Experimental Investigation on the Deformation , Strength , and Acoustic Emission Characteristics of Sandstone under True Triaxial Compression

-e study of deformation, strength, and other mechanical characteristics of sandstone under true triaxial compression is significant for understanding failure mechanisms in rock and evaluating the stability of underground structures. Conventional and true triaxial compression tests for sandstone are conducted for different stress states in this study using the self-developed true triaxial electrohydraulic servo test system combined with acoustic emission (AE) testing. -is study presents an in-depth and systematic investigation of deformation, strength, and AE characteristics. -e results show significant differences in deformation, strength, and acoustic emission characteristics for the rock under conventional triaxial and true triaxial compression tests, respectively. -e peak strength, axial strain, lateral strain, and incremental strain (in unstable crack growth stage) increase with increasing confining pressure under conventional triaxial compression, and the AE count gradually decreases while shear crack proportion gradually increases, indicating that increasing confining pressure gradually inhibits the shear slip effect along fractures, delays perforation of the rock shear fracture surface, and enhances the ability of the rock to withstand deformation and load. Under true triaxial compression, the peak strength increases and then decreases with increasing intermediate principal stress σ2 and the axial strain ε1 and lateral strain ε2 gradually decrease; besides, the lateral strain (expansion) of the rock is mainly in the minimum principal stress σ3 direction, and lateral expansion tends to decrease before increasing. AE events first weaken and then enhance with increasing σ2, and the proportion of shear cracks increases first and then decreases, indicating that the confining pressure gradually changes from the shear slip effect that controls crack offset to the damage effect that promotes crack tension with increasing σ2. In addition, the protective effect of confining pressure improves when σ3 increases.


Introduction
Rock material is a kind of brittle geological material, which has a complex composition and contains numerous defects, such as joints and cracks.Rock mechanical properties change with variations in external load and environmental factors because of these inherent characteristics.Rock engineering is a fundamental part of construction and is an important support for social development and progress.
ese projects are all related to research on fundamental rock mechanics problems [1].
e mechanical properties of the rock in Earth's crust are closely related to the 3D stress state.e deformation, strength, and other mechanical properties can be obtained by studying the deformation and failure of various rocks.Understanding rock failure mechanisms is significant for geotechnical engineering.At present, the study of rock damage in a 3D stress state is primarily carried out using conventional triaxial tests.Domestic and foreign scholars have studied the mechanical properties of rock under conventional triaxial compression by using conventional testing machines.Karman obtained the earliest stress-strain curves for Carrara marble under different confining pressures on an ordinary testing machine [2].Fredrich studied the mechanical properties of calcite marble under conventional triaxial compression and examined the effect of particle size on the brittle-ductile transition [3].Yang et al. [4].carried out conventional triaxial compression tests on sandstones by using a servo testing machine.
However, the influence of the intermediate principal stress is ignored due to the setup of the conventional testing machine.A cylindrical rock sample is subjected to different axial and lateral stresses such that the rock is in an axisymmetric stress state.So, only the strength and deformation for rocks in an axisymmetric stress state are measured, and the general stress states are not represented (σ 1 ≠ σ 2 ≠ σ 3 ).In a true triaxial compression test, each of the three principle stresses can be independently applied to the sample allowing for the failure mode to be accurately simulated and a more complex stress path to be measured.In recent years, Mogi [5,6], Haimson et al. [7,8], and Feng et al. [9] have carried out a large number of experimental studies on rocks using a true triaxial test machine.However, previous studies mainly focus on the effect of the intermediate principal stress on rock strength [10] and the establishment of true triaxial strength criterion to show the effect of the intermediate principal stress on rock strength [11,12].Furthermore, most true triaxial compression experiments examine strength and failure criteria for granite, marble, or other hard rocks, while failure and deformation characteristics for relatively soft rocks, such as sandstone and coal, remain largely unknown.
Underground projects such as roadways are mostly undertaken in sedimentary structures that consist of sandstone-filled channels, and the deformation problems in the roadways are more prominent.Due to the complex microstructure of and numerous defects, its physical and mechanical properties are more sensitive to external loads.Sandstone is one of the most widely distributed rocks in East, South, and Southwest China.With the rapid development of underground construction, understanding the response of sandstone to 3D stress states is of significance for the construction of underground foundations and roadways.Examining the deformation, strength, and other mechanical properties of sandstone under true triaxial compression can provide reference for the selection of rock mechanics parameters in future geotechnical engineering projects.
e rock damage induced by compression is essentially caused by the continuous development of microcracks, such that the rock fractures.erefore, the combination of macroscopic mechanical properties such as strength, deformation of the rock, and the development of microcracks in the rock can reveal the cause of the deformation and failure.Acoustic emission (AE) is an effective method to observe the development of microcracks in rock.AE is caused by the generation and expansion of microfractures when rock materials are under an external stress, and AE is accompanied by elastic wave or stress wave release.AE information reflects the damage and failure state of the rock, which is closely related to the densification of the original internal fissures as well as the generation, expansion, and penetration of the new fissures.
e influence of the intermediate principal stress on the development of internal microcracks in rocks can be revealed using AE information.Moradian et al. [13], Yang et al. [14], and Ranjith et al. [15] analyzed the evolution of internal cracks in rocks using AE.However, these studies focused on the evolution of rock fracturing under conventional triaxial compression.erefore, it is necessary to explore the development of internal microcracks in rock based on AE to reveal the root cause of rock deformation and failure under true triaxial compression.
In this study, sandstone is subjected to conventional and true triaxial tests with varying stress conditions using the self-developed true triaxial electrohydraulic servo test system.e development of internal cracks within the rock is monitored using an AE monitoring system.e deformation, strength, and AE characteristics of sandstone under three triaxial stress states are discussed.e effects of different confining pressures under conventional triaxial compression and different stresses in true triaxial compression on the variation of rock deformation, strength parameters, and internal crack development are discussed.

