Zhen Hung,Qixiong Gu,Yufn Wu,Yun Wu,Shijie Li,Kui Zho,Rui Zhng

a School of Resources and Environment Engineering,Jiangxi University of Science and Technology,Ganzhou 341000,China

b School of Earth Sciences and Engineering,Nanjing University,Nanjing 210023,China

c School of Earth Sciences and Engineering,Sun Yat-Sen University,Guangzhou 510275,China

d Kunming Survey,Design and Research Institute Co.Ltd.of CREEC,Kunming 650200,China

Keywords:Sandstone Acoustic emission Ib value Failure mode Fractal dimension

ABSTRACT In this study,uniaxial and triaxial compression acoustic emission(AE)tests were implemented to investigate the AE effect and failure characteristics of sandstone under different confining pressures (σ3).The evolution of AE parameters in the rock failure process and fracture fractal dimension characteristics after failure were analyzed.The results revealed that the activity of the AE signal is strongly related to σ3.The evolution of the Ib value can be divided into the I-fluctuation,II-stability,and III-decrease stages.In the first stage,the Ib value of the AE was relatively high,and the AE energy was low.Then,the Ib value tended to be stable;however,the fluctuation amplitude decreased,and the AE energy rapidly increased.In the stage of decrease,the AE energy sharply increased before the load approached the peak value,and the Ib value significantly decreased and dropped to the lowest point before the peak value.As σ3 increased,the rock’s failure mode changed from tensile failure to shear failure and became more coordinated.As the confining pressure increased,the shape dimension decreased,and the order degree of rock failure increased.The confining pressure exerted a certain control effect on the rock failure.

1.Introduction

Construction disturbances in underground projects,such as traffic,water conservancy tunnel excavation,hydrocarbon and coal resources development,cause the development and expansion of internal fissures in the surrounding rock.This results in the decrease of the structural integrity and bearing capacity of the rocks,which in turn greatly affects the stability of the project [1–3].Thus,it is of great importance to investigate the failure process and damage characteristics of rocks subjected to loading [4].Acoustic emission(AE)has attracted much attention from scholars worldwide,because it can achieve the continuous non-destructive detection of rock damage,and has been a popular research topic in related fields.The AE information obtained for rock under stress effectively reflects the evolution of micro-crack eruptions and crack extension penetration inside the rock [5–7].Currently,AE signal analysis is performed by analyzing the characteristic parameters such as AE events,AE energy,ringing count,bvalue (parameter related to seismic activity characteristics) [8–11],fractal dimension characteristics,and entropy values[12–14].Many studies have been carried out to understand the AE characteristics of rock failure processes.Eberhardt et al.[15] quantified the brittle fracture damage of rocks according to the information of the AE parameters before the peak stress.Song et al.[16] investigated the characteristics of parameters such as the energy rate and amplitude during the uniaxial compression of weakly cemented sandstone.Zhang et al.[17] investigated the main frequency and entropy change law of the AE signal during the destruction of dry and water-saturated gangue.Gao et al.[18]studied the fractal dimension characteristics of AE during the destruction of coal samples.Li et al.[19]and Li et al.[20]investigated the evolution law of thebvalue of AE during the destruction of different rocks.

Rock damage is the process of initial crack development,expansion,aggregation,connection,and penetration within the rock,and has significant nonlinear characteristics,from internal microscopic damage development to macroscopic fracture penetration [21].Fractals involve the study of the intrinsic laws of nonlinear systems and their unity of determinism and stochasticity[22–24],and their ability to measure the self-similarity of seemingly random and complex geometric contours at different angles and scales.Since the concept of fractal geometry was formed in 1983 [25],it has been applied to different degrees in the field of rock mechanics.Scholars domestically and abroad have conducted many studies from a fractal viewpoint to characterize the rock fracture,roughness of rock joints surface,fracture morphology,pore space,and other aspects [26–29],and various crucial research conclusions have been proposed.

Fig.1.Rock samples for tests.

