Mingzhong Gao,Jing Xie,Yanan Gao,Wenyong Wang,Cong Li,Bengao Yang,Junjun Liu,Heping Xie

a State Key Laboratory of Hydraulics and Mountain River Engineering,College of Water Resource and Hydropower,Sichuan University,Chengdu 610065,China

b Institute of Deep Earth Science and Green Energy,College of Civil and Transportation Engineering,Shenzhen University,Shenzhen 518052,China

c MOE Key Laboratory of Deep Underground Science and Engineering,Sichuan University,Chengdu 610065,China

d State Key Laboratory for GeoMechanics and Deep Underground Engineering,China University of Mining and Technology,Xuzhou 221116,China

Keywords:Mining rate Loading rate Fracture evolution Mining pressure Uniaxial compressive strength DIC

ABSTRACT During deep mining,the excavation disturbance stress path is the domination factor for the stability of the surrounding rock mass as well as the ground pressure.One of the important parameters of the stress path is the loading or unloading rate of the disturbed rock or coal,which depended on the mining rate.To achieve a well understanding of the mining rate and its effect on the coal behavior,a preliminary case investigation of the mechanical properties of the coal at the various mining rates in both the laboratory scale and field scale was performed.Based on the uniaxial compression test and the digital image correlation (DIC) method,the mechanical behavior of the coal samples,such as the evolution of the strength,surface deformation,crack propagation,and elastic strain energy of the coal under the various loading rates were analyzed.A threshold range of the loading rate has been observed.The uniaxial compressive strength (UCS) and releasable elastic strain energy (Ue) increase with increasing loading rate when the loading rate is below the threshold.Otherwise,the UCS and Ue may decrease with the loading rate.Under the low loading rate (≤0.05 mm/min),the tensile deformation of the original defects could result in crack coalescence,whereas failure of the coal matrix is the key contributor to the crack coalescence under the high loading rate(greater than0.05 mm/min).Afterwards,with the consideration of the bearing capacity(UCS) and energy release of the mining-disturbed coal mass (Ue),a power exponential relationship between the mining rate(MR)in the field and the critical loading rate(vc)in the laboratory was proposed.The application potential of the formulas was then validated against the field monitored data.Finally,based on the critical loading rate,the released strain energy,and the monitored pressure on the roof supports,a reasonable mining rate MR for the Ji15-31030 working face was determined to be approximately 3 m/d.

1.Introduction

The mineral resource is one of the necessary foundations for human society development as well as human subsistence [1,2].However,the present mining depth increases greatly during the last decades.Thus,deep mining is imperative [3-7].Mininginduced mechanical behavior,failure characteristics,disaster identification,and control are still important basic research topics related to deep mining [8-10].Generally,deformation,fracture propagation,and energy release are highly associated with mining-induced stress evolution,in which the mining rate is one of the main impact factors for the appearance of the mininginduced effect.However,the mechanical behavior of the coal mass under different mining rates is still not figured out yet.At the same time,how to choose an optimal mining rate for the actual mining work still lacks the necessary evaluation method.Some basic researches on the mechanical behavior of coal under different mining rates are still urgent to be done.

Different mining rates always result in different loading rates for coal mass.An increasing number of studies have been conducted to consider the effect of the loading rate in the laboratory and the mining rate in the actual engineering [11-14].Wang et al.[15] noted that increasing the mining rate on a fully mechanized caving face can effectively reduce the lower-stress area near the working face,reduce the rock failure zone area near the working face,and significantly increase the peak stress ahead of the working face,which directly showed that the mining rate strongly refers to the loading rate.Xie et al.[16] noted that increasing the mining rate can reduce the extent and rate of roof subsidence in the roof-control area of the working face support,and that roof collapse can occur without warning.They concluded that increasing the mining rate can reduce the rock failure zone surrounding the working face,reduce the extent of roof subsidence in the roof-control area,increase the peak advance support pressure,and shorten the distance between the working face and the location of the peak advance support pressure.Based on the micro-seismic monitoring method,Li et al.[17] investigated the effect of mining rate on the working face in high-intensity mining.They found that when the mining rate was slow,the micro-seismic events were widely distributed,highly developed in the coal seam,and distributed mainly in front of the working face.They also found that when the advancing rate was accelerated,the micro-seismic events were less distributed and were highly developed in the coal seam.Therefore,it can be suggested that the mining rate has a great impact on the loading rate,rock failure,and advance support pressure in front of the mining face.

Due to the complex environment of the actual mining process,there are still some difficulties or limitations in obtaining the actual mechanical behavior under the effect of the mining rate[18,19].While the pressure of the main roof on a coal seam is similar to loading a coal sample in a stiffness testing machine,generally the mining rate can correspond to the loading rate [20,21].Therefore,conducting investigations on the effect of the loading rate on the strength,fracture propagation,and energy release would be an effective method to learn about the effect of the mining rate in-situ.From the aspect of rock strength,the tensile strength of the samples increased significantly as the strain rate increased under direct and indirect tensile conditions [22-24].Zhou et al.[25]found that the tensile strength of granite decreased as the static prestress increased under coupled loading conditions.Through dynamic and static cyclic loading and unloading tests,Bagde and Petroš[26]found that the Young’s modulus and the uniaxial compressive strength (UCS) both increase as the loading frequency increases.