True Triaxial Electrohydraulic Servo Test System.
e tests presented in this study are carried out using the selfdeveloped true triaxial compression test system (Figure 1).e test system is primarily composed of a maximum principal stress, intermediate principal stress, minimum principal stress (σ 1 , σ 2 , σ 3 ) three-dimensional servo control load system, true triaxial pressure cell, automatic data acquisition system, and AE monitoring system.e σ 1 , σ 2 , σ 3 three-dimensional servo control load system forms an independent load frame.Piston rods are installed at one end of the three load frames, which is externally connected to the servo valve to produce independent servo loading.e three loading frames are perpendicular to each other.e positions of loading frames σ 1 and σ 3 are fixed, while the third loading frame (σ 2 ) is placed on a horizontal guide rail and has the able to slide along the guide rail to facilitate the operation and placement of the sample.e other end of the two loading frames (σ 2 and σ 3 ) is installed with reaction screws, which have an adjustable length to adapt to different specimen sizes.
Specimens used in this study are cuboids with a size of 50 × 50 × 100 mm.e specimen is placed in a cubic pressure chamber composed of a fully rigid structure, which consists of a box-shaped body and a loading plate.In order to avoid deformation of the rock samples leading to mutual extrusion of the loading plate during the test, a gap is left between the vertical and horizontal plates in the traditional true triaxial pressure chamber. is gap causes the uneven stress and strain in the test, resulting in a decrease in peak strength and an abnormal failure pattern in the sample [16].In order to overcome this defect, the true triaxial pressure cell adopts a rotary interlocking platen design, in which the loading plates on the 6 faces of the sample are arranged in a misplaced method.When the specimen is compressed, the loading plate moves synchronously with the specimen to avoid interference effects in each direction (Figure 1).e relative displacement between the loading plate and the specimen produces a friction force, which negatively influences the test result.To reduce the friction between the 2 Advances in Materials Science and Engineering loading plate and the sample, a 0.5 mm thick layer of lubricant is applied between the loading plate and the sample surface.e lubricant is composed of a 1 : 1 ratio of stearic acid and Vaseline [17].
A spoke-type pressure sensor with a precision of 0.01 kN is installed between the piston rod and loading block.A rope-type displacement sensor with an accuracy of 0.002 mm and a measurement range of 1,000 mm is xed to the piston rod and reaction force screw.A DS2-8B full information acoustic emission signal analyzer is used to examine the AE activity during tests.e AE system used in this study mainly consists of the AE host, preampli er, and AE sensor.e type of the AE sensor is RS-54A, and its monitoring frequency range is 100-900 kHz.e AE sensor is installed in the loading plate of the true triaxial pressure cell (an 8 mm diameter hole is set in the side of the plate).
e AE signal line is drawn out from the hole in the side of the plate, and the probe is in direct contact with the surface of the sandstone to ensure the accuracy of the AE data.e model of AE preampli er is 20/40/60 dB which can provide three di erent transmission gains; furthermore, it has the advantages of low noise, wide bandwidth, impact resistance, and small volume.During the test, the threshold is set to 40 dB to avoid the possibility of electronic/environmental noise.e AE signal is ampli ed by the preampli er with the gain of 40 dB.e time parameters for AE waveforms included peak de nition time (PDT), hit de nition time (HDT), and hit lockout (HLT), which are set to 50, 100, and 100 μs, respectively.

