Zhihu Le,Qinglei Yu,*,Wncheng Zhu,Hongyun Liu,Tinhong Yng

a Center for Rock Instability and Seismicity Research,Northeastern University,Shenyang 110819,China

b School of Engineering AMC,the University of Tasmania,Hobart,TAS 7005,Australia

Keywords:Granular backfill Dense degree Gradations Sandstone Compressive strength

ABSTRACT Backfilling is a common practice in the mining industry and the backfilling performance plays a significant role in supporting the surrounding rock mass.To evaluate the backfilling performance,an experimental apparatus has been developed to understand how backfill affects the compressive strength of sandstone specimens in the laboratory.Pebbles were selected to model the backfill and divided into six groups with different particle sizes using a set of standard sieves.The backfilling pebbles with three types of particle size compositions were then produced,i.e.single gradation,two adjacent gradations,and increasingly widening gradations.A series of compressive tests were carried out to study the mechanical behavior of the sandstone specimens confined by these pebbles.The effects of the gradations of the filled pebbles on the peak and residual compressive strengths were analyzed.It is found that the increasing amount of the compressive strength is over 10%in most cases,even up to 20%.Based on the experiment data,the increasing amount was also estimated theoretically under some assumptions and it further confirmed the experimental results.The effects are closely related to the gradations of the filled pebbles except for their dense degree.

1.Introduction

The cut-and-fill mining method is increasingly applied in major mining countries to control ground pressure and protect the environment [1].In China,authorities encourage new non-ferrous mines,even ferrous mines[2,3],to employ this method.However,it has been reported that evident ground subsidence and deformation occurred at a nickel mine in China although the mined void was backfilled immediately after excavation [4,5].During the mine-induced subsidence process,it strongly involves the interactions of the backfill with surrounding rock mass and these interactions may become very strong and complex.To deeply understand the subsidence mechanism and better design the backfill,it is necessary to study the interactions between them.

During the development of the cut-and-fill mining method,there are many pieces of literature focusing on new backfill techniques,materials,methods [6–9],the compaction and mechanical behavior of granular backfills[10–13]and cemented paste backfills[14–16],and improving the compressive strength of the surrounding rock[17].However,less attention has been paid to the interactions between the backfills and the surrounding rock mass.In fact,the backfill (e.g.hydraulic sand tailings or waste rock) used in the cut-and-fill mining method can be considered as granular materials[18,19].This granular backfill,similar to liquid,produces lateral pressure due to gravity to support mining stopes,which is defined as active pressure [20].However,when it is squeezed due to the deformation or failure of the stope walls,the granular backfill will produce passive pressure to strongly support the stopes [21].Moreover,this passive pressure may be greatly larger than the active pressure,which depends on the squeezing deformation[22].

With regard to the active pressure of backfill,the early theory was developed by Janssen [23] and Marston [24],which is used to calculate the pressure of particles in silos or closed conduits.During the cut-and-fill mining practices,however,the main purpose of calculating active pressure is to evaluate loads of the granular backfill applied on the barricades,which are usually used to retain the flowable fill(e.g.hydraulic sandfill or waste rock).Therefore,based on the early researches,many attempts have been made to evaluate the stress state of the granular backfill in underground mine stopes.Aubertin et al.[25] and Li et al.[26] derived analytical solutions to calculate the vertical and horizontal stresses of the granular backfill in vertical stopes.Ting et al.[27]discussed the effect of the wall inclination on the vertical stress of the granular backfill.Jahanbakhshzadeh et al.[28] proposed a new solution to derive the vertical and horizontal stresses in the backfilled stopes with the inclined walls of various inclination angles.Moreover,Ting et al.[29]and Rajeev et al.[30]designed laboratory models to study the arching phenomenon and the stresses within the granular fill in a model stope and modified the analytical solutions on the basis of their laboratory experiments.Furthermore,numerical methods have also been employed to analyze the stress distribution within the granular backfill with consideration of more complex conditions [31–33].