Meanwhile,based on the present studies,it can be found that there is a critical value of the loading rate.The mechanical behavior of the rock/coal will be quite different with the loading rates at the different sides of critical value.Regarding the energy characteristics,Li et al.[27] reported that granite exhibits relatively high energy absorption capacities at high strain rates.Ma et al.[28]conducted uniaxial compression tests on coal samples at various loading rates and confining pressures,and found that the elastic strain energy and dissipation strain energy of the coal first increase and then decrease as the loading rate continuously increases.Permeability,physical properties and Acoustic emission(AE)are also sensitive to the loading rates and strain rate[29-31],some researches noted that as the loading rate increases,acoustic emission (AE)events and main cracks occur earlier;and the failure mode of the coal changes from shear failure to tensile failure,and a highloading rate notably limits the development of AE activity in the rock.Huang and Liu [32] conducted uniaxial compression tests on a composite coal-rock mass at various loading rates values and found that the stress–strain characteristics of the composite coal-rock mass depended on the part of the system with the lowest stiffness.They also found that as the loading rate increased,the strain increment of the composite coal-rock mass gradually increased in the elastic,plastic,and failure phases,and the peak strain increased linearly.

On the other hand,there is always a gap between laboratory study and engineering practice.Therefore,the mechanical behavior of coal in laboratory is quite different from that in actual engineering,and how to simulate the engineering-scale mechanical behavior through the simulation of loading path or loading rate is a key task that should be solved.Besides,the application of the results of the mechanical behavior under different loading rates to the field is another key task to be solved.In this case study,from the perspective of macroscopic appearance and the internal essence of rock failure,the crack propagation and elastic strain energy of coal under various loading rates were considered.And the most important work was to bridge the gap between the laboratory results and the engineering demands with a proposal of the relationship between the loading rate and mining rate.The UCS of specimens at various loading rates was first investigated using multistage uniaxial loading tests.The information on the surface deformation,local strains,and crack propagation of the specimens was analyzed by using the optical monitoring.Next,the deformation,failure,and elastic energy release characteristics of the coal were investigated at various loading rates.Afterwards,based on the critical loading rate range for the UCS and releasable elastic strain energy,a reasonable mining rate for the Ji15-31030 working face was suggested.Finally,field monitoring of the actual mining rate and mining-induced pressure was conducted,and a reasonable mining rate for this mining face was determined.This paper aims to present a comprehensive understanding of the mechanical behavior of coal under different mining rates,bridge the gap between loading rate and mining rate,and provide advice on the optimal mining rate through laboratory evaluation.

2.Materials and experimental method

2.1.Specimen preparation

The coal samples used in this laboratory experiment were obtained from the Ji15-31030 working face (buried depth of 1050 m) of the No.12 mine of the China Pingdingshan Mining Group (Fig.1).Intact coal blocks (greater than 20 cm in length,width,and height) were selected.The coal samples were drilled and immediately placed in bubble wrap before being shipped to the laboratory.Cutting and polishing was performed to make standard cylindrical specimens(Φ50 mm×100 mm)in a rock mechanics laboratory [33].Based on a sample batch and the average specimen density,the specimens were divided into three groups.Table 1 summarizes the grouping information and relevant parameters.The specimens in group 1 were numbered 1–1 through 1–7 and had an average density of 1.79 g/cm3.The specimens in group 2 were numbered 2–1 through 2–7 and had an average density of 1.29 g/cm3.The specimens in group 3 were numbered 3–1 through 3–7 and had an average density of 1.36 g/cm3.

Table 1Specimen parameters.

2.2.Test procedure and measurement method

To thoroughly study the deformation characteristics and development of surface cracks in coal throughout the test process,a continuous monitoring and image analysis technology is needed.Peters and Ranson [34] and Yamaguchi [35] proposed the digital image correlation (DIC) method.The principle of this method is to obtain the surface displacement and strain fields of an object from two digital images,one taken before deformation and another taken after deformation.This is done using image-matching techniques and a registration algorithm based on the artificial speckles produced or the inherent random spots on the surface of the object[36].Currently,the DIC method is widely used in rock mechanics.Wang et al.[37] conducted uniaxial compression tests on wet sandstone samples and used the DIC method to calculate the local and global volumetric strains of the samples during the failure process.Wang et al.[38]and Gao et al.[39]used the DIC technique to study the characteristics and process of crack propagation in prefractured coal-rock masses.Similarly,Yuan et al.[40] measured the three-dimensional (3D) displacement and strain fields inside concrete samples under uniaxial compression conditions using digital volumetric speckle photography.The aforementioned researchers used the DIC technique in laboratory tests to observe mostly planar samples;therefore,they did not realize the advantages of 3D DIC.Relatively few available studies have used the DIC technique to investigate the surface deformation and failure of coal at various loading rates.

Fig.1.Location of the No.12 mine of the China Pingdingshan Mining Group.

In this study,uniaxial compression tests were performed using an electronic universal testing machine at the Mechanical and Material Test Center of Hohai University.Overall,the experimental procedure included three aspects.As shown in Fig.2,the noncontact optical strain mapping system consisted of two chargecoupled-device (CCD) cameras installed on the same horizontal axis with a certain angle between them.White LED light sources were placed at the sides of the cameras.Before the experiment,the distance between the cameras and the universal testing machine was adjusted to ensure that the specimen filled the entire field of view (FOV) of both cameras and that the specimen would remain in the FOV throughout the experiment.To fully understand the peripheral deformation of the specimen,another 3D optical strain mapping system was placed behind the universal testing machine.After setting up the equipment,the camera parameters were calibrated.In this process,a fixed-spacing pattern array board was used to correct for lens distortion and to determine the conversion relationship between the physical dimensions and image pixels.To comprehensively understand the changes in specimen strength at various values of loading rates v and considering the precision of the universal testing machine,a total of five loading rates were selected:0.01,0.02,0.05,0.10,and 0.20 mm/min.The highest loading rate was 20 times the lowest loading rate.

