Damage deformation properties and acoustic emission characteristics of hard-brittle rock under constant amplitude cyclic loading

2.1. Specimens and apparatus

The rock samples used in this test were extracted from a heading surface of a roadway in Gubei Mine, Huainan. The cores were processed into Φ50×100 mm standard samples in the laboratory, as shown in Fig. 1(a). The average longitudinal wave velocity and the density of specimens were 5.03×10³ m/s and 2.73×10³ kg/m³, respectively. Gridlines were drawn on the surface of the samples in advance so that the acoustic emission probes could be accurately fixed.

The tests were completed in an MTS 816 rock mechanics test system. The axial load was measured by the load weight installed on the test system, and the axial displacement was measured by the axial displacement extensometer matching with the testing machine. The radial displacement was measured by the circumferential extensometer installed on the specimens. The PCI-2 acoustic emission test and the analysis system used in this test were produced by a US company of physical acoustics. Six channels were used to collect the data in the test process, and each channel corresponded to a separate pre-amplifier and a sensor with a threshold of 40 dB. The acoustic emission probes were coupled to a specimen surface using vaseline, as shown in Fig. 1(b).

Fig. 1Cyclic loading test with diffesrent amplitudes

a) Limestone specimens with high strength and brittleness

c) Sketch of the cyclic loading path

b) AE sensor array and circumferential strain gauge installation

2.2. Testing methodology

Proper cyclic loading amplitudes should be set to explore the response of specimen under cyclic loading with different stress levels, especially the deformation and failure characteristics nearing the ultimate loading. Firstly, the uniaxial compression tests were conducted to obtain the average specimen strength, which was 161.3 MPa. Hence, the maximum values of the three amplitude cyclic loading were set to 70 MPa, 115 MPa and 160 MPa, respectively. All the minimum of cyclic loading were set to 30 MPa to limit the influence of the initial compaction section on the analysis of the experimental results. Therefore, the stress level (the ratio of maximum cyclic stress to static strength) was theoretically 0.43, 0.71 and 0.99, respectively. More than three specimens were selected for each amplitude test. The cycle number in each specimen was set to 10. After completion of the 10 cycles loading and unloading, the specimens were loaded at the same loading rate until failure. The loading and unloading rates were 1 kN/s, and the specific loading mode is shown in Fig. 1(c).

3.1. Stress and strain characteristics under uniaxial loading

The specimen stress-strain curve under uniaxial loading is shown in Fig. 2. In general, the stress-axial strain curve could be divided into three stages, namely the micropore fracture compaction section (OA), the linear elastic section (AB) and the post-peak failure stage (BC). The elastic stage of the limestone specimens in this test was wide, and the failure stage was not obvious compared to other rocks [25]. The specimens almost directly failed in the elastic section, only a local stress drop phenomenon occurred at point B. The failure process of the limestone specimen was more abrupt whereby a phenomenon of "burst" was observed, causing broken pieces to be dispersed at a long distance, thereby rendering difficult the depiction of the post-peak failure stage of stress-axial strain curve. When the axial loading on the specimen was 70.76 MPa, the radial strain suddenly increased, and the subsequent radial strain growth rate became larger, however the axial strain was not obvious, indicating that the radial deformation process was not stable. The stress-volumetric strain curves suggest that the transformation from the volume compression stage to the expansion stage of limestone is more sudden than for other rocks [18, 19].

Fig. 2Stress-strain curve of limestone specimen Ⅰ-4 under uniaxial loading

3.2. Stress and strain characteristics under cyclic loading

The stress-strain curves of the specimens under cyclic loading with different amplitudes are shown in Fig. 3. The data show that the hysteresis loops in the axial stress-strain curves are closer than that of other rock specimens such as sandstone [31] or rock salt [17]. As shown in Figs. 3(a) and 3(b), there is no abrupt change in strain or stress on the stress-axial or radial strain curves for cyclic loading with amplitudes of 40 MPa and 85 MPa, respectively. In particular, for specimen I-6 with an amplitude of 40 MPa, there is no abrupt change in stress or strain across the stress-strain curve. The axial and radial strains of the specimen Ⅰ-10 dropped at a stress of 142.5 MPa, and the radial strain was greater. The hysteretic loop in the stress-radial strain curve with an amplitude of 130 MPa was sparser than amplitudes of 40 MPa and 85 MPa, and a sudden increase occurred in the radial strain when the axial stress was nearing the peak value of the cyclic loading in the third cycle. Besides, the volumetric rock deformation exhibited an obvious slow expansion stage when the specimen was close to failure, as shown in Fig. 3(c).

