitude

p

Mean effective stress (kPa)

q

Deviator stress (kPa)

\( R_{a} \)

Roughness average: the arithmetic average of the absolute values of the profile heights over the evaluation length \(( {{\upmu {\rm m}}} ) \)

\( R_{q} \)

RMS Roughness: the root mean square average of the profile heights over the evaluation length \(( {{\upmu {\rm m}}} ) \)

\( R_{z} \)

Average maximum height of the profile: the average of the successive values of the vertical distance between the highest and lowest points of the profile within a sampling length calculated over the evaluation length \(( {{\upmu {\rm m}}} ) \)

RDC

Ring-down counts are the number of times the AE waveform crosses a voltage threshold level

ΔW

Increment of work done per unit volume transmitted to the granular material across its boundaries (i.e. boundary work)

ΔWd

Increment of distortional work per unit volume

ΔWv

Increment of volumetric work per unit volume

\( \varepsilon_{\text{a}} \)

Axial strain

\( \varepsilon_{r} \)

Radial strain

\( \varepsilon_{vol} \)

Volumetric strain

\( \varepsilon_{\upgamma} \)

Shear strain \( \left( {\varepsilon_{\text{a}} - \varepsilon_{r} = \frac{1}{2}\left( {3\varepsilon_{\text{a}} - \varepsilon_{vol} } \right)} \right) \)

\( \varepsilon_{q} \)

Deviatoric strain \( \left( {\frac{2}{3}\varepsilon_{\upgamma} = \frac{2}{3}(\varepsilon_{\text{a}} - \varepsilon_{r} ) = \varepsilon_{\text{a}} - \frac{1}{3}\varepsilon_{vol} } \right) \)

\( \uprho_{{\text{dry}_{\hbox{max} } }} \)

Maximum dry density \( \left( {{\text{Mg}}/{\text{m}}^{ 3} } \right) \)

\( \uprho_{{{\text{dry}}_{ \hbox{min} } }} \)

Minimum dry density \( \left( {{\text{Mg}}/{\text{m}}^{ 3} } \right) \)

\( \uprho_{\text{s}} \)

Particle density \( \left( {{\text{Mg}}/{\text{m}}^{ 3} } \right) \)

\( \upsigma_{r}^{\prime } \)

Radial effective stress (kPa)

\( \phi_{{\text{cv}}}^{\prime } \)

Constant volume friction angle

\( \phi_{\text{p}}^{\prime } \)

Peak effective friction angle

1 Introduction

Proportions of the energy dissipated during deformation of particulate materials are converted to heat and sound. The high-frequency (> 10 kHz) component of this sound energy is called acoustic emission (AE). The AE behaviour of particulate systems has been studied in the context of a range of disciplines, including: soil mechanics (e.g. [1, 2, 3, 4]), landslides (e.g. [5, 6, 7, 8]), faulting and earthquakes (e.g. [9, 10]), granular physics (e.g. [11, 12, 13]), additive manufacturing (e.g. [14]), mining (e.g. [15]) and pharmaceuticals (e.g. [16, 17]).

Densely packed particulate materials mobilise shearing resistance through inter-particle friction and interlocking (i.e. dilation, particle rearrangement and particle damage) [18]. AE monitoring offers the potential to sense particle-scale interactions that lead to macro-scale responses of granular materials, for example: particle–particle interactions such as sliding and rolling friction; particle contact network rearrangement (e.g. release of contact stress and stress redistribution as interlock is overcome and regained); degradation at particle asperities; and crushing [4, 5, 19]. Monitoring the evolution of these processes is particularly valuable in geotechnical engineering, where mobilisation of peak shear strength in dense soils causes shear zones to develop, which in turn leads to reduced shear strength and accelerating deformation behaviour as the soil mass becomes weaker under the same imposed boundary stresses; this ultimate limit state can have devastating consequences for people and infrastructure.

Smith and Dixon [4] demonstrated the benefits of using AE to monitor the behaviour of dense sands in triaxial experiments, and they proposed a framework to interpret the mobilisation of peak shear strength and to quantify rates of shear strain from AE measurements. The study also demonstrated the influences of the fabric (i.e. orientation and distribution of particle contacts) and state (i.e. physical condition, including stresses and void ratio) of sands on AE generation. However, stick–slip behaviour was not investigated because the natural quartz Leighton Buzzard sand that was studied exhibited negligible stick–slip events.

Glass beads are often used in the investigations of granular media behaviour (e.g. [10, 12, 19, 20, 21]) because of their relatively uniform and well understood properties. However, to date, interpretation of AE generated by glass beads has been qualitative (e.g. higher AE activity indicating a more significant stick–slip event [12]) and studies have not developed a quantitative framework for interpretation of material behaviour. The objective of the research reported here was to holistically develop quantitative interpretation of the AE behaviour of densely packed glass beads encompassing isotropic compression, shearing and associated stick–slip events. To achieve this, a programme of drained triaxial isotropic compression and shearing experiments were performed on samples of glass beads and AE measurements were compared with mechanical behaviours (e.g. stresses, strains and boundary work). The new quantitative methods will enable the evolution of particulate material behaviour to be interpreted from AE measurements, potentially removing or reducing the need for arduous measurements of stresses and strains, and hence benefitting a wide range of applications and industries.

2 Methodology

2.1 Apparatus

Triaxial tests enabled the systematic investigation of the evolution of AE with the stress–strain response of glass beads at a range of effective confining stresses and strain rates under drained conditions. The advantages of triaxial testing over simpler procedures, such as direct-shear testing, include the ability to control specimen drainage and stress conditions. A hydraulic GDS Bishop and Wesley [22] stress path triaxial apparatus was used to eliminate noise that could be generated by motor-operated systems. A schematic of the apparatus is shown in Fig. 1, which has a bespoke 50 mm diameter base pedestal incorporating both AE and pore-water pressure measurement.
Fig. 1

Schematic of the GDS Bishop and Wesley Stress Path triaxial apparatus and modified base pedestal to incorporate both AE and pore-water pressure measurement (after Smith and Dixon [4])

2.2 Glass beads

Glass beads were selected for this investigation as their mechanical behaviour has been studied extensively in the literature (e.g. [9, 19, 21]) and batches of different size fractions could be procured with consistent properties. Four poorly-graded, single-sized glass bead materials were selected to promote stick–slip behaviour during shearing, minimise the influence of different fabrics and to control mineralogy, shape, surface roughness and inter-particle friction.

