# Progressive Failure and Acoustic Emission Characteristics of Red Sandstone with Different Geometry Parallel Cracks under Uniaxial Compression Loading

Authors: Xizhen Sun; Fanbao Meng; Ce Zhang; Xucai Zhan; He Jiang
Journal: Advances in Materials Science and Engineering
 (2021)

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## Abstract

The geometric distribution of initial damages has a great influence on the strength and progressive failure characteristics of the fractured rock mass. Initial damages of the fractured rock were simplified as parallel cracks in different geometric distributions, and then, the progressive failure and acoustic emission (AE) characteristics of specimens under the uniaxial compression loading were analyzed. The red sandstone (brittle materials) specimens with the parallel preexisting cracks by water jet were used in the tests. The energy peak and stress attenuation induced by the energy release of crack initiation were intuitively observed in the test process. Besides, three modes of rock bridge coalescence were obtained, and wing crack was the main crack propagation mode. The wing crack and other cracks were initiated in different loading stages, which were closely related to the energy level of crack initiation. The propagation of wing crack (stable crack) consumed a large amount of energy, and then, the propagation of shear crack, secondary crack, and anti-wing crack (unstable crack) was inhibited. The relationship between the crack propagation mode and the geometric distribution of existing cracks in the specimen was revealed. Meanwhile, the strength characteristic and failure mode of fractured rock with the different geometric distributions of preexisting crack were also investigated. The energy evolution characteristics and crack propagation were also analyzed by numerical modeling (PFC2D).


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## Body

## 1. Introduction

In underground engineering, rock mass as the main geological body has a lot of randomly distributed macroscopic and microscopic initial damages [1, 2]. The propagation and unstable failure of initial damage can induce engineering geological disasters under the mining influence [3–5]. The initial damage can be conceptualized as rock fracture in the laboratory, and the fracture instability characteristics and progressive failure of rock mass with different geometric distributions have a great significance for the prediction and control of fractured rock instability disasters [6].In experimental tests, brittle rock-like materials with different crack geometric distribution are widely used, such as gypsum [7–11], concrete [12, 13], and glasses [14]. The crack angle, rock bridge mode, and crack distribution have been proved as the main factors affecting the crack initiation, propagation, and coalescence. However, artificial materials which have great differences with the initial rock materials are mainly used in these tests. The difference between artificial materials and initial rock leads to the diversity of the crack propagation.Studies on the rock (sandstone, marble, etc.) fracture propagation were mainly performed under different loading modes. Zhang and Zhao [15] studied the fracture toughness and failure micromechanisms of marble under different loading rates. Yang et al. [16] and Wu et al. [17] investigated the crack propagation of sandstone with oval flaws and a single hole under the uniaxial loading. Xu et al. [18] analyzed the compression-shear behaviors of brittle rocks under the static-dynamic loading by lab tests and numerical modeling. Zhou et al. [19] conducted the progressive cracking processes of granite with preexisting flaws. Vaneghi et al. [20] obtained the effects of loading amplitude and stress on the mechanical properties of sandstone and granodiorite. Li et al. [21] analyzed the dynamic strength and fracturing behavior of marble specimens with a single flaw. Hao et al. [22, 23] studied the time-dependent development of the excavation damaged zone (EDZ) around underground diversion tunnels in a columnar jointed rock mass and studied the fracture behaviour and crack propagation features of coal under coupled static-dynamic loading conditions. The single crack under the dynamic loading and tensile crack fatigue failure has been highlighted in most recent research of rock fracture propagation behaviors, while the complex crack propagation characteristics were rarely studied.Red sandstone with preexisting cracks was used to simulate the parallel joints of the fractured rock mass. The fracture propagation tests of specimens with different geometric distributions under the uniaxial compression loading were conducted by the AG-X250 loading system and PCI-2 AE system. The energy evolution process was analyzed by PFC2D numerical modeling. The progressive failure, AE characteristics, and energy evolution were obtained. Research results provide a reference for the prevention and control of rock mass instability under similar engineering conditions (uniaxial compression loading and parallel joints).