Fig. 3Stress-strain curves of specimens under cyclic loads of different amplitudes

a) 40 MPa amplitude

b) 85 MPa amplitude

c) 130 MPa amplitude

d) 130 MPa amplitude and the stress level is nearing 1

The peak stress of the specimen Ⅰ-17 was 190.38 MPa and was higher than the average strength because of the discreteness of the rock specimen, but the stress level was 0.84 and was still larger than the other two amplitudes. The strengths of parts of the specimens are lower than the maximum of the cyclic loading under an amplitude of 130 MPa and failed to implement the cyclic loading. Fortunately, the strength of the specimen I-13 seemed to be very close to the maximum of cyclic loading and the failure occurred near the third cycle peak stress, as shown in Fig. 3(d). The radial strain increased abruptly at the initial loading stage when the axial stress was about to reach the maximum of the cyclic loading. Nearing the maximum of the third cyclic loading, instability failure occurred after a short yield stage. Similarly to the other specimens, no sudden large change occurred in the stress-axial strain curve.

The above analysis of the stress-strain curves of the limestone specimens under uniaxial and cyclic loading shows that a strong elasticity was observed in the axial deformation regardless of the stress level cyclic loading. The influence of the stress level of cyclic loading on radial strain was significantly greater than that of axial strain, and the radial strain was prone to sudden increase. Although the radial deformation was significant under high-stress amplitude loading, it does not imply that Poisson’s effect was larger in a strict sense, because the slope of the stress-axial strain curve exhibited little change in the loading section (except the sudden change parts). The heterogeneity of the radial deformation showed that the appearance of the plastic regions or the micro-fracture surfaces in the specimens were local and mainly axial, while the majority kept integrity, maintaining the overall stiffness and stability of the specimen.

3.3. Axial and radial apparent residual strain under cyclic loading

The rock specimen was heterogeneous material that would produce residual deformation after removing the loading on it. All of the three amplitudes cyclic loading resulted in the radial and axial residual deformation after 10 cycles loading and unloading. However, the minimum of cyclic loading in this test was 30 MPa (incomplete unloading), and whether the peak or valley strain difference between hysteresis loops was a residual strain (unrecoverable) remained to be investigated. Therefore, the apparent residual strain was introduced to indicate the deviation in the strain between the hysteresis loops at peak or valley stresses of the cyclic loading, as shown in Fig. 4, where $\epsilon$ includes the radial strain and axial strain, while $\mathrm{\Delta }{\epsilon }_u^t$ and $\mathrm{\Delta }{\epsilon }_l^t$ are the total apparent residual strains at the upper limit and lower limit of cyclic loading, respectively.

Fig. 4Schematic diagram of apparent residual strain under cyclic loading

The radial and axial accumulative apparent strains under different stress levels are shown in Table 1, where $\mathrm{\Delta }{\epsilon }_{ua}^t$ and $\mathrm{\Delta }{\epsilon }_{ur}^t$ are the axial and radial total apparent residual strain at the upper limit of cyclic loading, respectively (loading section in the initial cycle and unloading section in the last cycle are not included), while $\mathrm{\Delta }{\epsilon }_{la}^t$ and $\mathrm{\Delta }{\epsilon }_{lr}^t$ are the axial and radial accumulative apparent residual strain at the lower limit of the cyclic loading, respectively. The variation of the axial accumulative apparent residual strain appears to be lesser than the radial apparent residual strain, which means that the cyclic loading had a greater effect on the radial strain than axial strain. $\mathrm{\Delta }{\epsilon }_{ua}^t$ is larger than $\mathrm{\Delta }{\epsilon }_{ur}^t$ under 0.43 and 0.71 stress level, but smaller under 0.84 stress level, which indicates that the apparent radial residual strain at the upper limit of the cyclic loading was partially recovered when the loading decreased and it was not strictly a residual radial strain which was unrecoverable. Similar results can be derived in the deformation process of the specimen Ⅰ-13, where the applied stress level exceeded 0.84.