Because the rock damage process is very complex and involves cross-scale processes,from microscopic to macroscopic,the parsing relationship between macroscopic failure and microscopic damage remains to be further studied.Additionally,the study of rock damage must be carried out from multiple viewpoints and in different directions.In this study,the evolution laws of the AE event rate,accumulated AE events,Ibvalue,and other parameters were investigated during the damage of yellow sandstone by conducting compression tests on sandstone under different confining pressure conditions,combined with AE monitoring technology.The macroscopic morphology and fractal dimension characteristics of rock fractures under different confining pressures were comprehensively analyzed to provide a useful theoretical reference for practical engineering in sandstone formations.

2.Materials and test methods

2.1.Sample preparation

Yellow sandstone was obtained from Meishan,Sichuan Province,China.Sandstone mainly consists of cuttings,feldspar,quartz,good homogeneity,and dark yellow in the natural state.Reducing the influence of specimen variability,the specimens were obtained from a piece of intact rock.A TX-ZS200A drilling and sampling machine,a JKDQ-1 T intelligent rock sample cutting machine,and a JKSHM-200 double-sided stone grinding machine were used to drill,cut,and polish the rock specimens to ensure that,after processing,the dimensional accuracy and flatness of the two ends of the specimens satisfied the recommendations of the International Society of Rock Mechanics(ISRM).The size and precision of the rock test were as follows:diameterD× lengthH=50 mm× 100 mm;end parallelism ≤0.05 mm;height error ≤0.3 mm.The processed rock specimens were placed in an oven under a constant temperature of 50 ℃,left to stand for 24 h,and then removed and number after cooling(“S”means the abbreviation of sandstone).The dimensions,quality,and compressional wave velocity of the rock specimens were measured.The specimens’ average density was 2.22 g/cm3,and the compressional wave velocity was 1990–2681 m/s.A rock specimen is shown in Fig.1,and the physical and mechanical parameters of the rock samples are listed in Table 1.Five sets of sandstone samples were selected for nuclear magnetic resonance(NMR) pore structure testing,and the results are shown in Fig.2.The NMR test results revealed that the average porosity of the five sets of test sandstone samples was approximately 21%.

Table 1Physical and mechanical properties of the sandstones.

Table 2Summary of the value of the fitting parameters.

2.2.Experimental setup and testing procedure

The loading system used in the test is a GDS triaxial rheometer produced in the United Kingdom (Fig.3).This system comprises three sets of supporting test systems for axial pressure,confining pressure,and osmotic pressure and is equipped with software to allow the effective operation of the test system.Moreover,the test system has high precision and data measurement accuracy,and can provide axial loads of 0–400 kN,confining pressures of 0–32 MPa,and osmotic pressures of 0–32 MPa.The system is equipped with a LVDT sensor,and can achieve the required measurement accuracy under high-and low-pressure environments.The AE test system uses the Micro-II Digital AE system developed by Physical Acoustics Corporation (PAC).The AE sensor uses a broadband UT-1000 sensor with a frequency range of 60–1000 kHz,the threshold value of 35 dB,preamplifier threshold value (gain) of 40 dB,and the waveform sampling rate of 2 MSPS(a million samples per second).The peak definition time (PDT),hit definition time (HDT),and hit lockout time (HLT) was set to 100,150,and 300 μs,respectively.The test was conducted by applying displacement loading,setting the axial loading rate to0.002 mm/s,and setting the four confining pressure levels of 2,4,6,and 8 MPa in the following test procedures:(1)specimen preparation and specimen installation;(2) pressure chamber filling and pressurization;(3)AE sensor deployment and testing;and(4)axial stress loading.

Fig.2.Transverse relaxation time T2 spectrum curves of sandstone specimens.

3.Results and analysis

3.1.Analysis of sandstone compression test results

The stress–strain curves of the sample are presented in Fig.4.It can be found that the sandstone went through four stages during the uniaxial and triaxial compression:initial crack closure and compaction stage,linear elastic deformation stage,stable crack extension stage (yield stage),and unstable extension stage (damage stage).There are obvious differences between the stress and strain curves of the uniaxial compression and triaxial compression.For example,under uniaxial compression,there was an obvious compaction phase in the pre-loading period,whereas in the triaxial compression test the compaction stage was not obvious and the stress–strain curve exhibited an approximately linear relationship before the peak stress,owing to the compaction of the primary pores and cracks inside the rock induced by confining pressure.Additionally,the degree of closure of the primary pore and the cracks of the rock under different confining pressures was not the same,and the compaction phase of the rock was not obvious at the early stage of loading,owing to a certain compaction effect exerted by the confining pressure on the initial fissure of the rock before loading.The peak strength of the yellow sandstone also exhibited an obvious increasing trend with the increase of the confining pressure.The peak strength of the yellow sandstone under uniaxial compression was approximately in the range of 58–80 MPa;the average peak strength was approximately 74.41 MPa,and the average peak strengths under the confining pressure of 2–8 MPa were 94.61,123.07,141.79,and 156.61 MPa.

