Influence of Fissure Number on the Mechanical Properties of Layer-Crack Rock Models under Uniaxial Compression

State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China College of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao 266590, China National Demonstration Center for Experimental Mining Engineering Education, Shandong University of Science and Technology, Qingdao 266590, China


Introduction
With the worldwide economic and social development, the shallow mineral resources are gradually depleted, and the depth of mining or tunnelling is deeper and deeper [1][2][3][4][5].Under the influence of excavation unloading condition, the deformation and failure modes of deep rock mass are different from those of shallow rock mass, which shows obvious discontinuous and nonlinear characteristics [6][7][8][9][10].Phenomena of layer-crack structure, zonal disintegration, rock burst, large deformation, and so on increase in deep exploitation.e layer-crack structures refer to spalling and slabbing structures of surrounding rock before the occurrence of rock bursts in this paper.Case studies have revealed that lots of rock bursts occurred in the high stress concentration area where layer-crack structures exist, as shown in Figure 1 [11][12][13][14][15]. Figures 1(a) and 1(b) show the phenomena of layer-crack structures in brittle rock mass, and Figures 1(c) and 1(d) show the phenomena of layer-crack structures in brittle coal mass.In general, layer-crack structures are closely related with the occurrence of rock bursts in brittle rock or coal mass.
Regarding research on brittle rock mass, theoretical analysis, numerical modeling, laboratory test, and field monitoring methods have been used to study the layer-crack structure and rock burst.In aspect of theoretical analysis, Stacey [16] proposed a simple and empirical criterion for fracture initiation in brittle rock and explained the phenomenon of layer-crack structure formation; Hou et al. [17] theoretically discussed the occurrence mechanism of layercrack rock bursts; Qiu et al. [18] proposed a comprehensive velocity assessment method to evaluate the rock burst wallrock velocity evoked by rock slab flexure sources; and Weng et al. [19] analyzed the occurrence mechanism and timedependency effect of layer-crack rock bursts based on the three-parameter viscoelasticity constitutive relationship and the slabbing thin plate mechanical model.In aspect of numerical modeling, Cai [20] concluded that the generation of tunnel surface parallel fractures and microcracks was attributed to material heterogeneity and the existence of relatively high intermediate principal stress, as well as zero to low minimum principal stress confinement, and Zhang et al. [21] analyzed the influence of intermediate principal stress, stress path, and principal stress axes rotation on the failure mechanism of layer-crack structure using numerical simulation.In aspect of laboratory test, numerous studies investigated the mechanical response of rocks to various loading and unloading conditions, and many layer-crack phenomena before rock bursts in different rocks were reported.For example, He et al. [22,23] divided the process of granite rock burst into four stages and analyzed the AE characteristics during the burst process of limestone through single-face dynamic unloading tests; Gong et al. [11] found that the process of rock burst and the layer-crack failure phenomenon of experimental rock samples were in good accordance with field observations; Zhao et al. [24] studied the influence of unloading rate on the characteristics of strain burst, and test results showed that the layer-crack phenomenon was influenced by the unloading rate; and Du et al. [25] summarized the main triaxial loading and unloading tests methods for determining the mechanical behavior of rock materials and researched the layer-crack phenomenon and rock burst induced by true-triaxial unloading and local dynamic disturbance.
Regarding research on brittle coal mass, scholars also have conducted significant work on the layer-crack phenomenon and rock burst.For example, Zhang et al. [26,27] found that the occurrence of rock burst in Sanhejian Coal Mine was local instability related to the layer-crack structure and analyzed the formation of layer-crack structure through fracture mechanics and laboratory tests; Peng and Lu [28] studied the formation and failure of layer-crack structure of surrounding rock under the influence of stress waves using LS-DYNA software; Bai et al. [29] presented three numerical models, that is, intact coal wall, coal wall including vertical discontinuities, and coal wall including criss-cross discontinuities, to investigate the failure mechanism of layer-crack structure of the coal wall based on extensive field surveys; and Mohamed et al. [13] found that there exist obvious layer-crack structures in the coal wall face through analyzing the current rib support practices in twenty coal mines in the USA.
As a consequence of the above researches, the meaningful results provide a good reference for understanding the mechanisms of layer-crack structure formation and rock burst occurrence.Although the viewpoint that layer-crack structures often exist before the occurrence of rock bursts is widely accepted by scholars, above researches mainly focus on the formation of layer-crack structure and the related influencing factors.ere is less literature trying to study the failure mechanism of layer-crack structure through laboratory test.erefore, four kinds of layer-crack rock models were established in this study for investigating the influence of fissure number on the mechanical properties of layercrack rock models through uniaxial compression tests.During the test process, the digital speckle correlation method (DSCM) and acoustic emission (AE) techniques were applied to record and analyze the information of deformation and failure processes.At last, the failure mechanism of layer-crack structure and the influence of fissure number were discussed based on the test results.2 Advances in Civil Engineering

