Crack evolution of soft–hard composite layered rock-like specimens with two fissures under uniaxial compression

Abstract

Acoustic emission and digital image correlation were used to study the spatiotemporal evolution characteristics of crack extension of soft and hard composite laminated rock masses (SHCLRM) containing double fissures under uniaxial compression. The effects of different rock combination methods and prefabricated fissures with different orientations on mechanical properties and crack coalescence patterns were analyzed. The characteristics of the acoustic emission source location distribution, and frequency changes of the crack evolution process were also investigated. The test results show that the damage mode of SHCLRM is related to the combination mode of rock layers and the orientation of fractures. Hard layers predominantly produce tensile cracks; soft layers produce shear cracks. The first crack always sprouts at the tip or middle of prefabricated fractures in hard layers. The acoustic emission signal of SHCLRM with double fractures has clear stage characteristics, and the state of crack development can be inferred from this signal to provide early warning for rock fracture instability. This study can provide a reference for the assessment of the fracture development status between adjacent roadways in SHCLRM in underground mines, as well as in roadway layout and support.

Graphical abstract

Keywords

soft−hard composite layered rock mass / double cracks / crack evolution / acoustic emission / digital image correlation

1 Introduction

Soft and hard composite laminated rock masses (SHCLRM) are complex media frequently encountered in underground mines during roadway excavation [1]. Fracture sprouting and extension around the tunnel under the actions of ground stress and excavation disturbance, and the development of fracture penetration in the rock mass are the main factors leading to engineering disasters in such underground circumstances [2–4]. Existing researches on fracture extension are mainly focused on single rock masses [5–8], while few studies have paid attention to SHCLRM [9,10]. Hence, further research is needed for engineering problems in special underground mines. It is necessary to design new tests to investigate the fracture extension evolution characteristics of adjacent roadway envelopes in SHCLRM. This study intends to provide an important reference value for the assessment of fracture development state between adjacent roadways in SHCLRM in underground mines and for roadway layout and support. Figure 1 shows the layout of an underground mine tunnel.

The effects of fractures on the mechanical properties and damage modes of rock have been extensively studied using experimental research [11–16] and numerical simulations [17–21]. Numerical methods have many advantages over experimental testing, and many researchers have achieved fruitful results using numerical methods, such as the cracking particles method (CPM) [22,23], cracking element methods (CEMs) [24,25], the global cracking elements method (GCEM) [26], dual-horizon peridynamics (DH-PD) [27,28], the non-uniform horizon peridynamic (NHPD) [29], non-local operator methods (NOM) [30,31] and the phase field model (PFM) [32]. The simulation of crack initiation, propagation, branching and coalescence by these numerical methods has deepened the understanding of crack extension laws and provided methods and ideas for solving complex engineering problems. Cheng et al. [33] investigated the effects of fracture opening on the mechanical properties of rocks using uniaxial compression tests. Lin et al. [34] established the corresponding compaction stress field equation by comparative analysis of the stress field at the crack tip in the tensile state, and they derived the relationship between the crack initiation angle of the open crack tip and the inclination angle of the prefabricated defect. Shang et al. [35] and Pakdaman et al. [36] investigated the type I, type II, and mixed (I + II) fracture characteristics of rocks using semicircular bending tests, revealing the microscopic mechanism of rock fracture behavior. Zhou et al. [37] studied the fracture characteristics of prefabricated multi-fracture poly methyl methacrylate. Aliha et al. [38] predicted the fracture load of rock materials containing fractures based on the average strain energy density criterion, and they verified the accuracy of the prediction by fracture tests of diagonally cracked triangular specimens under a symmetric three-point bending load. SHCLRM are transverse isotropic rock masses with anisotropic behavior [39–44]. Douma et al. [45] reported that the difference in the strength of soft and hard laminae controls crack extension, and the presence of laminae can hinder crack extension. Wang et al. [46] investigated the damage pattern of prefabricated single-fracture laminated rocks with different laminar face dips under uniaxial compression, and the results showed that the laminar face plays a decisive role in crack extension. Hu et al. [10] investigated the effect of different dip angles of prefabricated fissures and different rock strengths on the damage mode of double-layered composite rock masses, and the results showed that the damage mode was mainly affected by the difference in strength between the soft and hard rock layers. The above-mentioned studies provide an in-depth analysis of the damage mode, crack extension process, and the influence of fractures on the mechanical properties of rock masses containing fractures; however, they mainly focused on single or single laminated rock masses containing fractures. There is a paucity of research on the evolution of crack extension in SHCLRM containing fractures.