The elastic modulus (Et),deformation modulus (Es),and peak strain are important parameters for describing the process of rock damage,including the deformation characteristics of the rock damage process.The relationships between σ3andEt,Es,and peak strain are analyzed below.The elastic modulus and deformation modulus calculated under uniaxial compression has a large dispersion and deviate from linearity.Therefore,the uniaxial part of the relationship betweenEt,Es,and σ3is excluded.Fig.5a shows the relationship betweenEtof sandstone and σ3.As can be seen,Etsignificantly increased with σ3,and an obvious linear relationship between the confining pressure and the modulus of elasticity was observed through the linear fitting,with the fitted correlation coefficient exceeding 0.99.The fitted equation for the elastic modulus isEt=1.9064σ3+72.6556 Et=19064σ3+72.6556and the fitted correlation coefficientR2=0.9959.The mean elastic modulus of the yellow sandstone increased from 76.5 to 87.6 GPa with the increase of the test confining pressure from 2 to 8 MPa.Importantly,the effect of σ3onEtis related to the internal structure of the rock.For the yellow sandstone,the increase of the confining pressure contributed to the densification of internal defects,such as pores and fissures inside the rock sample,to a certain extent,and the limiting effect of the confining pressure increased the stiffness of the rock to a certain extent.Thus,the elastic modulus of the rock increased accordingly.

Fig.3.GDS triaxial testing apparatus.

Fig.4.Stress–strain curves of rock specimens under triaxial compression (σ1 is the peak stress of the rock under differentconfining pressures,and σ3 is the test confining pressure of rock).

Fig.5.Relationships between elastic and deformation moduli and confining pressure.

Fig.5b shows the relationship betweenEsand σ3.Similar to the relationship betweenEtand σ3,as σ3increased,the rock’sEsexhibited an increasing trend,with a faster increase occurring in the range of 2–4 MPa and a slower increase was occurring in the range of 4–8 MPa,which indicates a tendency toward stabilization.The fitting equation of the deformation modulus isEs=-0.2614+4.8728σ3+53.3732 and the fitting correlation coefficientR2=0.9257.The average deformation modulus of the yellow sandstone increased from 62.5 to 75.6 GPa when σ3increased from 2 to 8 MPa.The effect of σ3onEsis essentially consistent with that of the elastic modulus.The increase of the confining pressure densified the internal fracture and pore structure of the rock,which made the preliminary densification stage increasingly unobvious and thus caused the increase of the deformation modulus.The test results are essentially consistent with the test results obtained by Zhao et al.[30].

The peak strain is the strain value corresponding to the time at which the rock stress reached its peak.Fig.6 shows the relationship between the peak strain of the sandstone and σ3.As shown in Fig.6,the law of peak strain variation is essentially consistent with the law governing the variation of the modulus of elasticity and deformation modulus with the variation of the confining pressure.As the confining pressure increased,the peak strain exhibited an increasing trend,the peak strain of the rock under the uniaxial 2-MPa condition was elevated,and the average peak strain value ranged from 0.83 under the uniaxial condition to 1.53 under the 2-MPa condition.Then,as the test confining pressure increased(0–8 MPa),the peak strain slowed down as the test envelope pressure increased (0–8 MPa) and the peak strain only increased by 0.05,from 6 to 8 MPa.The fitting formula of the yellow sandstone peak strain and confining pressure is ε1= -0.02+0.3059σ3+0.8796,and the fitting correlation coefficientR2=0.9758.This indicates that the confining pressure had an obvious controlling effect on the deformation damage.As the confining pressure increased,the rock deformation exhibited the characteristics of transformation from the brittle state to plastic failure,and the rock damage is strongly influenced by the stress state of the rock.

Fig.6.Relationship between the peak strain and confining pressure of sandstones.