Specimen Preparation and Testing
2.1.Specimen Preparation.Since it is di cult to directly fabricate joints in intact rocks, the intermittent jointed rocks are generally prepared using arti cial rock-like materials in laboratory tests.In order to carry out experimental study on the mechanical properties of layer-crack models, the specimens were made of high-strength gypsum, and the watercement ratio is 5 : 9. e reason for choosing high-strength gypsum as modeling material is that a wide range of brittle rocks can be easily prepared and the experimental results can be conventionally compared with the previous studies [30,31].Besides, the overall dimensions of the specimens were 50 mm wide × 100 mm height × 50 mm thickness.e height-width ratio is set to 2.0 to guarantee a uniform stress state in all specimens interior.e single ssure geometry is mainly described by three parameters: ssure length, ssure width, and ssure angle (note: the term " ssure" is used to describe the arti cially created aw or crack, and the term "crack" is adopted to describe the new fracture or failure in the loading process).Since the research object of this paper is the layer-crack rock model, the ssure angle is set to 90 °.
Moreover, this paper mainly researches the in uence of ssure number on the mechanical properties of layer-crack rock models, the ssure length and width are all set to 80 mm and 0.5 mm, respectively, but the number of ssures varies.Four kinds of specimens were designed, including intact specimens, one ssure specimen, two ssure specimens, and three ssure specimens, as shown in Figure 2. In order to ensure the accuracy of the test, three specimens were prepared for each kind of specimen.
e nal results were obtained based on the consistency for two or three same specimens.We design this kind of test scheme, because the damage depth of roadway surrounding rock generally is stable and the number of layer-crack plates varies, which means that the test scheme in this study is reasonable.

Test Equipment and Procedure.
e uniaxial compression experiments were conducted on an RLJW-2000 servocontrolled rock pressure testing machine at the College of Mining and Safety Engineering, Shandong University of Science and Technology [32]. is testing system can record stress and strain data automatically.To obtain the mechanical behavior of layer-crack rock models with the change of ssure number under uniaxial compression in detail, the tests were done for four kinds of specimens, as shown in Figure 2. All specimens were loaded with a strain rate of 1 × 10 −5 •s −1 .e tests were carried out under a natural state.
Moreover, the digital speckle correlation method (DSCM) measurement was conducted to analyze the deformation characteristics before peak stress.DSCM is a particle-tracking method that uses digital images to evaluate full-eld displacement.One side of each specimen was selected to be sprayed with black paint as underpainting and then speckled with white spots according to the DSCM method [33].One thing needs to be explained is that if there is debris stripping in the speckle surface, the deformation elds are hard to be processed out.At the same time, the PCI-2 AE testing system (produced by American Physical Acoustic Corporation), with A/D resolution 18 bit and signal-to-noise ratio (SNR) less than 60 dB, was applied to record the AE signals.e experiment system for uniaxial compression tests is given in Figure 3.