Acoustic emission (AE) and digital image correlation (DIC) are effective methods for studying crack extension [47–51]. By analyzing the AE source location and wave velocity laminar imaging, Yang et al. [52] found that the crack development and stress evolution processes in rocks have discrete phases, and that local damage and excessive local stress differences in rocks accelerate rock damage. Wang et al. [53] investigated the mechanical properties, AE characteristics, crack dynamic extension process, damage mode, and damage evolution law of prefabricated rock samples with different crack inclination angles under uniaxial compression. Xing et al. [54] used DIC on centrally cracked Brazilian disc (CCBD)-type rock specimens and determined the effect of loading rate on the strength and damage mode of the rock. Miao et al. [55] investigated the effect of loading rate on the strength and damage mode of the rock by AE and DIC, and investigated the effect of fracture filling material and fracture dip angle on fracture extension in sandstone.

Depending on the geological conditions and mining methods, roadways may be arranged in soft or hard formations, and the relative locations of multiple roadways may be different [56–60]. Therefore, in this study, uniaxial compression was performed on laminated class rock specimens with different soft and hard rock combination methods, and with fissures of different orientations. Crack extension was monitored by AE and DIC during loading, and the AE signals generated during crack extension and the strain on the specimen surface were analyzed to obtain the spatial and temporal evolution characteristics of crack extension in SHCLRM.

2 Materials and methodology

2.1 Geometries of the specimen and flaw

Two types of rock combinations were set up: hard layer–soft layer–hard layer, and soft layer–hard layer–soft layer, with the fissure at the layered interfaces. The fissure penetrated the specimen, and the length was fixed at 10 mm, the opening was 2 mm, the depth was 60 mm, and the inclination was 45°. The rock bridge inclination was either 60°, 75°, 90°, 105°, or 120°. Cubic specimens with model dimensions of 60 mm × 60 mm × 120 mm were cast. The specimens were named according to the rule of “combination method-bridge angle” (e.g., HSH-60 represents the combination method of hard layer–soft layer–hard layer, and a bridge inclination angle of 60°). Table 1 lists the design scheme of the specimen. Figure 2 shows a schematic diagram of the combination of hard and soft rock layers.

2.2 Specimen preparation

To study the fracture extension and AE characteristics of laminated composite rock masses, fractures need to be prefabricated inside the specimens. Because it is difficult to prefabricate fissures in the original rock specimens, and the accuracy requirements cannot be met, rock-like models are mostly used for the study of fractured rock masses [61]. In this study, cement mortar was used to produce the samples; the hard layer ratio was composed of 42.5R ordinary silicate cement: gypsum: quartz sand = 1∶0∶0.4, and the water–cement ratio was 0.32. The soft layer ratio was 42.5R ordinary silicate cement: gypsum: quartz sand = 1∶0.3∶0.4, and the water–cement ratio was 0.46. The basic physical and mechanical parameters of the rock-like specimens are listed in Table 2.

Figure 3 shows the test mold and specimens. To ensure the accuracy of prefabricated fissures and soft and hard rock layer locations, the prefabricated fissures and laminated surfaces were formed by division plates and iron sheets with length, width, and thickness of 90 mm × 60 mm × 0.8 mm, and 90 mm × 10 mm × 2 mm, respectively. The spacers and iron sheets were fixed with 3D printing molds. When producing the sample, the iron mold was first cleaned and fixed, coated with a mold release agent, and then the 3D printed mold was installed on the iron mold to form a combined mold, as shown in Fig. 3(a). The division plates and iron sheets were inserted into the slot of the mold; the material was prepared according to the ratio of the hard and soft layers; the prepared material was poured into the mold separately, vibrated on a small vibration table for 30 s, and the division plates were removed while vibrating. After 8h, the prefabricated fracture iron sheets were removed, the surface was smoothed, and the mold was removed after 24 h, after which the rock-like specimen was maintained in a constant temperature maintenance box for 28 d. The rock-like specimens after maintenance are shown in Fig. 3(b). The surface of the finished speckles was evenly sprayed with white matte paint, and after 10 min, the surface was evenly sprayed with black matte paint. The finished speckled specimen is shown in Fig. 3(c).

