Study on Mechanical Properties of Fractured Sandy Mudstone Based on Triaxial Compression Experiment

Abstract

The technological requirements for mining are becoming more and more complex as underground coal mining depth increases. The issue that the concentration of mining stress causes an increase in the degree of rock fracture formation in the stope is one of them, and it has a significant impact on the mine’s production safety and efficiency. Using a pseudo-triaxial compression experimental platform, the effects of confining pressure on the strength, deformation, and fracture propagation route of fractured sandy mudstone were investigated in order to explore the mechanical characteristics of fractured rock mass. The findings demonstrate that the stress and strain curves of split sandy mudstone vary from those of intact specimens in that they are stepped and have several stress decreases. High frequency and low energy levels are released by fractured sandy mudstone, while high frequency and low energy levels are released by unbroken rock. The strength of sandy mudstone is less sensitive to confining pressure when prefabricated fissures are present. Specimens with fractures have a roughly 80% reduction in shear strength while confining pressure remains constant. The fracture propagation route of the intact rock is parallel to the section where the highest shear stress is found, whereas the fracture propagation path of the fractured sandy mudstone progressively expands from the constructed fracture tip to the specimen border. The degree of fracture development in fractured sandy mudstone is greater under the same stress mechanism, and the rock breaks more readily.

1. Introduction

Complex geological conditions exist in coal mines that are mined underground. The rock is in its original three-way stress condition before mining and its stress state changes after mining. The major stress differential will cause rock fissures, which will subsequently result in tensile shear failure, diminishing the surrounding rock’s stability and adversely affecting the safety of subterranean production [1,2,3,4,5,6,7]. Disasters including roof breakage, roof water inrush, and gas outbursts are among the mining operations mishaps that are directly linked to the formation of nearby rock fissures [8,9,10,11,12]. Studying the impact of fractures on the physical properties of the surrounding rock in stope is thus very important.

Numerous tests and numerical simulation studies have been conducted to investigate the mechanical characteristics of fractured rock, primarily from two angles: varying loading techniques and varying fracture incidence. In his research, Wang Yuan [13] examined the mechanical characteristics and compression failure forms of fractured rock bodies at varying loading rates. He discovered that, in cases where fracture occurrence is constant, the strength of the rock will increase as the loading rate increases, and that the strength of the rock is most affected by a fracture inclination angle of 30°. The mechanical characteristics and energy changes of fractured rock under uniaxial compression were investigated by Wang Erbo [14]. The findings indicated that the likelihood of tensile shear mixed failure in the rock increases with the size of the fracture inclination. Prefabricated fractures reduced the energy storage limit of the rock specimens and had an impact on their rate of energy dissipation. Wang Dianxin [15] examined the strength and deformation characteristics of rock under various stress routes and investigated the impact of arc fractures on the mechanical properties of sandstone using traditional uniaxial compression and triaxial compression tests. The findings demonstrate that arc fractures have a higher peak strength under triaxial compression than they do with unloading confining pressure. The rock strength is weakened by the linear crack’s arch height. Luo Danyi [16] investigated the connection between rockburst and fracture incidence at open face using a prefabricated granite single crack experiment. The findings of the study indicate that the granite’s strength is more degraded with a smaller crack dip angle and that the elastic energy produced by a rockburst decreases with increasing crack proximity to the open face. The elastic energy generated by the rock burst is clearly amplified when the crack is filled with resin. In a uniaxial experiment, Wang Zhaohui et al. [17] investigated the stress–strain relationship of fractured rock. They discovered that the rock exhibits a bimodal form on the stress–strain curve under uniaxial pressure, that the fracture expansion has the optimal expansion Angle, and that tensile shear causes the majority of the rock’s damage within this range. In order to simulate the complicated failure morphology of rock with fracture, Wang Susheng [18] used an enhanced phase-field fracture model. He also conducted a theoretical analysis of the coupling connection between the phase field and the fracture displacement field.