Mechanical Properties of Layer-Crack Specimens under Uniaxial Compression
e axial stress-strain curves of rock-like specimens with di erent ssure numbers subject to uniaxial compression stress are illustrated in Figure 4. Table 1 lists the uniaxial compressive strength (σ c ), the elastic modulus (E), and the peak strain (ε 1max ) corresponding to the strain of peak stress of layer-crack specimens with di erent ssure numbers.In Table 1, AV is de ned as the average value.From Figure 4 and Table 1, we can conclude that the ssure number greatly affects the mechanical properties of layer-crack rock models.We will elaborate this problem in detail in the following.

Axial Stress-Strain
Curves.e whole stress-strain curves consist of four stages for layer-crack specimens, including the compaction stage, elastic deformation stage, plastic deformation stage (i.e., stress stiffening and stress softening stages), and failure stage, which are similar to intact specimens, as shown in Figure 4.All the stress-strain curves experience a stress drop phenomenon after peak stress, showing brittle failure characteristics.However, the drop amplitude for intact specimens is larger than that for layer-crack specimens.
e drop amplitude value for intact specimens is 7.65 MPa, but this value for layer-crack specimens varies from 0.73 to 4.01 MPa.In addition, it also illustrates that the fissure number obviously influences the mechanical properties of layer-crack specimens, that is, the uniaxial compressive strength, elastic modulus, and peak strain.
Moreover, there also exists a slight stress drop phenomenon for layer-crack specimens before reaching the peak stress.e larger the fissure number, the earlier the appearance of the slight stress drop phenomenon.For example, when the fissure number is one, two, and three, their corresponding strains are 1.77 × 10 −2 , 1.68 × 10 −2 , and 1.55 × 10 −2 , respectively.Probably, there are two reasons causing this phenomenon.First, the layer-crack rock model is divided into multiple supporting bodies due to the existence of vertical fissures, but it is very difficult for materials to reach complete homogeneity, thus causing the incompatible deformation and asymmetric load of each supporting body during the compression process.One of the supporting bodies might enter into yield failure first while the whole layer-crack rock model still has a good bearing capacity. at is why, the slight stress drop phenomenon might appear before the complete failure of the specimen.Second, the larger the fissure number, the thinner the each supporting body of the layer-crack specimen.In other words, the bearing capacity of supporting bodies decreases as the fissure number increases.erefore, the appearing time of slight stress drop phenomenon decreases with the increase of fissure number.

Influence on Mechanical Properties.
Figure 5 shows the influence of fissure number on the mechanical parameters of layer-crack specimens, and number zero means intact specimen.Compared with intact specimens, the uniaxial compressive strength and elastic modulus of layer-crack specimens all decrease, but the variation law of peak strain is not clear.For example, the uniaxial compressive strength and elastic modulus of intact specimens are 15.9 MPa and 1.55 GPa, respectively, but they are 9.11-12.18  e ssure number in uences the strength and deformation parameters of layer-crack specimens in varying degrees: when the ssure number increases, both the uniaxial compressive strength and elastic modulus decrease with the increase of ssure number, but the peak strain increases rst and then decreases.Speci cally speaking, when the ssure number increases from one to three, the uniaxial compressive strength and elastic modulus decrease from 12.18 MPa to 9.11 MPa and from 1.44 GPa to 0.90 GPa, respectively, whose corresponding dropping percentages are 25.21% and 37.50%.
e peak strain, however, increases from 1.98 × 10 −2 to 2.14 × 10 −2 rst and then decreases to 1.93 × 10 −2 as the ssure number increases from one to three.