The principle of the two-dimensional (2D) DIC method is to obtain the surface displacement and strain fields by comparing two digital images.Image-matching techniques and a registration algorithm are used,which are based on the artificial speckles produced or the inherent random spots on the surface of the object.Fig.3a is taken ibefore deformation,which is called the reference image.Fig.3b is taken after deformation,which is called the target image.In the reference image I1,a subarea(f1)with n×n pixels is selected,and its central point is denoted as an ‘O’.Assuming that the grayscale values of the subarea remain constant or change linearly during deformation,a subarea (f2) in I2that is most strongly correlated with the selected subarea can be found using a pointby-point search;the central point of this subarea is denoted as an ‘O’.In a simple strain state,the displacement of any pointPin the reference image I1(from the central pointO) satisfies [41]

Fig.2.Experimental mechanical and monitoring system.

whereu(x,y) and v(x,y) are the horizontal and vertical coordinates after deformation,respectively;u0and v0the horizontal and vertical coordinates before deformation,respectively;Δxand Δythe increments in the horizontal and vertical coordinate directions,respectively;εxxand εyythe strains in thex-andy-directions,respectively;and εxyand εyxthe shear strains.Thus,the displacement field of the entire image can be obtained by moving the subarea.Then,the strain field of the entire image can be calculated using Eq.(1).

Currently,a 3D DIC method using the binocular stereo vision principle has been developed based on the 2D DIC technique[41].The principle of the 3D DIC method is described as follows[42].First,two high-speed cameras or high-resolution,industrial CCD cameras are set up with a certain angle between them.The two-camera system is calibrated using a checkerboard or dot calibration board.Then,these two cameras are used to simultaneously record the same scene within the space.Next,the target subareas in the two images of the sample surface taken at the same time are obtained using a matching algorithm.Finally,the spatial coordinates of the surface points are calculated based on the internal and external parameters of the cameras.The key technologies of 3D DIC include image acquisition,camera calibration,image matching,and 3D strain calculation [43].For the DIC method,image matching is performed mainly based on the grayscale information in the neighborhoods of specific points,which are also called points of interest (i.e.subareas).To distinguish one subarea from another,each should contain sufficient,non-repetitive,isotropic textural information to characterize its uniqueness.After 3D reconstruction of the object before and after deformation,the strains and displacements for these points can be calculated.This is because the 3D spatial information is known for the surface points of the object before and after deformation.

Fig.3.Schematic diagram of relevant matching before and after deformation.

Fig.4.Speckled specimen.

In this experiment,it was necessary to produce artificial speckles on the specimen surfaces using the following method.Each specimen was placed horizontally and painted from above using white spray paint.This allowed the paint to fall evenly on the surface.Fig.4 shows a speckled specimen.

3.Mechanical results analysis

3.1.Preliminary investigation

As illustrated in Fig.5,owing to the heterogeneity of each specimen and the distribution difference of local pore fracture structures,the UCS of coal from the Ji15-31030 working face is relatively low and exhibits an obvious change range.The UCS of group 1 exceeds 15 MPa at various loading rates.The UCS of group 2 is in the range of 6–12 MPa.The UCS of group 3 is in the range of 3–12 MPa.Based on the data in Table 1,the results suggest that a higher density implies a higher UCS.The reason for this phenomenon may be that a higher density corresponds to a smaller amount of internal damage,such as pores and fractures,and a smaller amount of internal damage will result in a higher strength.Moreover,the stress–strain curves of the three groups of specimens also have some differences.The stress–strain curve of each specimen has a notable section that curves upward when the stress is relatively low,implying that the natural microcracks and pores were closed owing to the external force.As the compression continues,the curve of each specimen becomes nearly linear,indicating that the specimen is in the elastic stage.For the specimens in group 1,the stress suddenly decreases during the linear stage and then subsequently increases.This phenomenon occurs because the specimens are heterogeneous and stress concentrations develop at certain surface locations.Once the load exceeds the compressive strength of the coal (σuc),the specimens fail,and the stress in the specimens is rapidly released.Another reason is that the specimens in group 1 have a higher density and tend to exhibit a relatively brittle failure.Regarding the specimens in groups 2 and 3,the stress–strain curves of the specimens also drop vertically,but the specimens still have a certain residual strength.

Table 2UCS values of specimens.

Fig.5.Stress–strain curves of the specimens at various values of loading rates.

3.2.Role of loading rate

The loading rate is a dominant factor in the strength of rock and coal [44–47].As shown in Fig.6,the compressive strength σucof the specimens does not continuously increase as loading rates increases.Instead,with the increasing loading rates,the compressive strength first increases and then decreases,and there is an obvious threshold range of vcthat occurs (0.05–0.10 mm/min).It should be noted that the compressive strengths of the specimens in the group with higher densities are more sensitive to the loading rate.After the loading rate exceeds vc,the bearing capacities of the specimens exhibit an obvious decreasing trend.For instance,specimen 1–5 has a compressive strength of 17.8 MPa at a loading rate of 0.02 mm/min.As the loading rate increases to 0.05 mm/min,the compressive strength of specimen 1–4 increases to 28.8 MPa.However,as the loading rate increases further to 0.10 and 0.20 mm/min,the compressive strength of the specimens 1–3 and 1–1 decreases to 22.8 and 21.0 MPa,respectively.For groups 2 and 3,the compressive strength of the specimens also increases first and then decreases with increasing the loading rates.Similar to the group 1 specimens,the compressive strength of the specimens in group 2 reaches a maximum value at a loading rate of 0.05 mm/min.The detailed testing results are summarized in Table 2.