Regarding the occurrence of fractures, Tang Shuangchen [19] investigated the mechanical characteristics of both intact and cross-fractured rock using a uniaxial compression experiment. The findings of the experiment demonstrated that the tensile inverse airfoil crack dominated the fracture development and that the peak strength and elastic modulus of the cross-fractured rock were relatively small under uniaxial compression. In order to characterize the geometry of granite blasting cracks, Saba Gharehdash [20] integrated the SPH damage model with the finite element approach to determine the rock failure state and derive the real-time rock permeability. Using the DFN discrete grid modeling method, Etienne Lavoine [21] quantified the stress perturbations on the fracture network scale. The study’s findings demonstrated that the rock failure stress fluctuated in relation to the fracture’s density, with the greater the density, the greater the perturbations, which could be quantitatively predicted using a tensor. Ana Carolina Loyola [22] enhanced the fracture mechanics model of rocks by evaluating the REV of fractured rocks using the central limit theorem and by proposing a method to decrease the amount of reference volume simulations. In their study of the mechanical properties of fractured rock mass under biaxial compression, Wang Xiaoming et al. [23] found that, in comparison to uniaxial compression, there is a certain amount of lateral strain limitation and a delay in the overall failure of the fractured rock mass under biaxial compression. The macroscopic expression of the microscopic interaction of the contact forces between particles is the stress–strain relationship of cracked rock mass.

In conclusion, a large number of researchers both domestically and internationally have thoroughly studied the mechanical characteristics of rock with fissures under various circumstances, producing fruitful findings. However, the majority of current fractured rock mechanical tests concentrate on uniaxial and biaxial fractures, with little attention paid to the triaxial fractured rock’s mechanical characteristics. Additionally, underground coal mining has a wide variety of rocks. Few experimental studies on sandy mudstone with low strength are conducted at the moment, and the majority of studies concentrate on sandstone and granite with high rock strength. As a result, the study target for this work was polished prefabricated rock samples that had cracks in them. The mechanical characteristics of the cracked rock samples were then examined under various confining pressures, and a comparison analysis was carried out with entire rock samples. The findings of the study may ensure safe and effective underground mining operations and provide a theoretical foundation for the stability management of surrounding rock that is broken.

2. Experimental Instrument and Scheme Design

2.1. Preparation of Rock Samples

Several specimens with and without cracks are prefabricated for control experiments, as shown in Figure 1. The roof sandy mudstone of the 761 working face of the Linhuan coal mine in Anhui province is chosen in this paper to create standard cylindrical specimens with a height of 100 mm and a diameter of 50 mm from the roof rock collected underground. Among them, the specimen with the fracture has a 30 mm length, 4 mm thickness, and a 30 degree angle. It is located in the center of the column’s side. The number “WL100-X” in the picture refers to a rock specimen that has a crack, whereas “W100-X” refers to a specimen that does not.

2.2. Experimental Scheme and Equipment

The experimental investigation employed the French Rock600-50 (Top Industrie, Vaux-le-Pénil, France) three-axis multi-field coupling mechanical apparatus, which included a three-axis pressure chamber, axial loading system, measurement control system, and test software (refer to Figure 2). The confining pressure is loaded by hydraulic pressure to guarantee that the rock specimen’s lateral confining pressure is consistent in all directions. Simultaneously, to mitigate the interference resulting from hydraulic oil penetration of the specimen, the specimen’s side was coated with thermal insulation rubber film, and a circumferential deformation sensor was affixed to its surface to monitor the circumferential strain. The acoustic emission sensor was installed at the base of the cylinder block to facilitate data acquisition and to monitor the AE energy change throughout the entire loaded failure process of the specimen.

Five confining pressure conditions were established in the experiment: σ2 = σ3 = 0 MPa, 8 MPa, 16 MPa, 24 MPa, and 30 MPa, respectively. One group of specimens with fractures and one group of specimens without cracks were subjected to confining pressure in each group. According to

Table 1. Triaxial test specimen parameters of fractured sandy mudstone.