Fig.7.Relationship between peak strength of sandstones and confining pressure.

Nowadays,the Mohr-Coulomb(MC)strength criterion is one of the most widely used strength criteria.According to the MC,the rock damage process is the result of the joint action of normal stress and shear stresses.Thus,the MC can describe the damage characteristics of brittle,plastic materials based on the assumption that the intermediate principal stress does not affect the strength of the rock,depending on whether the rock damage occurs when the normal stress and shear stresses reach their ultimate value at an interface within the rock[31].The maximum shear force carried by the rock can be determined by the cohesion and internal friction angle;the MC criterion is expressed as follows:

where τmis the shear stress of rock material;cthe cohesive force of the rock material;σ the normal stress at the breaking surface of the rock material;and φ the internal friction angle of the rock material.

In this study,the strength characteristics of sandstone under different confining pressures were analyzed based on the MC,and the MC expressed by the normal stress can be written as follows:

wherekis the influence coefficient of the confining pressure on the axial carrying capacity;dthe theoretical uniaxial compressive strength of the rock material;σ1the peak stress of the rock under different confining pressures;and σ3the test confining of rock.

Eq.(2) was used to fit the relationship between the peak stress of the rock and σ3,as shown in Fig.7.Additionally,it can be seen that the equation fitting correlation coefficient isR2=0.9883,which indicates a high degree of fitting,and that the MC can better describe the damage variation law of yellow sandstone.The fitting results of the MC for yellow sandstone isk=10.5794,d=75.781 8 MPa,and the fitting equation is σ1=10.5794σ3+75.7818.

3.2.Analysis of acoustic emission test results

3.2.1.Acoustic emission event rate

The AE frequency,amplitude,and other related parameters of crack development and expansion in rocks at different stages of stress damage have obvious differences,and the AE characteristics at different stages contain important information on the rock damage process.In this study,the AE characteristics during the damage of rocks under different confining pressures were analyzed using the AE event rate and cumulative AE event number,which reflect the frequency and total amount of AE signals,respectively.The evolution of the AE event rate and cumulative AE events in sandstone under different confining pressures is shown in Fig.8.

It can be found from Fig.8 that the stress curves and AE counts of the rocks under different confining pressures exhibit similar variation characteristics.At the early stage of loading,only a few of AE events occurred in the initial densification stage of the rocks under different confining pressures,because the AE signal at the early stage of loading was mainly generated by the closure and densification process of the initial cracks inside the rocks,which released a small amount of transient elastic waves under the action of compression and friction.However,the overall decreasing trend of the AE event rate with the increase of σ3indicates the direct relationship of the AE event rate with σ3.As the axial load increased,the compaction stage ended and the linear elastic stage began to form.At this stage,the stress–strain curve was approximately linear,and the rock specimen mainly underwent elastic deformation.The external load was not sufficient for forming new microcracks in the rock specimen,the AE event rate and the cumulative number of AE events were in a relatively stable state,and the cumulative number of AE events exhibited a relatively stable period of increase.After the end of the linear elastic stage,the yellow sandstone began to enter the plastic deformation stage.At this stage,the new microcracks inside the sample began to increase and eventually penetrated and connected to each other to form macroscopic cracks as the number and size of microcracks increased.Additionally,the overall rock rupture exhibited an unstable development stage wherein the AE activity entered the active stage,and the AE event rate and cumulative AE events appeared to surge (Fig.8).Before the axial load approached the peak,the AE event rate surged to the peak,as shown in Fig.8.By the time that the axial load peaked,the rock sample had completely lost its bearing capacity,and the AE event rate appeared to increase to a certain extent.Overall,the AE activity of rocks in the initial pressure-density stage and the elastic stage was relatively calm,and the AE signal was mainly generated by the closure of the initial fissure and the sprouting of a small number of microcracks.The active degree of the AE signal in the initial pressuredensity stage is strongly related to σ3,and the increase in σ3suppressed the active degree of the AE signal in the initial pressuredensity stage to a certain extent.In the plastic stage,microfractures within the rock sprouted,developed,expanded,and connected to produce macroscopic cracks [32–34].Additionally,the AE activity entered the active stage,and the AE event rate and cumulative AE events appeared to surge.

Fig.8.Variation of stress and AE events of sandstone under different confining pressures.