2.3 Testing System

The test system included a loading system, an AE system, and a DIC system. The loading system was a YZW-30A microcomputer-controlled electronic rock straight shear instrument, which supports two control modes of displacement and load, and this test was displacement controlled at a rate of 0.02 mm/min. The AE system was a United States Physical Acoustics Express-8 AE monitoring system, with six AE probes to receive AE signals; the probe surfaces were evenly coated with a coupling agent and fixed with transparent tape. The lead break test was used to determine the integrity and accuracy of the system test, and the AE event definition value and event blocking value were adjusted so that the positioning point error was less than 2 mm. The AE threshold was set at 40 dB, and the preamplifier was set to 40 dB. The DIC system was an XTDIC three-dimensional full-field strain measurement system that can perform full-field three-dimensional strain calculations while acquiring images. The charge-coupled device camera had a resolution of 2448 × 2048 pixels and recorded scatter images at a rate of 1 frame per second. Figure 4 shows a diagram of the test system.

3 Results: strength and crack evolution behavior

3.1 Mechanical performance analysis

The mechanical test results for the SHCLR specimens containing double fissures are shown in Table 3. The compaction stress is the critical point at which the specimen enters the elastic strain stage from the compressive stage, the fracture initiation stress characterizes the beginning of microcrack extension within the specimen, and the damaging stress characterizes the beginning of rock dilation and the long-term strength of the rock body. The crack initiation stress level is the ratio of crack initiation stress to peak strength, and there are some differences between the crack initiation stress levels of specimens from two different soft and hard layer combinations. The difference in fracture initiation stress level between “HSH-60” and “SHS-60” specimens with the same angle of 60° was 16.13%. The compaction stresses of the specimens with different combinations of rock layers or different orientations of cracks did not vary significantly, and the average compaction stress was 1.8 MPa.

The uniaxial compaction stress–strain relationship curves of the laminated class rock specimens are shown in Fig. 5. As shown in Fig. 5, the peak stress of the fractured rock specimens is significantly lower than that of the intact rock specimens, and the peak stress tends to decrease initially and then increase with an increase in the rock bridge angle. Using the “HSH” combination method as an example, the peak strength of the intact rock specimen was 15.1 MPa. The peak strength decreased by 3.51 MPa and the peak strain increased by 4.75 × 10⁻³ as the bridge angle increased from 60° to 105°. The peak strength increased by 0.61 MPa and the peak strain increased as the bridge angle increased from 105° to 120°. The maximum strength loss of the fractured specimens was 39% that of intact rock specimens.

3.2 Failure modes analysis

DIC was used to record the crack eruption, extension, and connectivity of the SHCLRM containing double fissures under uniaxial compression, and the strain field of the crack extension process was calculated using digital images. Figure 6 shows the final damage mode of the SHCLRM containing double fissures, which is the maximum principal strain profile obtained by the DIC system when the specimens were damaged. The DIC results show that the damage to the specimens was caused by the crack extension generated by the prefabricated fissures. Most of the cracks in the hard layers were due to tensile damage caused by tensile crack extension, and most of the soft layers exhibited shear damage caused by shear crack extension. According to Zhang and Wong’s study [62], the first crack generated during loading of rock masses containing prefabricated fissures was caused by prefabricated fissures and then propagated in the vertical direction. In addition, the first crack initiation location was limited to the crack tip and included the middle of the cracks. The results of this study are consistent with the results of Zhang and Wong’s study [62]. In particular, the first crack in SHCLRM containing double fractures was generated around the prefabricated fracture in the hard layer, not necessarily at the tip of the prefabricated fracture, but also possibly in the middle of the prefabricated fracture. However, most of the cracks were generated at the tip of the prefabricated fracture and propagated along the vertical direction. This may be related to the difference in mechanical properties of soft and hard laminations, where the compressive strength of the hard laminations is greater than that of the soft laminations, while the tensile strength of the hard laminations is smaller than that of the soft laminations. Therefore, the first tensile cracks in soft and hard composite laminations are always produced at the tip or middle of prefabricated fractures in the hard laminations. In addition, the laminae have a certain barrier effect on crack extension, which is in agreement with the findings of Douma et al. [45] For example, the wing crack generated by the precast fracture above SHS-75 was blocked when it extended downward to the interface between the hard and soft layers, while the wing crack generated by the precast fracture below extended upward through the laminate surface. The crack extension to the laminate surface may continue to extend through the laminate surface or may be separated by the laminate surface and not continue to extend. This may be related to the stress field and the difference in the mechanical properties of the two media in the laminate surface.

