Confining Pressure Tests Research Articles

Study on the Influence of Matrix on Mechanical and Failure Characteristics of Miscellaneous Fill

Abstract The matrix has a great influence on the mechanical and failure characteristics of the miscellaneous fill. Based on the laboratory medium-sized triaxial test, the confining pressure tests of 100, 200, and 400 kPa were carried out on the miscellaneous fill under three kinds of matrix with block stone content of 30 %, and the influence of the matrix on the mechanical properties of miscellaneous fill was analyzed. A biaxial test with a confining pressure of 200 kPa was carried out on three kinds of matrix miscellaneous fill samples using the particle flow method, and the influence of miscellaneous fill on the failure characteristics was studied. The test results show that the relation curve of the miscellaneous fill (σ1–σ3)∼εa can be considered as a hyperbola. The miscellaneous fill whose matrix is clay and silty soil always shows shear shrinkage. When the confining pressure is 100 kPa, the miscellaneous fill in the sandy soil matrix shows the property of shrinkage first and then dilatancy. When the confining pressure is 200 kPa and 400 kPa, it shows shear shrinkage. Through numerical simulation, it is found that when the matrix is clay, the shear zone is obvious and the shear failure surface is stable. When the matrix is silty soil, the contact cracks become thinner and the shear bands increase. When the matrix is sandy soil, compared with clay matrix, the overall crack is finer and the shear fracture surface is irregularly distributed.

Mechanical properties of cemented backfill under different unloading rates after cured at different temperatures

In the process of deep filling mining in coal mine, due to the influence of mining and other factors, the confining pressure on both sides of cemented backfill decreases. It is necessary to master the mechanical characteristics of cemented backfill under unloading conditions in different temperature environments to ensure the stability of cemented backfill. To simulate the unloading process of cemented backfill in the deep highland environment of coal mine, triaxial unloading confining pressure tests of cemented coal gangue- fly ash backfill at different unloading rates after curing at different temperatures (20 ℃, 35 ℃ and 50 ℃) were carried out by the Rock Triaxial Testing System, and the mechanical characteristics of cemented backfill unloading were systematically studied. The findings of the study show that, for the same unloading rate, the peak strength of cemented backfill specimen reduces initially before increasing with curing temperature rises. After curing at the same temperature, the peak strength of cemented backfill specimen varies exponentially with an increase in unloading rate. The deformation modulus and volume strain at different unloading rates satisfy an exponential function relationship, while the generalized Poisson's ratio and volume strain satisfy a quadratic function relationship. Under unloading conditions, there was no large fracture or fragmentation of cemented backfill, only cracks appeared on surface. At the same unloading rate, cemented backfill specimen cured at 35 ℃ and 50 ℃ exhibits significantly more shear cracks after failure compared to the material cured at 20 ℃. As the unloading rate increases, the proportion of shear cracks generated during unloading failure of cemented backfill specimen cured at 35 ℃ and 50 ℃ gradually increases. In addition, the theoretical curve of the four-stage cemented backfill unloading constitutive model established in sections is essentially compatible with experimental curve, confirming the theoretical model's reasonableness. The study's findings provide a theoretical basis for evaluating stability of cemented backfill after unloading in deep high temperature (35–50 ℃) environments.

Effects of initial unloading level on the mechanical, micro failure and energy evolution characteristics of stratified rock mass under triaxial unloading confining pressure

In order to study the strength, micro crack distribution and energy evolution characteristics of stratified rock mass under unloading confining pressure conditions, triaxial compression tests and triaxial unloading confining pressure tests at different initial unloading levels were carried out. The experimental results indicated that the triaxial unloading confining pressure plus axial stress is a stress path between the stress state of uniaxial compression and triaxial compression. With the increasing initial unloading level, the specimen is closer to the stress state of triaxial compression, the peak stress, peak axial strain, peak circumferential strain and peak volume strain increase linearly, Poisson’s ratio decreases linearly, failure type of specimens shows 4 typical characteristics. When the bedding plane inclination is 45°, 3D reconstruction and quantitative characterization of micro cracks of stratified rock mass specimens are conducted based on CT scanning results. Variations of area fraction along the specimen height show 3 typical characteristics. The stratified rock mass mainly stores and dissipates energy before the peak stress, and mainly releases and dissipates energy after the peak stress under different conditions. With the increasing initial unloading level, the input energy, elastic energy, dissipative energy and energy dissipation rate at the peak stress increase approximately linearly.

