Effect of Cyclic Lateral Loading on the Compaction Behaviour of Waste Rock Backfill Materials in Coal Mines

Crushed waste rock (CWR) can be used as backfill for goafs allowing disposal of solid waste and control of surface subsidence. Waste rocks for backfilling (WRBs) have a certain density before use if cyclic lateral loads are applied to CWRs, therefore, by employing a self-designed bidirectional loading test system for granular materials, the influence of the number of lateral loading cycles on the compaction characteristics of WRBs was explored. Through testing, changes in mechanical parameters of WRBs during lateral and axial loading were attained to analyse the influence of lateral loading on lateral strain, axial strain, porosity, and lateral pressure coefficient during their compaction. The test results showed that: (1) the lateral loading exerted a significant influence on the porosity, strain, and lateral pressure coefficient of crushed WRBs during lateral and axial loading; (2) under lateral load, the more cycles of lateral loading applied, the greater the lateral strain and the reduction in lateral porosity of samples; (3) during axial loading, for samples subjected to multiple cycles of lateral loading, owing to the porosity of WRBs having been decreased in advance to improve their density, the final axial strain was low; (4) after compaction, the particle size distributions of CWR samples after different numbers of cycles (1, 3, 5 and 7) of lateral loading all shifted upwards compared with those obtained before compaction, implying that rock particles were crushed. However, the number of cycles of lateral load did not affect crushing of particles before, and after, compaction.