Specimen Preparation.
Sandstone is selected for examination in this study.Specimens are composed of feldspar and quartz, as well as a small amount of montmorillonite.e sandstone has a medium grain structure with grain size ranging from 0.1 to 0.35 mm and a relatively dense massive structure.Grains are relatively uniform with an identical macroscopic uniformity and an average density of 2380 kg/m 3 .Samples are

Strength and Criterion
Verification.In order to analyze the strength characteristics of sandstone under conventional triaxial and true triaxial compression and to further verify the accuracy of the test results for the triaxial test system, rock strength and the strength-tting curve under the two loading conditions are obtained (Figures 3 and 4).e peak strength increases linearly with increasing con ning pressure under conventional triaxial compression (Figure 3).e Mohr-Coulomb criterion is used to t the relationship between the con ning pressure and rock strength under the conventional triaxial compression.e tting correlation coe cient is R 2 0.994, which re ects the relationship between rock strength and varying con ning pressure under conventional triaxial compression.
Because the in uence of the intermediate principal stress on the rock strength is not considered in the Mohr-Coulomb criterion, the Mohr-Coulomb criterion is only applicable to the special case in which σ 2 σ 3 , and it cannot accurately re ect the strength characteristics of the rock.Domestic and foreign scholars have come to realize the signi cance of the intermediate principal stress on ultimate compressive strength.Mogi [5,6], Al-Ajmi and Zimmerman Advances in Materials Science and Engineering [18], Oku et al. [19], Lee and Haimson [20], and Chang and Haimson [21] considered that a true triaxial failure criterion can be expressed as a linear function (the Mogi-Coulomb criterion) between octahedral shear stress τ oct and the average e ective normal stress acting on the shear plane σ m,2 : where τ oct and σ m,2 are the octahedral shear stress and the average e ective normal stress on the shear plane, respectively, and a is the intercept of Mogi's linear criterion tting straight line and τ oct axis, and b is the slope of straight line.By comparing the Mohr-Coulomb criterion and Mogi-Coulomb criterion, the relationship between them is concluded: According to the suggestions from ISRM, the Mogi-Coulomb criterion is used to t the strength of the rock (including conventional and true triaxial strength) (Figure 4(b)).According to the tting results, the Mogi-Coulomb criterion (R 2 0.964) re ects the strength characteristics of the rock under true triaxial loading conditions relatively well and is consistent with the test results of Mogi, Haimson, and Chang.ese results are further veri ed by the reliability and accuracy of the experimental system used in this study.
e values of c and φ of the sandstone under two different strength criteria are shown in Table 2 and are obtained by combining (1)-( 4) according to the parameters in the tting equations in Figures 3 and 4(b).e tting coe cient of the two strength criteria is high.erefore, the values of c and φ of the sandstone are relatively close to each other.
e Mogi-Coulomb criterion applies to both the conventional and true triaxial test and is more universal.
e Mohr-Coulomb criterion is a special case of the Mogi-Coulomb criterion.
e strength characteristics of rock under true triaxial compression are shown in Figure 4(a), and the variation is di erent from that of conventional triaxial condition.e peak rock strength increases and then decreases with increasing σ 2 under true triaxial loading.When σ 3 10 MPa and 20 MPa, the peak rock strength rst increases to the maximum and then gradually decreases with increasing σ 2 .In ection points are located at 40 MPa and 50 MPa, respectively.e ascending segment tends to increase linearly with increasing σ 2 , and the slopes of the peak strength are 1.208 and 1.993, indicating that improving σ 3 has a more signi cant protective e ect on the rock.