Cyclic confining pressure and rock permeability: Mechanical compaction or fines migration

The apparent rocks permeability, measured under cyclic loading, tends to constantly decrease with each subsequent loading/unloading cycle, the main reason for this, the researchers consider irreversible deformations. However, this understanding is not complete, as attention is not paid to the method of determining the permeability. Under cyclic loading, permeability is measured by fluid flow, which is able to carry colloids and they can clog pore throats and reduce permeability, but this is not taken into account in the study of porous rocks. Colloidal migration is also not taken into account in routine core tests, although colloids can significantly reduce the apparent permeability of rocks during migration. Also it is impossible to determine exactly which of the factors (mechanical compaction or colloid migration) contributed to the change in apparent permeability. The purpose of this research is to provide experimental evidence that under cyclic loading, permeability decreases not only due to mechanical compaction, but also due to colloid migration within the porous medium. For this task, a methodology has been developed, the feature of which is that between loading/unloading cycles, the core is blowning with a large pressure gradient. It has been established that under cyclic loading, the apparent permeability of rock samples changes as a result of colloid migration up to 20 %. The dynamics of permeability becomes unpredictable and weakly depends on the confining pressure when changing the direction and regime of the gas flow. At the end of the multi-cycle confining pressure test, the apparent permeability of 3 out of four core samples, despite the decrease during injection, recovered to the initial value which also confirms that the apparent permeability has affected by colloid migration. A mechanism for changing the apparent permeability during gas injection and cyclic confining pressure is proposed. The outcomes indicate that colloid migration should be taken into account during core tests not only in cyclic loading but also in routine coreflooding tests.

Experimental investigation on the triaxial unloading mechanical characteristics of sandstone immersed in different brines

In this study, the stress–strain curves of sandstone soaked in 5% NaCl and 5% K2SO4 solutions under different loading and unloading paths were obtained by carrying out different paths of unloading confining pressure tests on sandstone specimens. Thereafter, the strength, deformation, and failure characteristics of the specimens were analysed. First, the unloading capacity of sandstone specimens soaked in 5% NaCl was found to be greater than those soaked in 5% K2SO4, and the unloading amount increased in the order of increasing axial pressure unloading confining pressure < constant axial pressure unloading confining pressure < constant deviatoric stress unloading confining pressure. When unloading the confining pressure, the strain change rate of the sandstone specimens soaked in 5% K2SO4 was greater than that of the sandstone specimen soaked in 5% NaCl, and the strain change rate had the following trend: increasing adding axial pressure and unloading confining pressure > constant axial pressure unloading confining pressure > constant deviatoric stress unloading confining pressure. The deformation modulus and Poisson's ratio of the sandstone specimens during unloading exhibited an exponential change with increasing unloading ratio. The deformation modulus and Poisson’s ratio of the sandstone soaked in 5% NaCl during the unloading period was respectively greater and less than those of the sandstone soaked in 5% K2SO4. Second, the total energy absorbed by 5% NaCl soaked sandstone specimens was always less than that soaked in 5% K2SO4 under different unloading paths. The effect of immersing the specimens in different solution on acoustic emission and failure characteristics was unclear. Compared with the dry sandstone specimens, the sandstone specimens soaked in brine solutions lower mineral composition and higher, clay mineral content. The contents of plagioclase and calcite contents in the sandstone specimens soaked in 5% NaCl was similar to those in dry sandstone, but no plagioclase or calcite was detected in the specimens soaked in 5% K2SO4.