With regard to the passive pressure of backfill,there is little literature on experimental or field studies published.Song et al.[34]analyzed the interactions between the rock pillar and cemented paste backfills by using a self-made experimental device.However,for the case of granular backfill,most attempts were made using numerical methods to study the influence of the backfill on the pillar strength.Kostecki and Spearing [35] employed a threedimensional (3D) Mohr-Coulomb elastic plastic model with the interfaces between the pillar and backfill to investigate the influence of the backfill on the coal pillar strength and found that the non-cohesive backfill had little influence on the increase of the pillar strength.Mo et al.[36] obtained similar conclusions using a two-dimensional (2D) strain softening model based on the Mohr-Coulomb failure criterion.However,Wang et al.[37] also numerically investigated the influence of roadway backfill on the strength of a coal pillar using a 3D strain softening model with nonassociated shear and associated tension flow rules based on the Mohr-Coulomb failure criterion,and concluded that the pillar strength could increase around 20% to 35% when the percentage of non-cohesive backfill is up to 90%.The same software (FLAC3D&2D) with similar models were used in these modellings,which,unfortunately,led to discrepancies.

The reliability of the numerical modelling depends on the selected constitutive model and input parameters.Although the backfill is assigned zero cohesion in their modellings to simulate granular backfill,it may be still in doubt whether the constitutive model can accurately describe the physical behavior of the granular backfill.In this case,experimental study may be an effective method to clear the discrepancies.Therefore,in this study,an experimental apparatus was developed to model how the granular backfill supports a pillar in the laboratory and understand the interactions between them.Using this apparatus,a serial of experiments were carried out to preliminarily study the behavior of the sandstone specimens confined with common pebbles.On the basis of the experimental results,the influence of the particle gradation of the backfill on the sandstone specimen strength was primarily discussed.

2.Equipment and material

2.1.Experimental equipment

The experimental apparatus for modelling how granular backfill supports rock specimen consists of a modeling cell for holding granular backfill and rock pillar,a load controlling unit,and a data acquisition unit.

The modeling cell is shown in Fig.1a,in which a cylinder wall,a couple of floating ring platens,a fixed ring plate,and six vertical bolts are used together to restrict the backfill.The rock specimen is placed in the center while the granular backfill is filled into the space between the sample and the cylinder wall.The inner diameter of the cell is 360 mm,and the cylinder wall with a thickness of 3 mm is made of 45# carbon steel,which has an elastic modulus of 207 GPa and Poisson’s ratio of 0.26,respectively.The diameter of the rock pillar sample can be 100,125,or 150 mm.During the experiments,the modelling cell is installed in YAW-5000 servo-controlled testing system(Fig.1a)and the axial loading is applied on the down bar,which runs through the centric holes of the modelling cell acting on the rock specimen sample.The axial load can be applied in either stress or strain controlled mode and the maximum available axial load is 5000 kN.The load and displacement are automatically recorded by the data acquisition unit.

To capture the response of the backfill,the cylinder wall is especially designed and consists of three arc walls with an identical size,that is,it is a cylinder cell that composed of three arc walls with 120° in radian (see the section view of modeling cell in Fig.1a).Each arc wall is fixed using two vertical bolts running through four small bolt holes,which is like a shell with four corner points fixed.When the backfill is squeezed by the lateral deformation of the rock sample,the passively induced pressure will pass through the backfill to the arc wall,depending on the failure plane orientation during the post failure stage.Three strain gauges are installed on each arc wall to measure its deflection.The configuration of the strain gauges on each wall was shown in Fig.1b,and the data are recorded by the data acquisition unit to evaluate the mechanical response of the backfill.

2.2.Backfill preparation

The common pebbles were adopted to model granular backfill because the contacts between pebbles are relatively simple(point-point contacts and few point-face contacts),and regular results may be obtained.In the laboratory,the pebbles were further sorted into six gradations using standard sieves as shown in Fig.2a and b,whose sizes are 4.75–9.5,9.5–13.2,13.2–16,16–20,20–26.5,and 26.5–31.5 mm.The solid density of the pebbles is 2.67 g/cm3.