Stress-Strain
Curve.In this study, the stress-strain curves under conventional and true triaxial compression with di erent con ning pressure conditions are shown in Figures 5 and 6, where the yellow origin represents the peak strength of the rock.Rock stress-strain characteristics for four con ning pressures under conventional triaxial compression are similar (Figure 5).e steepness of the curve in the elastic deformation stage is greatly a ected by the con ning pressure.e larger the con ning pressure, the steeper the curve is, which indicates that the elastic modulus of the sandstone increases with increasing of con ning pressure.e di erence in steepness of the lateral curve is not obvious, which shows that the e ect of con ning pressure on the steepness of the lateral deformation of sandstone is small.e axial strain, lateral strain, and peak strength of the rock increase with increasing con ning pressure, which shows that the increase in the conventional triaxial con ning pressure improves the ability of the rock to withstand deformation and loading in both the axial and lateral directions.
Figures 6(a)-6(d), respectively, show the relationships between the di erential stress (σ 1 − σ 3 ) and principal strain (ε 1 , ε 2 , and ε 3 ) as well as volumetric strain (ε V ) under true triaxial compression.Considering that di erent intermediate principal stresses under true triaxial compression are taken, the test process is divided into one section with a loading by force (o → a(a ′ ) → b(b ′ )) and other section with a loading by displacement (b(b ′ ) → c(c ′ )).To facilitate the analysis, the rock's stress-strain characteristics are only analyzed for the loading by the displacement section.
e condition of the rock in the initial compaction stage is not obvious due to the e ect of loading (Figure 6(a)).e rock enters the elastic stage quickly, and the axial curve is Axial strain, ε 1 (%) 6 Advances in Materials Science and Engineering linear under di erent σ 2 conditions.e steepness of the axial curve is e ected by σ 2 .e steepness of the axial curve increases and gradually decreases with increasing σ 2 .e variation law is di erent from that of conventional triaxial compression.e elastic modulus gradually increases and then decreases with increasing σ 2 , and the variation law is consistent with peak strength.e strain during loading by displacement gradually reduces with increasing σ 2 , and the lateral expansion of the rock gradually plays a more dominant role.e strain curve in the direction of intermediate principal stress gradually steepens with increasing σ 2 (Figure 6(b)).e increase of σ 2 limits the deformation (expansion) in the σ 2 direction.After the peak stress is reached, the rock experiences compression in the intermediate principal stress direction especially when σ 2 equals 50 MPa or 60 MPa, indicating that brittle failure of the rock occurs under such intermediate principal stress conditions, and the rock extends rapidly along the minimum principal stress direction, which leads to the rapidly compressed in the intermediate principal stress direction after the peak.
e strain curve in the direction of minimum principal stress steepens and gradually shallows with increasing σ 2 (Figure 6(c)).e lateral expansion of the rock mainly in the direction of the minimum principal stress is due to the increase of σ 2 .Because σ 2 > σ 3 , the expansion of the rock in the direction of minimum principal stress is promoted by increasing σ 2 .At the same time, the lateral expansion of rock could be limited by σ 2 , which can be regarded as the conning pressure.Results show that when σ 2 is 20 MPa∼40 MPa, the increase of σ 2 plays a protective role for the rock and limits deformation in the direction of σ 3 (lateral restraint e ect).When σ 2 is 50 MPa or 60 MPa, the increase of σ 2 plays a damaging role for the rock and accelerates deformation in the direction of σ 3 (damage e ect).
In Figure 6(d), the change in rock volumetric strain (ε V ) is shown.ε V rst increases and then decreases, showing that the rock undergoes gradual compression rst, and then begins to expand with increasing di erential stress.e in ection point of ε V is the point where rock volume stops compression and begins to expansion.e in ection point of volumetric strain is more easily reached with the increasing σ 2 .
e stress-strain curve of the rock under at σ 3 20 MPa is similar to that of σ 3 10 MPa (Figure 7).e rock axial strain curve is steeper, which indicates that the elastic Advances in Materials Science and Engineering modulus of the rock increases.
e peak strength, axial strain, and lateral strain of the rock increase with increasing σ 3 , and the strain corresponding to the in ection point of ε V greatly improved.e increase of σ 3 enhances the ability of the rock to bear stress and improves the carrying capacity of the rock.e variation of elastic modulus under conventional triaxial and true triaxial compression is shown in Figure 8.
e elastic modulus increases with increasing con ning pressure under conventional triaxial compression (Figure 8(a)).e variation is similar to that of strength, which shows that there are microcracks in the rock and the con ning pressure closes the cracks to some extent, causing some slippage between cracks.If the con ning pressure increases, cracks would close more fully, and slippage between the cracks decreases.e increase of con ning pressure makes slip along the cracks reduce due to the inhibition of the frictional force.
erefore, the axial deformation of the specimen decreases, and the elastic modulus of the rock increases.
e elastic modulus of the rock rst increases and then decreases with increasing σ 2 under true triaxial compression, in which σ 3 is 10 and 20 MPa, and the values of the two peak points are both σ 2 40 MPa (Figure 8(b)).When σ 2 is 20∼40 MPa, the number of slippage cracks in the rock is e ectively reduced by improving σ 2 , and slip along the microcracks is inhibited, which leads to an increased elastic modulus.e e ect of con ning pressure is similar to that of conventional triaxial compression.When σ 2 exceeds 40 MPa, the con ning pressure promotes the expansion of microcracks in the rock, and the elastic modulus gradually decreases (Figure 6(c)).By comparing the variation laws of elastic modulus when σ 3 is 10 MPa and 20 MPa, it is apparent that the latter elastic modulus is larger, indicating that the increase of σ 3 makes the cracks close more fully and reduces slip.When σ 2 is 40∼60 MPa, the decrease of the latter elastic modulus is slower than the former, which indicates that the increase of σ 3 , to some extent, slows down the variation trend of " rst increase and then decrease" under true triaxial compression and plays a protective role to the rock.