Many cracks were produced at the crack tip during the damage process of the rock specimens containing prefabricated fissures. Wong and Einstein [63] classified the cracks produced at the crack tip, including three types of tensile cracks, three types of shear cracks, and one type of mixed crack. Based on the types of cracks produced in the upper and lower prefabricated fissures, the damage modes of the specimen fissures can be classified into four types: shear, tensile, mixed, and no agglomeration. Table 4 indicates the four coalescence modes of the double fractures of the rock-like specimens. The combination of the rock layers and the orientation of the fissures significantly influence the coalescence mode of the prefabricated fissures in SHCLRM containing double fissures. When the middle was a soft layer, the β = 90° and β = 105° specimens showed tensile coalescence, while when the middle was a hard layer, these specimens displayed no coalescence. The same fissure orientation with different combinations of soft and hard rock layers showed completely different coalescence patterns, which may be caused by the difference in the mechanical properties of the soft and hard rock layers. The hard layer rocks were more susceptible to tensile damage, and the crack extension direction produced by tensile stress was mostly along the vertical direction. Therefore, when the middle was a hard layer with β = 90° and β = 105°, the cracks produced tensile agglomeration. The most common agglomeration pattern was mixed agglomeration, which occurred in both rock combination methods, while shear agglomeration only occurred in the specimens with a soft middle layer and tensile agglomeration only occurred in the specimens with a hard middle layer, and tensile and shear agglomeration are special cases of mixed agglomeration. The crack coalescence patterns of specimens with different combinations of soft and hard layers and prefabricated fissures in different orientations showed clear regular characteristics, and the crack coalescence patterns generated by fissures in other orientations can be predicted from the test results.

3.2.1 Shear coalescence

The principal strain and displacement evolution of a typical shear-agglomerated HSH-60 specimen are presented in Fig. 7. The displacement diagrams in the X- and Y-directions show that the displacements along the X-direction of the rock on each side of the tensile crack were significantly different, while there were few differences in the displacements along the Y-direction. Furthermore, the displacements along both directions on each side of the shear crack were significantly different, which more directly indicates the type of crack. As shown in the main strain evolution diagram, the tip of the prefabricated fracture in the upper hard layer first produced two larger strain profiles. The larger main strain profile in the soft layer gradually extended downward, while the larger main strain profile in the hard layer did not change much. The first crack appeared as a T₂-type tensile crack in the hard layer, which extended along the vertical direction, indicating that the tensile strength of the hard rock is smaller than that of the soft rock. The next to appear was the S₃-type shear crack, which extended vertically downward and changed direction when reaching the laminated surface, indicating that the laminated surface hindered the extension of shear cracks. Shear cracks S₁ and S₂ appeared last, and S₂ extended in the direction of the rock bridge, connecting the two prefabricated fractures. The types of cracks in the soft and hard laminae show obvious differences, with S₁, S₂, and S₃ in the soft laminae, all of which are shear cracks, and T₂ in the hard laminae, all of which are tensile cracks, indicating that the types of cracks produced by the prefabricated fissures are directly related to the nature of the laminae.

3.2.2 Tensile coalescence

Figure 8 shows the main strain and displacement evolution of a typical tensile agglomerated SHS-105 specimen. The central hard layer between the two prefabricated fissures produced a large principal strain initially, and the first crack was a T₃-type tensile crack produced by the upper prefabricated fissure. The displacement diagram shows that with the increasing loading stress ground, the rock on both sides of the T₃-type tensile crack was displaced in the X-direction, and showed a small displacement difference in the Y-direction. However, the first crack was a T₃-type tensile crack produced by tensile stress, and this crack developed vertically, connecting the two prefabricated fissures; therefore, this agglomeration pattern was still attributed to tensile agglomeration. The types of cracks produced in the precast fissures are still related to the nature of the soft and hard rock layers, with all S₃-type shear cracks in the soft layers and T₂ and T₃ tensile cracks in the hard layers. Tensile cracks appeared first.