Fig.6.Compressive strength (σuc) of the coal specimens.

4.Failure results analysis

Based on the compressive mechanical analysis results,it has been suggested that the UCS has a nonlinear relationship with the loading rate.Moreover,various loading rates will also have a great impact on the deformation characteristics and crack propagation.In this section,the surface deformation at various loading stages under a constant loading rate and various loading rates are compared.Afterwards,the surface crack evolution under a constant loading rate and the final failure characteristics under various loading rates are discussed.

4.1.Coal surface deformation characteristics at various loading stages with a constant loading rate

From Fig.7,it can be seen that the coal compression process consists of approximately four stages:compaction,linear elasticity,plastic yielding,and post-peak.To investigate the surface deformation and strain of the coal at each stage,specimen 1–5 was used as an example,and the deformation and failure of this sample during the entire loading process were analyzed.The specimen was loaded at a loading rate value of 0.02 mm/min.The total time from the start of loading to failure was approximately 2800 s.SectionsOA,AB,BC,andCDcorrespond to the compaction,linear elastic,plastic yielding,and post-peak failure stages,respectively.Within the first 80 s of the 100-s period of loading,the pressure head came in close contact with the specimen and its axial surface displacement was relatively uniform.However,the surface displacement of the specimen exhibited an obvious change at 87 s of loading.During the compaction stage,the curve was notably concave upward.This stage lasted for a relatively long time.The next stage did not begin until the strain reached 0.3%–0.4%.During the compaction stage,the primary pores and microcracks inside the specimen were closed.During the linear elastic stage,the stress–strain curve exhibited a nearly linear trend.This stage includes mostly vertical deformation of the specimen and compression of particles inside the specimen.The stress–strain curve had two relatively small fluctuations during the linear elastic stage,suggesting that relatively minor fractures might have occurred at times corresponding to these two small fluctuations,resulting in stress release.During the plastic yielding stage,the number of cracks inside and on the outer surface of the specimen increased,and these cracks extended and coalesced.Additionally,the load on the specimen increased.During the post-peak failure stage,the main cracks in the specimen coalesced,and surface spalling occurred.Additionally,the bearing capacity of the specimen decreased rapidly but still retained a certain residual strength.

Fig.7.Stress and surface deformation of the specimen 1-5.

The axial and horizontal strains during the entire loading process were also obtained and discussed.As shown in Fig.7,the surface deformation of the specimen over a period of 100–2500 s is presented.As the upper pressure continuously increased,the axial surface displacement of the specimen continuously increased,the surface deformation of the specimen was incongruous,and the axial deformation decreased from the upper-right corner to the lower-left corner of the specimen.Generally,the results of axial strain and horizontal strain were quite heterogeneous around the surface of coal specimen.During the compaction stage(the loading time is less than 1000 s),there are some local compression parts and tension parts jointly existed on the surface and the bearing structure was under a gradual adjustment,and the specimen end effect was obvious.With the effect of continuous loading(the loading time was less than 2000 s),the axial compressive strain around the coal surface matrix became obvious,the horizontal strain exhibited some uncertain deformation adjustments until a potential crack occurred.With the effect of continuous loading,the incongruous axial surface deformation of the specimen ultimately resulted.At 2000 s,a long and narrow area appeared in the lowerleft corner of the specimen in the horizontal strain nephogram.When the coal specimen entered the post-peak stage,the horizontal tensile strain occurred around the macroscopic crack,and an obvious axial compression strain also occurred around the crack which can also increase the horizontal tensile deformation.Moreover,when the specimen was compressed,the entire surface of the specimen was not compressed in the axial direction.Instead,there was no obvious deformation in a few areas,and a fraction of these areas were never stretched (indicated in red).

The stress–strain curve of the specimen and its surface deformation were correlated.However,the nodes in the curve did not show a one-to-one correspondence with surface deformation or fracture formation and development in the specimen.This phenomenon may occur because the stress–strain curve of the specimen reflects its overall deformation and failure during loading,but it also relates to the crack formation,extension,and coalescence that occur inside the specimen.

4.2.Coal surface deformation and strain characteristics at various loading rates

Based on the understanding of the evolutionary process of coal surface deformation characteristics under the same loading rate,the differences in those characteristics under various loading rates were discussed.The horizontal,axial strain,and shear strain in the specimens of group 3 at five loading stages(axial displacements of 0,0.2,0.4,0.6,0.8,and 1.0 mm)are shown in Figs.8–10.Generally speaking,the initial joint structure (original defects) and heterogeneity of the coal specimen are important factors affecting the surface deformation.It can be clearly seen that the surface deformation of the coal specimen is not coordinated under uniaxial loading,which will inevitably lead to stress concentration.The spatial distribution of the initial joints always determines the growth of the final macrocracks,and the heterogeneity often leads to the phenomenon of stress concentration and non-uniform deformation on the surface of the specimen.The horizontal strain results show that the specimens perform mostly tensile failure under various loading rates.Also,because of the existence of the initial joints or original defects,the local axial strain on the surface of the specimens also performs a small number of tensile areas.