Strength and Deformation Characteristic in Unstable Crack Growth Stage.
e deformation properties of rock are closely related to the growth and development of internal cracks.e rock failure process is associated with the closure, fracture initiation, expansion, and interactive perforation of cracks.
e failure process is divided into the following stages [22]: (1) microcrack closure compaction stage; (2) elastic deformation stage; (3) stable crack growth stage; (4) unstable crack growth stage; (5) postpeaking stage.When the axial stress gradually increases to the rock damage stress σ cd , the stress-strain curve enters the unstable crack growth stage, marking the beginning of shear and expansion of the rock sample.In this stage, the cracks are unstable.8

Advances in Materials Science and Engineering
Even if the rock is no longer loaded, the internal cracks in the rock specimen cannot hold stable for a signi cant amount of time and continue to expand over time.erefore, the damage stress is also called the long-term strength of the rock.Examination of rock deformation, strength, and crack development in this stage is of great signi cance to understanding its failure mechanism.is study focuses on the analysis of rock strength, deformation, and acoustic emission characteristics in this stage.e variation rule of damage strength and peak strength under conventional triaxial and true triaxial compression is shown in Figure 9. Damage strength σ cd and peak strength σ p of the rock under conventional triaxial compression increase with increasing con ning pressure (Figure 9(a)).Because there are microcracks in the rock, development of cracks is e ectively prevented, and the expansion of internal cracks of the rock is restrained laterally by improving con ning pressure.
Variation of damage strength σ cd and peak strength σ p for rocks under true triaxial compression (σ 3 10 MPa and 20 MPa) is di erent from rocks under conventional triaxial compression (Figure 9(b)).Damage strength σ cd and peak strength σ p both increase rst and then decrease.When σ 3 is 10 MPa, the damage stress σ cd and peak strength σ p show an obvious trend of " rst increasing and then decreasing," and the con ning pressure constrains the expansion of internal cracks when σ 2 is small.While the lateral restraint gradually transforms into a damaging force on the rock with increasing σ 2 , the expansion of internal cracks in the rock is promoted, leading to decreasing σ cd and σ p .By comparing variations in damage and peak strength under true triaxial compression, it is apparent that σ 3 equal to 10 MPa and 20 MPa corresponds to σ 2 equal to 40 MPa and 50 MPa, respectively.e latter values of σ cd and σ p are higher and vary more gradually than the former values.In particular, the values of σ cd and σ p decrease when the former σ 2 exceeds 40 MPa, while the values of σ cd and σ p reduce slightly when the latter σ 2 exceeds 50 MPa, indicating that the damage e ect of the latter con ning pressure is signi cantly weakened, and improving σ 3 limits the development of internal cracks.
e strain characteristics corresponding to damage and peak stress of the rock under conventional triaxial compression are shown in Figure 10.e axial strain and lateral strain corresponding to damage and peak stress of the rock under conventional triaxial compression vary linearly with con ning pressure, all of which increase with increasing con ning pressure.Volumetric strain uctuates greatly.e lateral strain of the peak point ε 3 p increases more quickly than the axial strain ε 1 p with increasing con ning pressure, which indicates that the lateral strain dominates during the unstable crack growth stage and the admission value of lateral expansion increases.At the same time, the volumetric strain increment of the rock Δε v ( ε v p − ε v cd ) in this stage increases with increasing con ning pressure, which indicates that the ability of the rock to withstand deformation increases gradually due to increasing con ning pressure under the conventional triaxial compression.
Incremental strain variation in the unstable crack growth stage under the conventional triaxial compression is shown in Figure 11.e axial strain increment Δε 1 increases slightly with increasing con ning pressure in this stage, while the lateral strain Δε 3 increases quickly.e volumetric strain increment Δε V increases quickly with increasing con ning pressure due to Δε v Δε 1 + 2Δε 3 , which indicates that the lateral expansion of the rock in the unstable crack growth stage under the conventional triaxial compression is obvious, and the ability to withstand lateral deformation increases signi cantly due to increasing con ning pressure.
e strain characteristics of rock damage point and peak point under true triaxial condition are shown in Figure 12.Because the deformation characteristics of the rock in the loading segment by displacement are only analyzed, the values of σ 3 and σ 2 are 20 MPa under the conventional triaxial compression in this study, and the strain law is not discussed because of its abnormality.Axial strains of the damage point and the peak point under true triaxial compression decrease with increasing σ 2 .Variation is similar when σ 3 is 10 and 20 MPa, and the latter axial strains of the damage point and peak point ε 1 cd and ε 1 p are higher than the former ones.e lateral strains ε 2 cd and ε 2 p in the direction of σ 2 decrease gradually with increasing σ 2 .Deformation Advances in Materials Science and Engineering in the rock re ects expansion in the σ 2 direction, and the expansion is limited by an increasing σ 2 .e restriction is more pronounced when σ 3 equals 20 MPa (Figure 12(b)).e change laws of the two kinds of conditions where σ 3 is 10 or 20 MPa are di erent in the direction of σ 3 (Figure 12(c)).When σ 3 is 10 MPa, the lateral strain in the minimum principal stress direction ε 3 p (expansion) of the rock peak point rst increases and then decreases with increasing σ 2 .When σ 2 is 50 MPa or 60 MPa, the lateral strain exhibits a sharp decrease, indicating that the rock reaches the peak point at a fast speed and its ability to withstand deformation is signi cantly weakened.When σ 3 is 20 MPa, the lateral strain ε 3 p (expansion) of the rock peak point rst increases and then decreases with increasing σ 2 .Here, while σ 2 is 60 MPa, the lateral strain decreases slightly, indicating that the lateral strain ε 3 p of the peak point reduces the ability to withstand lateral strain.However, due to increasing σ 3 , the rock su ers only a slight decrease in lateral deformation capacity.e law of rock volumetric strain is similar to that in the minimum principal stress direction (Figure 12(d)).When σ 3 is 10 MPa, the peak volumetric strain ε v p rst increases and then decreases with increasing σ 2 .When σ 3 is 20 MPa, the peak volumetric strain ε v p slightly decreases with increasing σ 2 , whose value is higher than the former one (σ 3 10 MPa), which indicates that the rock's ability to support expansion and deformation could be improved by increasing σ 3 .
e variation in strain increment in the unstable stage under true triaxial compression is shown in Figure 13.e axial strain increment Δε 1 and lateral strain increment Δε 2 in the intermediate principal stress direction in this stage are similar when σ 3 is 10 and 20 MPa and decreases with increasing σ 2 .e di erence in strain increment Δε 3 in the direction of the minimum principal stress is large.Strain increments rst increase and then decrease, but the former decreases signi cantly when σ 2 is 50 MPa and 60 MPa, which indicates that the ability to bear lateral deformation signi cantly decreases due to damage from con ning pressure.e latter decreases slightly when σ 2 is 60 MPa, which indicates that the damage caused by con ning pressure could be signi cantly weakened due to an increase in σ 3 .e volumetric strain increment is similar to that in the direction of σ 3 .