3.2.3 Mixed coalescence

Figure 9 shows the main strain and displacement evolution diagrams of a typical hybrid agglomerated SHS-60 specimen. The main strain diagram suggests that large strains were first generated near the precast fracture and in the middle of the rock bridge, but none of them had cracks. With an increase in the loading stress, the specimen was suddenly damaged when the energy accumulated inside the specimen reached the critical damage value, and the crack extension was completed rapidly. The mixed agglomeration mode showed shear cracks S₁, S₂, S₃, and tensile cracks T₂ in the hard layer, and shear cracks S₁ and tensile cracks T₁ in the soft layer, which showed obvious differences from tensile and shear agglomeration, and the crack extension process was more complicated.

3.2.4 No coalescence

Figure 10 shows a typical principal strain and displacement evolution diagram for a non-agglomerated HSH-105 specimen. The two larger principal strain contours appear first at the tips of the prefabricated fissures in the upper hard layer, and the T₁-type tensile crack is the first crack produced, extending vertically upward, followed by shear cracks S₁ and S₃, extending to the lower left and lower right sides, respectively. No cracks were produced in the lower prefabricated fissure; both shear cracks produced in the upper prefabricated fissure were staggered with the lower prefabricated fissure and did not agglomerate. As with tensile and shear agglomeration, only shear cracks were produced in the soft layer, and only tensile cracks were produced in the hard layer.

4 Results: Acoustic emission characteristics

4.1 Acoustic emission location analysis

The spatiotemporal evolution of cracks and the corresponding time-varying AE characteristics were analyzed by combining the stress–strain curves of laminated rock specimens, the 3D positioning of the AE source, and the surface principal strains of the specimens monitored by DIC. All four agglomeration modes were formed by extensional penetration of tensile cracks or shear cracks; therefore, only tensile and shear agglomeration are analyzed here, and the typical shear agglomeration specimen HSH-60 and tensile agglomeration specimen SHS-105 were selected as examples for analysis. The spatial and temporal evolution of the source AE and the main strain cloud at five key points on the stress–strain curve, compaction stress, fracture initiation stress, damage stress, peak stress, and stress at the end, were selected for analysis. The specimen rupture process can be divided into four stages: compression-density stage, elastic strain stage, damage development stage, and post-damage stage, corresponding to stages I, II, III, and IV in Fig. 11, based on the stress–strain curve and the variation characteristics of the accumulated AE counts. Figure 12 summarizes the spatiotemporal evolution distribution of the source AE and the main strain cloud at the damage critical point of the HSH-60 specimen, while Fig. 14 presents the spatiotemporal evolution distribution of the source AE and the main strain cloud at the damage critical point of the SHS-105 specimen.

The typical shear coalescence axial stress and AE event rate variation curves are shown in Fig. 11. A small number of seismic sources are distributed around the fracture in the compression-density stage, and the number of seismic sources around the prefabricated fracture in the upper part is more than that in the lower part, with few distribution of seismic sources in the central soft layer. The number of seismic sources was 104 by the σ_cc point (σ = 1.83 MPa, ε = 4.33 × 10⁻³); the cumulative AE count from the σ_cc point to σ_ci in the pre-elastic strain stage grew approximately linearly, as shown in the auxiliary line segment AB in Fig. 11. indicating that the microcrack inside the specimen developed steadily at low speed. When loaded to the σ_ci point (σ = 7.41 MPa,ε = 7.83 × 10⁻³), the distribution of seismic sources around the crack increased, and the number of sources was 295, and a relatively large principal strain appeared at the tip of the upper prefabricated fissure. The accumulated AE count from the point σ_ci to σ_cd in the post-elastic strain stage accelerated, and when loaded to the σ_cd point (σ = 10.35 MPa, ε = 9.67 × 10⁻³), the AE count increased abruptly to 1.2253 × 10⁴, the source distribution around the fracture continued to increase, the number of sources was 716, and the microcrack around the fracture accelerated to extend and sprout, but had not yet nucleated to result in formation of macroscopic cracks. The cumulative AE count in the damage development stage increased at a faster rate, and when loaded to the σ_c point (σ = 12.77 MPa, ε = 12.17 × 10⁻³), the specimen changed from ductile to brittle. The specimen started to experience damage, the first crack appears at the tip of the upper crack, a T₂-type tensile crack, and the number of sources increased to 1641. The cumulative AE count rose exponentially in the post-damage stage, and the AE count appeared to peak at 3.069 × 10⁴. The specimen progresses rapidly through the internal microcrack. When loaded to the σ_ce point (σ = 10.28 MPa, ε = 13.25 × 10⁻³) the specimen was damaged. The loading ended with 2576 sources; the two prefabricated fissures were then connected by S₂-type shear cracks, the middle soft layer showed shear damage, and the upper and lower hard layers showed tensile damage.