A multiscale framework for atomistic–continuum transition in nano-powder compaction process using a cap plasticity model

In this paper, a computational atomistic-continuum multiscale framework is presented for the simulation of the nano-powder compaction process using a cone-cap plasticity model. The atomistic representative volume element (RVE) comprises of nano-powder particles that is used to perform the molecular dynamics analysis in order to capture the mechanical behavior of nano-powder material. The periodic boundary condition is applied over the atomistic RVE to satisfy the inter-scale kinematic compatibility, and the stress tensor is derived according to the inter-scale energetic consistency principals from the nanoscale at each material point of the powder component. A multiscale framework is performed using the constitutive law of the coarse-scale domain enhanced by the molecular dynamics results of the fine-scale domain. The coarse-scale constitutive law is conformed to the cone-cap plasticity model as a robust and capable constitutive relation in modeling the powder compaction process, in which the cap plasticity parameters are determined using the data derived from the molecular dynamics simulations. The mechanical response of nano-powder particles within the RVE is obtained from the confining pressure test and true-triaxial test, where a sensitivity analysis is accomplished on the computed parameters of the cone-cap plasticity model. The enhanced cap plasticity model is then employed to simulate various industrial nano-powder components that illustrates the performance and efficiency of the proposed multiscale computational homogenization method.

Determination method of rock characteristic stresses based on the energy growth rate

Introduction: Precisely determining the characteristic stress value of a rock progressive failure process has important theoretical and practical significance for reasonably defining the rock deformation and failure stage, mechanical mechanism, and design parameters.Methods: Based on the energy characteristics in the process of rock deformation and failure, this paper proposes a new method of rock characteristic stress (EGR) around the index of elastic energy storage capacity, elastic energy growth rate, and dissipative energy growth rate. First, the rationality of the new method is verified by the indoor uniaxial and triaxial loading test data of coal and marble. Second, five different determination methods, namely, lateral strain method, lateral strain difference method, crack strain method, energy dissipation rate method, and volumetric strain method, are compared to further verify the scientific nature of the new method. Finally, the method is applied to the conventional triaxial unloading confining pressure test and true triaxial loading and unloading test of marble, and the new method is fully extended to verify its universality.Results: The results show that the theoretical basis of the EGR characteristic stress determination method is rigorous and sufficient, and the value process is objective and reasonable. Compared with different methods, the EGR method can accurately define the process of rock asymptotic failure, and its corresponding characteristic stress level is well-consistent and in a reasonable range.Discussion: The EGR method is applicable to the conventional triaxial unloading confining pressure test and true triaxial loading and unloading test and has good universality.

A dynamic constitutive model for high-density rigid polyurethane foam subjected to impact loading

This study experimentally and numerically investigated the dynamic response of high-density rigid polyurethane foam (RPUF). Firstly, drop-weight tests were conducted under three impact velocities, 2.42 m/s, 3.43 m/s, and 4.85 m/s. Test results showed that the dent depth and absorbed energy rise as impact velocity increases. Then the constitutive model for high-density RPUF based on an ideal elastoplastic constitutive model is proposed based on the measured mechanical properties, including quasi-static uniaxial compression tests, quasi-static uniaxial tensile tests, triaxial confining pressure tests, and split-Hopkinson pressure bar tests. Finally, the numerical simulation of the drop-weight tests was conducted. It was shown that the proposed dynamic constitutive model can accurately describe the dynamic performance of a high-density RPUF subjected to impact loading.