The physical properties of the glass beads are shown in Table 1 and their particle size distributions are shown in Fig. 2. The mean particle sizes (i.e. d50) were 2.67 mm (GB 4510), 1.61 mm (GB 4506), 0.81 mm (GB 4503) and 0.52 mm (GB 45015). Particle size and packing properties were quantified using soils testing methods to BSI [23]. Particle shape parameters (range and mean) were quantified from measurements of 40 particles taken across the four particle size ranges. Roundness and sphericity were computed using the method described in Zheng and Hryciw [24] from 2D microscope images of the particles. Roundness is quantified as the average radius of curvature of particle surface features relative to the radius of the largest circle that can be inscribed in the particle. Sphericity (circle ratio) is quantified as the diameter ratio between the largest inscribing and smallest circumscribing circles [24, 25, 26, 27]. The range of roundness measurements was 0.92 to 1.00 and the mean was 0.99. The range of sphericity measurements was 0.90 to 0.99 and the mean was 0.97. Roughness was computed using high-resolution optical 3D measurements of the particles acquired with an Alicona Infinite Focus system. Roughness parameters Ra, Rq and Rz are the roughness average, RMS roughness and average maximum profile height, respectively. The range of Ra (μm) measurements was 0.16 to 1.23 and the mean was 0.57. The range of Rq (μm) measurements was 0.21 to 1.64 and the mean was 0.78. The range of Rz (μm) measurements was 0.56 to 5.09 and the mean was 2.39. Scanning electron microscope (SEM) images of a glass bead particle are shown in Fig. 3.
Table 1

Physical properties of the glass beads

 

Particle size

Packing

Description

Size range (mm)

\( {\text{C}}_{\text{u}} \)

\( {\text{C}}_{\text{c}} \)

\( \uprho_{\text{s}} \)

\( \uprho_{{{\text{dry}}_{ \hbox{min} } }} \)

\( \uprho_{{{\text{dry}}_{ \hbox{max} } }} \)

\( {\text{e}}_{ \hbox{min} } \)

\( {\text{e}}_{ \hbox{max} } \)

Glass Beads

GB 4510

2.40–2.90

1.318

0.954

2.500

1.510

1.531

0.633

0.656

GB 4506

1.55–1.85

1.325

0.985

1.530

1.558

0.605

0.634

GB 4503

0.75–1.00

1.431

0.931

1.550

1.572

0.590

0.613

GB 45015

0.40–0.60

1.410

0.944

1.550

1.584

0.578

0.613

Fig. 2

Particle size distributions of the glass beads

Fig. 3

Scanning electron microscope (SEM) images of a glass bead particle. The length of the white bar in the bottom panel of each image shows the scale: 1 mm in (a), 100 μm in (b), 10 μm in (c), and 1 μm in (d). Note that cracking visible in (d) is in the gold–palladium sputter coating on the surface of the particle, which is required for SEM imagery

2.3 Testing procedure

Specimen preparation followed the same procedure to that described in Smith and Dixon [4] for sand samples. The cylindrical specimens were 50 mm in diameter and 100 mm tall. Samples were prepared in a membrane-lined split-mould mounted on the base pedestal. Moist compacted samples were tamped into the mould to a target relative density, Dr, of approximately 85% in 10 equal layers to produce densely packed assemblages of glass beads. Back pressure of 400 kPa was imposed under a constant effective stress of approximately 20 kPa to achieve saturation until a minimum pore-pressure parameter, B, of 0.97 was measured [18, 28, 29, 30].

Isotropic compression was performed by increasing the cell pressure to achieve a target effective stress (e.g. 100, 200 or 300 kPa), which led to excess pore-water pressure generation and consolidation. The drainage pathway was through the upper porous disc and top cap (Fig. 1) and the volume of water leaving the samples was measured by the back-pressure controller. Pore-water pressure measurement was at the base of the specimens.

The shearing stage was initiated after no further volume change took place and 100% of the excess pore-water pressure had dissipated. Shearing was performed strain-controlled through application of constant rates of axial displacement of 1, 3 and 6 mm/h, which were selected to ensure drained shearing. The appropriate corrections for the membrane and changes in specimen area were applied to the measurements [28].

A summary of the triaxial tests performed in this investigation is shown in Table 2. The peak and critical state friction angles obtained are typical and consistent with those reported for glass beads in the literature (e.g. [9, 21, 31]).
Table 2

Summary of the drained triaxial isotropic compression and shearing tests performed in this study

Test No.