## 2. Specimen Preparation and Experimental Setup

### 2.1. Specimen Preparation

The size of the red sandstone specimen was 50 mm (width) × 22 mm (thickness) × 100 mm (length,L1). The water jet cutting system was employed to obtain preexisting cracks, which were 20 mm in length (L2) and 1 mm in aperture (A) (Yongda Dynamo Electric, Foshan, Guangzhou, China, as shown in Figure 1), and the angle with the horizontal direction was 45°, as shown in Figure 2. Three groups of specimens (three specimens in each group) were made with different geometric distributions. Table 1 lists the main parameters of red sandstone.Figure 1
Water jet cutting system (the cutting accuracy and repetitive positioning accuracy were ±0.1 mm and ±0.05 mm, respectively; the working water pressure was less than 0.4 MPa).Figure 2
Red sandstone specimens with preexisting cracks: (a) Group 1; (b) Group 2; (c) Group 3.Table 1
The main parameters of red sandstone.
Density2.40 g/cm3MaterialOriginal brittle rock from Junan County, Linyi City, ChinaParticle sizes0.07–0.30 mm [24]Uniaxial compressive strength77.95 MPaSpecimen size: 50 mm (diameter) × 100 mm (height)Tangent elastic modulus6.55 GPaUniaxial compression loading tests under the ISRM standardUniaxial tensile strength3.76 MPaSpecimen size: 50 mm (diameter) × 25 mm (height)Brazilian disc test under the ISRM standard


### 2.2. Loading and Monitoring System

The loading controlled mode (simulated the stress increase in underground engineering excavation) was set at an average loading rate of 0.05 kN/s by the AG-X250 loading system [25]. The crack propagation process was observed by using a high-speed video camera. In this test, the PCI-2 AE system (one Nano 30 sensor was used, as shown in Figure 3) was used to monitor the AE characteristics, and the couplant was applied between the sensors and the specimen surface to ensure the quality of the AE signal [11]. The AE parameters are shown in Table 2. The ambient noise and loading system noise were less than 30 dB (the threshold value was 40 dB). The AG-X250 loading system, PCI-2 AE system, and high-speed video camera (Figure 3) were used to collect data synchronously until the failure of specimens.Figure 3
Loading and monitoring system.Table 2
The AE parameters setup.
Resonant frequency100–400 kHzSampling frequency106 sThreshold value40 dBFloating threshold value5 dB


## 2.1. Specimen Preparation

The size of the red sandstone specimen was 50 mm (width) × 22 mm (thickness) × 100 mm (length,L1). The water jet cutting system was employed to obtain preexisting cracks, which were 20 mm in length (L2) and 1 mm in aperture (A) (Yongda Dynamo Electric, Foshan, Guangzhou, China, as shown in Figure 1), and the angle with the horizontal direction was 45°, as shown in Figure 2. Three groups of specimens (three specimens in each group) were made with different geometric distributions. Table 1 lists the main parameters of red sandstone.Figure 1
Water jet cutting system (the cutting accuracy and repetitive positioning accuracy were ±0.1 mm and ±0.05 mm, respectively; the working water pressure was less than 0.4 MPa).Figure 2
Red sandstone specimens with preexisting cracks: (a) Group 1; (b) Group 2; (c) Group 3.Table 1
The main parameters of red sandstone.
Density2.40 g/cm3MaterialOriginal brittle rock from Junan County, Linyi City, ChinaParticle sizes0.07–0.30 mm [24]Uniaxial compressive strength77.95 MPaSpecimen size: 50 mm (diameter) × 100 mm (height)Tangent elastic modulus6.55 GPaUniaxial compression loading tests under the ISRM standardUniaxial tensile strength3.76 MPaSpecimen size: 50 mm (diameter) × 25 mm (height)Brazilian disc test under the ISRM standard


## 2.2. Loading and Monitoring System

The loading controlled mode (simulated the stress increase in underground engineering excavation) was set at an average loading rate of 0.05 kN/s by the AG-X250 loading system [25]. The crack propagation process was observed by using a high-speed video camera. In this test, the PCI-2 AE system (one Nano 30 sensor was used, as shown in Figure 3) was used to monitor the AE characteristics, and the couplant was applied between the sensors and the specimen surface to ensure the quality of the AE signal [11]. The AE parameters are shown in Table 2. The ambient noise and loading system noise were less than 30 dB (the threshold value was 40 dB). The AG-X250 loading system, PCI-2 AE system, and high-speed video camera (Figure 3) were used to collect data synchronously until the failure of specimens.Figure 3
Loading and monitoring system.Table 2
The AE parameters setup.
Resonant frequency100–400 kHzSampling frequency106 sThreshold value40 dBFloating threshold value5 dB


