Introduction

Rock mass can undergo deformation, yielding, and even failure under the action of external forces1. Studying these mechanical properties is of great significance for the theoretical calculation and design of rock mechanics engineering2,3,4,5,6. Many scholars have studied on the mechanical properties, such as strength properties and deformation properties, under external factors such as load, water flow, and temperature. The research methods used mainly include indoor tests, in-situ field tests, scientific tests, theoretical analysis and engineering verification. The indoor tests are mainly based on uniaxial compression tests7,8,9,10,11,12,13,14, conventional triaxial compression tests15,16,17 and splitting tests18,19,20.

Accurate analysis of strength characteristics and deformation properties can provide a theoretical basis and guidance for the design and construction of rock mechanics and engineering. The full stress-strain curve and the identification of microcracks and crack directions help to better analyze the strength characteristics and deformation properties21,22. Many researchers have carried out related studies. Pasiou & Triantis23 verified that the AE technique and the pressure stimulated currents (PSC) can well detect the formation of cracking and damage process in brittle materials. Both techniques can provide information regarding the initial stages of microcrack generation, propagation and coalescence, with the aim of using these as fracture precursors24. He et al.22 carried out uniaxial compression tests of four types of rocks under axial strain control mode and lateral strain control mode respectively and analyzed the characteristics of complete stress and strain curves, strength, brittleness and failure modes. Xie et al.21 summarized the status and development in theories, test apparatuses, data processing and method selection of the existing testing methods for evaluation of the uniaxial compressive strength (UCS) of rocks and recommended the method selection for UCS measurement.

Over the years, the study of mechanical properties with respect to the effect of confining pressure has never ceased through different techniques, such as AE techniques and numerical simulation techniques, and some valuable research results have been obtained. Ismail et al.25 carried out laboratory experiments to study the effect of confining pressure on stress-drop after compressive fracturing in a wide range of sedimentary, metamorphic and igneous silicate rocks. Asef et al.26 investigated the impact of confining stress on the rock mass deformation modulus and found that the rock types tested display significant increase in stiffness under confinement. Hokka et al.27 discussed the effects of confining pressure and strain rate on rock strength and found that the strength increases with confining pressure. Taheri et al.28 conducted a series of uniaxial and triaxial tests on different rocks and studied the effects of strength and confining pressure on crack stress thresholds. For the rocks having different strength values and subjected to different confining pressures, on average, ratio of crack damage to peak strength is found to be 0.80. Yang et al.29 carried out triaxial compression tests accompanied by AE monitoring on carbonaceous shale rock specimens with different confining pressures and water-bearing conditions to explore the mechanical properties and damage evolution characteristics. The results suggest that the mechanical properties intensify with increasing confining pressure and observed that AE activities mainly occur in the post-peak stage and the maximum AE counts and AE energy decrease with confining pressure. Huang et al.6 also conducted uniaxial and triaxial compression AE tests to investigate the AE effect and failure characteristics of sandstone under different confining pressures. Ma et al.30 analyzed the combined coal–rock’s dynamic mechanical properties by using the SHPB system and found that compressive strength and elastic modulus of the combined body increase gradually with increasing confining pressure and the elastic modulus seems to be stable as confining pressure increases at low strain rate. Yuan et al.31 adopted numerical simulation method to focus on the effect of confining pressure on dynamic deformation of rocks. Wang er al32 analyzed the impacts of confining pressure and gas on coal-rock combination and found that the confining pressure effect also greatly determines the formation of the final failure pattern of combination specimens after macroscopic failure. Wang et al.33 explored the impact of cyclic stress amplitude (CSA) on the macro-meso failure characteristics of deeply buried rock under confining pressure unloading process and found that the lateral expansion induced by confining pressure unloading has a great impact on rock volumetric deformation, damage propagation, and failure properties. Ma et al.34 carried out a series of experimental tests and numerical simulations that aim to reveal the failure mechanical behavior, crack development, AE event attributes and failure properties of oil shale under various confining pressures.