Fig.2c shows the representative shapes of the pebbles in six grades.It can be seen that the shapes of the pebbles in the same grades are quite different due to the fact that the pebbles were produced naturally.Moreover,it is noticed that the differences between the shapes of the pebbles with small diameters are small while they are great for the pebbles with large diameters.

2.3.Rock specimen preparation

The rock used in the study was obtained from a quarry in Yunnan province,China.In this study,the gradation with big particle size is 26.5–31.5 mm.Generally,it is required that the dimensions of granular material should be 5 times the particle size to represent granular material behavior [38,39].For the case of rock samples with 100 mm diameter,the width of the annular space between the rock sample and the cylinder wall is 4.1–4.9 times the pebble size to basically meet the requirement.Therefore,the rock specimens were fabricated into cylindrical samples with 100 mm in diameter and 200 mm in height,as shown in Fig.3a.Ninety-six specimens were made in total and the average density is 2.25 g/cm3.

Before the loading test,P-wave velocity was measured using a C61 nonmetallic ultrasonic detector for all ninety-six specimens,which revealed that the P-wave velocity varied from 1.30 to 2.56 km/s.Moreover,it was noted that the P-wave velocity of most samples was less than 2 km/s and only five specimens was larger than 2 km/s.Therefore,the specimens with the P-wave velocities larger than 2 km/s were classified into one group and the rest were divided into seven groups,in which the interval of the P-wave velocity between groups is 0.1 km/s.The amount of the specimens in each group is then counted and plotted in Fig.3b.To minimize the influence of the scattered variation of the sandstone’s mechanical properties on the testing results,the specimens with the P-wave velocities ranging between 1.6 and 1.8 km/s were selected for the loading experiments.

Fig.1.Experimental apparatus.

The basic mechanical properties of the selected sandstone specimens were firstly measured using a standard testing machine following International Society for Rock Mechanics(ISRM)standards,which shows that the sandstone has the uniaxial compressive strength (UCS) of about 57.33 MPa,the elastic modulus of about 7.83 GPa,and Poisson’s ratio of 0.27.Such lower elastic modulus and UCS prove in a way that sedimentary diagenesis is weak for this type of sandstone,and it may result in a highly heterogeneous microstructure of sandstone and the variations of P-wave.

2.4.Experimental schedule

In this study,the sandstone specimens confined by the pebbles with a single gradation,two adjacent gradations,and increasing gradations were loaded axially to systematically examine the influence of the grading pebbles on the strength and deformation of the sandstone specimens.Six groups of compressive experiments were carried out for the tests with single gradation,five groups for two adjacent gradations,and six groups for increasing gradations.In each group,the tested specimens from the group with P-wave of 1.6–1.7 or 1.7–1.8 km/s were not further marked.However,three specimens were tested for each grading scheme under the identical condition,and the average values are used as the test results in order to further minimize the influence of the variations among specimens on the results.The displacement-control loading mode was adopted and the loading rate was 0.5 mm/min.For each test,the height and the mass of the filled pebbles between the specimen and the cylinder wall are measured to estimate the dense degree(The dense degree is defined as the fraction of the solid volume of the filled pebbles over the total volume of the filled pebbles.)of the filled pebbles.Table 1 presents the grading schemes and the dense degree of filled pebbles for experiments.

Table 1Grading schemes and dense degree of the filled pebbles for experiments.

It should be noted that the filling process of the pebbles in each test may affect the testing results to some extent.The pebbles were filled into the space between the specimen and the cylinder wall(see Fig.1a)layer by layer to ensure the uniform and dense distribution of the pebbles,which is illustrated in Fig.4.In the tests,the filled pebbles are unintentionally prestressed during the tests due to the weight of the adjustable ring plate and the upper float ring plate (see Fig.1a),which is 70 kg in total.Therefore,considering the fixed load on the adjustable ring plate,7.3 kPa pressure was applied on the filled pebbles in each test.