Analysis of Crack-Characteristic Stress and Energy Characteristics of Sandstone under Triaxial Unloading Confining Pressure

The deformation and failure of underground engineering are usually caused by unloading. In this work, triaxial unloading confining pressure tests are carried out to simulate the failure process of rock mass caused by unloading, analyze the crack-characteristic stress, and study the energy evolution of rock under unloading and the pre-peak and post-peak energy characteristics combined with the energy theory. The results show that, when the confining pressure increases from 5 MPa to 20 MPa, crack closure stress σcc, crack initiation stress σci, dilatancy stress σcd, and peak stress σp are 6.34 times, 2.75 times, 1.93 times, and 1.66 times higher than the original, respectively. By comparing the increase in crack-characteristic stress, it can be found that the confining pressure has a large effect on the crack closure stress and crack initiation stress, while the dilatation stress and peak stress have relatively little influence. From the perspective of energy evolution, the pre-peak axial absorption energy U1 increases exponentially, the elastic energy Ue is similar to U1, and the circumferential consumption energy U3 and dissipation energy Ud are small. After reaching the peak stress, the growth rate of U1 decreases slightly, Ue decreases rapidly, and U3 increases rapidly but only as a small fraction of the total energy, while Ud grows almost exponentially and rapidly becomes the main part of the energy. Under each crack-characteristic stress state, the energy characteristic parameters gradually increase with the increase in confining pressure, which is manifested by the increase in slope in the linear fitting formula of energy characteristic parameters. The release process of the releasable elastic energy after the peak stress can be divided into three stages of “slow–fast–slow”, and the energy release process shows an obvious confining pressure effect.

Mechanical Response and Failure Characteristics of Granite under Unloading Conditions and Its Engineering Application

Excavation in engineering significantly changes the initial stress state of rock, which makes rock inevitably in complex unloading conditions, thus it is of great significance to make a profound investigate of the mechanical characteristics of rock under unloading condition. This paper carried out two different stress paths including conventional triaxial compression and unloading confining pressure tests on granite specimen from Sanshandao gold mine, and systematically analyzed the strength characteristics, deformation characteristics and energy evolution laws. Results show that the brittle failure characteristic of granite under unloading confining pressure are more obvious, and the peak strength, axial deformation and other parameters are smaller than those of triaxial compression test. Especially the deformation modulus decreases with the increase of unloading confining pressure, which is no longer a constant parameter in the sense of continuum. Therefore, the unloading-induced weakening coefficient of engineering rock mass is proposed, and the relationship between the coefficient and the reduction ratio of confining pressure is quantified. Then, the unloading-induced weakening algorithm is developed in FLAC3D to simulate the stability of a deep mine stope. It is found that results of the unloading-induced weakening model are much closer to the engineering practice, which has certain theoretical and practical reference significance for the stability analysis of rock mass engineering.

Constant void ratio vs. constant confining pressure tests on partially saturated silty soil

The presence of soil solids, water, and air complicates understanding unsaturated soil dynamics. A thorough understanding of unsaturated soil behavior is essential for the fruitful design of slopes, embankments, and retaining structures. A series of constant void ratio and constant confining pressure triaxial compression tests were carried out under constant water content conditions (pore air pressure drained and pore water pressure undrained) to study the shear strength and deformation characteristics of a partially saturated silty soil. Test specimens were prepared with a water content of 15%, 20% (Optimum water content), and 25%, with the corresponding degree of saturation of 37, 49, and 62.5%. The degree of compaction of all specimens was kept at 83% while the dry density was 1.29 g/cm3, and the void ratio was around 1.045. All the samples were isotropically consolidated under 500kPa by keeping deviatoric stress at 0kPa. The constant void ratio test results showed that the deviatoric stress reached a peak value followed by a sudden decrease within the axial strain of 0-1.5%. In contrast, the deviatoric stress increased continuously until reaching the critical state without depicting any peak for constant confining pressure tests. However, in both cases, the lower the water content at the time of specimen preparation, the higher the shear resistance.