Material

\( \upsigma_{\text{r}}^{\prime } \) (kPa)

Axial displacement rate (mm/h)

Initial \( {\text{D}}_{\text{r}} \) (%)

\( \phi_{\text{p}}^{\prime } \) b

\( \phi_{\text{cv}}^{\prime } \) b

M b

1

GB 45015

100

1

84.4

31°

23°

0.89

2

GB 45015

200

1

84.4

3

GB 45015

300

1

84.4

4

GB 4503

100

1

83.7

31°

23°

0.89

5

GB 4503

200

1

83.7

6

GB 4503

300

1

83.7

7

GB 4506

100

1

84.8

31°

23°

0.89

8

GB 4506

200

1

84.8

9

GB 4506

300

1

84.8

10

GB 4506

300

3

84.8

11

GB 4506

300

6

84.8

12

GB 4510

100

1

85.9

31°

23°

0.89

13

GB 4510

200

1

85.9

14

GB 4510

300

1

85.9

15a

GB 4506

84.8

aIsotropic load–unload–reload (LUR) cycles of \( \upsigma_{\text{r}}^{\prime } \)

bFriction parameters obtained from drained triaxial shearing tests performed in this study at three different cell pressures

2.4 Energy calculations

Equations 13 were used to quantify the work done during the triaxial experiments for comparison with AE measurements. The increment of work done per unit volume transmitted to the granular material across its boundaries (i.e. boundary work) was computed using Eq. 1. Boundary work per unit volume has two components: distortional work per unit volume, which causes a change of sample shape (Eq. 2); and volumetric work per unit volume, which causes a change of sample volume (Eq. 3) [32, 33, 34, 35].
$$ \Delta W = \Delta W_{d} + \Delta W_{v} $$
(1)
$$ \Delta W_{d} = q\delta \varepsilon_{q} = \frac{2}{3}q\delta \varepsilon_{\gamma } $$
(2)
$$ \Delta W_{v} = p^{\prime } \delta \varepsilon_{vol} $$
(3)
where \( \delta \varepsilon_{\gamma } \), \( \delta \varepsilon_{q} \) and \( \delta \varepsilon_{vol} \) are increments of shear strain, deviatoric strain and volumetric strain, respectively. The increments of work done per unit volume were multiplied by the current sample volume in each increment [35]. This allowed direct comparison with the AE generated by each sample, and hence the AE generated for an increment of work done per unit volume.

2.5 Acoustic emission measurements

A band-pass filter was used to constrain the measured AE to within the frequency range of 10–100 kHz. Filtering signals below 10 kHz is essential to remove extraneous low-frequency environmental noise that could be generated in a laboratory by machinery. The focus of this investigation was frictional and stick–slip interactions within assemblages of glass beads; particle damage and fracturing were minimised through application of relatively low effective confining stress (100–300 kPa). Mao and Towhata [36] found that particle crushing has a much higher frequency content (> 100 kHz) than inter-particle friction and particle rearrangement (< 100 kHz). It is notable that particle damage was minimal in the experiments reported here (confirmed through post-test particle size distributions), and hence filtering above 100 kHz was appropriate for this study.

The AE sensor was installed inside the base pedestal as shown in Fig. 1; a 5 mm wall of stainless steel separated the surface of the sensor and the top surface of the pedestal. The sensor was a MISTRAS R3α piezoelectric transducer, which is sensitive over the frequency range of 0–100 kHz and has a resonant frequency of 30 kHz. The sensor converts the mechanical AE to a voltage waveform that can be processed.

The AE measurement system was a bespoke setup comprising a pre-amplifier (20 dB gain), a main amplifier (3 dB gain), an analogue-to-digital converter with 2 MHz sampling frequency, and a laptop with a LabView program to condition, process and record the AE waveform. The two amplifiers were used to improve the signal-to-noise ratio. The LabView program was set to further attenuate signals outside of the 10–100 kHz range and record the full AE waveform within this frequency range.

Two key AE parameters of interest are ring-down counts (RDC) and b-value. RDC per unit time are the number of times the AE waveform crosses a programmable threshold level (set to 0.01 V in this study, above background environmental and electronic noise as shown in Fig. 4) within a predefined time interval and are a measure of the AE signal energy. The b-value can be obtained from the full AE waveform data [37] and is a convenient way to describe the amplitude distribution in a single value. When the AE waveform is dominated by low amplitude events the b-value is large. As the proportion of higher amplitude events increases, indicating an increase in energy, the b-value reduces. The b-value was computed at 1-min intervals using Eqs. 5 and 6.
$$ {\text{logN = c - bm}} $$
(5)
$$ {\text{m = logA}} $$
(6)
where A is the amplitude, m is a log-scale measure termed magnitude, N is the number of AE events with magnitude greater than m, c is the point that the log(N) vs. m relationship intersects the y-axis, and the coefficient b (b-value) is the negative slope of the log(N) vs. m relationship.
Fig. 4

Example waveforms recorded using the AE measurement system showing the 0.01 V threshold level: a background environmental and electronic noise, and b during deformation of granular media (after Smith and Dixon [4])

Quantifying the b-value is appropriate as the measured log(N) vs. m relationships follow a power law, as demonstrated through multiple studies reported in the literature on AE monitoring of particulate materials (e.g. [3, 4, 12, 19, 20]).

3 Results

3.1 Isotropic compression

Figure 5 shows example time series measurements from isotropic compression performed on GB 4503 (d50 = 0.81 mm) (Tests 4, 5 and 6). Space precludes inclusion of time series measurements from all tests; however, the general trends in behaviour were the same, and results from all isotropic compression tests (Tests 1–9 and 12–14) are compared in relation to the change in mean effective stress and volumetric work done in Fig. 6. Excess pore-water pressures developed as the imposed cell pressure increased in each test. With time the mean effective stress increased as the excess pore-water pressure dissipated, and the specimen consolidated to a drained condition.
Fig. 5

Time series measurements from isotropic compression tests to effective confining pressures of 100, 200 and 300 kPa performed on GB 4503 (d50 = 0.81 mm) (Tests 4, 5 and 6). a mean effective stress, b excess pore-water pressure, c volume change (%), d cumulative AE (RDC), and e cumulative volumetric work (Joules)

Fig. 6

Results from isotropic compression tests to effective confining pressures of 100, 200 and 300 kPa performed on glass beads (Tests 1–9 and 12–14). a Total generated AE (RDC) versus change in mean effective stress (kPa). b Total generated AE (RDC) versus volumetric work done (Joules)

The small increase in volume shown at 4 min and decrease at 7.5 min in the measurements for cell pressure to 300 kPa in Fig. 5c (i.e. solid black line) are a function of the measurement system. During tests, the volume of de-aired water in the back-pressure controller is automatically modified at regular intervals in order to maintain a constant back-pressure in response to changes in cell pressure. Note that the b-value measurements were not significantly modified by isotropic compression; however, they were influenced by stick–slip behaviour in shear (described later).