## 3. Experimental Results and Discussion

### 3.1. Progressive Failure Laws

According to stress strain characteristics, the test process was divided into three stages: initial compression, elastic deformation, and peak failure, as shown in Figure4. The crack propagation was concentrated in the peak failure stage. The wing crack of Group 1 and Group 3 was initiated in the elastic deformation stage (the wing crack of Group 2 was initiated near the peak stress), and axial stress decreased transitorily. The average stress of each group changed with geometry distributions. The average peak stress of Group 2 (15.11 MPa) was the lowest one, and that of Group 1 (23.12 MPa) was the highest one. Peak stress and their average are shown in Figure 5.Figure 4
Three stages in the test process.Figure 5
Peak stress and the average.The homoplastic characteristics were observed in each group. Figures6–8 show the typical progressive failure modes of these groups.Figure 6
The progressive failure mode of Group 1: (a) 8.55 MPa; (b) 20.70 MPa; (c) 28.12 MPa.
(a)(b)(c)Figure 7
The progressive failure mode of Group 2: (a) 9.64 MPa; (b) 10.08 MPa; (c) 11.79 MPa.
(a)(b)(c)Figure 8
The progressive failure mode of Group 3: (a) 6.85 MPa; (b) 15.73 MPa; (c) 20.24 MPa.
(a)(b)(c)In this section, the preexisting crack was denoted bypc, wing crack by wc, shear cracks by sc, the mixed cracks (containing two crack modes: shear and tensile) by mc, the anti-wing crack by ac, the secondary crack (initiated from the newly generated cracks during the tests) by sec.Figure6 shows the progressive failure process of Group 1. When the first group of axial stress reached 8.55 MPa, wing cracks were initiated. At this time, the axial stress was reduced to 8.54 MPa. As the stress continued to increase to 20.70 MPa, mixed crack propagation resulted in the rock bridge coalescence. When the axial stress reached 28.12 MPa, the specimen was damaged.Figure7 shows the progressive failure process of Group 2. When the second group of axial stress reached 9.64 MPa, wing cracks were initiated with the rock bridge coalescence and anti-wing cracks were propagated simultaneously. The wing crack and secondary crack (initiated from the neonatal crack or the other part of preexisting crack except for the crack tip) were propagated when the stress was increased to 10.08 MPa. When the axial stress reached 11.79 MPa, the specimen was damaged.Figure8 shows the progressive failure process of Group 3. When the third group of axial stress reached 6.85 MPa, the wing cracks were initiated. The anti-wing crack was initiated when the stress was increased to 15.73 MPa. When the axial stress reached 20.24 MPa, the wing crack and anti-wing crack were propagated to the rock bridge coalescence, and the specimen was damaged.The wing crack was the main propagation mode in the tests, accompanied by anti-wing crack, shear crack, secondary crack, and mixed crack. The wing crack as stable propagation mode was initiated primarily in the elastic deformation stage, and secondary crack and shear crack as unstable propagation modes were mostly initiated nearby the peak failure stage. Besides, there were three types of the rock bridge coalescence: mixed crack, anti-wing crack, and anti-wing crack-secondary crack.


### 3.2. AE Instability Characteristics

The AE phenomenon can reveal the microcrack propagation in the rock failure process, and it also was used as an effective way to investigate the rock fracture [26–28]. The AE parameters from the lab tests can be used as the key indexes for the disaster prevention and control of fractured rock mass instability [29]. The energy index which defined in the study of [4] was employed to investigate the instability characteristics in this test. Compared with other parameters (e.g., amplitude), the energy index can reflect the energy size of crack initiation and propagation effectively [30]. The coevolution law of energy index and axial stress was obtained in the crack propagation process.The typical specimens with the different geometric distributions of preexisting cracks were analyzed under the uniaxial compression loading, as shown in Figure9. When the wing crack of the specimen started to crack, the energy index of the three groups was 1670, 6940, and 108, respectively. At the same time, the stress of the first group of specimens decreased with crack initiation. When the rock bridge coalescence appeared, the energy index of the first and second group was 6050 and 6940. When the specimens were damaged, the energy index of three groups of specimens was 9380, 15353, and 11927, respectively.Figure 9
Results of the uniaxial compression loading test for red sandstone with the different geometric distributions: (a) Group 1; (b) Group 2; (c) Group 3.
(a)(b)(c)Table3 shows the stress and energy index of different crack modes. The energy was accumulated in the specimen internal during the loading process, and the energy was released during the crack initiation, rock bridge coalescence, and specimen failure, leading to the energy index peak and stress attenuation. The released energy was determined by the crack modes.Table 3
The stress and energy index of different crack modes.
Crack modeGroup 1Group 2Group 3ParametersWing crack8.559.646.85Stress (MPa)16706940108Energy indexRock bridge coalescence20.709.64—Stress (MPa)60506940—Energy indexSpecimen failure28.1211.7920.24Stress (MPa)93801535311927Energy index