Seepage characteristics of fractured rock mass with non-equal width filling under cyclic loading

Fractured rock mass with non-equal width filling often appears in the tunel engineering, the non-equal width ratio is the ratio of the filling width at the seepage inlet to the outlet. To study the seepage characteristics of FFRM (filling fracture rock mass) in the surrounding rock of the Gaoligongshan railway tunnel, the samples of FFRM with different non-equal width ratios were prepared indoors. The permeability coefficient formula of the non-equal width ratio FFRM was deduced for the permeability measurement. Then the triaxial seepage apparatus was used to conduct high and low confining pressure test. Results show that the permeability coefficient of FFRM with non-equal width ratios is a function of multi-parameter interaction, such as seepage outflow, inlet width and filling porosity. The permeability and confining pressure at LCP (low confining pressure) and HCP (high confining pressure) is the power and translation exponential function, respectively. While the relationship between the permeability and non-equal width ratio under confining pressure-seepage condition is the quadratic function. After the first cycle, the permeability loss of the samples under HCP is larger than that of the LCP, and the recovery degree is less than that of the LCP. The SSC (stress sensitivity coefficient) decreases with the increase of the confining pressure, the recovery degree is poor after the first cycle unloading. The trend of the subsequent cycle is almost consistent and the recovery degree is good, which is more obvious under the action of the HCP. The conclusions obtained in this study provide a reference for the stability evaluation of the surrounding rock in the underground engineering.

Failure Mechanism and Acoustic Emission Precursors of Coal Samples considering Bedding Effect under Triaxial Unloading Condition

Bedding increases coal seam anisotropy, which leads to significant differences in the evolution laws of mining stress and strata movement. This work analyzed the dip angles of different layers to analyze the mechanical properties of the coal seam under unloading. The coal sample was subjected to triaxial compression and unloading damage acoustic emission testing. The brittleness characteristics of the coal sample failure in different bedding directions differed significantly. Compared with axial parallel bedding coal samples, axial vertical bedding and inclined stratification reached an ultimate strength. The stress–strain curve decreased sharply and showed visible brittle-drop characteristics. The average strengths of the axially inclined bedding and the parallel layered coal sample decreased compared with the axial vertical bedding coal sample and were 10.20 and 16.12 MPa, respectively, which implies a greater susceptibility to failure during unloading confining pressure tests. Acoustic emission monitoring indicated that the axial vertical bedding and inclined bedding showed sudden destruction of different coal samples, a reduction in axial parallel bedding ductility coal sample characteristics, and stronger unloading damage on the axis parallel to the bedding coal sample. Further, using the acoustic emission ring count rate and the cusp catastrophe theory, the unloading failure prediction of coal samples is carried out. The prediction results are not different from the experimental results, which shows that this method is feasible.

Rock Unloading Failure Precursor Based on Acoustic Emission Parametric Fractal Characteristics

Abstract The mechanical response characteristics and occurrence mechanism of coal and rock under unloading conditions are key to evaluating the stability and control of engineering rock excavation. Triaxial unloading confining pressure tests of coal and rock based on different unloading rates and different initial confining pressure conditions were conducted with fractal theory, research into the fractal characteristics of coal and rock acoustic emission time series under an unloading confining pressure, and the correlations with the unloading failure of coal and rock. The correlation dimension of the acoustic emission signal showed a variation law of a sudden increase, followed by a decrease, increase, and continuous decrease during the experiment. The average time differences between the time when the correlation dimension of coal and sandstone decreased and the actual fracture time of the rock sample were 13.6 s and 16.7 s, respectively. The change in correlation dimension showed the change in internal damage and fracture of the rock sample during the test. The HURST exponent of the acoustic emission time series was calculated at the beginning of the loading. The HURST index showed an overall stable trend and fluctuated around 0.5. A sudden drop in the HURST index resulted when the axial load reached 85% of the peak stress of the rock sample. When the HURST index dropped suddenly (minimum less than 0.2) and then increased rapidly (maximum above 0.8), the rock sample was close to rupture. A HURST index of 0.8 can be used as an index of rock sample unloading and fracture.