Although the above results indicate that the confining pressure has an important effect on the mechanical properties and focus the study on the analysis of the AE characteristics and mechanical properties of the pre-peak, there are still some issues that deserve further study. For example, what are the differences in the AE characteristics and mechanical properties of the residual stage under different confining pressures? How do the AE characteristics change in the process of unloading the confining pressure? In this study, uniaxial and triaxial compression tests and AE emission tests were conducted on muddy shale to analyze in depth the AE characteristics and mechanical properties under different confining pressures. The relationship between mechanical parameters and confining pressures was quantitatively analyzed. The evolution law of rock microcracks under load—including closure, propagation, penetration, and complete failure—is described by the characteristics of AE signals35. AE signals can reflect the cracks developing situation and are widely used for analyzing the evolution of cracks36,37,38,39,40,41. So based on the AE data, the similarities and differences in AE signals under different confining pressures were analyzed. More importantly, the AE characteristics and mechanical properties at the residual stage and the AE characteristics under confining pressure unloading process were analyzed. It is hoped that this study will provide a theoretical basis for the design, construction and payment of engineering projects.

Test materials, equipment and design

Preparation of rock specimens

The rocks used in the tests were taken from the muddy shale of the Silurian Luojiaping Formation in the Pengshui area, Chongqing, with clear bedding and cracks distribution. Rock sampling was conducted in the laboratory of Chongqing University. According to the International Society of Rock Mechanics (ISRM)42, all specimens were processed into standard cylinders with dimensions of Φ50mm×100 mm. To ensure the relative consistency of the properties, all the specimens were obtained from the same rock block and were taken along the bedding direction. Due to the swelling and disintegration because of water, anhydrous polishing was used during the specimen production process. A total of 21 specimens were obtained, which were divided into 7 groups. Some specimens are shown in Fig. 1.

Fig. 1
figure 1

Display of some specimens.

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Test equipment

The MTS815 electro-hydraulic servo rock mechanics test system and the PCI-II AE system produced by American acoustic physics company PAC (physical acoustic corporation) were used as the testing system, as shown in Fig. 2. The PCI-2 AE system on a card is a 2-channel data acquisition and digital signal processing system on a single full-size 32-bit PCI-Card and the wide bandwidth of 1 kHz to 3 MHz allows the board to use the full potential of any MISTRAS AE sensor43.

Fig. 2
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Test equipment.

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Test steps

Firstly, two AE probes were arranged symmetrically on the wall of triaxial cylinder. A layer of butter was applied between the AE probes and the triaxial cylinder, and then the AE probes were tightly attached to the triaxial cylinder with adhesive tape. Due to the presence of noise in the test environment, the AE instrument was calibrated before the confining pressure was applied. When the AE threshold was set at 30 dB, no AE signal was received. Therefore, to eliminate the influence of ambient noise, the AE threshold during the tests was set to 30 dB.

Secondly, the confining pressure loading was applied to the predetermined value at a loading rate of 10 MPa/min using a stress-controlled method. Next, displacement-controlled loading was used to apply axial load at a loading rate of 0.1 mm/min until the post-peak residual stage.

Finally, the axial load was kept constant and the confining pressure was unloaded. The confining pressure unloading was performed in a stress-controlled manner at a rate of 10 MPa/min (the confining pressure unloading rate was 1 MPa/min for a confining pressure of 1 MPa). The test was completed when the confining pressure was reduced to zero. It is important to note that the loading and unloading process was synchronized with the AE signals monitoring.

The schematic diagram of the test system is shown in Fig. 3.

Fig. 3
figure 3

The schematic diagram of the test system.

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AE characteristics under uniaxial and conventional triaxial compression

AE characteristics during the process of loading confining pressure

No AE signal is detected during the process of increasing confining pressure to 1 MPa. The variation of the ring-down counts and amplitude over time during the process of increasing confining pressure to the predetermined value is shown in Fig. 4. It can be seen that the AE signals during the process of loading confining pressure have periodic characteristics. During the process of increasing confining pressure to a predefined low value, basically no or very small amounts of AE signals are detected, while during the process of increasing confining pressure to a predetermined high value, AE signals with different energy occur, and with the increase of confining pressure, the released AE energy increases as well. The main reason for this phenomenon is that during the process of loading confining pressure, the specimen was compacted and produced fewer microcracks, resulting in the detection of a small amount of AE signals.