3.Experimental results

3.1.Stress-strain curves

Fig.5a presents the stress-strain curves of the specimens when the specimen confined with the single gradation (13.2–16 mm)pebbles and two adjacent gradations (20–26.5 and 26.5–31.5 mm mixed) pebbles,and the stress–strain curves of the specimens under the axial compressive condition without pebbles.The stress–strain curves of the rock specimens confined by the granular fills with single gradation,two adjacent gradations,and increasingly widening gradations are plotted in Fig.5b–d,respectively.Similar to the complete stress–strain curve of rock,the compressive process of sandstone specimen confined by filled pebbles can be divided into four stages,i.e.compacted stage of rock (OAstage),elastic deformation stage of rock (ABstage),failure stage of rock(BCstage),and post-peak stage of rock(CEstage),as shown in Fig.5a.

It can be seen that the pebbles confining the specimens have positive influences on the peak and residual compressive strength.The peak compressive strength of specimens has been increased and the residual compressive strength has been highly increased,which is larger than 5 MPa during theDEstage (Fig.5a).These increases are contributed by the active and passive pressures from the pebbles.In the experiments,the active pressure was contributed by the pre-existing pressure (about 7.3 kPa mentioned in Section 2.4) as well as the weight of the filled pebbles,and the passive pressure was produced due to the pebbles squeezed by the lateral deformation of the rock specimens.

During the pre-peak stage,all the stress–strain curves are similar.However,they are quite different during the post-peak stage.During this stage,the axial force,the confining pressures from the squeezed pebbles as well as the frictions on the failure planes have reached a relative equilibrium for the case with the specimens confined by the pebbles.Therefore,with the increasing axial displacement,the residual compressive strength is generally constant.Only a few stepped descents or subsequent linear ascents occur on the curves.The stepped descents may result from the fragmentation of some pebbles with their strengths attained due to the stress concentrations,which are induced by local contacts between the pebbles subjecting to squeeze.After that,the granular system of pebbles becomes relatively stable for the stress concentrations within them are released,and will be interlocked again under squeezing conditions.With the lateral deformation of the rock specimens increasing,the pebbles are squeezed more densely to produce larger passive pressures,which results in the occurrences of subsequent linear ascents.

Fig.2.Pebble backfill preparation.

Fig.3.Rock specimens.

3.2.Failure patterns

Fig.6 shows the failure patterns of the specimens confined by the filled pebbles with various gradations and under uniaxial compressive conditions.This type of sandstone specimens either confined by pebbles with various gradations or under uniaxial compressive conditions mainly exhibit single-slope shear failure.A difference is that tensile cracks near the shear plane in the case of uniaxial compression are more than those in the cases with filled pebbles.This may be related with that the filled pebbles passively provide pressure on the surface of the sandstone specimen to improve the stress state within the sandstone specimen.

Fig.7a shows the indentations on the sandstone specimen,which indicates the strong interaction of the filled pebbles with the specimens.This violent interaction influences the stress status within the specimens and subsequently influences their failure(see Fig.6).During the loading process,some pebbles were also crushed,as shown by yellow arrows in Fig.7b.It induces that the force chains in the filled pebbles adjust and redistribute.The corresponding behavior at the macroscopic level is the stepped descents and ascents on the stress–strain curves during the postpeak stage (see Fig.5).

3.3.Effect of gradations on compressive strength

Fig.8 shows the effect of gradations on the compressive strength of sandstone specimens.It should be noted that the compressive strengths in Fig.8 are the average values of those obtained in three tests with the identical conditions.Meanwhile,the UCS of sandstone and a 10%increase of the UCS are also horizontally plotted in Fig.8 as a solid red line and a dash blue line for reference.