3.2.2.Analysis of Ib value of acoustic emission

In 1944,Gutenberg et al.[35]analyzed the pattern between the earthquake frequency and the earthquake magnitude and proposed the concept of using the value of thebparameter to describe the proportion of the focal dimension distribution.Since then,thebvalue has been widely used as important prior information for earthquakes by researchers in the field of seismic activity and hazard assessment.The mechanism of the rock damage process under stress is similar to that of earthquake occurrence,and the acoustic signal generated by rock damage is also defined as microseismic activity.Therefore,Mogi [36] and Scholz [37] introducedbvalues into the field of rock engineering based on AE monitoring technology,and used the correlation between the magnitude of the AE signal’s amplitude and the fracture scale to replace the earthquake magnitude in the original calculation equation with the AE signal amplitude.Thus,they investigated the change of the internal microfracture scale during the force damage of rocks by considering thebvalue characteristics of AE.Generally,it is thought that the increase of thebvalue reflects an increase in the proportion of small-scale events,which indicates the dominance of smallscale fracture development and expansion within the rock material and means that the rock material is in the stable state of microfracture expansion.The decrease of thebvalue reflects an increase in the proportion of large-scale events,which indicates the dominance of large-scale fracture expansion within the rock material and means that the rock material is in the macrofracture expansion state.When thebvalue stably changes with a small change amplitude,this shows that the specimen is in a more stable and progressive fracture expansion state.However,because thebvalue was originally defined in seismology,various application problems emerge when it is directly introduced into the AE signals of engineering materials.Hence,Shiotani et al.[38] proposed an “improvedbvalue”,namely,theIbvalue,which is more applicable to the analysis of the AE signals of rock and concrete materials.The formula for calculating theIbvalue is expressed as follows:

wheren(a) denotes the cumulative AE events abouta;β a certain number of AE events,where β in the range of 50–100 is considered as a suitable value for fitting the Gutenburg-Richter formula [38];α1and α2the constants;μ and ε the statistical mean value and standard deviation of amplitudes,respectively;w1andw2the sublayer and upper amplitudes,respectively;andN(w1)andN(w2)the cumulative number of the upper layer and sublayer amplitudes,respectively.

In this study,equal time intervals were used to calculate the AEIbvalue of the damage process of the rock under different confining pressures with 6 s as the time interval,according to the aboveIbvalue calculation formula.The change law of the AEIbvalue for the damage process of yellow sandstone under different confining pressures is shown in Fig.9.It can be seen from Fig.9 that during the stress damage of rock with σ3,theIbvalues exhibit a similar variation law,which can be separated into three stages:Ifluctuation,II-stability,and III-decrease.

In the fluctuation stage (stage I),the AEIbvalue fluctuated upward and downward as the load increased.The range of upward and downward fluctuation was large,and theIbmaintained a relatively high value mainly because the rock was in the crack compression and linear elastic stage at the beginning.Additionally,the primary microcrack and pore structure inside the rock was in the process of densification and closure,and the AE signal in this stage was generated by the densification of the primary microcrack and pore structure,which corresponds to small-scale fracture change.Hence,theIbfluctuated upward and downward and had a high value.In this stage,the AE energy was low,and had good synchronization with the fluctuation stage of theIbvalue.The comparison of different confining pressure conditions reveals that there existed some variability in the change of theIbvalue at the initial stage of loading.The stage without theIbvalue appeared at the initial stage of loading under the 8-MPa condition,owing to the effect of the higher σ3.This produced the initial compression density of the microfracture and pore structure inside the rock before loading,and resulted in the stage without the AE signal at the initial stage of loading,which was then used to obtain the calculation results without theIbvalue.As the confining pressure increased,the AEIbvalue exhibited more upward and downward fluctuation,and theIbvalue fluctuated in the range of 0.04–0.20 at 8 MPa,but remained within 0.04–0.12 at 2 MPa,which is similar to the calculation results obtained by Zhang et al.[39]for the AEbvalue of rock under different confining pressures.The fluctuation of theIbvalue at the early stage of loading is strongly influenced by the compaction effect of the confining pressure.Owing to the initial confining pressure,the microfractures inside the rock material appeared to undergo densification,and microfractures with a relatively larger size were more likely to densify under the action of the confining pressure.As the confining pressure increased,the densification of the rock material by the confining pressure became more significant,which in turn led to the larger fluctuation of theIbvalue at the early stage of loading as σ3increased.