Test Piece Number	Whether There Is Crack	Confining Pressure (MPa)
WL100-1	Yes	0
WL100-2	Yes	8
WL100-3	Yes	16
WL100-4	Yes	24
WL100-5	Yes	30
W100-1	No	0
W100-2	No	8
W100-3	No	16
W100-4	No	24
W100-5	No	30

, a total of 10 groups of loading experiments were conducted. The rate was set to 0.01 mm/min, and the axial loading mode was displacement loading. The residual strength was progressively maintained until the rock specimen was damaged, at which point it was discharged. The stress loading continued. The acoustic emission signal data collection and tension loading were conducted concurrently.

3. Analysis of Triaxial Test Results

3.1. Analysis of Stress–Strain and Acoustic Emission Characteristics of Specimens

The failure of rock under loading is often accompanied by a large amount of strain energy release and fracture expansion, which can be captured by triaxial compression experiment and numerical simulation [24,25,26,27]. The axial and circumferential stress–strain curves of fractured sandy mudstone were derived by summing the data collected under various confining pressure conditions in order to investigate the mechanical properties and energy evolution of the material. The acoustic emission characteristic parameters are subject to change as a result of the axial strain, as illustrated in Figure 3. The tensile strain is assigned a negative value, while the compressive strain is assigned a positive value.

Numbers W100-1 and WL100-1 in Figure 3 correspond to stress–strain curves under a confining pressure of 0 MPa, and so on. There are five groups of test curves under different confining pressures. In these curves, ε1 represents the axial strain value of the specimen, ε2 represents the circumferential strain value of the specimen, and εv represents the volumetric strain value of the specimen. Additionally, σb represents the crack closure stress of the specimen, σc represents the yield stress of the specimen, and σt represents the peak stress of the specimen. The figure also includes three acoustic emission characteristic parameters: impact count rate, AE accumulated energy, and ringing count. As shown in Figure 3, when rock specimens with cracks are subjected to an axial stress loading less than σb, they undergo crack compaction stage where both axial strain (ε1) and volume strain (εv) increase while generating tensile strain (ε2) perpendicular to the maximum principal stress in circumferential direction. The number of acoustic emission events during this stage is small and cumulative AE energy increases slowly. When axial stress loading exceeds σb, there is an approximately linear relationship between axial stress and axial strain indicating that rock is in elastic deformation stage where compressive strain as well as tensile strain maintain a linear increase. Before the stress loading reaches the yield stress point σc, the number of acoustic emission specimens is small. The micro-cracks in the rock do not expand, and the cumulative AE energy increases faster than that in the compaction stage. When the stress is loaded to the yield stress point σc, it enters the plastic deformation stage. The strain curve deviates from linearity and reaches its peak at σt. After reaching the yield point, both toroidal strain and volumetric strain turn from compression to tensile deformation, indicating that rock dilatancy occurs after yielding. Subsequently, as fissures rapidly develop post peak, elastic strain energy is released leading to a sharp increase in acoustic emission events and an abrupt rise in cumulative AE energy when fissure expansion occurs rapidly. Finally, both toroidal and volumetric tensile strains reach their maximum value near σt.

The mechanical properties and acoustic emission characteristics of intact rock specimens are essentially the same as those of fractured rock during the compaction stage and elastic deformation stage. Based on the series of accumulated AE energy, it is observed that the strain energy stored by intact rock specimens during deformation is greater than that of fractured rocks. During the post-peak crack acceleration stage, there is an intensive release of energy from the entire specimen after reaching peak strength. The energy series of the entire specimen is higher than that of a cracked rock specimen, leading to a rapid decrease in strength.