AE Behavior
AE is a phenomenon that microcracks generate during crack development, which is accompanied by the release of an elastic wave or stress wave.Deformation and failure of the  e AE information during compression and failure of the rock is used to predict the rock failure process, which is of great importance to monitoring deformation in mines and other geotechnical engineering [23].
e typical curve of the cumulative AE events with the change of strain under di erent loading conditions is shown in Figure 14. e characteristics of the rock in unstable crack growth stage (the same below) are only selected in this study.AE events increase sharply in this stage, and interactions among cracks increase.AE events weaken gradually with increasing con ning pressure under conventional triaxial compression, and the cumulative AE counts decrease gradually when the peak value is reached.With a con ning pressure of 10 MPa, the cumulative AE counts are signi cantly higher than the one with higher con ning pressure.Since the constraint on lateral deformation with low con ning pressure under conventional triaxial compression is small, it is easy to produce new microcracks and generate slip along cracks, creating a more active acoustic emission signal.High con ning pressure reduces the generation of internal fractures and shear slip, producing relatively low AE counts.e higher the con ning pressure, the stronger the binding e ect is, which enhances the rock's capacity to withstand deformation and loading.
AE count decreases rst and then increases under true triaxial compression.When σ 3 is 10 MPa, AE events increase with increasing σ 2 (Figure 14(b)).When σ 2 is 20∼40 MPa, the cumulative AE counts gradually reduce with increasing σ 2 .ere is no "sudden increase" phenomenon, and the rock produces many continuous AE counts.In combination with the AE characteristics under conventional triaxial compression, numerous shear slip cracks are produced in this stage (which would be analyzed in detail below), and microcracks converge and perforate within the rock, leading to the formation of macroshear and slip surfaces.When σ 2 is 50 and 60 MPa, the cumulative AE counts increase rapidly, and there is a "sudden increase" phenomenon indicating that the increase of σ 2 inhibits the deformation in the σ 2 direction but promotes the lateral expansion in the σ 3 direction.
e rock produces many tensile cracks whose convergence and perforation cause fracture surfaces to form.e con ning pressure gradually evolves from a constraining force to a damaging force, greatly weakening the carrying capacity of the rock.When σ 3 is 20 MPa, AE events change slightly with increasing σ 2 .Here, when σ 2 is 30∼50 MPa, the typical AE event curves (Figure 14(c)) are similar to each other, and more shear and slip cracks are formed.e constraining e ect of con ning pressure to internal cracks is enhanced, and the development of cracks is suppressed by increasing σ 2 .When σ 2 is 60 MPa, the cumulative AE counts increase rapidly, but there is no "sudden increase" phenomenon, indicating that the con ning pressure damages the rock and promotes the development of rock cracks.For σ 3 10 MPa, the damage e ect is greatly weakened by improving σ 3 and the rock is protected.
In order to further analyze the destruction of sandstone under di erent loading conditions, the value of RA (the ratio of the rise time and the amplitude) and the average frequency value AF (the ratio of the ringing count and the duration) of the AE parameters are used to describe the type of microcracks within the rock.In general, AE signals with low AF and high RA or with high AF and low RA usually represent the generation or development of shear or tensile cracks, respectively [24][25][26].Energy levels are combined to analyze the distribution law for RA under three kinds of AE levels which are 0.1∼1, 1∼10, and >10 mV 2 •ms (ignore < 0.1) (Figure 15).Microcracks in the rock under the three loading conditions are stretched and expanded.e AE count which has an AE energy of over 10 mV 2 •ms, 1∼10 mV 2 •ms, and 0.1∼1 mV 2 •ms is small, large, and dense.According to the energy level, the proportion rule of the rock shear cracks under di erent loading conditions is shown in Figure 16.
e proportion of the shear cracks under conventional triaxial compression with AE energy greater than 10 mV 2 •ms varied little with increasing con ning pressure, which is in 27%∼32%.e proportion of shear cracks gradually increases (from 25% to 37%) with AE energy from 1 to 10 mV 2 •ms.e proportion of the shear cracks is relatively small and irregular with AE energy varying from 0.1 to 1 mV 2 •ms (only AE of more than 1 mV 2 •ms would be analyzed in the following paper).Although a former study believed that the rock sample Advances in Materials Science and Engineering re ects the shear failure characteristics under conventional triaxial compression at the macrolevel, analyses in this study show that the macroshear failure of the rock samples at the microlevel is caused by tension, expansion, or a large number of connecting internal microcracks.e presence of shear cracks is often accompanied by a large number of tensile cracks, which is consistent with the existing literature [27,28].
e cracks need to overcome the con ning pressure.e law of the proportion of shear cracks in which AE is over 1 mV 2 •ms increases with increasing con ning pressure indicates that cracks gradually overcame the shear constraints of con ning pressure.On the contrary, the shear slip is gradually inhibited due to increasing con ning pressure and delaying penetration of the cracks and rupture of the rock surface, in a ecting playing a protective role in rock.
ere are signi cant di erences in the change laws for RA under true triaxial compression in which σ 3 is 10 and 20 MPa.When σ 2 is 20∼40 MPa, the former (σ 3 10 MPa) proportion of the shear cracks gradually increases (from 28% to 35%) with increasing Δε 3 with AE energy greater than 1Δε v .e role of con ning pressure is similar to conventional triaxial compression.Slippage of rock cracks can e ectively be inhibited by increasing σ 2 , which delays the formation of macroshear and slip surfaces and plays a protective role in the rock.When σ 2 is 50 and 60 MPa, the proportion of shear cracks decreases dramatically (12% and 9% resp.) with its AE energy more than 1 mV 2 •ms, indicating that the rock records mainly tension and expansion, accompanied by a small amount of shear cracks.Tension cracks within the rock are constantly fused, and the macroscopic tension and failure surface instantaneously forms, which explains why the cumulative AE counts appeared as a "sudden increase" (Figure 14(b)).e e ect of con ning pressure on the cracks within the rock gradually evolves from a constraining force to a damage force.e latter (σ 3 10 MPa) has a relatively smooth change in RA.When σ 2 is 20∼50 MPa, the proportion of the shear cracks gradually increases (from 26% to 37%) with increasing σ 2 with AE energy of more than 1 mV 2 •ms.By comparing with σ 3 10 MPa, the proportion of shear cracks increases, indicating that the slip e ect may be inhibited by increasing σ 3 and the rock is restricted laterally.When σ 2 is 60 MPa, the proportion of shear cracks (20%) in which AE energy is more than 1 mV 2 •ms decreases.It is signi cantly larger than the former proportion with conditions the same as σ 2 , indicating that the damage e ect of con ning pressure is weakened because of increasing σ 3 , although the rock is damaged by the con ning pressure, to some extent, which led to the increase of the tensional cracks of the rock.