For the sandstone specimens confined by the filled pebbles,the compressive strength has increased exactly (above the solid red lines).The increasing amount of compressive strength (i.e.the increment of the compressive strength divided by the UCS)ranges from 1.2%to 19.3%.If the dash blue lines(10%increase of the UCS)are referenced considering a 10%test error,the increasing amount in 13 gradations (four in Fig.8a and b,respectively,and five in Fig.8c) is over 10%.

For the cases with the single gradations and two adjacent gradations,in general,the compressive strength of the sandstone specimens slightly decreases with the size of the pebbles in each gradation increasing (Fig.8a and b).For the third case,the compressive strength slightly increases with the gradation increasingly widening(Fig.8c).It can be seen that the test results from the case with two adjacent gradations are more scattering than those from the case with the single gradation,which may be related with the size range of the filled pebbles.

For the case with rock specimen confined by the filled pebbles,the pressure that the filled pebbles provide depends on the lateral deformation of the rock specimen.The deformation and lateral deformation of intact rock are tiny at the pre-peak stage.When this tiny lateral deformation acts on the filled pebbles,very small pressure can be produced.Therefore,the filled pebbles were thought to hardly affect the compressive strength of the specimens.However,this effect of the filled pebbles on compressive strength has been observed apparently and presents certain regularity with the gradations of the filled pebbles (Fig.8).By analyzing the data,it is found that,during rock dilatancy in the pre-peak stage,the passive pressure has been generated within the filled pebbles,which is recorded by the strain gauges installed on the arc walls of the cylinder (Fig.1).

Fig.4.Filling process of pebbles.

Fig.9 shows the curves of the axial stress of the specimen at the gradations of 4.75–9.5,4.75–13.2,and 4.75–31.5 mm and the corresponding hoop strain of the three arc walls with time.To give more details,the curves near the peak stress are separately magnified and plotted on the right.At the peak stress,the gauges on the three arc walls have violent responses.By statistical analysis,the violent responses of the gauges on the three arc walls occurred 8 s ahead of the peak stress (from the uprush point of hoop strain to the peak stress in Fig.9).These responses indicate that the filled pebbles have been suddenly squeezed to passively produce pressure before the peak stress.In turn,this pressure was acting on the specimen to enhance its compressive strength.

The pressure that filled pebbles acts on the specimen can be estimated under some assumptions according to Newton’s Third Law of Motion,the generalized Hooke’s law [40],and the thinwalled vessel theory [41].Fig.10 shows the free body diagram of granular backfill during tests.The pressure () on the outer surface of the granular backfill is the resistance of the cylinder wall and the pressure (σ3) on the inner surface of the granular backfill is the interaction between backfill and rock specimen.To theoretically analyze this pressure,and σ3are both assumed to be uniformly distributed on the outer and inner surfaces.Due to that the granular backfills maintain balance throughout the tests,the force acting the inner surface of filled pebbles should be equal to that acting on the outer surface.These two forces are related to σ3and,the perimeter of the outer and inner surfaces as well as the height of the filled pebbles.Therefore,the ratio of σ3tocan be determined to be equal to the diameter ratio of the cylinder wall(D)to the rock specimen(d).In this study,the diameters of the cylinder wall and rock specimen are 360 mm and 100 mm respectively,so the ratio of σ3tois 3.6.

According to the generalized Hooke’s law [40] and thin-walled vessel theory[41],the outer pressure()can be calculated based on the data of strain gauges attached to the cylinder wall.In this study,the cylinder consists of three arc walls,not a complete thin-walled cylinder,so the value of outer pressure () is an approximation,just to explain the effect of backfill on the compressive strength of rock.Fig.11 shows the estimation of the inner pressure (σ3).In Fig.11,the maximum value of hoop strains at the three uprush points is adopted for each grading type.From Fig.11,it is observed that the changing trend is basically consistent with compressive strength (Fig.8a–c).

Fig.5.Stress-strain curves of uniaxial compression and sandstone specimens confined by pebbles.