The stress–strain relationship of fractured sandy mudstone differs from that of intact rock. The axial strain ε1 exhibits an inverted triangle shape near the peak stress, while the curve of intact rock samples shows an inverted U shape under the same confining pressure. This indicates that the failure form of fractured sandy mudstone is closer to brittle failure than that of intact rock. Additionally, after the loading exceeds the elastic deformation stage, a stress drop occurs in the rock specimen with cracks before reaching peak stress, which is caused by the closure of pre-existing cracks exceeding their yield strength σc. After fracture closure, occlusal contact under the fracture surface produces normal stress, strengthening the bearing capacity of the rock and causing a subsequent rise in stress value. Post-peak stress drop phenomena are more frequent in fractured sandy mudstone samples, with each stress drop accompanied by a surge in acoustic emission energy. In comparison to intact rock samples, energy release in fractured sandy mudstone occurs gradually step by step whereas it is released intensively as a single event for intact rocks; indicating that fractured rock samples have broken several times after reaching peak stress. According to acoustic emission data, both energy series and number of events for cracked samples are smaller than those for intact ones; suggesting that micro-cracks are more distributed in intact rock samples.

Based on the test results of specimens with cracks and intact specimens under varying confining pressures, it is observed that as the confining pressure increases, the values of σc and σt for all rock samples become closer. The σc of intact rock samples clearly increases, while the slope of the straight line intersecting σt decreases, and the strain required to reach the peak point becomes larger. This suggests a transition from brittleness to ductility in rock failure under confining pressure, leading to an increase in carrying capacity. Conversely, for specimens with cracks, plastic deformation is not significant initially; however, when the confining pressure exceeds 8 MPa, stress loading before reaching the peak point becomes more linear and stress drop amplitude reduces. This indicates an improvement in bearing capacity for rocks with cracks at higher confining pressures. These findings are consistent with research by Wang Yiyang [20] on fractured rocks under different confining pressures. Furthermore, analysis of ε2 and εv data under different confining pressures reveals that ε2 for specimens with cracks is larger than that of intact specimens due to expansion of tensile wing cracks dominated by prefabricated cracks. In contrast, failure in intact specimens tends towards instantaneous shear failure.

3.2. Influence of Confining Pressure on Specimen Strength and Deformation

It is evident from the examination of stress–strain curves that, under varying confining pressures, the mechanical characteristics of specimens with fractures and unbroken specimens differ. As seen in Figure 4, the peak strength of specimens under various confining pressures was extracted for examination in order to more intuitively depict the impact of confining pressure on the strength of sandy mudstone.

Figure 4 illustrates how the peak strength σt of the sandy mudstone specimen rises as confining pressure does. A specimen with cracks has a lower peak strength than an intact specimen, and its average strength is only 15% of the intact specimen’s strength. When the confining pressure is 8 MPa, the strength of both intact and fractured specimens rises the highest in comparison to the strength under uniaxial conditions. There is a 53% increase in peak strength for whole specimens and a 28% increase for broken specimens. It is evident that confining pressure has less of an impact on the strength of cracked sandy mudstone.

The peak axial and circumferential strains of intact and fractured sandy mudstone at various confining pressures are shown in Figure 5. The picture shows that the axial strain of the intact specimen progressively rises with increasing confining pressure, whereas the axial strain of the fractured specimen gradually decreases. This suggests that prefabricated fractures are more difficult to break and shut at higher confining pressures. The impact of fracture on the collapse of rocks progressively diminishes.

The lateral strain of the intact rock specimen is positively associated with the confining pressure, while the lateral strain of the fissure specimen rises first and subsequently declines as the confining pressure increases, based on the peak circumferential strain data. Consistent with the axial strain data, the dilatation of fissured rock reduces as the confining pressure loading exceeds 16 MPa. The rock is less susceptible to expansion deformation when axial strain is reduced, which also encourages circumferential strain reduction.