At the same time,the surface deformation of the specimens shows significant differences under various loading rates.With an increase in loading rate,the stress sensitivity of the initial joint structures and coal matrix skeletons showed a certain competitive state.When the loading rate was lower than the critical loading rate vcin the early stages of loading,the axial displacement is 0.2 and 0.4 mm,the initial joint structure exhibited a strong stress sensitivity and the tensile strain region appears instantly,which determined the development of macroscopic cracks in the later stages of loading.The horizontal strain was mostly concentrated around the potential macro-crack,the strain was already concentrated at the initial stage of loading,which also showed a significant sensitivity.At the same time,the shear strain results suggested that there was also some local shear deformation around the initial joint.Besides,both shear strain occurs around the initial joint,which also showed the heterogeneous deformation before the final macroscopic failure.From the perspective of axial strain,the axial strain is mainly concentrated near the potential macro-cracks and also intensifies the generation of circumferential tensile strain under a low loading rate.This failure pattern was obvious in Fig.8a and b,Fig.9a,and Fig.10a and b.

Fig.8.Failure process of the Group 1 specimens at various loading rates.

When the loading rate was higher than the critical loading rate vc,the initial joint structure cannot produce a response at the beginning of loading and exhibited almost no significant expansion of the tensile strain area,thus the discontinuous distribution of the coal matrix became the main bearing structure.The horizontal strain was mainly produced by the macroscopic cracks of the matrix.The horizontal strain was still an important factor leading to the macro-coalescence,but its response rate is obviously slowed down.In addition,axial compressive strain occurs extensively in the specimen surface,which also prevents the formation of penetrating cracks to a certain extent.At the same time,the shear strain results suggested that only a few discontinuous and discrete parts of shear strain happen on the surface of the coal specimen and there is no potential fracture.This failure pattern was obvious in Fig.8d and e,Fig.9c–e,and Fig.10d and e.

Fig.9(continued)

Finally,with a rapid reduction of the effective area of the coal matrix,the ultimate compressive strength of the specimen would be easily reached and destruction of the specimen would finally be achieved.The evolutionary process of the surface deformation characteristics of specimens under various loading rates may also reflect the reason for the phenomenon of a nonlinear correlation between the UCS and the loading rate.

4.3.Surface crack propagation on the specimen

Despite surface deformation,surface crack evolution is the most important information related to failure characteristics and strength.The failure patterns of the specimens in group 1 are shown in Fig.11.It is obvious that the failure pattern was significantly affected by the loading rate.It is common for cracks to eventually propagate through the entire surface.When the loading rate increased,the number of secondary cracks decreases and the main cracks dominated the failure of the specimen (Fig.11c–e).There was also a strong spalling phenomenon under a high-loading rate(Fig.11e).The reason for this may be that when the loading rate was low,the rapid macro-mechanical fractures along the joint surface(or original defects)played a dominant role and resulted in the final development of macrocracks.When the loading rate is high,the local heterogeneity of a coal sample will lead to initial damage within the coal matrix and the failure of the coal matrix will gradually accumulate to form a macrocrack.

Then,corresponding to the actual field engineering situation,various mining rates of the coal seams will affect the development rates of mining stress,resulting in various states of fracture behavior,energy release,and disaster appearance in the coal mass.Therefore,how to guide the best advancing rate of the actual mining face based on differences in the mechanical behavior of coal samples under various loading rates is a topic worthy of discussion.

4.4.Relationship between the failure pattern and loading rates

It is obvious that the compressive strength values of the specimens in all three groups increased first and then decreased as the loading rates increased.This result is different from those in previous studies,which suggested that a larger loading rate can result in greater strength [48–51].Some potential reasons for the abovementioned phenomenon are given hereafter:

(1) A relatively low loading rate value may result in sufficient development of natural defects (e.g.microcracks and pores)as well as bearing structure(coal matrix).The internal damage will increase first until macroscopic failure occurs.This failure can be exhibited two types:failure caused by cracks induced by the propagation and connection of original defects,and failure caused by cracks induced by the failure of the coal matrix (the main bearing structure),among which the former is the primary failure patterns (Fig.12a).Therefore,the bearing capacity,i.e.the strength,is relatively small in this situation.On the other hand,as shown in Fig.10a,when the axial displacement changed from 0.4 to 0.8 mm,it is obvious that local original defects gradually developed and finally generated an obvious macroscopic crack.Fig.12a and Fig.10a can support the first predicted pattern to some extent.

(2) When the loading rate is gradually increasing,the degree of development of the original defect is gradually decreasing,which is not the main reason for the final failure.As shown in Fig.10b and c,the initial damage was located at a number of parts of the surface of the coal specimen,and the final failure was generated close to some small cracks.In addition,from the final failure patterns in Fig.11b and c,the long cracks along the original defects are not the only failures on the surface of the coal specimen and some small cracks of local matrix failure also occurred.The failure of the specimen with the mechanism mentioned above can be abstracted as the second pattern in Fig.12.