Fig.6.Failure pattern of the sandstone specimens confined by pebbles with various gradations.

Fig.7.Interaction between sandstone specimen and filled pebbles.

Besides,the possible range of the outer pressure () can be estimated based on the experimental data according to the above-mentioned theory.The minimum and maximum values of hoop strain at the uprush points are selected from all the tests and the rock failure is assumed to obey the Mohr-Coulomb Criterion.When the internal friction angle is set to be 30°,40°,and 50°,the possible range of the increasing amount of compressive strength can be obtained and the results are shown in Table 2.The theoretical results of the increasing amount of compressive strength range from 3.19% to 55.05%,depending on the internal friction angle.

Although the theoretical results are obtained under some assumptions,they provide references for the experiments.The increasing amount of compressive strength of sandstone specimens confined by filled pebbles obtained experimentally is about 1.2% to 19.3%,which is smaller than the results obtained theoretically.Therefore,it is concluded that the experimental results are reasonable and reliable.

3.4.Relation between compressive strength of sandstone and dense degree of backfill

According to Table 1,the dense degree of the filled pebbles is between 0.55 and 0.60.For the cases with the single gradation and two adjacent gradations,the dense degree of filled pebbles generally decreases with its increasing particle size.However,the dense degree of filled pebbles increases for increasingly widening gradations.

Table 2Theoretical results of the increasing amount of compressive strength for the experiments.

Fig.12 shows the relationship between the compressive strength of the sandstone specimens and the dense degree of the correspondingly filled pebbles.The data is linearly fitted and the linear correlation coefficient is up to 0.9983.In general,the compressive strength obtained under the confinement of filled pebbles increases with the dense degree increasing.However,for specific gradations,the relationship between the compressive strength and dense degree becomes inverse,especially for the cases of the test results at the gradations of 20–26.5,16–26.5,and 4.75–20 mm as shown by the red dashed box in Fig.12.These inverse phenomena may be related to the ratio of the width (i.e.130 mm in the tests) of the annular space to the diameter of the pebbles.In this case,only five or six pebbles can be stacked along the radial direction of the annular space,which may not completely represent the mechanical behavior of the massively stacked granular material.

It should be pointed out that granular materials have specific characteristics.The force transfer of granular materials mainly depends on force chains between particles,not completely on continuous strains like solid rocks.The composition of particle size can influence the force chains morphology and intensity in granular materials[42–46].On the premise that there is no relative motion between particles,the granular materials with small particle size can be packed densely with relatively weak force chains.In this case,the dense degree plays a dominant role in producing passive pressure.However,the granular materials with large particle sizes cannot be packed densely but produce strong force chains within them.In this case,the strong force chains play a dominant role in producing passive pressure.Therefore,the particle size composition of the granular backfill is also a vital factor influencing the compressive strength of rock specimens,which should be paid more attention.

Fig.8.Effect of pebbles with various gradations on the compressive strength of sandstone specimens.

Fig.9.Axial stress of the sandstone specimen and the hoop strain of the arc walls with time confined by pebbles.

3.5.Effect of gradations on residual compressive strength

In the cut-and-fill mining practice,it is common that there exists a gap between the stope roof and the top of the backfill.Due to excavation disturbance,blasting vibration as well as rock rheology,specimens confined by backfill often fail to induce the stope roof subsidence until the gap disappears to reach equilibrium.The specimens experience a post-failure stage,which involves the residual compressive strength.Fig.13 shows the effect of the different gradations of the filled pebbles on the residual compressive strength of the rock specimen.Due to the complex interaction of the filled pebbles with the sandstone specimens during the post-peak stage,the residual strength of the sandstone specimens is not constant (Fig.5).Thus,the residual strengths at three strain levels are selected,which are 0.028,0.033,and 0.038 and are approximately 1.74εp–2.54εp(εpis the peak strain).