3.3.
In uence on Failure Modes. Figure 6 shows the failure modes of intact specimens and layer-crack specimens.Splitting failure accompanied with local shear failure is the main failure mode for intact specimens, as shown in Figure 6(a).It can be seen from Figure 6(b) that the failure mode of one ssure specimen is similar to intact specimens but mainly is the splitting failure of one to two of the two supporting bodies divided by the vertical ssure.However, the failure mode of two ssure specimens is splitting failure or shear failure of one to three of the supporting bodies, as shown in Figure 6(c), which is similar to three ssure specimens.e failure mode of three ssure specimens is also splitting failure or shear failure of one to four of the supporting bodies, as shown in Figure 6(d).
In addition, it can also be seen from Advances in Civil Engineering body B accompanied with the shear failure of supporting body C, as shown in Figure 6(c).is phenomenon might be caused by the incompatible deformation and asymmetric load of each supporting body, because the layer-crack rock model could not reach complete homogeneity.
3.4.Influence on Deformation Fields.Figure 7 shows the horizontal and vertical deformation fields of intact specimens and layer-crack specimens before peak stress from the DSCM measurement.As shown in Figure 7(a), from the compaction stage to peak stress, the deformation of specimen surface for intact specimens is almost uniform.In the compaction stage, the deformation of specimen surface for layer-crack specimens is also uniform, as shown in Figures 7(b)-7(d).When entering into the elastic deformation stage, however, the deformation field of specimen surface for layer-crack specimens begins to show a nonuniform phenomenon due to the noncomplete homogeneity.is is to say, deformation gradient difference appears in the specimen surface for layercrack specimens in the elastic deformation stage.As entering into the yield stage, the nonuniform deformation phenomenon becomes more serious.
Moreover, Figures 7(b)-7(d) also shows that the fissure number greatly affects the deformation field of layer-crack specimens, especially the appearing time of the nonuniform deformation phenomenon in the specimen surface.For example, the nonuniform deformation phenomenon appears when the axial stress reaches at 0.4-0.6σc for one fissure specimen or two fissure specimens, but for three fissure specimens, this phenomenon appears when the axial stress reached at 0.2-0.4σc .As shown in Figures 7(c) and 7(d), the deformation field cannot be recorded at 0.8-1.0σc for two fissure specimens or three fissure specimens due to this phenomenon, which might lead to debris stripping in the speckle surface of supporting bodies.In general, the DSCM results reveal that under the same loading and lithology conditions, if the number of layer-crack plate increases, the instability probability will be enhanced, that is, the occurrence risk of rock bursts increases.8, a further study to look into the AE activity law of intact specimens and layer-crack specimens during the uniaxial loading process was conducted.As shown in Figure 8(a), the AE behavior of intact specimens mainly consists of three stages: minor active stage, quiet stage, and major active stage.At the beginning of the axial loading process, only a few AE events could be recorded, which is owing to the closure of primary defects.e initial AE activity process is defined as the minor active stage.As the axial load continues increasing, the AE behavior enters into the second stage, that is, the quiet stage.During this stage, the AE behavior is quite stable accompanied with the elastic deformation stage.However, the AE events continue increasing rapidly after the quiet stage, which means the AE behavior starts to enter into the major active stage.In this stage, the inner damage of the intact specimen develops, which induces the rapid increase of AE events.In general, the AE activity law of intact specimens is similar to other research results.

Influence on AE Characteristics. According to Figure
According to Figures 8(b)-8(d), the AE behavior pattern of layer-crack specimens is characterized by three peaks, showing a great difference with intact specimens.ere also exists the minor active stage caused by the closure of primary defects before the first peak stage.However, it is worth mentioning that new cracks begin to generate during the first peak stage and that the quiet stage seems to have disappeared.A more active stage, that is, the second peak stage, just follows the first peak period, revealing that the crack growth rate is accelerated.In the second peak stage, the phenomenon of slight stress drop is more obvious except for three fissure specimens.With the continuing increase of axial load, the AE events reach the largest until the layer-crack specimen fails with an appearance of through cracks.At the same time, more and more AE events are produced during this process, and that is the third peak stage.In addition, Figures 8(b)-8(d) also reveal that the fissure number greatly influences the AE characteristics of layer-crack specimens.e AE events are denser and denser with the increase of fissure number in each peak stage, especially in the first and second peak stages.is result also might be induced by the incompatible deformation and asymmetric load of each supporting body.