(3) However,after the loading rate reaches a certain value critical vc,the simultaneous failure of a high number of bearing structures (coal matrix) could be the main reason for the decrease in compressive strength [52].During this process,although the original defects have nearly no time to develop,the degree of failure of the original bearing structure increases significantly owing to the high energy of the high-loading rate and the rapid reduction in the bearing area.The effective bearing structure is severely damaged,and the bearing capacity decreases (Fig.12c).On the other hand,as shown in Fig.10d and e,the original defects did not sustain much development,and a number of strain concentrations for the coal matrix occurred around the surface of the coal specimen.In addition,from the final failure patterns in Fig.11d and e,it can be suggested that the local failure of the matrix was the main phenomenon and coal matrix spalling was obvious.Therefore,this kind of failure can be abstractly described as failure pattern 3 in Fig.12.

Fig.10.Failure process of the Group 3 specimens at various loading rates.

Fig.10 (continued)

5.Analysis of the mining rate effect and application to actual engineering:A case study

Fig.11.Final failure characteristics of the specimens at various loading rates.

Fig.12.Schematic view of the final failure pattern under various loading rates.

The coal mining process is actually a mechanical behavior,and various mining rates will affect the mining stress distribution/redistribution rate and result in various states of fracture,energy release,and disaster appearance in the coal mass.However,the mining rate is not only referring to the mining efficiency but also the safety problems,which is a contradictory proposition.

From the perspective of mining rates,a larger mining rate is needed to guarantee the coal output but a large mining rate usually means a quick stress environment adjustment,which is testing the bearing capacity of the coal mass in front of the mining face and also the supporting structure of surrounding rock.At the same time,a large mining rate will also result in a quick energy concentration,which is very dangerous for some disasters (such as rock bursts).Owing to the conditions of actual engineering,there are so many impact factors,and the bearing capacity and energy concentration during the mining process cannot be directly determined.The loading rate in laboratory can be generalized to the advancing speed of mining face.As a result,based on the laboratory experiment,the mechanism of loading rates or mining rates can be discussed.

From the perspective of the results of this manuscript,it can be suggested that there is an obvious non-linear relationship between the loading rates and coal strength,the coal strength is increasing first and then decreasing with the increase of loading rates.A critical loading rate is presented.Similar characteristics also refer to the elastic strain energy.In order to guarantee the coal mining output,maintain a large bearing capacity and a relatively low elastic strain energy,determining a reasonable loading rate or the mining rate is much of importance.Combining the UCS and elastic strain energy,this manuscript is trying to find an impossible approach to determine the reasonable mining rate from the perspective of laboratory research.

5.1.Investigation of the relationship between the in-situ mining rate and loading rate in the laboratory

Simulating the stress environment and relating the usual loading paths or patterns found in actual engineering projects in the laboratory is one of the most common issues in this type of research.As we know,the stiffness and strength of overlying strata and bottom strata of the coal seam are usually much higher than those of coal mass.Thus,it is a common solution for people to model the stress paths of mining disturbance by using a servocontrol rock mechanics facility [53-55].Meanwhile,the study of roof-coal-bottom structure also usually assumed that the roof and floor were rigid body [56-61].

Additionally,in previous research,the stiffness and strength of overlying strata and bottom strata of the coal seam are usually much higher than those of coal mass.There is a huge difference in elastic modulus between the roof-floor rock and coal [62-64].Based on the geological data of Pingdingshan Coal Mine,the elastic modulus of the roof-floor sandstone is nearly 110 GPa,the elastic modulus of the coal is nearly 6 GPa.Thus,it may be reasonable that the deformation of roof strata and floor strata in front of mining face can be ignored when comparing with the deformation of the coal seam.Here,another assumption should be added:the roof and floor of coal seam in front of the mining face can be regarded as a rigid body with no deformation.After excavation and the redistribution of the in-situ stress,the stress state of the coal in these areas can be simplified as one specimen in a state of the uniaxial compression state (Fig.13).This simplify should be referred to some assumptions:the contact between coal seam and roof plate meets the continuity condition;the deformation of coal seam is synchronous with the displacement of roof;the displacement between roof and floor is regarded as the deformation of coal seam;the overlying strata and bottom strata of coal seam in front of mining face can be regarded as a rigid body with no deformation.

In this manuscript,a preliminary investigation of the relationship between the mining rate and loading rate was conducted.The loading rate can be understood as a reflection of the mining rate of the working face or the tunneling rate.When mapped to the field scale,the loading rate can provide a reference for determining safe mining rate values.As shown in Fig.13,the engineering and geological conditions of a specific coal seam can be considered constant within a certain length range.Then,the roof rock layer in front of the mining face is considered to be in complete contact with the coal seam,and the deformation of the roof and seam is congruous.Thus,the deformation between the overlying strata and bottom strata near the mining face can be treated as compression of the coal pillar.

As for the mining disturbed underground space,the displacement or deformation of the surrounding rock,rock strata,or the coal mass is also induced by the unloading and re-distribution of the in-situ stress.Therefore,the study of the deformation of the roadway or the coal pillar can be established on the view of the stress path of mining disturbance,which is also the basic mechanism of the deformation of underground rock or coal mass.The stress path effect is modeled by using complex loading conditions,such as different loading rates or loading paths.Meanwhile,the roof-to-floor convergence can be understood as the vertical deformation of the coal seam.From the perspective of field data,the monitoring points are usually set near the side wall of the coal seam with two points on the roof-to-floor,and the vertical deformation rate can be calculated by the displacement between the monitoring points.As a result,the loading rate and the compressive deformation of the coal pillar can be used to develop an equivalent method to create a link between laboratory and actual engineering scenarios.Based on previous research,the relationship between the coal seam thickness and the height of laboratory experimental specimens is given by [52]

where v is the loading rate used in the laboratory experiment(mm/d);hthe height of the specimen(m);Hthe height of the coal seam(m);ξ the non-homogeneous coefficient,which ranges from 10 to 20 (ξ is set to 10 in this research);andVmaxthe maximum rate by which the coal pillar is compressed(mm/d).Considering the results of previous studies[16,65],the relationship between the advancing rate of mining face and the maximum subsidence deformation of overlying strata or the deformation rate can be fitted with a power law,a power-law relationship can be assumed between the mining rate and loading rate.Li et al.[20]and Li et al.[52]obtained the following relationship between mining rate and loading rate by fitting

whereaandbare the correlation coefficients;andMRthe rate of advance of the mining face.