Fig. 4
figure 4

AE signals during the process of increasing confining pressure to the predetermined value. (a) 5 MPa; (b) 10 MPa; (c) 20 MPa; (d) 40 MPa; (e) 50 MPa.

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AE characteristics during uniaxial and conventional triaxial compression

AE is commonly defined as transient elastic waves induced by the rapid release of local stress energy44. AE signals are positively correlated with local failure in rocks and can be analyzed with signal parameters, such as ring-down counts45. When microcracks propagate or localized internal failure occurs within the rock, elastic waves are generated, causing the AE signals to exceed the threshold multiple times, thereby increasing the ring-down counts. Therefore, ring-down counts can serve as an indirect indicator of localized internal failure within the rock46,47. A large number of ring-down counts means many local failures occur inside rocks48.

The AE amplitude, cumulative ring-down counts, energy rate and other parameters obtained from the tests. Because the AE characteristics is consistent, and considering the space limitation, the relationship of amplitude, cumulative ring-down counts, and stress versus time in uniaxial and conventional triaxial compression (1 MPa, 5 MPa, 10 MPa, 20 MPa) were analyzed, as shown in Fig. 5. From the tests, the AE characteristics during deformation and failure under different confining pressure conditions can be derived.

Fig. 5
figure 5

The relationship of amplitude, cumulative ring-down counts, stress versus time under different confining pressures: (a) uniaxial compression; (b) 1 MPa; (c)10 MPa; (d) 20 MPa.

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  1. (1)

    There is almost no AE signal at the initial stage of the stress-strain curve, but the AE signals start to be generated when the axial stress continues to be applied up to the cracking strength σci. When the axial stress continues to be applied up to the damage strength σcd, the slope of the cumulative ring-down counts curve increases rapidly. For example, during uniaxial compression, the slope of the cumulative ring-down counts-time curve of rock specimen PS-0-2 starts to change at 280.05 s, which corresponds to a stress value of 33.83 MPa, about 84.3% of the peak strength. During conventional triaxial compression tests, the damage strength of specimens is about 90% of the peak strength. For example, with a confining pressure of 1 MPa, the slope of the cumulative ring-down counts-time curve increases rapidly at 238 s, which corresponds to a stress value (damage strength) of 53.87 MPa, about 83.13% of the peak strength (64.8 MPa); With a confining pressure of 5 MPa, the slope of the cumulative ring-down counts-time curve increases rapidly at 300 s, which corresponds to a stress value (damage strength) of 64.58 MPa, about 89.31%of the peak strength (72.31 MPa); Similarly, at a confining pressure of 10 MPa, the damage strength (84.55 MPa) is about 91% of the peak strength (92.91 MPa). This is somewhat different from the findings of Taheri et al.28, but is consistent with Yang et al.‘s findings29. In addition, the cumulative ring-down counts curve shows a small section with a slowly increasing slope before reaching the peak strength, and the slope of the curve is approximately zero. The curve is approximately step-like, that is, the overall AE signal level is low at this moment, indicating that the specimen is about to be failure.

  2. (2)

