2.1 Test apparatus

In this study, MTS 322 digital control test systems with special test fixtures were used to conduct VASTs. During testing, an AE system was applied to record and save AE signals which were used to illustrate the crack propagation evolution process, and the sampling threshold, sampling rate and sampling length of AE system were set as 40 dB, 3×10⁶ samples/s and 4000, respectively. Magnet AE sensor fixtures were used for fixing the AE sensors on the surface of the rock specimens. A DIC measurement system consisting of a charge-coupled device (CCD) camera, an illumination light source, an image acquisition card, and a control computer was also used to perform a real-time analysis of the rock failure process.

2.2 Specimen preparation

In this paper, we choose the most selected sandstone as the test material. The cubic rock specimens with a side length of 50 mm and two slits with a depth of 2 mm along the horizontal midlines utilized in the testing were from the same rock block, and had good integrity and homogeneity (Figure 1). The non-parallelism and non-perpendicularity of specimens were less than 0.02 mm on both sides. Before the installation of AE sensors, the AE sensors needed to be tested for broken lead, and to make the AE sensor closely stick to the surface of the rock specimen and exhaust the air, a film of coupling agent should be placed on the contact surface of the sensor. The ring iron washer and the custom AE sensor fixture were used to secure the AE sensor to the rock specimen’s surface during installation. One surface of the rock specimen was spray-painted for DIC analysis.

Figure 1全屏查看

Rock specimens used in VASTs

2.3 Experimental scheme

Before loading, the petroleum jelly was applied on the surfaces of the rock specimen in contact with the loading blocks for anti-friction treatment to reduce the influence of friction on the experimental results. The displacement-control loading mode was chosen, and the loading rate in VASTs was set as 0.15 mm/min. VASTs were conducted with five different test angles of 30°, 45°, 50°, 60° and 70° in this study [33]. Tests were repeated under the same test conditions to minimize accidental errors. In addition, the Brazilian splitting test and conventional triaxial compression test were also carried out to analyze the difference in mechanical properties of red sandstone under different stress states.

3.1 Shear strength parameters

The experimental results are listed in Table 1. The equivalent shear failure stress τ_e and equivalent normal failure stress σ_e were used to draw the shear strength envelope of the red sandstone (only the data under the test angle above 45° were used), and the shear strength envelope was approximately a straight line. Based on the Mohr-Coulomb criterion, the cokesion (c) and internal friction angle (φ) of the red sandstone were calculated to be 15.163 MPa and 37.585°, respectively (Figure 2(a)). The data under different test angles in Figure 2 were the average value of the two specimens.

Figure 2全屏查看

Testing results: (a) Shear strength curve; (b) Relationship between test angle α and σ_e, P_s and τ_e

Figure 2(b) shows that with the increase of the test angle, both σ_e and P_s gradually decreased, and the decreasing trend of σ_e was shaped as a straight line, and the decreasing trend of P_s was a parabola curve. The changing trend of τ_e with the increase of the test angle was quite different, i.e., increased first and then decreased, and the test angle of 50° was the dividing point. The τ_e increased approximately linearly or decreased approximately linearly. In this study, the smaller the test angle was, the lower the shear stress applied to the specimen was. The low-level shear stress played a similar role as confining pressure, so the P_s of 30-1 was smaller than that of 45-1.

3.2 AE characteristics

From the difference in AE characteristics of different specimens, it can be concluded that the change of test angle in VASTs can cause the transformation of the rock failure mode. The development of microcracks and the overall damage of sandstone under compression-shear conditions can also be monitored by AE system. In this study, the AE hit characteristics, AF-RA characteristics (AF is the ratio of AE rise time to amplitude, and RA is the AE average frequency), amplitude-frequency characteristics, and peak frequency characteristics of different specimens were analyzed.

3.2.1 AE hits

The change curve of AE hits with the test time and the total AE hits in the VASTs under different test angles are shown in Figures 3 and 4, respectively. The number of AE hits produced in the early and mid-term stages can be affected by the test angle. When the test angle is equal to or lower than 50°, in the early and mid-term stages, the number of AE hits is higher, and when the test angle is greater than 50°, the number of AE hits produced in the early and mid-term stages is less. This rule can also be found in the total number of AE hits. VASTs with a test angle below 50° produce more total AE hits exceeding 50000, while those with test angles greater than 50° produce less total AE hits around 20000.