Under the abovementioned assumptions,the coal seam deformation of an in-situ working face is used to determine the correlation coefficientsaandb.The mining height for the working face is 3 m.WhenMR=1.5 m/d,the maximum deformation rate from the roof to the floor is 18 mm/d.WhenMR=2 m/d,the maximum deformation rate from the roof to the floor is 35 mm/d.As a result,the relationship between mining rate and loading rate for the working face can be obtained as

where the units ofMRand v are mm/d and mm/min,respectively.

Based on Eq.(4),the relationship between the loading rate in the laboratory and the mining rate in the actual engineering is developed.However,when determining the optimal mining rate,not only is the bearing capacity (i.e.the UCS) of the coal needed but also the elastic strain energy should remain at a relatively low value to prevent rock bursts.These two influencing factors are usually in a state of mutual restraint.As a result,the evaluation of the optimal mining rate for a laboratory loading test can be described as

Fig.13.Schematic view of the equivalent relationship between axial loading in the laboratory and 430 compressive deformation in-situ.

whereMs-optimalis the optimal mining rate in-situ;σuc-maxthe maximum axial compressive strength with a change in loading rate;andUe-minthe minimum releasable elastic strain energy with the change in loading rate.

The releasable elastic strain energy within the principal stress space can be noted as [66]

Referring to the uniaxial loading condition,Eq.(7) can be simplified as

Based on Eq.(8),the released elastic strain energies were calculated and are listed in Table 3.The results suggest that the released elastic strain energy first increased an increasing trend and then decreased with an increase in loading rate.Generally,a high UCS usually means a high elastic strain energy.The maximum value of the UCS occurred in the loading rate range of approximately 0.05–0.1 mm/min,and the maximum value ofUealso occurred within the same range and was much higher than those at other loading rates.To reduce the risk of a quick release of elastic strain energy and also to maintain the bearing capacity of the rock,the optimal loading rate was suggested to be approximately 0.02–0.05 mm/min based on Eq.(5).Using Eq.(4),it can be suggested that with anMR=3 m/d(2.94–4.36 m/d),the compressive strength of the coal pillar was relatively high for bearing the mininginduced stress in front of the mining face.Additionally,the level of accumulatedUeremained within the moderate range with no rockburst risk.To further evaluate the suggestion of an optimalmining rate for this mining face,monitoring of the actual mining rate and the pressure on hydraulic supports at the Ji15-31030 working face was conducted.

Table 3Calculation results of the released elastic strain energy.

5.2.Mining-induced pressure evolution under various mining rates at the Ji15-31030 working face

To verify the optimal mining rate for the laboratory based on the UCS and elastic dissipation energy,72-day continuous in-situ monitoring of the hydraulic support pressure and mining rate was performed on the Ji15-31030 working face.During this period,the working face advanced by 95 m.Fig.14,is a schematic diagram of pressure monitoring of a hydraulic support at the working face,in which a total of 70 sets of ZY6800/20/40 ordinary hydraulic supports and 76 sets of ZC5200/20/40 backfill hydraulic supports were used on the entire working face.This experiment focused on pressure monitoring of the No.1–20 hydraulic support near the ventilation roadway.The pressure monitoring consisted basically of automatically recording the pressure every 10 min through a pressure gauge installed in the lower cavity of each group of support columns.The daily recorded data of the mining rate at the Ji15-31030 working face are shown in Fig.15.The mining rate at the working face fluctuated between 0 and 3.2 m/d.Some of the workdays had a mining rate of zero because the working face had some additional operations such as borehole drilling for pressure unloading and gas drainage,and it took the entire workday to complete these tasks.The recommended optimal mining rate range was reached,and the average rate was approximately 1.3 m/d.

Fig.14.Schematic view of pressure monitoring of a hydraulic support.

Fig.15.Mining rate record during the monitoring period.

Fig.16.Monitoring results of the hydraulic supports.

Fig.16 shows the changes in hydraulic support pressure with the advance of the mining face.Three sets of hydraulic support pressure monitoring data were selected.Part of the interval was a straight line.The pressure data during this period were not recorded during a monitoring fault when the mining face was advancing to 20–30 m.The curve of hydraulic support pressure exhibited a periodic fluctuation with the continued advance of the mining face,and each growth interval represents one advance process of the mining face.When the mining face advanced to 60–80 m,the pressure on each hydraulic support fluctuated at a high level and then reaches a dynamic equilibrium state.The faster the mining face advanced,the longer the mining distance was per unit time and the more fracturing occurred in the overlying strata.Finally,the greater pressure acted on the hydraulic support.However,with a further increase in distance,the pressure recovery in the goaf limited the fracture from continuing to expand upward;therefore,the hydraulic support pressure did not continue to increase beyond a certain distance.Instead,it fluctuated with the periodic collapse of the old roof within a certain range.Additionally,under various mining rates,the pressure of the hydraulic support exhibited mostly periodic fluctuation characteristics.Furthermore,the hydraulic support pressure increased to a certain extent with the advancement of the mining face,and the amplitude and range of the fluctuations were relatively stable.When the mining rate of the mining face reached 3.2 m/d,the maximum pressure fluctuation range of the hydraulic supports was less than 40 MPa,which is generally within the safe bearing range.Therefore,according to the experimental analysis results and in-situ monitoring results,it is recommended that the average mining rate of the Ji15-31030 working face be increased from 1.3 to approximately 3 m/d.