It can be observed that the AE sources were first distributed around the two prefabricated fissures and continuously extended around them. The AE sources distributed around the upper prefabricated fissure were more than those distributed around the lower prefabricated fissure, and only a small number of AE sources were distributed in the middle soft layer. The AE counts and cumulative AE counts of the crack extension process showed strong stage-specific characteristics. The AE counts increased and then decreased in the compression-density stage, and increased steadily, indicating microcrack closure inside the specimen. The counts were fewer in the pre-elastic strain stage, and increased approximately linearly, indicating microcrack extension inside the specimen at a low and steady speed. The counts gradually increased in the post-elastic strain, damage development, and post-damage stages, and the growth rate of accumulated AE counts gradually accelerated, indicating that the number and extension rate of microcracks inside the specimen increased, and the microcracks gradually extended and connected to form macroscopic cracks and large damage.

The typical tensile coalescence axial stress and AE event rate variation curves are shown in Fig. 13. The AE characteristics and source distribution in the compression-density stage were similar to those of HSH-60, with a small number of sources distributed around the fissure and few AE source distribution in the middle layer; the number of sources was 108. The cumulative AE event rate increased abruptly to 1.71273 × 10⁵ at the {\sigma }_{\mathrm{c}\mathrm{c}}^{\prime } point (σ = 1.35 MPa, ε = 3.92 × 10⁻³), and the specimen entered the elastic strain stage. From {\sigma }_{\mathrm{c}\mathrm{c}}^{\prime } to {\sigma }_{\mathrm{c}\mathrm{i}}^{\prime } (σ = 4.61 MPa,ε = 7.42 × 10⁻³) was the pre-elastic strain stage, and the cumulative AE count increased approximately linearly, as shown in the auxiliary line segment A´B´ in Fig. 13. The newly added sources in this stage were mostly distributed near the upper fissure and the rock bridge, and the number of sources was 227. With the stress loading to the {\sigma }_{\mathrm{c}\mathrm{d}}^{\prime } point (σ = 5.83 MPa, ε = 8.92 × 10⁻³), stress concentration appeared at the crack tip, the new sources in the post-elastic strain stage were mainly near the rock bridge, and the number of sources was 507. In the damage development stage, along with the appearance of stress drop, the AE event rate reached a peak of 4.1168 × 10⁴, and when loaded to the {\sigma }_{\mathrm{c}}^{\prime } point (σ = 6.53 MPa, ε = 10.58 × 10⁻³), the first crack was a slightly T₃ tensile crack, sprouting from the middle of the prefabricated fissure in the upper soft layer, extending vertically downward; the distribution of seismic sources near the rock bridge continued to increase, and the number of sources was 1184. The cumulative AE count in the post-damage phase also increased exponentially, and the specimen was damaged when loaded to the {\sigma }_{\mathrm{c}\mathrm{e}}^{\prime } point (σ = 3.91 MPa, ε = 11.67 × 10⁻³). The loading ended, and the number of sources was 1809; the two prefabricated fissures were then connected by T₃-type tensile cracks, and the S₃-type shear cracks at the tips of the upper and lower soft layer cracks extended to form shear damage.

It can be observed that the distribution of AE sources of tensile agglomeration in the compression-density stage was similar to that of shear agglomeration; both had a small number of AE sources distributed around the prefabricated fractures, while from the elastic stage, the additional AE sources were mainly distributed in the area near the rock bridge, which coincided with the location where the first crack appeared. The AE counts and cumulative AE counts during crack extension in tensile and shear coalescences were similar in characteristics, and both showed strong phase characteristics, with the tensile coalescences showing a sudden increase in AE counts at the end of the compacting phase, which may be caused by the closure of microfractures in the soft layer.