Conclusion
In this study, the conventional triaxial and true triaxial tests of sandstone under di erent stress states are carried out using the self-developed true triaxial electrohydraulic servo test system.Deformation, strength, AE characteristic parameters, and development of the internal cracks are studied under di erent con ning pressures, intermediate principal stresses, and minimum principal stresses.e primary research results are summarized as follows: (1) e strength of the sandstone increases with increasing con ning pressure under conventional e strength under the true triaxial condition is consistent with the Mogi-Coulomb criterion.e rock is protected obviously, and the peak strength of the rock is greatly improved by increasing σ 3 .
(2) e deformation characteristics of the rock under the two loading conditions are quite different.Under conventional triaxial compression, the axial strain and lateral strain as well as the elastic modulus increase with increasing confining pressure before failure, showing that the ability of the rock to withstand deformation capacity of the rock is gradually improved because of the increase in confining pressure under conventional triaxial compression.Under true triaxial compression (σ 3 equal 10, 20 MPa), the elastic modulus of the rock first increases and then decreases, and the axial strain ε 1 and lateral strain ε 2 decrease gradually with increasing σ 2 .e lateral strain (swelling) of the rock is mainly along the σ 3 direction, and the tendency of the lateral expansion is to decrease first and then to increase.In the unstable crack growth stage, the lateral strain ε 3 p and strain increment Δε 3 , Δε V first increase and then decrease, but the former appears as "cliff" decrease when σ 2 is 50 and 60 MPa, while the latter decreases slightly when σ 2 is 60 MPa.e variation of strain increment Δε 3 , Δε V in the stage is similar, indicating that when σ 2 is large, the former ability to bear lateral deformation is weakened significantly, while the latter can greatly reduce the role of confining pressure damage at this time and provide a protective effect to the rock due to increasing σ 3 .
(3) In this study, the AE characteristics of rocks in unstable crack growth stage under conventional and true triaxial compression are analyzed.It is found that microcracks in the sandstone reflected mainly stretching and expansion under the two loading conditions (the characteristics of AE signals are high AF and low RA); however, the AE characteristics are significantly different.e trend of AE activity for rocks under conventional triaxial compression is "gradually reduced" with increasing confining pressure, and the shear and slip effect of the cracks is gradually inhibited.AE events first weaken and then enhance with increasing σ 2 under true triaxial compression in which σ 3 is 10 and 20 MPa.When the former σ 2 is 20∼40 MPa, the cumulative AE counts gradually decrease with increasing σ 2 , and the proportion of the shear cracks increases gradually.
When σ 2 is 50 and 60 MPa, the cumulative AE counts increases rapidly, and there is a "sudden increase" phenomenon.e proportion of the shear cracks decreases dramatically, showing that the confining pressure gradually evolves from the shear and slip effect inhibiting shear cracks to damage the rock promoting the formation of tensional cracks with increasing σ 2 , resulting in an instant of macrotension rupture formation.But, the damage of confining pressure is weakened by increasing σ 3 (the latter σ 3 � 20 MPa).