As the axial load increased,theIbvalue entered the stable stage (stage II) and gradually stabilized,the fluctuation range gradually decreased,and a relatively gentle stage appeared before theIbvalue decreased.However,the AE energy appeared to rapidly increase,which reflects that the rock material was in a more stable progressive microfracture expansion state corresponding to the stage of stable crack expansion in the process of rock force damage.At this stage,the internal fracture of the rock was in the stable expansion state;therefore,theIbvalue remained relatively stable and the AE energy was in the increasing stage.

As the axial load kept increasing,theIbvalue entered the decreasing stage(stage III),and the AE energy exhibited an obvious surge at this stage,which reflects the further development,connection,and penetration of the small fissures that developed inside the rock toward forming larger fissures.At this stage,the AE signal was mainly generated by the expansion of larger fissures,which produced higher-energy AE,and theIbvalue appeared to decrease.When the axial load approached closer to the peak intensity,the fissures inside the rock material further expanded to form macroscopic penetration fissures,and theIbvalue dropped to the minimum.

Fig.9.Variation of Ib value of sandstones under different confining pressures.

Fig.10.Failure modes of sandstone under different confining pressures.

Fig.11.Digital image process of rock fracture planes.

4.Failure characteristics of sandstone

4.1.Failure modes

After the test was completed,the rock specimens that had deformed and became damaged under different confining pressures were removed from the pressure chamber.The heat shrink tube and sensors on the surface were removed,and the damaged rock samples were processed and analyzed.To compare and investigate the differences in the rock rupture characteristics under confining pressure and without confining pressure,a uniaxial compression test(σ3of 0 MPa)was conducted on the yellow sandstone.The failure patterns of the rock specimens obtained under different confining pressures are shown in Fig.10.As can be seen,when σ3was 0 MPa,the rock was mainly in the form of brittle tensile damage,the rock surface exhibited multiple vertical penetration fissures,and the fissure surfaces at the middle of the specimen were more densely distributed and intersected with each other.The central fissure intersection exhibited a slight decrease,the overall shape of the block was cut,the specimen fractured,and the middle of the specimen exhibited certain dilatancy.When σ3was 2 MPa,the crack density on the surface of the specimen was significantly reduced,the cracks were mainly 3–5 through cracks,and the specimen did not exhibit central dilation.When σ3was 4 MPa,the main fractures in the specimen consisted of a single shear surface fracture and one vertical through the fracture,and the middle of the vertical through fracture was connected to several secondary fractures.When the confining pressure was 8 MPa,two single shear surfaces appeared on the surface of the specimen.The two shear surfaces penetrated each other,which divided the rock specimen into two parts,and the angle of the shear surface further increased with respect to 6 MPa.As can be seen,the uniaxial conditions of the sandstone were mainly dominated by brittle tensile damage.The main fractures were mainly vertical through fractures,and the middle of the vertical fractures was connected to several secondary fractures with an obvious central dilation.As the confining pressure increased,the yellow sandstone gradually exhibited typical shear damage,and the main fractures of the specimens formed gradually from single shear fractures.Additionally,the number and density of the fractures exhibited a decreasing trend with σ3,and the dip angle of the single shear fractures exhibited a small increase as the confining pressure increased.This is consistent with the results obtained by scholars such as Mogi [40].

Fig.12.Grayscale image of the fracture surface of sandstones.

Fig.13.Relationship between lgN(A) and lgr of rocks under different confining pressures.

4.2.Fractal dimension characteristics of post-failure rocks

The box-counting dimension is gradually becoming one of the main methods for calculating the fractal dimension,owing to its benefit of being able to accurately and easily measure the fractal dimension of self-similar images [22].The method of calculating the box-counting dimension entails covering the curves with fractal dimension characteristics consisting of squares (shapes) or boxes with different side lengthsr.The number of boxesN(A)with different side lengthrcovering the curves with the fractal dimension is recorded,and the slope of the (-lgr,lgN(A)) distribution points is calculated from the relationship betweenNr(A) and its corresponding squares (shapes) or boxes.Thus,the corresponding fractal dimension was estimated,and the calculation formula is given as follows:

whereN(A) is the number of boxes in the fractal dimension;andrthe side length of the box.