Constitutive Model of N15 Propellant considering the Confining Pressure Effect

To describe the effect of confining pressure on the mechanical responses of N15 propellant, a constitutive model considering the confining pressure effect was first established for N15 propellant based on the elastic-viscoelastic correspondence principle. Then, the mechanical properties of N15 solid propellant under different confining pressures were obtained using confining pressure test system, and the obtained results indicate that the initial modulus of propellant did not change with confining pressure, but the maximum tensile strength, rupture strength, the maximum elongation, and elongation at break increased with increasing confining pressure. In conjunction with propellants’ mesoscopic structure and cross-section analysis, the mechanical mechanism of confining pressure effect on propellant was initially disclosed. Due to confining pressure, the particle dewetting inside the propellant was reduced, the hole propagation was delayed, and crack extension inhibited germination, proving that confining pressure has a strengthening impact on the propellant. Finally, assuming that the model parameters were dependent on pressure, the model parameters acquisition and validation were conducted. The results demonstrated that constitutive model can describe confining pressure influence on the mechanical properties of N15 propellant accurately.

Mechanical Characteristics of Frozen Sandstone under Lateral Unloading: An Experimental Study

The lateral unloading strength and deformation of surrounding frozen rock are the key parameters for safety evaluation of frozen shaft construction. A low-temperature and high-pressure rock triaxial test system was used to simulate freezing construction, and a constant axial pressure unloading confining pressure test was carried out on frozen sandstone. The effects of freezing temperature, initial confining pressure, and unloading rate on the strength, deformation, and failure modes of frozen sandstone are studied. The main results of the study are as follows: (1) under the initial confining pressure of 20 MPa, the temperature of the sandstone decreases from 20°C to –5°C, and the peak stress and elastic modulus of triaxial compression increase by approximately 3 times. Under lateral unloading conditions, the peak stress of frozen sandstone is about 2∼3 times that of 20°C sandstone, and the peak strain of 20°C sandstone is smaller than that of frozen sandstone. The temperature of frozen sandstone decreases and the rate of increase in the peak stress of triaxial compression is slightly less than the rate of increase in the peak stress of lateral unloading. (2) The initial confining pressure of frozen sandstone increases, the growth rate of axial and radial strain increases, the radial strain dominates the failure process, and the lateral unloading strength decreases significantly. (3) The lateral unloading rate of frozen sandstone increases, the peak strength increases, and the axial and radial strain decrease. At a low unloading rate, partial creep deformation occurs. (4) The frozen rock sample undergoes tensile splitting failure under lateral unloading. According to the stress-strain curve of the frozen rock sample, the relationship between changes in the deformation modulus and changes in the confining pressure unloading amount during the unloading process of the rock sample is obtained.

Research on Energy Conversion and Damage Features of Unloading Instability of Sandstone under High Stress

In order to explore the failure characteristics of sandstone under unloading conditions in deep zone with high stress, constant axial pressure and unloading confining pressure tests were conducted on a yellow sandstone sample under different initial confining pressures using the French ROCK600-50 triaxial tester, and the mechanical properties, energy conversion characteristics, and damage evolution law of sandstone failure under unloading conditions were obtained. The test results showed that the axial deformation, the confining pressure for failure, and the shear fracture energy during the failure process of sandstone under the unloading state were positively correlated with the initial confining pressure; the dilatancy amount and speed and the radial deformation were negatively correlated with the initial confining pressure, exhibiting the characteristics of dilatancy under low confining pressure and compression under high confining pressure. Before the unloading point, almost all the energy absorbed by the rock under low initial confining pressure was converted into elastic energy, while part of the energy absorbed under high initial confining pressure was converted into dissipated energy, and the higher the confining pressure, the greater the proportion of the dissipated energy converted. The higher the initial confining pressure, the greater the elastic energy, radial deformation energy, and dissipated energy at the rock fracture point. The larger the unloading confining pressure, the greater the postpeak failure energy and surplus energy of sandstone, and the greater the increase in the proportion of elastic energy converted into surplus energy. The higher the confining pressure, the larger the damage value at the unloading point; the damage speed in the unloading stage was significantly greater than that in the loading stage.