The above analysis suggests that the radial strain during the loading process from low stress to high stress could be expressed by the following equation:

where $\mathrm{\Delta }{\epsilon }_r$ is the difference of the radial strains between high and low stresses, ${\epsilon }_{re}$ is the elastic strain, ${\epsilon }_{rp}$ is the plastic strain and $\mathrm{\Delta }{\epsilon }_{rr}$ is the recoverable radial apparent residual strain.

4.1. Acoustic emission characteristics under uniaxial loading

The characteristic parameters of the acoustic emission include Hit, Event, Counts, Energy, Duration and Rise time, where the AE Counts represents the number of oscillations of the signal above the threshold and can be used to evaluate the activities of the acoustic emission. Therefore, the AE Counts during the deformation and the failure process of the specimen was mainly analysed in this study.

As shown in Fig. 5(a), the accumulative AE Counts curve under uniaxial loading could be divided into three stages, including the gentle development stage (OA), the constant-velocity growth stage (AB) and the accelerated growth stage (BC). The compaction process of the micropores and micro-fissures under the lower loading would lead to the generation of a certain amount of elastic wave (Fig. 5(b)). The AE Counts increases suddenly at point A, which may be due to the occurrence of local axial failure surface according to the radial deformation characteristics in Fig. 2. The accumulative AE Counts exhibited a noticeable stepwise increase after point B, which indicates that unstable deformation state occurred in this transient stage. The accumulative elastic energy released with the complete instability and the failure of the specimen, which resulted in a large amount of elastic waves and the accumulative AE Counts subsequently increased to the maximum.

Fig. 5Variation of axial stress, AE counts and accumulative AE counts with time under uniaxial loading

a) Chart of changes throughout the time period

b) Plot of changes in time period from 0 to 200s

4.2. Acoustic emission characteristics under uniaxial loading

Fig. 6 shows the various characteristics of the AE Counts with time under three amplitudes cyclic loading. When the amplitude was 40 MPa (Fig. 6(a)), a small amount of AE counts were produced in the initial cyclic loading section (OP), while AE phenomenon rarely occurred in the next cyclic loading and unloading stage (PQ). When the stress on the specimen exceeded the upper limit of cyclic loading, AE Counts began to increase obviously (QR), indicating the presence of a Kaiser effect in the rock specimens [32].

Fig. 6(b) shows that when the cyclic loading amplitude was 85 MPa, the AE Counts in the initial cycle loading section were almost ten times of that when the amplitude was equal to 40 MPa due to the greater upper limit of cyclic loading. The AE phenomenon was weak during the stage from the initial cycle unloading section to the third cycle unloading section, but it was relatively larger near the upper limits of the fourth, fifth and sixth cycles, thereby causing the accumulative AE Counts to increase in a ladder shape while the growth rate was getting gradually smaller. In the last four cycles, the curve of the accumulative AE Counts gradually tended to be gentle, and scarcely no AE Counts generated in each cycle. The AE counts began to accelerate when the axial stress was about 140 MPa until failure occurred. In general, the AE phenomena can be measured near the peak point in each cycle under 85 MPa amplitude loading, especially in the 4th, 5th, and 6th cycles which are the most obvious. It can be seen that the Felicity effect [33] has appeared under this amplitude cyclic loading.

Fig. 6The variation of stress, AE Counts and accumulative AE Counts with time under cyclic loading with different amplitudes

a) 40 MPa amplitude

b) 85 MPa amplitude

c) 130 MPa amplitude

d) 130 MPa amplitude and the stress level is nearing 1

When the amplitude was 130 MPa, the accumulative AE Counts of the specimens increased approximately linearly with time in the cyclic loading stage. The AE phenomenon appeared whether in the loading or unloading sections in each cycle, and the generation rates were generally the same. Also, a Felicity effect could be observed under this amplitude cyclic loading. In the loading to failure stage, the AE Counts increased rapidly when the stress exceeded the maximum of cyclic loading, so the Kaiser effect could still occur. Particularly for the specimen I-13, the upper limit of the cyclic loading was close to the uniaxial strength, so the AE characteristics were worth analysing. As shown in Fig. 6(d), the accumulative AE Counts in the initial loading stage, and the cyclic loading stage accounts for about 55 % of the total AE Counts. The AE characteristics of the specimen I-13 under the cyclic loading stage was similar to that of the specimen I-17, but the increasing rate of I-13 was relatively larger.