Introduction
The mining of coal resources results in the generation of waste rock from washing and mining operations.The waste rock tends to be transported from the underground mine and then piled up on the ground to thus form waste rock dumps [1][2][3].Waste rock dumps are frequently subjected to various disasters such as landslides, spontaneous combustion, and explosions.The presence of waste rock dumps not only occupies land, but also leads to serious environmental pollution [4][5][6].According to incomplete statistics, the accumulated stacking of waste rocks in China has exceeded 5.5 × 10 9 t, forming more than 1600 waste rock dumps, which occupy a land area of 15,000 ha [7,8].Moreover, the discharge increases at the rate of 4 × 10 8 to 8 × 10 8 t annually.If this waste rock fails to be appropriately disposed of, severe environmental issues arise [9][10][11][12], To solve the problems caused by discharge of waste rocks, we proposed direct backfilling of goaf with waste rock: waste rock is crushed and then transported to the underground coal face and then filled into goaf [13][14][15].The method not only can dispose of solid waste rocks but also can control stratum movement and surface subsidence.
method not only can dispose of solid waste rocks but also can control stratum movement and surface subsidence.Thus, the compaction characteristics of crushed waste rocks (CWRs) are a key factor influencing the backfill effect of goaf [16,17].If a certain lateral pressure is applied to CWRs backfilling goaf, the density and deformation resistance of CWRs can be improved (Figure 1).Additionally, the number of lateral loading cycles influences the compaction characteristics of CWRs: the compactness of CWRs constantly changes with the number of lateral loading cycles.In recent years, scholars have investigated the compaction characteristics of CWRs: by exploring mechanical properties of caved rock blocks in goaf, Pappas and Mark [18] obtained relationships between tangent and secant moduli with stress during the compaction of rock blocks.Moreover, they described the stress-strain relation by applying Salamon and Terzaghi formulae.Miao et al. [19] acquired the relationships between compaction stress and compaction-induced deformation and lateral pressure during the experimental compaction of crushed rocks.By carrying out compaction tests on loose rock blocks, Zhang et al. [20] suggested relationships between compression modulus and axial stress and axial strain and obtained relationships between compression modulus and rock strength and porosity.Ma et al. [21] revealed the stress-strain relationship by measuring the deformation characteristics of saturated crushed rock undergoing compaction and they analysed the influence of particle size and strength on the compaction characteristics of rock samples.By experimentally investigating the mechanism of crushing and compaction of waste rocks in coal mines, Jiang et al. [22] suggested that the whole compaction process of waste rocks can be divided into two stages: crushing-and solidification-based compaction.Fan and Mao [23] carried out creep tests on crushed rock blocks to obtain the relationships between creep deformation of rock samples under axial load and particle size by utilising a self-made apparatus for creep deformation of crushed rocks.By employing the YAS5000 testing machine (Changchun Kexin company, Changchun, China) and self-made compaction apparatus, Li et al. [24] investigated the influence of particle size on the compaction characteristics of waste rocks for backfilling (WRBs).They concluded that large particles of waste rock can form a skeleton structure of WRBs while small particles fill gaps between large particles.A reasonable size distribution of large and small particles is more favourable for improving the compressive properties of WRBs.By combining the MTS815.02testing system with self-made testing apparatus, Ma et al. [25] measured the compaction characteristics of limestone particles and revealed the influence of particle size distribution on porosity changes during compaction.No research has yet been reported on the influence of the number of lateral loading cycles on the compaction characteristics of crushed rocks.This is certain to influence the density and stiffness.
Considering this, by utilising a self-designed bidirectional loading test system for granular materials, tests of the compaction characteristics of CWRs were carried out.The purpose is to show the influence of the number of lateral load cycles on the compaction characteristics of crushed WRBs and analyse the changes in lateral strain, axial strain, porosity, lateral loading stress, and lateral pressure coefficient of WRB samples in lateral and axial loading processes.Additionally, the relationship between the lateral loading cycles and compaction characteristics of WRB samples was established, expecting to provide a theoretical basis for disposing waste rocks and improving the backfilling effect in goaf.In recent years, scholars have investigated the compaction characteristics of CWRs: by exploring mechanical properties of caved rock blocks in goaf, Pappas and Mark [18] obtained relationships between tangent and secant moduli with stress during the compaction of rock blocks.Moreover, they described the stress-strain relation by applying Salamon and Terzaghi formulae.Miao et al. [19] acquired the relationships between compaction stress and compaction-induced deformation and lateral pressure during the experimental compaction of crushed rocks.By carrying out compaction tests on loose rock blocks, Zhang et al. [20] suggested relationships between compression modulus and axial stress and axial strain and obtained relationships between compression modulus and rock strength and porosity.Ma et al. [21] revealed the stress-strain relationship by measuring the deformation characteristics of saturated crushed rock undergoing compaction and they analysed the influence of particle size and strength on the compaction characteristics of rock samples.By experimentally investigating the mechanism of crushing and compaction of waste rocks in coal mines, Jiang et al. [22] suggested that the whole compaction process of waste rocks can be divided into two stages: crushingand solidification-based compaction.Fan and Mao [23] carried out creep tests on crushed rock blocks to obtain the relationships between creep deformation of rock samples under axial load and particle size by utilising a self-made apparatus for creep deformation of crushed rocks.By employing the YAS5000 testing machine (Changchun Kexin company, Changchun, China) and self-made compaction apparatus, Li et al. [24] investigated the influence of particle size on the compaction characteristics of waste rocks for backfilling (WRBs).They concluded that large particles of waste rock can form a skeleton structure of WRBs while small particles fill gaps between large particles.A reasonable size distribution of large and small particles is more favourable for improving the compressive properties of WRBs.By combining the MTS815.02testing system with self-made testing apparatus, Ma et al. [25] measured the compaction characteristics of limestone particles and revealed the influence of particle size distribution on porosity changes during compaction.No research has yet been reported on the influence of the number of lateral loading cycles on the compaction characteristics of crushed rocks.This is certain to influence the density and stiffness.
Considering this, by utilising a self-designed bidirectional loading test system for granular materials, tests of the compaction characteristics of CWRs were carried out.The purpose is to show the influence of the number of lateral load cycles on the compaction characteristics of crushed WRBs and analyse the changes in lateral strain, axial strain, porosity, lateral loading stress, and lateral pressure coefficient of WRB samples in lateral and axial loading processes.Additionally, the relationship between the lateral loading cycles and compaction characteristics of WRB samples was established, expecting to provide a theoretical basis for disposing waste rocks and improving the backfilling effect in goaf.This paper first presents the sample preparation, test scheme and design of test apparatus in Section 2. The test procedure is stated in Section 3. The methods of calculating the compaction parameters including the strain and porosity are proposed in Section 4. The strain and porosity, changes in lateral stress and lateral pressure coefficient, changes in particle sizes are given in Section 5. Finally, Section 6 concludes with the implications of these findings.