Discussions
Scholars have reached a consensus that the layer-crack structure makes an essential contribution to rib spalling or rock burst in brittle coal or rock mass [13,[34][35][36][37][38][39]. Figure 9 illustrates the general occurrence mechanism of rock burst related to the layer-crack strucutre.e occurrence mechanism can be described as follows [40][41][42]: first, the layer-crack structure forms under the compression stress concentration of surrounding rock induced by the excavation unloading, as shown in Figures 9(a) and 9(b); second, the compression stress concentration further leads to the buckling deformation of layer-crack plates (i.e., rock plates divided by these vertical macro-cracks) and to the continuous accumulation of strain energy stored in layer-crack plates, as shown in Figure 9(c); third, when the strain energy stored in layer-crack plates reaches the storage limit, dynamic instability might take place under the influence of external disturbance, as shown in Figure 9(d).Although significant work has been done on the formation process of layer-crack structure and rock burst, there is little work trying to reveal the failure mechanism of layer-crack structure in detail, that is, to explain the process illustrated in Figures 9(c) and 9(d).erefore, this section mainly tries to explain this issue.
e experimental results show that the bearing capacity of layer-crack rock models distinctly decreases compared with intact rock models, which means that the instability probability is higher for layer-crack rock models.is phenomenon is also testified by the AE results.Except for the bearing capacity, DSCM results illustrate that when entering into the elastic deformation stage, nonuniform deformation phenomenon begins to appear in the specimen surface of layercrack specimens.However, the deformation field for intact specimens is uniform from the compaction stage to peak Advances in Civil Engineering stress.In general, the experimental results in Section 3 reveal two apparent reasons causing the dynamic instability of layercrack structure, that is, the nonuniform deformation and the asymmetric load of supporting bodies.erefore, the failure mechanism of layer-crack structure can be explained from the point of nonuniform deformation and asymmetric load.As shown in Figure 10, a simple failure mechanism of layer-crack structure is established under the uniaxial  Advances in Civil Engineering compression condition.Based on Figure 6, we have known that the failure of each supporting body of layer-crack specimens is stochastic, and thus assuming that the strain of supporting body B is larger than that of the supporting body A in Figure 10(a), that is, the stress σ B acting on the supporting body B is larger than that σ A acting on the supporting body A.
As the compression stress continues concentrating, the supporting body B enters into the yield failure rst while the supporting body A does not reach its limit bearing capacity. at is to say, the whole layer-crack structure still has a good bearing capacity, as shown in Figure 10(b).At the same time, the stress concentration degree of supporting body A increases rapidly due to the decrease of bearing capacity of supporting body B. e stress concentration exerted on the whole layercrack structure mainly transfers onto the supporting body A. Consequently, a large stress gradient di erence exists among the supporting bodies A and B. When the supporting body A reaches its limit bearing capacity, dynamic instability of the whole layer-crack structure will occur under the in uence of disturbance stress, as shown in Figure 10(c).
e failure mechanism of layer-crack structure containing more than two supporting bodies is similar.Furthermore, the ssure number (i.e., number of supporting bodies) also greatly a ects the stability of layer-crack structure according to the experimental results.e bearing capacity of layer-crack structure decreases as the ssure number increases, which means that the occurrence risk of dynamic instability also increases if the number of supporting bodies increases under the same stress and lithology conditions.ere are two main reasons causing this result.First, the appearing time of nonuniform deformation phenomenon decreases as the ssure number increases.us, one or more than two supporting bodies of the layer-crack structure will enter into the yield failure stage earlier.e stress concentration of supporting bodies, not coming into the yield failure stage, will be aggravated.Second, zones of stress gradient di erence increase as the ssure number increases.at is to say, unstable zones in the layer-crack structure will increase.erefore, if the ssure number of layer-crack structure increases, the occurrence risk of dynamic instability also increases.
Based on the analysis of the failure mechanism of layercrack structure, it reveals that rock bursts induced by the layer-crack structure can be mitigated by reducing the Advances in Civil Engineering number of layer-crack plate, avoiding the incompatible deformation and asymmetric load, and decreasing the impact energy.ree guidelines for controlling rock bursts induced by the layer-crack structure are proposed.First, control the number of layer-crack plate by optimizing the support system.Second, make the deformation of the layercrack structure more compatible by enhancing the bearing capacity of these layer-crack plates coming into the process of plastic deformation or yield failure. ird, decrease the strain energy stored in the mainly supporting layer-crack plates of layer-crack structure and in other possible energy provided bodies.Although preventing the formation of layer-crack structure is the best way for mitigating rock bursts, it is almost impossible.us, the three guidelines proposed in this section are rational.is paragraph only provides three guidelines, and there are still lots of work that needs to be done for finding out these suitable and applicable mitigation strategies, methods, and techniques, for mitigating rock bursts induced by the layer-crack structure.