Figure 6a shows the total AE generated during isotropic compression increased proportionally with the change in mean effective stress; however, these data also show that AE generation was influenced by particle size. Figure 6b shows the total AE generated plotted against the volumetric work done, which results in stronger correlation (e.g. R2 values of 0.92 and 0.96 for the presented linear and exponential relationships, respectively). The linear regression in Fig. 6b, which excludes the data corresponding to volumetric work greater than 0.5 J (i.e. those causing the exponential trend), shows that, in general, approximately 4900 RDC were generated per 1 Joule of volumetric work done on the glass beads. The exponential function in Fig. 6b best describes the data because both mean effective stress and density increase during isotropic compression, having a combined effect on AE generation (as described in Smith and Dixon [4]).

Figure 7 shows results from load–unload–reload cycles of cell pressure performed on GB 4506 (d50 = 1.61 mm) (Test 15), which demonstrates that the Kaiser Effect [38] occurs in glass beads under cycles of isotropic compression (i.e. AE activity is negligible until the current stress conditions exceed the maximum that has been experienced in the past). Imposed unload and reload stages of isotropic compression were 50 kPa and 100 kPa, respectively.
Fig. 7

Cumulative (AE) RDC versus mean effective stress (kPa) measurements for isotropic load-unload-reload cycles of cell pressure performed on GB 4506 (d50 = 1.61 mm) (Test 15)

3.2 Shearing

Figure 8 shows measurements versus shear strain from GB 45015 (d50 = 0.52 mm) (left, Tests 1–3) and GB 4510 (d50 = 2.67 mm) (right, Tests 12–14). Note the periodic cycling of deviator stress, which rapidly drops and then increases as shear strength is mobilised; these cycles in deviator stress are caused by stick–slip behaviour.
Fig. 8

Measurements versus shear strain (%) from drained triaxial shearing tests performed on GB 45015 (d50 = 0.52 mm) (left) and GB 4510 (d50 = 2.67 mm) (right) at effective confining pressures of 100, 200 and 300 kPa and axial displacement rate of 1 mm/h (Tests 1–3 and 12–14). a, b deviator stress (kPa), and c, d AE rate (RDC/min)

AE is generated in shear by particle-scale interactions and evolving mechanisms such as inter-particle friction, stick–slip events and particle rearrangement, and hence the AE measurements have a variable nature. Mean AE rate values are presented in Fig. 8c and d for when post-peak shear strength conditions were established, which demonstrate that AE activity increased with both particle size and confining stress level: mean post-peak AE rates for GB 4510 (d50 = 2.67 mm) were greater than those for GB 45015 (d50 = 0.52 mm) by factors of 6.4, 6.1 and 5.5 for effective confining stress of 100, 200 and 300 kPa, respectively; and an increase in effective confining stress of 100 kPa (i.e. from 100 to 200 kPa and from 200 to 300 kPa) caused the mean post-peak AE rates to increase by a factor of approximately 1.4.

Figure 8 shows that the amplitude of deviator stress cycles during stick–slip events increased with confining stress level and were significantly greater for GB 45015 (d50 = 0.52 mm) than for GB 4510 (d50 = 2.67 mm) (i.e. inversely proportional to particle size). The amplitudes of deviator stress cycles were greater in the GB 45015 (d50 = 0.52 mm) because its shear strength was controlled by failure along a concentrated shear zone, whereas GB 4510 (d50 = 2.67 mm) experienced a greater distribution of shear strains and hence particle dislocations as it failed by bulging.

The stick–slip events caused cycles in AE activity and hence were the principal cause for the variable nature in AE rate measurements. The coefficient of variation (CoV) (i.e. the ratio of standard deviation to the mean) of AE rate measurements during post-peak conditions was calculated as a measure of this variability and the calculated CoV values for GB 45015 (d50 = 0.52 mm) and GB 4510 (d50 = 2.67 mm) are presented in Fig. 8c and d, respectively. The calculated CoV values for GB 45015 (d50 = 0.52 mm) were greater than those for GB 4510 (d50 = 2.67 mm) by factors of 1.6, 2.1 and 2.1 for effective confining stress of 100, 200 and 300 kPa, respectively. In addition, an increase in effective confining stress caused the calculated CoV values to increase by factors of 1.5 (from 100 to 200 kPa) and 1.2 (from 200 to 300 kPa) for GB 45015 (d50 = 0.52 mm), and by factors of 1.1 (from 100 to 200 kPa) and 1.3 (from 200 to 300 kPa) for GB 4510 (d50 = 2.67 mm).

Figure 9 shows measurements versus shear strain from Tests 9, 10 and 11 (GB 4506; d50 = 1.61 mm) to demonstrate the influence of axial displacement rate. AE rates increased proportionally with the imposed displacement rate as more particle-scale interactions took place per unit time. AE generation increased with shear strain and reached peak values that were maintained from volume minimum (i.e. the transition from contractive to dilative behaviour) to peak dilatancy, whereupon AE generation gradually reduced and then remained around a constant mean value with further increments of shear strain. Average AE rates measured during post-peak shear strength behaviour are plotted against the applied axial displacement rate in Fig. 10, which results in a linear relationship with strong correlation (R2 of 0.99) over the range of data examined. Note that Smith and Dixon [39] observed a non-linear AE rate versus displacement rate relationship for granular media (i.e. a power curve intersecting the origin); therefore, the power curve plotted in Fig. 10 (R2 of 0.99) more accurately extrapolates the AE response at slower displacement rates.
Fig. 9