4.2 Acoustic emission frequency-amplitude analysis

The AE signal generated during the crack extension process reflected the size of the microcrack rupture scale inside the specimen [64]. The AE signal was converted from the time-domain signal to the frequency-domain signal, which can analyze the crack extension process more deeply, by fast Fourier transform. An AE signal of the HSH-60 specimen provides an example that can illustrate the process of primary frequency extraction. The AE signal generated by microcrack rupture was received by the AE sensor when loaded at 1.96 s, and the signal waveform is shown in Fig. 15(a), which is a time-domain signal. The time-domain signal was transformed into a frequency-domain signal by fast Fourier transform, as shown in Fig. 15(b), and the maximum value of the amplitude was used as the main frequency amplitude, with the corresponding frequency as the main frequency.

All waveforms were extracted from the main frequency using the above steps, and 2705 waveforms were received for the HSH-60 specimen, and 1020 waveforms were received for the SHS-105 specimen. The extracted main frequency signals ranged from 0 to 400 kHz, and the main frequency signals were divided into three frequency bands, 0–150, 150–250, and 250–400 kHz, corresponding to the relatively low, medium, and high frequencies, respectively. By analyzing the trends of low-frequency, mid-frequency, and high-frequency signals at each stage of crack extension evolution, it can provide a basis for early warning of rock fracture instability. Figure 15 demonstrates the waveform and spectrum of the AE signal. Figure 16 shows the variation in the frequency and amplitude of the crack extension AE.

The time-varying evolution of the axial stress and AE frequency domain of a typical shear agglomeration is shown in Fig. 16(a). The AE frequency domain signals generated in the compression-density stage (stage I) were 199 in total, of which 103 were high-frequency signals, accounting for 51.75%, and the maximum amplitude was 85 dB. The high-frequency signals were mainly generated in the early stage of loading, and the microcracks were closed. The AE frequency domain signals generated in the elastic strain stage were basically the same as those in the compression-density stage, 198 in total. They were dominated by high-frequency signals, accounting for 67.17%, and by the stable development of the internal microcrack of the specimen; however, the development rate and number were not large. In the damage development stage, the AE frequency domain signal increased to 868, still dominated by high-frequency signals, and crack sprouting extension accelerated. The post-damage stage generated a total of 1440 frequency domain signals, and the amplitude of the peak value was 97 dB; there was rapid extension of the crack, shear cracks became connected to the two prefabricated fissures, and shear coalescence formed.

The typical tensile agglomeration axial stress and AE frequency domain time-varying evolution are shown in Fig. 16(b). Unlike typical shear agglomeration, the specimen had only a small number of AE frequency signals in the compression-density stage and elastic strain stages, and the amplitude generally showed an increasing trend with a peak amplitude of 117 dB. The percentage of frequency bands in each stage of the crack extension process was also different from that of shear damage, with the elastic strain stage mainly producing high-frequency signals, accounting for 88.39%. On the other hand, the post-damage stage mainly produced low-frequency signals, accounting for 47.75%. The entire count of medium-frequency signals was an average of 12.85%. Table 5 shows the statistics of the main frequency change of the AE during crack extension.

The time-varying evolution of AE during the crack extension of shear and tensile coalescence shows that the number of low-frequency, medium-frequency, and high-frequency signals increased rapidly from the elastic stage to the damage development stage; the proportion of low-frequency and medium-frequency signals increased and the proportion of high-frequency signals decreased. The overall trend of the AE signal amplitude increased during the entire process of crack extension. The damage development stage was the stage of macroscopic crack formation; therefore the stage of crack extension can be inferred from the number and proportion of low-frequency, medium-frequency, and high-frequency signals combined with the amplitude change at the same time, to predict the rock rupture instability.

5 Discussion

5.1 Crack Initiation

A variety of existing theories for predicting the conditions of crack initiation and the direction of extension, such as the maximum tangential stress theory [65], the maximum energy release rate theory [66], and the minimum energy density theory [67], whose objects are the single lithologic layer, and they are not suitable for calculations of SHCLRM. Zhurkov et al. [68] proposed that crack formation should be divided into two stages. In the first stage, the microfractures develop slowly. Each microfracture is distributed randomly and independently of each other without interference. In the second stage, the interactions between the micro-ruptures are gradually strengthened due to the reduction of spacing. From Figs. 12 and 14, it can be seen that the micro-rupture both in compression-density stage and pre-elastic stage is distributed randomly around the two prefabricated fractures with a slow development rate. From the point of σ_ci, the rate of micro-rupture generation accelerates gradually until damage occurs. The micro-fracture nucleation theory can well explain the experimental phenomenon of the sprouting and extension of cracks in SHCLRM. In addition, the first cracks are all tensile-type cracks generated by tension stresses, and they extend along the vertical direction. This finding is consistent with the results of Zhang and Wong [62]. In particular, tensile wing cracks in SHCLRM will sprout at the tips of prefabricated fractures in hard layers first.