    Before reaching the stable residual strength stage, the post-peak stress undergoes a rapid drop and some unstable residual stresses. As shown in Fig. 6 (d), The residual stress at a confining pressure of 20 MPa stabilizes, then slowly decrease and stabilize again. The residual stress at low confining pressures does not remain constant with increasing strain, but decreases slowly, resulting in the continuous generation of a large AE signals. As the confining pressure increases, the rate of decrease decreases to zero, the generated AE signals decrease, the slope of the cumulative ring-down counts curve slows down, and the final curve approximates a horizontal straight line. At the confining pressures of 5 MPa, 10 MPa, and 20 MPa, the amplitudes during the residual phase are in the range of 30–38 dB, 30–42 dB, and 30–45 dB, respectively. The AE signals at this stage are mainly generated by the sliding friction of the rock blocks on both sides of the fracture surface. The AE signals at this stage are mainly generated by sliding friction. The fractured surfaces of the fractured rock blocks engage with each other at the concave and convex parts to produce AE signals. The higher the confining pressure, the closer the engagement between the fractured surfaces. When the gnawing occurs, the higher the confining pressure, the stronger the AE signals. This suggests that the formation mechanism of bearing capacity in the residual stage and AE signals are related to the confining pressure.

  3. (3)

    The AE signals are highly dependent on the confining pressure, the fracture surface, and the failure modes. From Fig. 5, it can be observed that the AE signals generated under high confining pressure are fewer than those under low confining pressure. One of the reasons for this phenomenon is that the increase in confining pressure hinders the formation of microcracks. Figure 6 shows the failure modes under different confining pressures. Under low confining pressure conditions, the specimens have a single fracture surface parallel to the center axis, multiple fracture blocks, and the fracture surface presents a stepped shape with high roughness. The AE signals generated after the peak are more frequent. However, under high confining pressure conditions, the specimens are inclined to a single fracture surface, with small fluctuation, unobvious steps, and a large amount of powder, which is smoother than the fracture surface under low confining pressure. The AE signals after the peak are reduced accordingly. As the confining pressure increases, the strain energy stored inside the specimens under axial stress increases. When the specimens undergo failure, the resulting AE energy becomes larger.

  4. (4)

    During the whole process of conventional triaxial compression, the ring-down count rate and energy count rate after the peak are relatively higher than those before the peak. As the confining pressure increases, the AE signals decrease, but the generated AE energy increases. For example, at a confining pressure of 5 MPa and 20 MPa, the amplitudes are in the range of 30–80 dB and 30–95 dB, respectively.

Fig. 6
figure 6

Failure modes of rock specimens under different confining pressures: (a) 1 MPa; (b) 5 MPa; (c) 20 MPa; (d) 40 MPa; (e) 50 MPa.

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AE characteristics during the process of unloading confining pressure

In the process of unloading confining pressure, the variation of the cumulative ring-down counts and amplitude over time are shown in Fig. 7. It can be seen that with the increase of the confining pressure, the release of AE energy in the process of unloading confining pressure increases, while the AE signals are shown to increase and then decrease, which is also closely related to the confining pressure, the fracture surface, as well as the failure modes.

When unloading confining pressure at low confining pressure, a large number of AE signals appear in the initial phase, while when unloading confining pressure at high confining pressure, the AE signals in the initial phase are less, but the AE energy generated is generally higher than that generated in the case of low confining pressure. A sudden increase in the slope of the cumulative ring-down counts curve occurs during the process of unloading confining pressure. The main reason for this phenomenon is that the process of unloading confining pressure is actually a process of continuous energy release. The confining pressure play an inhibitory role on the dissipation of energy. The greater the confining pressure, the greater the strain energy stored inside the specimen. While keeping the axial stress constant, the strain energy will be released rapidly during the process of unloading confining pressure. This phenomenon indicates that excavation operations in high confining pressure rock masses can easily induce instability of the surrounding rock mass and even rock burst.

Fig. 7
figure 7

Amplitude, Cumulative ring-down counts versus time during the process of unloading confining pressure: (a) 1 MPa; (b) 5 MPa; (c) 10 MPa; (d) 20 MPa; (e) 40 MPa; (f) 50 MPa.

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Mechanical properties under uniaxial and conventional triaxial compression

Strength properties

The damage strength σcd, peak strength σp, residual strength σrec, cohesion C and internal friction angle φ are very important mechanical properties in engineering design. These factors are related to whether the design and construction of rock engineering are scientific and safe, and are also important parameters for analyzing the strength properties of rocks.