Measurements versus shear strain (%) from drained triaxial shearing tests performed on GB 4506 (d50 = 1.61 mm) at an effective confining pressure of 300 kPa and axial displacement rates of 1, 3 and 6 mm/h (Tests 9–11). a Stress ratio (q/p′), b volumetric strain (%) (dilation shown as positive), and c AE rate (RDC/min)

Fig. 10

AE rate (RDC/min) versus displacement rate (mm/h) relationship (linear and power regressions) obtained from drained triaxial shearing tests at an effective confining pressure of 300 kPa and axial displacement rates of 1, 3 and 6 mm/h for GB 4506 (d50 = 1.61 mm) (Tests 9–11). The AE rate (RDC/min) values shown are averages calculated after mobilisation of peak shear strength (i.e. post-peak)

Figure 11 shows calculated work done (boundary, distortional and volumetric) versus shear strain during all tests performed on GB 4506 (d50 = 1.61 mm) (Tests 7–11) (i.e. under different imposed effective confining stresses and axial displacement rates), which shows that work done was governed by stress level but independent of axial displacement rate, as would be expected for the range of strain rates applied (i.e. negligible strain rate effects were observed). The average AE rate versus boundary work rate relationships for Tests 1–14 are compared in Fig. 12 during peak (i.e. volume minimum to peak dilatancy) and post-peak conditions. Linear regressions with R2 values of 0.95 and 0.90 were obtained during peak and post-peak conditions, respectively. The gradient of the relationship (i.e. AE generated per Joule) representing peak conditions in shear is 1.8 times greater than the relationship representing post-peak conditions. Moreover, when Fig. 12 is compared with Fig. 5, it can be concluded that glass beads generate between 18 (peak) and 10 (post-peak) times greater AE per Joule of work in shear than they do in isotropic compression.
Fig. 11

Measurements from drained triaxial shearing tests performed on GB 4506 (d50 = 1.61 mm) (Tests 7–11). a boundary work (J) versus shear strain (%), b distortional work (J) versus shear strain (%), and c volumetric work (J) versus shear strain

Fig. 12

Average AE rate (RDC/min) measurements versus average boundary work rate (J/min) measurements (Tests 1–14) at: a peak, and b post-peak

Figure 13 shows measurements of stress ratio, volumetric strain and AE rates up to 5% of axial strain during Test 3 (GB 45015, d50 = 0.52 mm, 300 kPa, 1 mm/h), which exemplify the observed AE rate behaviour during stick–slip events. In each stick–slip event, AE activity increased during shear strength mobilisation (i.e. during the periods in Fig. 13b when the stress ratio, q/p′, was increasing), particle climbing and dilation (i.e. the particles override at points of contact causing the volume to increase, which occurs in densely packed assemblages of particles in shearing), and then reduced with the subsequent deviator stress drop during particle sliding and contraction. Figure 14 shows the magnitude of AE rate change plotted against the amplitude of deviator stress cycles for all stick–slip events measured during Tests 1 to 3 (GB 45015, d50 = 0.52 mm), which results in a linear regression with R2 of 0.77.
Fig. 13

Measurements versus axial strain (%) from a drained triaxial shearing test performed on GB 45015 (d50 = 0.52 mm) at an effective confining pressure of 300 kPa and axial displacement rate of 1 mm/h (Test 3). a stress ratio (q/p′) from 0 to 1.2% axial strain, b stress ratio (q/p′) from 1.2 to 5.0% axial strain, c volumetric strain (%) (dilation shown as positive) from 0 to 1.2% axial strain, d volumetric strain (%) (dilation shown as positive) from 1.2 to 5.0% axial strain, e AE rate (RDC/min) from 0 to 1.2% axial strain, and f AE rate (RDC/min) from 1.2 to 5.0% axial strain. The black line in e and f shows moving averages of AE rates. The vertical grey boxes in b, d and f highlight the timing of deviator stress drops

Fig. 14

a Illustration of changes in deviator stress and AE rates during stick–slip events. b ΔAE rate (RDC/min) versus Δq (kPa) relationship for all stick–slip events measured from GB 45015 (d50 = 0.52 mm) (Tests 1–3)

Figure 15a focuses on a stick–slip event that took place between 1.8 and 2.1% of axial strain in Test 3 (GB 45015, d50 = 0.52 mm, 300 kPa) (i.e. the same test as that presented in Fig. 13), which exemplifies the observed b-value behaviour during stick–slip events. During the stress release phase (i.e. deviator stress drop), b-values increased due to the AE waveform being dominated by low amplitude events. As shear strength was mobilised (i.e. when the stress ratio, q/p’, was increasing), b-values reduced as the measured AE waveform became increasingly dominated by higher amplitude events.
Fig. 15

Measurements from a drained triaxial shearing test performed on GB 45015 (d50 = 0.52 mm) at an effective confining pressure of 300 kPa and axial displacement rate of 1 mm/h (Test 3): a stress ratio and b-value versus axial strain, and b AE amplitude-frequency spectra at axial strains of 1.88% and 2.02% (the insert focuses on the AE amplitude-frequency spectra between 10.0 and 11.5 kHz)

Figure 15b illustrates how the AE amplitude-frequency spectra changed during stick–slip events: the grey line shows the AE amplitude-frequency spectra at 1.88% axial strain (i.e. when the stress ratio was minimum in Fig. 15a), and the black line shows the AE amplitude-frequency spectra at 2.02% axial strain (i.e. during shear strength mobilisation). Above frequencies greater than approximately 11.5 kHz, significantly greater AE energy was generated during the shear strength mobilisation phase than in the stress release phase of the stick–slip event. Below frequencies of approximately 11.5 kHz, greater AE energy was generated during stress release (insert in Fig. 15b). The AE measurement system filtered frequencies below 10 kHz; however, previous studies have demonstrated high levels of AE at frequencies below 10 kHz during the stress release phase of stick–slip events (e.g. [7, 19, 21]). Note that the resonant frequency of the transducer was 30 kHz, which was the cause of the peak in AE response around this frequency.