Figure 3全屏查看

AE hits with time in VASTs with different test angles: (a) 30°; (b) 45°; (c) 50°; (d) 60°; (e) 70°

Figure 4全屏查看

Total AE hits in VASTs with different test angles

3.2.2 AF-RA distribution of AE signals

The AF-RA characteristics in VASTs with different test angles are shown in Figure 5. The core data (red data) in the AF-RA density map were mainly distributed below AF=100 kHz in VASTs with test angle 50°. The core data in VASTs with test angle >50° were mainly distributed around AF=100 kHz, and with the increase of test angle, the core data tend to be distributed with AF=100 kHz as the center line. The shear micro-cracks dominated the specimen failure in VASTs with a test angle lower than 50°, while partial tensile micro-cracks were produced as the test angle increased from 50° to 70°, and when the test angle was 60°, the proportion of tensile micro-cracks was largest.

Figure 5全屏查看

AF-RA characteristics in VASTs with different test angles: (a) 30°; (b) 45°; (c) 50°; (d) 60°; (e) 70°

3.2.3 Peak frequency distribution of AE signals

The distribution laws of the peak frequency in the VASTs with different test angles are shown in Figure 6. The AE signals with peak frequency of 0-100 kHz had the largest proportion in the VASTs with different test angles. It can be inferred that the specimens in VASTs experienced shear failure, which was dominated by shear micro-cracks. When the test angle increased from 50° to 70°, the percentage of AE signals with the peak frequency of 201-300 kHz increased, which indicated that the number of tensile micro-cracks increased. When the test angle was 60°, the proportion of AE signals with the peak frequency of 201-300 kHz was the largest.

Figure 6全屏查看

Distributions of peak frequency in VASTs: (a) 30°; (b) 45°; (c) 50°; (d) 60°; (e) 70°

3.2.4 Relationships between amplitude and frequency of AE signals

The amplitude-frequency relationships in VASTs with different test angles are shown in Figure 7 (N represents the number of AE counts; A represents the amplitude). The loading rate of all VASTs in this paper is 0.15 mm/min. At this loading rate, the chances of collision and extrusion between rock and pressure block are relatively high, and the resulting AE signal is likely to be monitored and collected by the AE system, so the AE characteristics need to be further analyzed. Given this, the correlation analysis between amplitude and frequency has been proved by many scholars to be effective for the monitoring of fatigue cracking and extension within various materials, and therefore this was used to check the abnormal AE signals.

Figure 7全屏查看

Amplitude-frequency relationships in VASTs with varying α: (a) 30°; (b) 45°; (c) 50°; (d) 60°; (e) 70°

From Figure 7, at all test angles of VASTs, the amplitude and frequency have a good correspondence in the logarithmic coordinate system with fitting coefficients higher than 0.72. Among them, when the test angle is 45°, the best correspondence is achieved, and the fitting coefficient reaches 0.85, which indicates that the AE signal collected in this test has the least noise signal. The AE signals monitored by the VASTs with the test angle of 30°, 50° and 60° have similar correspondence between the amplitude and frequency, which are all between 0.73 and 0.75. Therefore, by analyzing the correspondence between amplitude and frequency, we can assume that the AE signals monitored in the VASTs are all generated by the rupture activities occurring within the rock samples.

3.3 Failure properties based on DIC technology

In this study, the DIC measurement system was used to conduct a real-time analysis of the failure evolution process in VASTs. The pictures of the rock specimens’ final failure fragments were used as a reference for DIC analysis. Figure 8 presents the failure photos and DIC analysis results in VASTs with different test angles. The actual failure photos of the rock specimens and the DIC analysis results showed a high consistency in crack distribution.

Figure 8全屏查看

Analysis of failure modes in VASTs with different test angles

The crack network on the surface of the rock specimen is more complicated in VASTs with α < 45°, and the crack propagation direction deviates greatly from the ideal shear line connecting the slits, which was similar to the compressive failure. When the test angle reached 50°, the main crack is approximately a straight-through crack along the ideal shear line connecting the slits. The larger the test angle is, the simpler the crack network becomes, which is an ideal shear-failure mode. By comparing the fragment photos after rock failure, as the test angle increased, the number of fragments reduced, and the fragment size also decreased. When the test angle reaches 70°, the rock specimen is almost completely divided into two halves along the ideal shear line connecting to the slits, which is a pure shear-failure mode. To analyze the failure evolution process of red sandstone in VASTs, the DIC results of VASTs with test angles of 45° and 70° (with a relatively complex and simple crack network, respectively) were selected and shown in Figure 9.