It can be seen from Fig.13 that the residual strength of the sandstone specimens confined by the filled pebbles remains at 5–17 MPa,and it is about 9%–30% of UCS.From the figure,In general,the residual strength of the specimens firstly increases and then decreases with the gradations widening.For the cases with single gradations and two adjacent gradations,the residual strength exhibits a unimodal variation.The maximum occurs at the gradations of 13.2–16 mm (Fig.13a) and 16–26.5 mm(Fig.13b).For the cases with increasingly widening gradations(Fig.13c),the minimum of the residual strength occurs at the gradations of 4.75–9.5 mm and the peak values are not apparent.

Fig.10.Schematic diagram of and σ3.

This variation may be related to the flowability of granular material [47,48].During the post-peak stage,the filled pebbles are squeezed into each other.For the case with the smallest particle size,the granular material is of considerable flowability when subjected to squeeze and thus cannot provide relatively strong passive pressures on the specimens.For the case with the largest particle size,although the granular material is of little flowability,there are relatively large pore spaces.When subject to squeeze,some particles will be broken to fill the pore space.The squeezing deformation is substantially absorbed by the pore space,which makes the granular materials unable to provide relatively strong passive pressure on the specimen.

Fig.11.Effect of pebbles with various gradations on σ3.

Fig.12.Relation between the compressive strength of sandstone and the dense degree of the filled pebbles.

In this study,the intact samples were preliminarily adopted to examine the effect of granular backfill.It is found that the compressive strength of intact sandstone confined by filled pebbles increases up to 20% of the UCS and the residual strength is up to 30%of the UCS,about 5–17 MPa.Moreover,it should be noted that the effect of granular backfill on rock compressive strength depends on the lateral deformation of rock samples squeezing the backfill.In mining engineering,rock masses surrounding stopes consist of discontinuities with various scales.Rock masses have large lateral deformation when they are subject to compressive loads,which enable strong interaction between the granular backfill and rock masses.Therefore,the compressive strength and residual strength of rock masses confined by granular backfill may increase more than those of intact rock.In future work,the authors will fabricate jointed rock samples,similar to rock mass,to further study this effect using the self-developed experimental apparatus.

4.Conclusions

In this paper,an experimental apparatus has been developed to model how the backfill supports pillars in the cut-and-fill mining in the laboratory.Then using this apparatus,a series of laboratory tests were carried out to study the behavior of the sandstone specimens confined by the filled pebbles with three types of particle size composition.The following conclusions are drawn.

Fig.13.Effect of pebbles with various gradations on the residual compressive strength of sandstone specimens.

(1) The filled pebbles have an apparent influence on the compressive strength of the sandstone specimens.In most cases,the increasing amount of the compressive strength of the sandstone specimens confined by the filled pebbles is over 10%,even up to 20%,and it is confirmed by the theoretical estimation based on the data recorded by the strain gauges according to the thin-walled vessel theory and the Mohr-Coulomb Criterion.

(2) The filled pebbles also have an apparent influence on the residual compressive strength of the sandstone specimens.The residual compressive strength can remain about 9%–30% of UCS due to the stronger interaction between filled pebbles and sandstone specimens at the post-peak stage.

(3) The change of the compressive strength is basically consistent with the change of dense degree of the correspondingly filled pebbles,and it can be described by a linear equation.For some specific gradations,there exists an inverse change.This may be related to the ratio of pebble size to the volume of filled backfill.The ratio of particle size to the volume of granular backfill is an important factor to influence the performance of backfill,possibly similar to the representative element volume (REV) of the rock mass.It must be considered when studying granular materials.

Acknowledgements

This work presented in this paper was supported by the National Key Research and Development Program of China (No.2016YFC0801602),the National Science Foundation of China (No.52074060) and the Fundamental Research Funds for the Central Universities(Nos.N2101036 and N2101045).We are very grateful to the editor and anonymous reviewers for their affirmation of our works,and the careful examination,meticulous review comments,and constructive suggestions.This support is gratefully acknowledged.