Figure 16 compares the AE rate measurements obtained from Tests 1–14. AE rate measurements during peak conditions were greater than those during post-peak conditions in each test, evidenced by the negative AE rate difference between peak and post-peak conditions in Fig. 16a. The general trends of AE activity increasing with confining stress level, particle size and axial displacement rate are also evident in Fig. 16a. Figure 16b shows that the variability in AE rate measurements (i.e. CoV) due to stick–slip behaviour increased with confining stress level but reduced with particle size (i.e. the amplitude of AE activity cycles during stick–slip were inversely proportional to particle size). The most significant differences in CoV trends are between GB 45015 (d50 = 0.52 mm) and the other three particle sizes: GB 45015 (d50 = 0.52 mm) failed along a concentrated shear zone while GB 4503 (d50 = 0.81 mm), GB 4506 (d50 = 1.61 mm) and GB 4510 (d50 = 2.67 mm) all failed by bulging.
Fig. 16

Summary of measurements obtained from drained triaxial shearing tests performed on glass beads (Tests 1–14). a average AE rate (RDC/min) measured at peak and post-peak, and the AE rate difference between peak and post-peak; b coefficient of variation (CoV) of AE rate (RDC/min) measurements during post-peak behaviour

4 Discussion

A programme of drained triaxial tests have been performed on densely packed glass beads to establish quantified relationships for use in the interpretation of mechanical behaviour from AE measurements. The mechanical behaviour of the glass beads was consistent with findings reported in the literature: the obtained critical state friction angles of 23° and dilatancy components (\( \phi^{\prime}_{\rm{p}} \)  −  \( \phi^{\prime}_{\rm{cv}} \), Table 2) of 8° are typical for densely packed glass beads (e.g. [31]).

The original contributions from this study include: (i) the combination of AE rate and b-values has been measured from densely packed assemblages of glass beads for the first time in triaxial isotropic compression and shearing; (ii) the results show that AE generation in densely packed glass beads is proportional to the imposed stress level and displacement rate (e.g. an AE rate versus imposed displacement rate relationship has been quantified with an R2 value of 0.99); (iii) previous research has demonstrated that natural soils experience the Kaiser Effect (e.g. [1, 4]) and this study has extended knowledge to demonstrate its existence in densely packed glass beads (i.e. AE activity is negligible until the current stress conditions exceed the maximum that has been experienced in the past); (iv) relationships have been quantified between AE and boundary work (i.e. AE generated per Joule) for a unit volume of glass beads under isotropic compression and shear (R2 values ranging from 0.90 to 0.96), which show that glass beads generate greater RDC/J in shear than they do in isotropic compression (e.g. approximately 4900 RDC/J in isotropic compression, 49,000–89,000 RDC/J in shear) and the glass beads generated greater RDC/J in shear during peak conditions (approximately 89,000) than during post-peak conditions (approximately 49,000) because the specimens dilated and had a higher void ratio during post-peak conditions; and (v) the relationship between the amplitudes of cycles in deviator stress and AE activity during stick–slip events has been quantified (e.g. 1.24 RDC/min per kPa).

These findings mean that the AE interpretation framework proposed by Smith and Dixon [4] for natural sands can be extended to include densely packed glass beads and used to identify the transition from contractive to dilative behaviour (i.e. q/p′ = M), mobilisation of peak shear strength and quantify accelerating deformation behaviour that typically accompanies shear zone development. The influence of fabric (e.g. density and grading) was excluded as a variable from this investigation by focusing on four poorly-graded, single-sized glass beads; however, Smith and Dixon [4] demonstrated that AE generation increases with fabric coordination number (i.e. the number of particle contacts per particle). In addition, all four glass beads had comparable shape and roughness properties, and hence these were also excluded as variables from the investigation. However, it should be noted that the glass beads were not perfectly smooth spheres (e.g. Fig. 3) and their particle shape and surface features would have influenced inter-particle friction and hence AE generation.

The study results show that stick–slip behaviour significantly influenced the AE generated by densely packed glass beads in shear: in each stick–slip event, AE activity increased (i.e. AE rates increased, and b-values reduced) during shear strength mobilisation, particle climbing and dilation, and then reduced with the subsequent deviator stress drop during particle sliding and contraction. The results also show that above frequencies greater than approximately 11.5 kHz, significantly greater AE energy was generated during the shear strength mobilisation phase than in the stress release phase of stick–slip events, whereas below frequencies of approximately 11.5 kHz, greater AE energy was generated during stress release, which agrees with previous findings.

For example, Michlmayr et al. [12] and Michlmayr and Or [19] performed direct-shear experiments on glass beads using two AE measurement systems, one constrained to within 0–20 kHz (i.e. low-frequency) and one constrained to within 30–80 kHz (i.e. high-frequency). They found that AE activity was more significant in the low-frequency system during the stress release phase of stick–slip events, and in the high-frequency system during shear strength mobilisation and dilation. Johnson et al. [20] subjected layers of glass beads to granular shearing and monitored AE within 34–45 kHz; they observed significant AE activity during shear strength mobilisation and dilation. These relatively high-frequency monitoring systems (i.e. 30–80 kHz and 34–45 kHz) fall within the frequency range used in this study of 10–100 kHz, which strengthens the evidence to conclude that AE generated during the stress release phase of stick–slip events is predominantly low frequency (< 20 kHz), and AE generated during shear strength mobilisation and dilation is predominantly high frequency (> 20 kHz). Uniquely, the influence of stick–slip behaviour in densely packed glass beads on AE generation has been quantified in this study through a series of relationships (e.g. Figs. 13, 14, 15 and 16).

The implications of the findings have primarily been discussed within the context of soil mechanics with applications for geotechnical engineering and the potential to detect changes in behaviour for use in early warning of serviceability and ultimate limit state failures. However, the newly developed quantified interpretation of AE generated by glass beads has implications for a wide range of disciplines, for example: faulting and earthquakes, granular physics, additive manufacturing, mining and pharmaceuticals.