## 3.1. Progressive Failure Laws

According to stress strain characteristics, the test process was divided into three stages: initial compression, elastic deformation, and peak failure, as shown in Figure4. The crack propagation was concentrated in the peak failure stage. The wing crack of Group 1 and Group 3 was initiated in the elastic deformation stage (the wing crack of Group 2 was initiated near the peak stress), and axial stress decreased transitorily. The average stress of each group changed with geometry distributions. The average peak stress of Group 2 (15.11 MPa) was the lowest one, and that of Group 1 (23.12 MPa) was the highest one. Peak stress and their average are shown in Figure 5.Figure 4
Three stages in the test process.Figure 5
Peak stress and the average.The homoplastic characteristics were observed in each group. Figures6–8 show the typical progressive failure modes of these groups.Figure 6
The progressive failure mode of Group 1: (a) 8.55 MPa; (b) 20.70 MPa; (c) 28.12 MPa.
(a)(b)(c)Figure 7
The progressive failure mode of Group 2: (a) 9.64 MPa; (b) 10.08 MPa; (c) 11.79 MPa.
(a)(b)(c)Figure 8
The progressive failure mode of Group 3: (a) 6.85 MPa; (b) 15.73 MPa; (c) 20.24 MPa.
(a)(b)(c)In this section, the preexisting crack was denoted bypc, wing crack by wc, shear cracks by sc, the mixed cracks (containing two crack modes: shear and tensile) by mc, the anti-wing crack by ac, the secondary crack (initiated from the newly generated cracks during the tests) by sec.Figure6 shows the progressive failure process of Group 1. When the first group of axial stress reached 8.55 MPa, wing cracks were initiated. At this time, the axial stress was reduced to 8.54 MPa. As the stress continued to increase to 20.70 MPa, mixed crack propagation resulted in the rock bridge coalescence. When the axial stress reached 28.12 MPa, the specimen was damaged.Figure7 shows the progressive failure process of Group 2. When the second group of axial stress reached 9.64 MPa, wing cracks were initiated with the rock bridge coalescence and anti-wing cracks were propagated simultaneously. The wing crack and secondary crack (initiated from the neonatal crack or the other part of preexisting crack except for the crack tip) were propagated when the stress was increased to 10.08 MPa. When the axial stress reached 11.79 MPa, the specimen was damaged.Figure8 shows the progressive failure process of Group 3. When the third group of axial stress reached 6.85 MPa, the wing cracks were initiated. The anti-wing crack was initiated when the stress was increased to 15.73 MPa. When the axial stress reached 20.24 MPa, the wing crack and anti-wing crack were propagated to the rock bridge coalescence, and the specimen was damaged.The wing crack was the main propagation mode in the tests, accompanied by anti-wing crack, shear crack, secondary crack, and mixed crack. The wing crack as stable propagation mode was initiated primarily in the elastic deformation stage, and secondary crack and shear crack as unstable propagation modes were mostly initiated nearby the peak failure stage. Besides, there were three types of the rock bridge coalescence: mixed crack, anti-wing crack, and anti-wing crack-secondary crack.