5.2 Coalescence types

Several studies have been conducted to investigate crack coalescence patterns in single rock masses or laminated rock masses containing prefabricated double fractures [5,9,10,69,70]. In this study, nine types of crack coalescence were summarized, among which types I to VII are similar to types 3 to 9 of crack coalescence identified by Zhang and Wong [70], respectively. Types VIII and IX are newly discovered types. Table 6 shows the types of crack coalescence seen in this experiment. In type VIII, the interfacial crack plays a connecting role, and the tip of the prefabricated fissure above produces a T₂-type crack that extends vertically downward, while the tip of the prefabricated fissure below produces a T₁-type crack that extends vertically upward. Both the T₂-type crack and the T₁-type crack change the original direction of extension after intersecting the interfacial crack. The T₂-type crack stops extending when it extends downward to the laminar surface, indicating that the laminar surface plays a controlling role in crack extension. A similar phenomenon was observed by Douma et al. [45] in their experiments on soft and hard composite laminae without prefabricated fissures. In the IX-type agglomeration, three cracks are produced at the tip of the upper prefabricated fracture. The T₁-type cracks extended vertically upward, while the S₁-type and S₃-type cracks extended to the lower left and lower right, respectively. In addition, the lower prefabricated fracture did not produce cracks. The two new coalescence types are caused by the laminae of the SHCLRM and their property difference, which may not occur in a single rock mass.

The types of cracks produced at the crack tip showed a strong correlation with the rock properties. For example, the types of cracks produced in the hard layer were mostly tensile cracks, and the types of cracks produced in the soft layer were mostly shear cracks. It can be seen from Table 6 that shear agglomeration occurs only in specimens with soft layers in the middle, and tensile agglomeration occurs only in specimens with hard layers in the middle. According to the shear initiation criterion proposed by Bobet [71], tangential stress and pure shear stress can be calculated as Eqs. (1) and (2), where the three key parameters σ_crit, τ_crit, and r₀ are dependent on the material. The results indicate that tensile cracking starts to sprout when the maximum tangential stress reaches a critical value at a distance r = r₀, and shear cracking starts to sprout when the maximum pure shear stress reaches a critical value at a distance r = r₀. In this test, for the two specimens with the same rock bridge angle but different ways of soft and hard rock combination, the stress field at the crack tip before rupture occurs is the same, but the prefabricated fissure tips produce different types of cracks. These phenomena lead to different crack coalescence patterns, dependent upon the difference in material properties between soft and hard rocks.

(1)({\sigma }_{\theta }{)}_{\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{m}}{{}_{r=r_0}=({\sigma }_{\theta }{)}_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}}_{r=r_0}={\sigma }_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}},

(2)(\tau {)}_{\mathrm{m}\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{m}}{{}_{r=r_0}=(\tau {)}_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}}_{r=r_0}={\tau }_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}.

6 Conclusions

In this study, AE and DIC were used to monitor the crack extension of SHCLRM containing double fissures under uniaxial compression, and the damage mode of the specimens and the AE characteristics of the crack extension process were mainly analyzed. The following conclusions were reached.

1) The damage mode of SHCLRM containing double fissures is related to the nature of the rock formation and the orientation of the prefabricated fissures. The soft layers mostly showed shear damage, and the hard layers mostly showed tensile damage. The first crack always sprouted at the tip of the prefabricated fracture in hard layers.

2) Nine crack coalescence types are summarized, among which VIII and IX are newly discovered types. These two new crack coalescence types are related to the structure of SHCLRM and their property difference.

3) The lamina face plays a controlling role in the crack development. Whether the crack continues to extend when it reaches the lamina face may be related to the mechanical properties and stress field of the rock on both sides of the lamina face.

4) The crack development status can be inferred from the AE signal characteristics. The AE signal of the destruction process of SHCLRM has different variation characteristics. According to the similar principle, the fracture development state of the underground mine tunnel surrounding rock can also be assessed based on the AE signal.

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