This study has quantified links between particulate materials’ physical properties, imposed conditions (i.e. stress and strain) and generated AE. The authors acknowledge, however, that in many applications, such as with natural soils, the physical properties will be highly variable and largely unknown, which would make quantitative interpretation more difficult. Smith et al. [6] demonstrated that a generic AE rate versus displacement rate relationship can be obtained for a range of granular materials (e.g. sands and gravels with a range of angularities and particle size distributions), which means, for example, that AE monitoring could be used to quantify accelerating deformation behaviour in particulate systems with only a limited knowledge of their physical properties.

5 Conclusions

This study has gone beyond the state-of-the-art and established quantitative interpretation of AE generated by densely packed glass beads in isotropic compression and shear. This new knowledge will enable the evolution of particulate material behaviour to be interpreted from AE measurements, potentially removing or reducing the need for arduous measurements of stresses and strains, and hence benefitting a wide range of applications and industries. Results from a programme of drained triaxial tests on densely packed glass beads show that:
  • AE generation in densely packed glass beads is influenced by the imposed stress level, imposed displacement rate, mean particle size, the boundary work done and volumetric strain (i.e. dilation increases the void ratio and reduces the number of particle contacts per particle, and hence reduces AE activity);

  • AE activity in glass beads is negligible until the current stress conditions exceed the maximum that has been experienced in the past due to the Kaiser Effect;

  • Relationships between AE and boundary work (i.e. RDC generated per Joule) have been quantified for a unit volume of glass beads under isotropic compression and shear, which show that significantly greater RDC/J is generated in shear than in isotropic compression;

  • An AE rate versus displacement rate relationship has been quantified, which enables interpretation of accelerating deformation behaviour that typically accompanies shear zone development following mobilisation of peak shear strength in dense particulate materials;

  • Stick–slip behaviour significantly influenced AE generation in shear: in each stick–slip event, AE activity increased during shear strength mobilisation, particle climbing and dilation, and then reduced with the subsequent deviator stress drop during particle sliding and contraction. The amplitude of these cycles in AE activity were proportional to the amplitude of deviator stress cycles during stick–slip events, which were also proportional to the imposed stress level and inversely proportional to particle size.