According to the Mohr-Coulomb strength theory, there is a linear relationship between rock strength and confining pressure:

$${\sigma _{1f}}\,=\,k{\sigma _3}\,+\,b$$
(1)

In the equation, k and b are strength criterion parameters, σ1f is the maximum axial stress and σ3 is the confining pressure.

k and b are related to the cohesion C and the internal friction angle φ as follows:

$$k=\frac{{1+\sin \varphi }}{{1 - \sin \varphi }}$$
(2)
$$b = \frac{{2C \cdot \cos \varphi }}{{1 - \sin \varphi }}$$
(3)

Therefore, the values of the cohesion C and the internal friction angle φ can be calculated as,

$$\varphi =\arcsin \frac{{k - 1}}{{k+1}}$$
(4)
$$C=b\frac{{1 - \sin \varphi }}{{2\cos \varphi }}$$
(5)

The stress-strain curves under different confining pressures were obtained by processing and calculating the tests data, and typical curves were selected for illustration, as shown in Table 1; Fig. 8. Scatter plots were drawn and curves were fitted using the confining pressure as the horizontal coordinate and the damage strength, peak strength, and residual strength obtained from the tests as the vertical coordinate, as shown in Figs. 9 and 10, and 11, respectively.

Table 1 Shale parameters under uniaxial and conventional triaxial compression.
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Fig. 8
figure 8

Stress-strain curves of shale under uniaxial and conventional triaxial compression.

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Combined with Table 1; Fig. 8, it can be concluded that in the case of low confining pressure, the peak strength and residual strength are more greatly by the change of confining pressure. The stress-strain curves after rock fracture will have the shape of a wave peak, and there are small fluctuations in the stress-strain curves in the residual stage. However, in the case of high confining pressure, the confining pressure has less influence on the two and the stress-strain curves in the residual stage are smooth. The confining pressure has a more significant impact on residual strength. For example, when the confining pressure increases from 10 MPa to 20 MPa, the peak strength increases from 92.91 MPa to 114.22 MPa, an increase of 22.94%, and the residual strength increases from 39.19 MPa to 65.4 MPa, an increase of 66.88%. When the confining pressure increases from 20 MPa to 40 MPa, the peak strength and residual strength only increase by 23.45% and 36.68%, respectively. The main reason for this phenomenon is closely related to the fracture surface. Under the condition of low confining pressure, the fracture surface has significant undulations and high roughness. When the confining pressure is increased, the friction of the fracture surface increases, so that the residual strength is also improved. This also indicates that effective support for the surrounding rock mass under low confining pressure conditions can greatly improve the stability, thereby maintaining engineering safety.

Fig. 9
figure 9

The relationship of damage strength and confining pressure.

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Fig. 10
figure 10

The relationship of peak strength and confining pressure.

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Fig. 11
figure 11

The relationship of residual strength and confining pressure.

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According to Figs. 9 and 10, and 11, it can be seen that the damage strength, peak strength, and residual strength become larger with the increase of the confining pressure, and all of them can be fitted by a linear function. This is consistent with the findings of other scholars27,29,34. The damage strength, peak strength, and residual strength at a confining pressure of 0 MPa cannot be characterized by the fitted linear formula. Therefore, in order to obtain the influence of the confining pressure on the strength properties, it is recommended not to use the rock strength data under uniaxial compression.

Table 2 Shale strength parameters.
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The cohesion C and the internal friction angle φ are calculated from Eqs. (4), (5), as shown in Table 2. The results show that both the cohesion C and the internal friction angle φ in the residual phase are reduced, and the cohesion calculated at the residual strength is significantly lower than the value calculated from the peak strength, with a decrease of 69.64% in cohesion and a decrease of 9.1% in internal friction angle. It suggests that the main process of yield failure to residual stage is the weakening of cohesion, while internal friction angle is not significantly reduced.

Deformation properties

In order to clearly describe the deformation properties under different confining pressure conditions, elastic modulus E, Poisson’s ratio µ, peak strain εp, and residual strain εres were selected as deformation indexes to plot scatter plots and fit the curves, which are shown in Figs. 12, 13, 14, 15, respectively.