Sample Preparation and Test Scheme
Sandstone CWRs were used during testing of compaction characteristics, which were directly collected from the underground coal mine, as shown in Figure 2. The waste rock samples were produced during the excavation of rock roadway.During sample preparation in the laboratory, waste rocks needed to be crushed into particles with different sizes of less than 30 mm.The crushing of waste rock masses involved two steps: firstly, the waste rocks were crushed to 50 mm down by using a hammer; secondly, then to 30 mm down using a crusher-compactor.Finally, based on sandstone samples with particle sizes of 0~5, 5~10, 10~15, 15~20, 20~25 and 25~30 mm, the CWRs were screened and divided into six groups (Figure 3).This paper first presents the sample preparation, test scheme and design of test apparatus in Section 2. The test procedure is stated in Section 3. The methods of calculating the compaction parameters including the strain and porosity are proposed in Section 4. The strain and porosity, changes in lateral stress and lateral pressure coefficient, changes in particle sizes are given in Section 5. Finally, Section 6 concludes with the implications of these findings.

Sample Preparation and Test Scheme
Sandstone CWRs were used during testing of compaction characteristics, which were directly collected from the underground coal mine, as shown in Figure 2. The waste rock samples were produced during the excavation of rock roadway.During sample preparation in the laboratory, waste rocks needed to be crushed into particles with different sizes of less than 30 mm.The crushing of waste rock masses involved two steps: firstly, the waste rocks were crushed to 50 mm down by using a hammer; secondly, then to 30 mm down using a crusher-compactor.Finally, based on sandstone samples with particle sizes of 0~5, 5~10, 10~15, 15~20, 20~25 and 25~30 mm, the CWRs were screened and divided into six groups (Figure 3).This paper first presents the sample preparation, test scheme and design of test apparatus in Section 2. The test procedure is stated in Section 3. The methods of calculating the compaction parameters including the strain and porosity are proposed in Section 4. The strain and porosity, changes in lateral stress and lateral pressure coefficient, changes in particle sizes are given in Section 5. Finally, Section 6 concludes with the implications of these findings.

Sample Preparation and Test Scheme
Sandstone CWRs were used during testing of compaction characteristics, which were directly collected from the underground coal mine, as shown in Figure 2. The waste rock samples were produced during the excavation of rock roadway.During sample preparation in the laboratory, waste rocks needed to be crushed into particles with different sizes of less than 30 mm.The crushing of waste rock masses involved two steps: firstly, the waste rocks were crushed to 50 mm down by using a hammer; secondly, then to 30 mm down using a crusher-compactor.Finally, based on sandstone samples with particle sizes of 0~5, 5~10, 10~15, 15~20, 20~25 and 25~30 mm, the CWRs were screened and divided into six groups (Figure 3).Considering practical conditions on site, samples with particle sizes of 0~30 mm were applied.To take the influence of the particle size of WRBs into account, the samples with different particle sizes were uniformly mixed and prepared in mass ratio proportions of 1:1:1:1:1:1.
We investigated the influence of lateral loading cycles on compaction characteristics of WRBs.Based on the field condition of backfilling coal mining, the lateral loading was separately applied over 1, 3, 5 and 7 cycles.The sandstone samples had a particle size distribution in the range of 0~30 mm, on which the lateral stress was 2 MPa.The formulated test scheme is shown in Table 1.On the condition of keeping the lithology, particle size distribution, and lateral loading stress of samples unchanged, the influence of lateral load regime on the compaction characteristics of WRBs was analysed by changing the number of cycles of lateral load applied.

Design of Test Apparatus
Based on the mechanism of test system, a bidirectional loading test system for granular materials was developed, which consisted of an axial loading system, a loading box, a lateral loading system, and a data monitoring and acquisition system (Figure 4).The photo in the laboratory is shown in Figure 5.  Considering practical conditions on site, samples with particle sizes of 0~30 mm were applied.To take the influence of the particle size of WRBs into account, the samples with different particle sizes were uniformly mixed and prepared in mass ratio proportions of 1:1:1:1:1:1.
We investigated the influence of lateral loading cycles on compaction characteristics of WRBs.Based on the field condition of backfilling coal mining, the lateral loading was separately applied over 1, 3, 5 and 7 cycles.The sandstone samples had a particle size distribution in the range of 0~30 mm, on which the lateral stress was 2 MPa.The formulated test scheme is shown in Table 1.On the condition of keeping the lithology, particle size distribution, and lateral loading stress of samples unchanged, the influence of lateral load regime on the compaction characteristics of WRBs was analysed by changing the number of cycles of lateral load applied.