6.Discussion

As we know,a gap always exists between the laboratory-scale study and the engineering practice,and such gap is also the distance between the rock mechanics and the rock engineering.However,the results generated from the laboratory always present a positive reference even a direction solution for engineering.

In this paper,the mechanical behavior of the coal,which is collected from the filed site,under different mining rates is investigated in detail.For different loading rates,the evolution of mechanical parameters,the failure pattern,and the energy accumulation and release are analyzed and compared.Similar work can be also found in previous studies separately.The relationship between the rock mechanical behavior and loading rate is one of the most important research of laboratory rock mechanics.When it comes to the rock strength,some previous researchers thought it correlated positively with the loading rate [11–13].However,most of the research objects are belong to the high-strength rock,only a few pieces of research have concerned the relationship between the rock mechanical behavior and loading rate for the low-strength rock.The rock specimen of this work belongs to the low-strength type.When it comes to the rock strength,the testing results suggested that the uniaxial strength was increasing first and then decreasing,during which a threshold range of loading rate occurred.The results are quite similar to the results of the research work by Li et al.[14],in which the relationship between the uniaxial strength of coal and loading rate was not a linear pattern,and the loading rates 5×10-4to 1×10-3mm/s was the threshold rage.Besides,to prove this testing phenomenon,combined with the fracture timely detecting technique,the fracture evolution during the loading process,fracture number on the coal specimen surface,and the final fracture pattern of the coal specimen are used to explain the testing results.Based on these testing results,one of the most important works referring to the failure mechanism under different loading rates has been presented in Fig.12.As for the elastic strain energy of coal under different loading rates,the relationship between the elastic strain energy of coal and loading rate was still not a linear pattern,the similar conclusions of elastic strain energy,dissipation strain energy,or acoustic emission (AE) events under different loading rate can be found in previous work [7,28,32].

However,such results are not sufficient for engineering applications.Therefore,bridging the gap between the laboratory study and engineering practice is another aim of this paper.As illustrated in Section 3,a critical range of the loading rate is proposed.Thus,it may imply that there should be an optical mining rate for the field.Based on the field monitor and the experimental results,the relationship between the loading rate and mining rate is proposed.Also,the relationship is verified and applicated based on the monitored data and the deformation energy.The optical mining rate is thus proposed.Meanwhile,it should be noted that there are some research limitations of this work and there are also some additional researches that should be applied in the future.Firstly,for the actual engineering,the assumption that the roof and floor of coal seam in front of the mining face can be regarded as a rigid body with no deformation is not strictly to the actual situation.The deformation and failure of the roof layer should be concerned when determining the real axial deformation of coal.Secondly,the coal used in laboratory tests is not considering the initial porosity and fracture,the relationship between the pore-fracture system and loading rates still needs intensive research.Thirdly,an optimal mining rate is a value for coal seam with a large-scale,linking the research results in laboratory and the actual engineering still needs intensive field monitoring or numerical simulations in the future work.Generally speaking,this paper proposed a methodology for the evaluation of the mining rate.The application potential is demonstrated by the field monitoring.Meanwhile,it should be noted that the relationship between the loading rate and mining rate is just for the case of the Ji15-31030 working face.This case study can be a reference for the design of the mining rate.

7.Conclusions

To investigate the mechanical behavior of coal under different loading rates,uniaxial loading tests and 3D DIC tests were conducted.Afterward,based on field monitoring,the relationship between the mining rate and loading rate was determined.The main results can be concluded as follows.

(1) The compressive strength of the coal did not increase constantly with increasing loading rate.There was a certain threshold range of the critical loading rate vc.If the loading rate was greater than vc,the compressive strength might decrease with increasing the loading rate.The approximate value range of vcin this study was 0.05–0.10 mm/min.

(2) The surface deformation of the specimens implied that the failure mechanism would be dominated by the loading rate.When the loading rate was lower than vc,the tensile strain region around the initial joint structure appeared quickly.When the loading rate was higher than vc,the discontinuous distribution of the coal matrix became the main bearing structure.

(3) The loading rates had a significant effect on surface deformation and crack propagation.At lower loading rates,the original defects were more stress-sensitive and usually generated the final crack propagation.At relatively high values of loading rates,the coal matrix became the main bearing structure and only a few main cracks appeared on the surfaces of the specimens at failure.

(4) Based on the UCS and releasable strain energy,a relationship between the mining rate and loading rate in laboratory tests was preliminarily proposed.Combined with the field monitoring for this case study,the mining rates were evaluated using mining-induced pressure monitoring,and a reasonable mining rate for the Ji15-31030 working face was suggested to be approximately 3 m/d.

Acknowledgements

This work was financially supported by National Natural Science Foundation of China (Nos.U2013603,52004167,52078477,51827901,and U1965203) and Sichuan International Technological innovation Cooperation Project (No.2018HH0159).