σ 1 = 2 =Figure 3 :Figure 4 :Figure 2 :
Figure 3: Peak strength σ 1 as a function of the minimum principal stress σ 3 under conventional triaxial stress and the best-t linear function strength criterion (Mohr-Coulomb) for sandstone specimens.

Figure 5 :
Figure 5: Stress-strain curves for sandstone from conventional triaxial compression experiments.

Figure 9 :
Figure 9: Variation rule of rock damage strength and peak strength under conventional triaxial and true triaxial conditions.

Figure 10 :
Figure 10: In uence of the con ning pressure on strain corresponding to each characteristic stress under conventional triaxial compression experiments: (a) axial strain; (b) lateral strain; (c) volumetric strain.

Figure 11 :
Figure 11: Variation in strain increment in the unstable crack growth stage under the conventional triaxial compression.

Figure 12 :
Figure 12: Strain characteristics of rock damage point and peak point under true triaxial compression: (a) axial strain; (b) lateral strain (the intermediate principal stress direction); (c) lateral strain (the minimum principal stress direction); (d) volumetric strain.

Figure 13 :Figure 14 :Figure 15 :
Figure 13: Variation in strain increment of rock in the unstable crack growth stage under true triaxial compression.

Table 1 :
Tested sandstone specimens and conditions in this research.

Table 2 :
Fitting results and parameter values of two strength criteria of sandstone.