Figure 9全屏查看

The failure evolution process of VASTs with α=45° and α=70°

For VASTs with the test angle of 45°, when the stress is loaded to 20% uniaxial compressive strength (σ_ucs,) the strain concentration field of the red sandstone specimen is mainly distributed near the two cut slits with a depth of 2 mm, and the area of strain concentration area is relatively large, with a centrosymmetric distribution, which indicates that under the action of the load, the rock specimen produces stress concentration at the cut slit. And when the stress is loaded from 20% to 60% σ_ucs, the strain-concentrated field converged to the centerline of the specimen. When the stress increased from 60% σ_ucs to the peak load, the strain-concentrated field distributed along the centerline “thinned” into a strip, which divided the specimen into two parts of the same size, and at this time the strip is the true reflection of the generated main crack.

4.1 AE characteristics of sandstone under different stress states

In VASTs, the sandstone is subjected to a compression-shear stress state, and the changes of AE parameters indicate that the sandstone experiences shear failure, and the proportion of tensile micro-cracks increases with the increase of test angle. In order to comprehensively understand the AE characteristics of sandstone under different stress states, Brazilian indirect tension tests (BITTs) using the same sandstone were carried out. The analysis results of AE hits, AF-RA, AE peak frequency and AE amplitude-frequency relationship in BITTs are shown in Figure 10. The BITT core data in the AF-RA data density map are mostly concentrated near the vertical axis, and the overall AF level is distributed around 200 kHz. The AE signals produced by the BITT have a peak frequency that is generally above 200 kHz, of which the AE signals distributed in 201-300 kHz are the most. Overall, these results indicate that the red sandstone in BITT mainly produced tensile micro cracks.

Figure 10全屏查看

AE characteristics of BITTs: (a) AE hit; (b) AF-RA; (c) AE peak frequency distribution; (d) AE amplitude-frequency relationship

The AE impact number of sandstone under tensile stress state is much smaller than that under compression-shear stress state, and the AF-RA scatter data are obviously distributed along AF axis. The peak frequency of AE signal in rock under tensile state is much higher than that under compression-shear state.

4.2 c and φ in different tests

In the study of rock mechanics, the internal friction angle of the rock reflects the strength under the condition of anisotropic unequal stress, while cohesion reflects the ability of the rock to withstand anisotropic unequal stress. The determination of these two parameters is of great significance for the study of underground engineering stability. In general, conducting a series of VASTs at different test angles and triaxial compression tests (CTTs) at different confining pressures are two common methods for determining the angle of internal friction and cohesion of rocks. We analyze the results of internal friction angle and cohesion determined by these two methods to provide a reference for the design and construction of underground works.

In the VASTs, the cohesive force c and the internal friction angle φ of the rock can be determined from the scatter diagram of the equivalent shear stress τ_e and equivalent normal stress σ_e. The cohesion force c refers to the intercept of the τ_e-σ_e line on the τ_e axis and the φ is the angle between the τ_e-σ_e line and the σ_e axis. The conventional (CTT) can also be applied to measure the c and φ based on the results of the major principal stress σ₁ and the minor principal stress.

Table 2 shows the c and φ results of red sandstone based on different tests. The c and φ measured in VAST and CTT have a certain difference. The c and φ determined by VAST were 40.74% and 17.01% lower than those determined by CTT, respectively. When the confining pressure is less than or equal to 8 MPa, the cohesion measured in CTTs is close to that measured in VASTs (less than 25.70%), while when the enclosure pressure is larger than 8 MPa, it is the internal friction angle determined by CTTs that is close to the internal friction angle determined by VASTs (less than 1.04%). CTT and VAST are two common laboratory experiment methods to obtain rock shear strength parameters. The values of the above two parameters calculated by the former under different confining pressures are different, and the values of the above two parameters calculated by the latter without shear angle are also different, which is related to the experimental design scheme. Based on the failure mode of sandstone in Section 3.3, it can be seen that at 50°-70°, the failure of the sample presents obvious shear failure along a straight line. Therefore, we have a reason to believe that the shear strength parameter calculated in this angle range is reasonable. As a reference, it can be seen that the cohesion of sandstone calculated when the confining pressure is less than 8 MPa is more reasonable, and the internal friction angle calculated when the confining pressure is greater than 8 MPa is more reasonable.

Table 2全屏查看

Cohesive force and internal friction angle results of red sandstone in VAST and CTT

Parameter	VAST		CTT
	All angles	50°-70°	All confining stresses	σ38 MPa	σ3>8MPa
c/MPa	15.163	20.762	25.586	20.409	36.114
φ/(°)	37.585	39.513	45.288	51.499	37.981

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