Fig. 12
figure 12

The relationship of elastic modulus and confining pressure.

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Fig. 13
figure 13

The relationship of Poisson’s ratio and confining pressure.

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Fig. 14
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The relationship of peak strain and confining pressure.

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Fig. 15
figure 15

The relationship of residual strain and confining pressure.

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As can be seen from Figs. 12 and 13, the elastic modulus and Poisson’s ratio show an obvious non-linear growth relationship with the increase of the confining pressure, both of which can be fitted in the form of a power function. When the confining pressure exceeds 20 MPa, the difference in elastic modulus gradually decreases, mainly due to the closure of cracks under high confining pressure. The elastic modulus and Poisson’s ratio do not increase with the increase of confining pressure, but tend to a stable value. The test results of Lindholm et al.49 on hard basalt showed that the elastic modulus does not vary with confining pressure. The test results of Huang et al.6 on sandstone showed that the elastic modulus increases linearly with increasing confining pressure. The test results of Ma et al.30 on combined coal–rock showed that the elastic modulus also increases with increasing confining pressure, and it seems to be stable as confining pressure increases at low strain rate. Therefore, for dense and intact brittle rocks, the magnitude of the confining pressure has no significant effect on the elastic modulus. However, from Fig. 12, it can be seen that the effect of confining pressure on the elastic modulus is not negligible. This should be related to the fact that shale is a typical transverse isotropic medium and the laminated surfaces contain abundant micro-defects. The effect of confining pressure on elastic modulus reflects the number of micro-defects in a sense of degree, which deserves further in-depth study.

As can be seen from Figs. 14 and 15, the peak strain and residual strain increase with the increase in the confining pressure, showing a significant positive linear relationship. These results can provide a theoretical basis for numerical simulation tests and geotechnical theory calculations to accurately select the elastic modulus, Poisson’s ratio and other rock mechanical parameters.

Conclusion

In this study, the AE characteristics and mechanical properties of muddy shale under uniaxial and triaxial compression are analyzed, focusing on the mechanical properties and AE characteristics at the residual stage, as well as the AE characteristics during the process of unloading confining pressure. The main conclusions are as follows:

  1. (1)

    The peak strain and residual strain are linearly related to confining pressure, and all of them increase with the increase of confining pressure. The elastic modulus and Poisson’s ratio increase nonlinearly with the increase of confining pressure, which can be fitted in the form of a power function. However, it does not increase indefinitely, but tends to a stable value. These results can provide a theoretical basis for numerical simulation tests and geotechnical theory calculations of muddy shale to accurately select the elastic modulus, Poisson’s ratio and other rock mechanical parameters.

  2. (2)

    The damage strength, peak strength, and residual strength show a significant positive linear growth relationship as the confining pressure increases. The cohesion calculated at the residual strength is significantly lower than the value calculated from the peak strength, with a decrease of 69.64% in cohesion and a decrease of 9.1% in internal friction angle, indicating that the main process from yield failure to residual stage is the weakening of shale cohesion, while the internal friction angle does not decrease significantly. This is also an important factor affecting the stability of shale formations.

  3. (3)

    During the residual phase, AE signals are continuously generated. The AE signals generated under low confining pressure are more than those under high confining pressure. As the confining pressure increases, the AE signals decrease, the slope of the cumulative ring-down counts-time curve slows down, and the final curve approximates a horizontal straight line.

  4. (4)

    In conventional triaxial compression tests, as the confining pressure increases, the AE energy increases, but the AE signals increase first and then decrease. A sudden increase in the slope of the cumulative ring-down counts-time curve occurs during the process of unloading confining pressure. During the unloading process under different confining pressures, a large number of AE signals occur at different times.

  5. (5)

    The greater the confining pressure, the greater the strain energy stored inside the specimen. While keeping the axial stress constant, the strain energy will be released rapidly during the process of unloading confining pressure. This phenomenon indicates that excavation operations in high confining pressure rock masses can easily induce instability of the surrounding rock mass and even rock burst.