The data of cracked and intact specimens at the elastic deformation stage were fitted and analyzed in order to investigate the impact of confining pressure on the elastic modulus E of rock. As a result, the elastic modulus E of sandy mudstone under various confining pressures was obtained, as illustrated in Figure 6. The picture illustrates a positive correlation between the confining pressure and the elastic modulus E of both the crack specimen and the whole specimen. In other words, a higher confining pressure corresponds to a higher elastic modulus. The intact specimen’s growth slope is greater than the fractured specimen’s, suggesting that the intact specimen’s elastic modulus is more susceptible to confining pressure. The average elastic modulus of unbroken sandy mudstone under the same confining pressure is 3.51 times that of cracked rock. The aforementioned findings demonstrate that confining pressure can increase the elastic modulus of sandy mudstone. Conversely, the elastic modulus of fractured rock is less susceptible to confining pressure because of the higher density of microcracks and numerous secondary cracks brought on by tensile stress during the failure process. On the other hand, the medium inside the rock is more compact, the secondary fractures have low density, and the whole specimen contains shear cracks throughout the failure process. Therefore, the resistance to deformation of cracked sandy mudstone is much lower than that of whole rock, the larger the confining pressure.

The greatest stress at which a rock can return to its initial condition upon unloading is known as the yield strength of rock, or elastic limit [28]. It is also a crucial metric for assessing the mechanical characteristics of rock. The rock will undergo a transition in volume deformation from compression to tensile deformation when the axial stress loading surpasses the yield stress. This will result in the appearance of volume strain at an inflection point, and the accompanying axial stress is the yield stress, or σc [29]. As an example, the specimen’s stress–strain curve at 0 MPa confining pressure is used, as shown in Figure 7.

Figure 7 compares, analyzes, and positions the axial strain, axial stress, and volume strain of the whole specimen W100-1 under uniaxial conditions. Under uniaxial conditions, the specimen’s total yield stress value (σc) is 34.58 MPa, whereas the highest compressive volume strain is 0.0138. Using this technique, the yield stress of samples with unbroken rocks and fractures under various confining pressures was determined and graphed, as Figure 8 illustrates.

The yield stress variations of whole and fractured rocks under various confining pressures are shown in Figure 8. It is evident that the yield strength of both unbroken and fractured rocks rises as confining pressure increases. The density of the internal structure of intact rock is reflected in the larger yield strength growth rate of intact rock compared to fractured rock, which is compatible with the peak strength study findings. The rate at which the σc values of intact and fractured rocks decrease is often slower as the confining pressure rises over 16 Ma. This is because, under increasing confining pressure, the strain hardening stage is reduced, the yield stress of rocks progressively approaches the peak stress, and the failure of rocks gradually becomes ductile.

3.3. Influence of Confining Pressure on Shear Strength of Specimens

The triaxial compression failure of rock results in a high number of tensile and shear fractures. Shear failure occurs when the shear stress on the shear plane is greater than the shear strength, resulting in the shear fractures. When assessing the mechanical characteristics of rock, shear strength is a crucial metric to consider. The molar Coulomb criterion, which represents shear strength τ, is used to calculate the shear strength of both whole rock and broken sandy mudstone:

$${\mathsf{\tau }=\mathrm{m}\mathsf{\sigma }}_3{+\mathsf{\sigma }}_0$$

(1)

The uniaxial compressive strength of the rock specimen, expressed in MPa, is denoted by σ0 in Formula (1), and m is the effect coefficient of confining pressure on sandy mudstone. The following is the connection between the cohesive force C, the internal friction angle (φ) of the rock, and the m value:

$$\phi =\arcsin {\displaystyle \frac{m-1}{m+1}}$$

(2)

$$C={\sigma }_0{\displaystyle \frac{1-\sin \phi }{2\cos \phi }}$$

(3)

When Formulas (2) and (3) are combined, it is evident that the bigger the rock’s uniaxial compressive strength, the higher its cohesion C, and the greater the value of m, the greater the internal friction angle and the rock’s shear strength. A statistical analysis of the m values of both whole and cracked rock samples at various confining pressures is shown in Figure 9.