It can be seen that the accumulative AE Counts in the cyclic loading stage was gradually increased with increasing amplitude, and the total AE Counts at completion of the failure process also increased gradually. New microcracks kept opening and closing under the cyclic loading and unloading, during which the AE phenomenon was generated. When the upper limit of the cyclic loading was close to the specimen strength, the AE phenomenon could occur at any stress under the cyclic loading stage, and the generation rate in the unloading section was the same as that in the loading section. The Kaiser effect was exhibited significantly under the cyclic loading of lower amplitude, and the Felicity effect began to reflect with increasing cyclic loading amplitude, but both of them occurred at any amplitude.

4.3. Relationship between specimen AE characteristics and radial deformation

Regardless of the cyclic loading amplitude, there was no great sudden change in the stress-axial strain curves, and the specimen seemed stable and scarcely damaged before reaching peak stress. However, the AE Characteristics showed that the specimen damage before peak loading could not be ignored, especially under larger amplitude. Therefore, it is difficult to reflect specimen damage process according to the axial deformation characteristics. It can be easily found that the sudden increase point of the radial strain corresponds to a large AE Counts. For example, the radial strain of the specimen Ⅰ-17 suddenly increased near the maximum of the cyclic loading in the third cycle and the corresponding AE Counts also suddenly increased. However, the axial strain did not exhibit such abrupt change. It can be seen that the radial deformation of the specimen was more closely related to the AE characteristics. Also, the final split failure mode (Fig. 7(c)) of the limestone specimens shows that the radial deformation was more significant when the specimen was close to failure. Therefore, the acoustic emission phenomenon of the limestone specimens is mainly due to the formation of new microcracks in the axial or approximate axial direction.

At a lower stress level, the initiation and propagation of the most microcracks did not appear, so the AE phenomenon was very rare under the cyclic loading stage, or the phenomenon was too weak to be detected (less than 40 dB). With increasing stress level, some microcracks began to appear and expand but did not form a larger failure surface which could significantly impact the specimen instability and failure, therefore specimens under amplitude of 85 MPa tended to be relatively stable after several cyclic loading and unloading. With the stress level further increasing, additional microcracks were created, which subsequently expanded, merged and developed in a stable trend in each cycle, both in the loading sections and unloading sections.

Under the loading sections of the cyclic loading, one can easily understand that the new cracks were initiated at the tips of the original microfractures under the axial loading. Tension and shearing action was mainly exhibited in the fracture surfaces, which resulted in energy-releasing and elastic wave generation, as shown in Fig. 7(a). For the unloading sections, the accumulative AE Counts in the unloading sections was almost the same as that in the loading sections under higher amplitudes and stress levels, such as specimen Ⅰ-13 and Ⅰ-17, thereby showing that the specimens also released energy and could generate a large number of waves in the deformation recovery process of the unloading sections. However, the AE generation mechanism in the unloading sections was different from that of loading sections. Fig. 7(b) shows the possible specimen deformation and the crack initiation and expansion characteristics during the unloading section. With the slow recovery of the axial deformation, the radial deformation recovered gradually. Since rock is a heterogeneous material, the energy agglomeration is different in the different parts under axial loading, and the various parts will produce different deformation recovery in the unloading process. Therefore, an uneven axial deformation may occur on both sides of the fracture surfaces, leading to the shear or tension actions at the tips of the fractures (location 1) and the extrusion dislocation between the crack surfaces (location 2). Besides, in the radial deformation recovery process, the shear action (location 3) may also appear between the adjacent fracture tips in the opposite direction from the loading process. Therefore, the plastic area will also be produced near the fracture surfaces and tips in the unloading sections, which caused the specimen damage to be intensified.

The new crack generation and propagation process are complex during the cyclic loading, and only the several possible forms are listed above. In general, the radial deformation of the limestone specimens was more unstable under the cyclic loading than axial deformation, and the vertical new cracks tend to initiate and propagate more easily, which leads to the specimen damage and the occurrence of AE phenomena.

Fig. 7Crack initiation and propagation in deformation and failure process of specimens during loading and unloading process

a) Loading section

b) Unloading section

c) Brittle splitting failure morphology of limestone