Conclusions
In this study, the mechanical properties of layer-crack rock models with different fissure numbers were investigated with uniaxial compression tests based on the phenomenon that rock bursts generally occur in stress concentration areas where layer-crack structures often exist.During the experimental process, the DSCM and AE techniques were applied to record and analyze the deformation and failure processes.e following conclusions can be drawn: (1) Compared with intact rock models, the bearing capacity, deformation field, and AE behavior of layercrack rock models show a great difference.First, the bearing capacity of layer-crack rock models is lower.Second, the nonuniform deformation phenomenon exists from the elastic deformation stage to peak stress for layer-crack rock models during the compression process but does not appear from compaction stage to peak stress for intact rock models.ird, the AE behavior of intact rock models consists of three stages, that is, active stage, quiet stage, and major active stage, but for layer-crack rock models, the AE behavior patter is characterized by three peaks without quiet stage after the minor active stage.
(2) e failure modes of intact rock models and layercrack rock models are similar.Splitting failure accompanied with local shear failure is the main failure mode for intact rock models.For layer-crack rock models, splitting failure or shear failure of one or more than two of the supporting bodies is the mail failure mode.In addition, the failure of each supporting body of layer-crack rock models is stochastic.(3) e fissure number greatly affects the mechanical properties of layer-crack rock models.When the fissure number increases from one to three, the uniaxial compressive strength and elastic modulus decrease about 25.21% and 37.50%, respectively.Meanwhile, the appearing time of nonuniform deformation phenomenon in the specimen surface also decreases as the fissure number increases.For example, the nonuniform deformation phenomenon appears when the axial stress reaches at 0.4-0.6σc for one fissure specimen or two fissure specimens, but for three fissure specimens, this phenomenon appears at 0.2-0.4σc .In aspect of AE behavior, the AE events are denser and denser with the increase of fissure number in each peak stage, especially in the first and second peak stages.(4) e failure mechanism of layer-crack structure can be described as follows.First, as the compression stress continues concentrating, one or more than two of the supporting bodies enter into the yield failure first while the remaining supporting bodies still have a good bearing capacity. is result causes the rapid increase of local stress concentration degree in the layer-crack structure.At the same time, some zones of stress gradient difference also exist.Second, when the remaining supporting bodies reach their limit bearing capacity, dynamic instability of the whole layer-crack structure will occur under the influence of disturbance stress.Furthermore, if the number of supporting bodies increases, the occurrence risk of dynamic instability will be enhanced.

Figure 2 :Figure 3 :
Figure 2: Sketch of test specimens.(a) Sketch of layer-crack rock models and (b) part of the test specimens.

Figure 10 :Figure 9 :
Figure 10: Schematic diagram of the failure mechanism of layer-crack structure: (a) under compression concentrating condition, (b) yield failure of supporting body B, and (c) dynamic instability of the whole layer-crack structure.

Table 1 :
Figure 4: Axial stress-strain curves of layer-crack specimens with different fissure numbers.Test results of basic mechanical properties of layer-crack specimens under uniaxial compression.