## 3.2. AE Instability Characteristics

The AE phenomenon can reveal the microcrack propagation in the rock failure process, and it also was used as an effective way to investigate the rock fracture [26–28]. The AE parameters from the lab tests can be used as the key indexes for the disaster prevention and control of fractured rock mass instability [29]. The energy index which defined in the study of [4] was employed to investigate the instability characteristics in this test. Compared with other parameters (e.g., amplitude), the energy index can reflect the energy size of crack initiation and propagation effectively [30]. The coevolution law of energy index and axial stress was obtained in the crack propagation process.The typical specimens with the different geometric distributions of preexisting cracks were analyzed under the uniaxial compression loading, as shown in Figure9. When the wing crack of the specimen started to crack, the energy index of the three groups was 1670, 6940, and 108, respectively. At the same time, the stress of the first group of specimens decreased with crack initiation. When the rock bridge coalescence appeared, the energy index of the first and second group was 6050 and 6940. When the specimens were damaged, the energy index of three groups of specimens was 9380, 15353, and 11927, respectively.Figure 9
Results of the uniaxial compression loading test for red sandstone with the different geometric distributions: (a) Group 1; (b) Group 2; (c) Group 3.
(a)(b)(c)Table3 shows the stress and energy index of different crack modes. The energy was accumulated in the specimen internal during the loading process, and the energy was released during the crack initiation, rock bridge coalescence, and specimen failure, leading to the energy index peak and stress attenuation. The released energy was determined by the crack modes.Table 3
The stress and energy index of different crack modes.
Crack modeGroup 1Group 2Group 3ParametersWing crack8.559.646.85Stress (MPa)16706940108Energy indexRock bridge coalescence20.709.64—Stress (MPa)60506940—Energy indexSpecimen failure28.1211.7920.24Stress (MPa)93801535311927Energy index


## 4. Numerical Modeling Tests and Analysis

The PFC2D (version 5.0) was used to simulate the crack propagation characteristics [31–34]. The parameter calibration of numerical modeling was based on the uniaxial compressive test (ISRM standard), and the calibration results are shown in Figure 10. The number of particle ball was 10788, and the physical mechanical parameters are in Table 4.Figure 10
The calibration results between numerical modeling and laboratory test.Table 4
Physico-mechanical parameters of red sandstone specimens.
ParameterValueSpecimen size (H×D) (mm)50×100Particle diameter ratio (Rmin/Rmax)1Stiffness ratio1Contact modulus of the particle (GPa)1.60Parallel bond deformation modulus (GPa)1.60Densityρ/Kg m32500Coefficient of friction0.15Particle contact damping0.2Bonding tensile strength/MPa3.24Parallel bond stiffness ratio1The cohesive energy, strain energy, friction energy, kinetic energy, and boundary energy were analyzed in the numerical modeling process (other energy is negligible). The boundary energy was the energy on the model. The strain energy and cohesive energy were related to crack initiation and propagation. As the main energy mode, strain energy and cohesive energy increased with the deterioration degree of the model. The friction energy reacted after the crack initiation, and the friction effect was the main supplier of the residual strength. The kinetic energy was closely related to the dynamic equilibrium in the model.The geometric distribution of cracks had a greater effect on energy parameters, as shown in Figure11. The boundary energy, cohesive energy, and strain energy all increased gradually before the peak stress, however, the energy growth gradually decreased with the change of crack geometric distributions of specimens from Group 1 to Group 3. At the same time, the peak energy of specimens from Group 1 to Group 3 also decreased gradually. Before the peak stress, the kinetic energy and friction energy of the microparticles increased slowly. It indicated that the boundary energy before the peak stress was mainly provided by the cohesive energy and strain energy, and the energy supply of the samples with three geometric distributions was gradually weakened. Subsequently, the cohesive failure occurred, leading to an increase in friction between particles, especially the particles near the macrocracks. Meanwhile, the appearance of microcracks between particles weakened the coherence of particles, and the equilibrium of particle force was broken. The velocity of these particles increased gradually and the kinetic energy increased accordingly, even a few particles at the boundary of the model can completely break away from the bonding force and the model. After the peak stress, the cohesive energy and strain energy began to decrease, and the friction energy and kinetic energy began to increase rapidly.Figure 11
The energy evolution characteristics during numerical modeling process: (a) integrated specimen; (b) Group 1 specimen; (c) Group 2 specimen; (d) Group 3 specimen.
(a)(b)(c)(d)The crack propagation modes obtained in numerical modeling were consistent with those in the laboratory tests. The preexisting crack tips were initiated due to the stress concentration. The tensile crack was the main crack mode, accompanied by shear crack, anti-wing crack, and secondary crack. However, the mechanism and material homogeneity between numerical modeling and laboratory tests had some differences, and the results varied in two conditions (laboratory tests and numerical modeling), as shown in Figure12.Figure 12
The crack propagation characteristics of the numerical modeling: (a) specimens in Group 1; (b) specimens in Group 2; (c) specimens in Group 3.
(a)(b)(c)