Notes

Acknowledgements

The authors acknowledge the excellent technical assistance provided by Mr Lewis Darwin and the Loughborough Materials Characterisation Centre. Alister Smith gratefully acknowledges the support of an EPSRC Fellowship (Listening to Infrastructure, EP/P012493/1). Data reported in this study can be made available by the authors on request.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Koerner, R.M., McCabe, W.M., Lord, A.E.: Acoustic Emission Behavior and Monitoring of Soils. In: Drnevich, V.P., Gray, R.E. (eds.) Acoustic emissions in geotechnical engineering practice ASTM STP 750, pp. 93–141. ASTM International, West Conshohocken (1981)CrossRefGoogle Scholar
  2. 2.
    Tanimoto, K., Tanaka, Y.: Yielding of soil as determined by acoustic emission. Soils Found. 26(3), 69–80 (1986)CrossRefGoogle Scholar
  3. 3.
    Naderi-Boldaji, M., Bahrami, M., Keller, T., Or, D.: Characteristics of acoustic emissions from soil subjected to confined uniaxial compression. Vadose Zone J., 16(7), 1–12 (2017)CrossRefGoogle Scholar
  4. 4.
    Smith, A., Dixon, N.: Acoustic emission behaviour of dense sands. Géotechnique  https://doi.org/10.1680/jgeot.18.P.209 (2019)
  5. 5.
    Smith, A., Dixon, N., Meldrum, P., Haslam, E., Chambers, J.: Acoustic emission monitoring of a soil slope: Comparisons with continuous deformation measurements. Géotech Lett 4(4), 255–261 (2014)CrossRefGoogle Scholar
  6. 6.
    Smith, A., Dixon, N., Fowmes, G.: Early detection of first-time slope failures using acoustic emission measurements: large-scale physical modelling. Géotechnique 67(2), 138–152 (2017)CrossRefGoogle Scholar
  7. 7.
    Michlmayr, G., Chalari, A., Clarke, A., Or, D.: Fiber-optic high-resolution acoustic emission (AE) monitoring of slope failure. Landslides 14(3), 1139–1146 (2017)CrossRefGoogle Scholar
  8. 8.
    Dixon, N., Smith, A., Flint, J. A., Khanna, R., Clark, B., Andjelkovic, M.: An acoustic emission landslide early warning system for communities in low-income and middle-income countries. Landslides  https://doi.org/10.1007/s10346-018-0977-1 (2018)CrossRefGoogle Scholar
  9. 9.
    Adjemian, F., Evesque, P.: Experimental study of stick-slip behaviour. Int. J. Numer. Anal Methods Geomech. 28(6), 501–530 (2004)CrossRefGoogle Scholar
  10. 10.
    Johnson, P.A., Savage, H., Knuth, M., Gomberg, J., Marone, C.: Effects of acoustic waves on stick–slip in granular media and implications for earthquakes. Nature 451(7174), 57 (2008)CrossRefADSGoogle Scholar
  11. 11.
    Bonneau, L., Catelin-Jullien, T., Andreotti, B.: Friction-induced amplification of acoustic waves in a low Mach number granular flow. Phys. Rev. E 82(1), 011309 (2010)CrossRefADSGoogle Scholar
  12. 12.
    Michlmayr, G., Cohen, D., Or, D.: Shear-induced force fluctuations and acoustic emissions in granular material. J. Geophys. Res. Solid Earth 118(12), 6086–6098 (2013)CrossRefADSGoogle Scholar
  13. 13.
    McNamara, S.C.: Acoustics and frictional sliding in granular materials. Granul. Matter 17(3), 311–324 (2015)CrossRefGoogle Scholar
  14. 14.
    Everton, S.K., Hirsch, M., Stravroulakis, P., Leach, R.K., Clare, A.T.: Review of in situ process monitoring and in situ metrology for metal additive manufacturing. Mater. Des. 95, 431–445 (2016)CrossRefGoogle Scholar
  15. 15.
    Li, J., Huang, Y., Chen, Z., Li, M., Qiao, M., Kizil, M.: Particle-crushing characteristics and acoustic-emission patterns of crushing gangue backfilling material under cyclic loading. Minerals 8(6), 244 (2018)CrossRefGoogle Scholar
  16. 16.
    Serris, E., Périer-Camby, L., Thomas, G., Desfontaines, M., Fantozzi, G.: Acoustic emission of pharmaceutical powders during compaction. Powder Technol. 128(2–3), 296–299 (2002)CrossRefGoogle Scholar
  17. 17.
    Papp, M.K., Pujara, C.P., Pinal, R.: Monitoring of high-shear granulation using acoustic emission: predicting granule properties. J. Pharm. Innov. 3(2), 113–122 (2008)CrossRefGoogle Scholar
  18. 18.
    Sadrekarimi, A., Olson, S.M.: Critical state friction angle of sands. Géotechnique 61(9), 771 (2011)CrossRefGoogle Scholar
  19. 19.
    Michlmayr, G., Or, D.: Mechanisms for acoustic emissions generation during granular shearing. Granul. Matter 16(5), 627–640 (2014)CrossRefGoogle Scholar
  20. 20.
    Johnson, P.A., Ferdowsi, B., Kaproth, B.M., Scuderi, M., Griffa, M., Carmeliet, J., Guyer, R.A., Le Bas, P.Y., Trugman, D.T., Marone, C.: Acoustic emission and microslip precursors to stick-slip failure in sheared granular material. Geophys. Res. Lett. 40(21), 5627–5631 (2013)CrossRefADSGoogle Scholar
  21. 21.
    Cui, D., Wu, W., Xiang, W., Doanh, T., Chen, Q., Wang, S., Liu, Q., Wang, J.: Stick-slip behaviours of dry glass beads in triaxial compression. Granul. Matter 19(1), 1 (2017)CrossRefADSGoogle Scholar
  22. 22.
    Bishop, A.W., Wesley, L.D.: A hydraulic triaxial apparatus for controlled stress path testing. Géotechnique 25(4), 657–670 (1975)CrossRefGoogle Scholar
  23. 23.
    BS EN ISO 17892: Geotechnical investigation and testing – laboratory testing of soil. London, UK: BSI (2016)Google Scholar
  24. 24.
    Zheng, J., Hryciw, R.D.: Traditional soil particle sphericity, roundness and surface roughness by computational geometry. Géotechnique 65(6), 494–506 (2015)CrossRefGoogle Scholar
  25. 25.
    Krumbein, W.C., Sloss, L.L.: Stratigraphy and Sedimentation, 2nd edn. Freeman and Company, San Francisco, CA, USA (1963)Google Scholar
  26. 26.
    Cho, G.C., Dodds, J., Santamarina, J.C.: Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. J. Geotech. Geoenviron. Eng. 132(5), 591–602 (2006)CrossRefGoogle Scholar
  27. 27.
    Cavarretta, I., Coop, M., O’Sullivan, C.: The influence of particle characteristics on the behaviour of coarse grained soils. Géotechnique 60(6), 413–423 (2010)CrossRefGoogle Scholar
  28. 28.
    Head, K. H.: Manual of Laboratory Testing. Volume 3: Effective Stress Tests, ELE International Ltd (1986)Google Scholar
  29. 29.
    Been, K., Jefferies, M.G., Hachey, J.: Critical state of sands. Géotechnique 41(3), 365–381 (1991)CrossRefGoogle Scholar
  30. 30.
    Skempton, A.W.: The pore-pressure coefficients A and B. Geotechnique 4(4), 143–147 (1954)CrossRefGoogle Scholar
  31. 31.
    Wu, K., Abriak, N., Becquart, F., Pizette, P., Remond, S., Liu, S.: Shear mechanical behavior of model materials samples by experimental triaxial tests: case study of 4 mm diameter glass beads. Granul. Matter. 19(4), 65 (2017)CrossRefGoogle Scholar
  32. 32.
    Muir Wood, D.: Soil behaviour and critical state soil mechanics. Cambridge University Press, Cambridge, UK (1990)zbMATHGoogle Scholar
  33. 33.
    Bolton, M.D.: A Guide to Soil Mechanics. Universities Press, Oxford (2003)Google Scholar
  34. 34.
    Powrie, W.: Soil Mechanics: Concepts and Applications. CRC Press, Boca Raton (2013)CrossRefGoogle Scholar
  35. 35.
    Hanley, K.J., Huang, X., O’Sullivan, C.: Energy dissipation in soil samples during drained triaxial shearing. Géotechnique 68(5), 421–433 (2017)CrossRefGoogle Scholar
  36. 36.
    Mao, W., Towhata, I.: Monitoring of single-particle fragmentation process under static loading using acoustic emission. Appl. Acoust. 94, 39–45 (2015)CrossRefGoogle Scholar
  37. 37.
    Pollock, A.A.: Acoustic emission-2: acoustic emission amplitudes. Non-destr. Test. 6(5), 264–269 (1973)CrossRefGoogle Scholar
  38. 38.
    Lavrov, A.: The Kaiser effect in rocks: principles and stress estimation techniques. Int. J. Rock Mech. Min. Sci. 40(2), 151–171 (2003)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Smith, A., Dixon, N.: Quantification of landslide velocity from active waveguide-generated acoustic emission. Can. Geotech. J. 52(4), 413–425 (2015)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.School of Architecture, Building and Civil EngineeringLoughborough UniversityLoughboroughUK

Personalised recommendations