Figure 9 shows that, while the range of variations between the two is limited, the m value of intact sandy mudstone progressively falls with an increase in confining pressure, whereas that of cracked sandy mudstone gradually rises. It can be seen that the sensitivity of the m value to confining pressure is very low, much lower than the sensitivity of peak strength to confining pressure, as the m value change degree of the intact rock specimen under different confining pressures is 5.7%, while the m value change degree of the fractured rock specimen under different confining pressures is only 3.1%. Under various confining pressures, the shear strength of both whole and fractured rock is computed and averaged. The average cohesive force C1 is 12.4 MPa, the average internal friction angle φ1 is 35°, and the shear strength of complete rock is τ1 = 3.84σ3 + 49.38, according to the data. The average cohesion force C2 is 3.9 MPa, the average internal friction angle φ2 is 6°, and the shear strength τ2 = 1.26σ3 + 8.52. According to the findings, with the same confining pressure, the shear strength of cracked sandy mudstone is only 20% that of unbroken rock.

3.4. Effect of Confining Pressure on Crack Propagation Characteristics of Specimens

The process of ongoing crack growth and buildup that leads to macroscopic fracture is fundamental to rock failure. Based on the mechanical reasons of fractures, cracked and undamaged sandy mudstones are classified into three types to explain their failure patterns under varying confining pressures: Three types of cracks: shear, tensile, and secondary. The tensile crack typically runs parallel to the direction of the maximum principal stress, the shear crack typically runs at a specific angle to it, and the secondary crack, which is related to the degree of stress concentration at the crack tip, typically widens after the main crack forms. Figure 10 displays the fracture development features of several rock specimens.

The failure mechanisms of entire specimens under various confining pressures are W100-1~5. Figure 10a illustrates that the majority of the specimen’s fractures are found on the cylinder’s top and bottom surfaces. On the side of the cylinder of specimen W100-1, there were two conjugate shear fractures and two secondary cracks after the specimen’s failure under uniaxial compression. The shear fracture and one secondary crack were oriented at a 23° angle with respect to the specimen’s axis. A single shear crack dominates the fracture pattern as confining pressure increases, and the angle between the shear crack and the axial stress is 45 degrees, suggesting a deflection of the maximum shear stress in one direction. Simultaneously, the surrounding secondary cracks almost vanish, suggesting that the presence of confining pressure raises the rock’s particle density and the shear fracture tip’s initiation stress.

The failure forms of specimens with fractures under various confining pressures are WL100-1~5. Figure 10b illustrates that the primary failure mode of specimens with cracks is tensile fractures near prefabricated cracks. At the prefabricated fracture tip of the WL100-1 specimen, four secondary tensile cracks developed, and the crack propagation route progressively advanced towards the cylinder’s top and lower boundary surfaces. In comparison to the intact rock specimens, the WL100-2~5 specimens produced more shear cracks with increasing confining pressure, extending from the specimen boundary to the precast crack and connecting with the tensile crack surrounding the precast crack. This suggests that the rock fracture occurs in a tension–shear mixing mode under varying confining pressures.

4. Conclusions

(1)

While the stress–strain curve of intact sandy mudstone is mostly smooth, the stress–strain curve of fractured sandy mudstone is stepped and experiences a stress decrease throughout the failure process. According to the acoustic emission data, intact sandy mudstone releases strain energy at a low frequency and high energy level, while cracked sandy mudstone releases strain energy at a low frequency and high energy level.

(2)

Prefabricated cracks lessen the susceptibility of the strength of the sandy mudstone to confining pressure, and the dilatation and deformation of the fractured sandy mudstone are restricted by the confining pressure. Prefabricated fractures reduce the shear strength of rock and increase the likelihood of shear failure under the same confining pressure.

(3)

The crack propagation patterns of fractured sandy mudstone vary from those of intact sandy mudstone. The crack propagation of fractured sandy mudstone is characterized by tensile cracks centered on prefabricated fractures, while unbroken rock is dominated by through-shear cracks. When the confining pressure is steady, the secondary fissure of sandy mudstone with fissure develops quicker, increasing the rock’s fracture degree.

(4)

Limited to the experimental conditions, this paper initially investigates the mechanical properties of sandy mudstone with fractures under the same lateral confining pressure. Subsequently, it will examine the influence of two lateral principal stresses on the strength of sandy mudstone and consider the impact of fracture length, angle, and location on its mechanical properties. This approach aims to ensure that the experimental results are more consistent with the actual situation of underground mining.