## 5. Discussion of Fracture Patterns

For specimens with the different geometric distributions of the preexisting cracks, the strength and propagation modes were extremely different in the lab tests and the PFC2D (version 5.0) was used to simulate the crack propagation characteristics.In the first group, the wing cracks and mixed crack initiation led to the stress attenuation and propagated stably, which rarely affected the strength of the specimens. The energy was consumed partially during the crack propagation process, preventing the premature coalescence of the rock bridge. The rock bridge coalesced in the peak failure stage, in which the axial strength was the highest. Besides, the crack propagation mode was relatively simple.In the second group, the wing cracks and anti-wing crack were initiated nearby peak stress, and their propagation led to the obvious stress attenuation. The specimen failure occurred after the propagation of wing cracks and anti-wing crack. In this group, the crack propagation mode was the most complicated; the rock bridge was more likely to coalesce, leading to the rapid failure of these specimens. Therefore, the strength was the minimum one.In the third group, the preexisting cracks were propagated independently at the initial loading stage, and the wing cracks were initiated and propagated steadily. The consumed energy inhibited the initiation of anti-wing cracks and secondary cracks. The anti-wing cracks were initiated nearby the peak stress and greatly influenced the strength of the specimen. The propagation mode of specimens was relatively complicated.The energy concentration occurred at the preexisting crack tips during the tests, and the initiation of wing crack occurred at the low or relatively low energy level. Therefore, the wing cracks were initiated and propagated steadily in the elastic deformation stage, and the strength of specimen was rarely affected. More energy was required for the initiation of anti-wing cracks and secondary cracks, and most of them were initiated nearby the peak stress. As a result, the rapid failure of specimens was caused. When the same energy was input, the energy level of shear crack initiation can be fleetly reached in the system without the dissipated energy of stable crack propagation. Therefore, the energy consumption of stable crack propagation restricted the unstable crack initiation to a certain extent, and the propagation mode and strength were changed with the different geometric distributions of cracks in specimens.


## 6. Conclusions

The crack propagation tests of red stone specimens with different geometric distributions were conducted under the uniaxial compression loading, and progressive failure laws and AE characteristics were investigated in lab tests. The conclusions are drawn as follows:(1)
The wing cracks are the main propagation mode, accompanied by the anti-wing cracks, mixed cracks, and secondary cracks. Three modes of rock bridge coalescence are observed: mixed crack (Group 1), anti-wing crack (Group 2), and anti-wing crack-secondary crack (Group 3). The energy is released by crack initiation and accumulated during the loading process, resulting in the energy index peak and the stress attenuation (the carrying capacity of the specimen decreases shortly). The energy level is determined by the crack propagation modes.(2)
The crack initiation and propagation include the following processes: energy concentration at the tip, crack initiation, and energy release. The energy released by wing crack initiation is lower than that by other cracks (anti-wing cracks, secondary cracks, and mixed cracks), and most of them are observed in the elastic deformation stage. Meanwhile, most of the other cracks are initiated in the peak failure stage, which is also determined by the energy level of crack initiation.(3)
The crack propagation modes are affected by the geometric distribution of preexisting crack in specimens. The difficulty of rock bridge coalescence and the stability of crack propagation are the key factors to determine the specimen strength and failure mode. The stable crack propagation consumes the energy and reduces the energy level, and the unstable crack initiation is inhibited partially. The crack propagation stability of specimens in Group 2 is the lowest, and the strength of specimens in Group 2 is the smallest.(4)
The results of PFC simulation results show that the boundary energy, cohesive energy, and strain energy of the specimen increase gradually with the loading before the peak stress, and the microcracks caused by cohesive failure are relatively few. A large number of particles are bonded and broken at the peak stress, and the movement and friction between particles increase gradually. After the peak stress, the cohesive energy and strain energy begin to decrease, and the friction energy and kinetic energy begin to increase rapidly.



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