First,a translucent copy paper (with the same size as the surface of the specimen)was wrapped around the surface of the damaged specimen,and a sketch pencil was used for tracing along the fracture surface of the rock sample.Subsequently,a scanner was used to scan the finished copy paper and convert the image of the fracture morphology of the copy paper into a picture file(Fig.11a).Fig.12 shows the gray-level image of the fracture surface morphology of a typical rock sample.The image file was imported into a MATLAB binarization program that was developed to convert the fracture surface morphology image from a gray-level image to a binary image,as presented in Fig.11b,and the logical data from the binarization process were converted into binary data to be used in the calculation of the fractal dimension.Thus,the binary data of the fracture surface morphology were extracted.The lgN(A)-lgrcurves of various typical rock samples and the fitting equations are shown in Fig.13 and Table 2.The slope of the curve is the fractal dimension of the fracture surface.From Fig.13 and Table 2,it can be seen that the correlation coefficients calculated in the figure are higher than 0.98,which indicates that the fracture surfaces,which formed by the force damage of the sandstone under different surrounding pressures,have obvious fractal dimension characteristics.

Fig.14 presents the variation of the surface fractal dimension(D) of the fractured rock samples under different confining pressures.As can be seen,the fractal dimension of the fracture surface fluctuated in the range of 1.35–1.42 with an average value of approximately 1.39 at 0 MPa.At 2 MPa,Dexhibited an obvious decreasing trend with an average value of approximately 1.30.At 4 MPa,Dfluctuated in the range of 1.25–1.30 with an average value of 1.26.Compared withDat 0,2,and 4 MPa,Dat 6 and 8 MPa decreased further.Therefore,within a certain confining pressure range,the fractal dimension of the damaged rock sample’s surface tended to decrease as σ3increased,and the calculated fractal dimension is essentially consistent with the macroscopic damage results and similar to the findings of Zhou et al.[41].Because the fractal dimension is a parameter used to characterize the degree of order and disorder of a nonlinear system,as the fractal dimension increases,the system’s degree of disorder increases.Similarly,a smaller fractal dimension value indicates a higher degree of order in the system.Hence,it is understood that as σ3increases,the orderly degree of rock damage exhibits an increasing trend.That is,the confining pressure exerts a certain controlling effect on the rock damage pattern.

Fig.14.Relationship between fractal dimension and different confining pressures.

5.Conclusions

In this study,an AE test on the compression damage process of rocks was carried out under different confining pressures using a typical yellow sandstone found in southwest China.The evolution law of the AE events andIbvalues during the damage process was investigated,and the macroscopic damage characteristics and fissure fractal dimension characteristics of the rocks were analyzed under different confining pressures.The main conclusions can be drawn as follows:

(1) At the initial compaction stage,the active degree of the AE signal is closely related to the confining pressure.The change characteristics of theIbvalue can be divided into three stages,namely,the I-fluctuation,II-stability,and III-decrease stages.In the fluctuation stage,theIbvalue of the AE fluctuates upward and downward with the increase of the load,and theIbvalue of the AE remains relatively high,while the AE energy is low.In the stability stage,theIbvalue tends to stabilize,and the fluctuation amplitude decreases,while the AE energy appears to increase rapidly.Before the load approaches the peak stress,the AE energy exhibits a significant surge.In this phase,theIbvalue exhibits a significant decline and decreases to the minimum before the peak stress.

(2) As σ3increases,the damage form of sandstone transforms from predominantly tension-type damage to predominantly shear-type damage,and the number of fissures continues to decrease.

(3) The fractal dimension of the damaged sandstone’s surface decreases as σ3increases.As the confining pressure within a certain range increases,the orderly degree of sandstone damage exhibits an increasing trend,and σ3exerts a certain controlling effect on the rock damage pattern.

Acknowledgements

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (No.41702326),the Jiangxi Provincial Natural Science Foundation (No.20202ACB214006),the Innovative Experts,Long-term Program of Jiangxi Province (jxsq2018106049),the Supported by Program of Qingjiang Excellent Young Talents,Jiangxi University of Science and Technology,and the Innovation Fund Designated for Graduate Students of Jiangxi Province (YC2020-S451).