Mechanical Characteristics of Coal Samples under Triaxial Unloading Pressure with Different Test Paths

In order to understand the influence of unloading path on the mechanical properties of coal, triaxial unloading confining pressure tests with different initial confining pressure and different unloading rate were carried out. The test results show that the triaxial unloading strength of coal samples under different test conditions is lower than conventional triaxial tests, but the brittleness characteristics are more obvious. This result indicates that the coal samples are easily damaged under unloading conditions. In the axial loading stage of the confinement unloading tests, the axial strain plays a leading role. However, during the confining pressure unloading stage, the circumferential deformation is large, which is the main deformation in this stage. Higher unloading rates of confining pressure are associated with shorter times between the peak stress position and sample complete failure. This shows that samples are more easily destroyed under higher unloading rates and the samples are more difficultly destroyed under lower unloading rates. In addition, with increasing unloading rate, the peak principal stress difference and confining pressure at failure decrease gradually, whereas the confining pressure difference at failure increases gradually. Compared with conventional triaxial compression tests, the cohesion of coal is reduced and the internal friction angle is increased under the condition of triaxial unloading test.

Behavior of transversely isotropic shale observed in triaxial tests and Brazilian disc tests

Shale rock is widely distributed in nature and must be taken into account in some rock engineering applications. In this research, three kinds of experiments, namely the conventional triaxial compression test, reducing confining pressure test, and Brazilian test were conducted on a type of shale rock specimen with a horizontal bedding plane and a vertical bedding plane collected from Lushan city, Jiangxi Province, China to further investigate the bedding effect on the mechanical properties of shale rock. An acoustic emission (AE) monitoring system was used to study the fracture process under the conventional triaxial compression test, whereas a digital image correlation (DIC) system was employed to monitor the deformation of disk faces during the failure process under the Brazilian test. Another key issue addressed in this research is the failure process and mechanism of shale specimens with horizontal and vertical bedding planes under the reducing confining pressure test. The conventional triaxial compression test shows that the bedding plane could easily affect the elasticity modulus and failure pattern, and the failure of the bedding plane can lead to stronger energy release and a higher AE count level. The reducing confining pressure test shows that the dissipated energy magnitude of unloading Path II (reducing confining pressure and increasing axial stress) is much larger than that of unloading Path I (reducing confining pressure and keeping axial strain constant), and that continuous energy input and larger energy dissipation led the specimens under unloading Path II to fail faster than those under unloading Path I. The Brazilian test further revealed that the bedding plane has a significant effect on the tensile strength and failure pattern of shale rock.

Fractal Characteristics of Coal and Sandstone Failure under Different Unloading Confining Pressure Tests

To analyze the fractal characteristics of coal rock failure under unloading conditions, triaxial unloading confining pressure tests were carried out on coal and sandstone rock samples under different unloading rates and initial confining pressures. We examined the distribution of the surface cracks and fragmentation of the coal and sandstone samples that failed under different triaxial unloading confining pressure tests. The results showed that the fractal dimension of the surface cracks in coal and sandstone decreased as the initial unloading confining pressure increased. Thus, shear failure is more obvious in coal or sandstone with high‐stress conditions caused by unloading confining pressure than in coal or sandstone with low‐stress conditions. However, the fractal dimension of the surface cracks increased with the unloading rates. Additionally, the fractal dimension of the fragmentation in the coal and sandstone samples had a negative correlation with the initial unloading confining pressure. When the initial confining pressure was relatively low, the samples underwent splitting and shear failure; when the initial confining pressure was higher, the failure mode was mostly shear failure and the fragmentation of the samples was less homogeneous. In contrast, the fractal dimension of the fragmentation in the coal and sandstone increased with higher unloading rates. The lithology had a significant effect on the fractal dimension of the surface cracks and on the fragmentation. Samples with more internal fissures had more surface cracks and the fragmentation was more homogeneous when the rock failed compared with samples with less fissures under the same experimental conditions.