Design of Test Apparatus
Based on the mechanism of test system, a bidirectional loading test system for granular materials was developed, which consisted of an axial loading system, a loading box, a lateral loading system, and a data monitoring and acquisition system (Figure 4).The photo in the laboratory is shown in Figure 5. Considering practical conditions on site, samples with particle sizes of 0~30 mm were applied.To take the influence of the particle size of WRBs into account, the samples with different particle sizes were uniformly mixed and prepared in mass ratio proportions of 1:1:1:1:1:1.
We investigated the influence of lateral loading cycles on compaction characteristics of WRBs.Based on the field condition of backfilling coal mining, the lateral loading was separately applied over 1, 3, 5 and 7 cycles.The sandstone samples had a particle size distribution in the range of 0~30 mm, on which the lateral stress was 2 MPa.The formulated test scheme is shown in Table 1.On the condition of keeping the lithology, particle size distribution, and lateral loading stress of samples unchanged, the influence of lateral load regime on the compaction characteristics of WRBs was analysed by changing the number of cycles of lateral load applied.

Design of Test Apparatus
Based on the mechanism of test system, a bidirectional loading test system for granular materials was developed, which consisted of an axial loading system, a loading box, a lateral loading system, and a data monitoring and acquisition system (Figure 4).The photo in the laboratory is shown in Figure 5.  axial load of 1,000 kN was used.Moreover, the testing machine has a big test bench suited to testing coarse granular materials.
(2) Loading box The loading box contains the granular materials and is composed of a foundation, a rib, an arc-shaped support, a front side plate, left and right side plates, an upper cover plate, a side-push plate, and M18 bolts.(3) Lateral loading system The lateral loading system can provide lateral load on the granular samples, and consists of a hydraulic pump unit, an oil cylinder for loading, a control box, a pressure gauge, a hydraulic oil tube, and an overflow valve.
(4) Data monitoring and acquisition system The data monitoring and acquisition system can monitor and acquire experimental data during loading and in real time, and is composed of a pull-rod displacement sensor, a spoke-type pressure sensor, a pressure transmitter, FX2N-5a analogue input and output modules, a FX2N-32MR controller, MCGS configuration software, and a laptop.

Test Procedure
To explore the influence of lateral loading times on compaction characteristics of crushed WRBs, compaction tests were carried out on WRBs under different numbers of cycles (1, 3, 5, and 7) of lateral load.On this basis, the influence of lateral loading cycles on compaction characteristics of WRBs was obtained.The compaction test method of solid backfill materials promulgated by China's National Energy Administration [26] was adopted to test the compaction characteristics of crushed waste rocks used for backfilling.The specific test steps are as follows: (1) Preparation of CWR samples The preparation scheme of samples is summarised in Section 2.1.
(2) Placing the prepared CWR samples into the loading box layer-by-layer The loading box needed to be assembled before loading the samples and also the displacement and pressure sensors were reset to zero.Afterwards, the prepared samples were packed into the loading box after being divided into 3~6 layers.The samples were subjected to pre-compaction after (1) Axial loading system The axial loading system is the basis of the bidirectional loading test system, which can apply sustainable and stable axial stress to these granular samples.In the test, the WAW-1000D electro-hydraulic servo-controlled universal testing machine with a travel range of 0~250 mm and an axial load of 1,000 kN was used.Moreover, the testing machine has a big test bench suited to testing coarse granular materials.
(2) Loading box The loading box contains the granular materials and is composed of a foundation, a rib, an arc-shaped support, a front side plate, left and right side plates, an upper cover plate, a side-push plate, and M18 bolts.
(3) Lateral loading system The lateral loading system can provide lateral load on the granular samples, and consists of a hydraulic pump unit, an oil cylinder for loading, a control box, a pressure gauge, a hydraulic oil tube, and an overflow valve.
(4) Data monitoring and acquisition system The data monitoring and acquisition system can monitor and acquire experimental data during loading and in real time, and is composed of a pull-rod displacement sensor, a spoke-type pressure sensor, a pressure transmitter, FX2N-5a analogue input and output modules, a FX2N-32MR controller, MCGS configuration software, and a laptop.

Test Procedure
To explore the influence of lateral loading times on compaction characteristics of crushed WRBs, compaction tests were carried out on WRBs under different numbers of cycles (1, 3, 5, and 7) of lateral load.On this basis, the influence of lateral loading cycles on compaction characteristics of WRBs was obtained.The compaction test method of solid backfill materials promulgated by China's National Energy Administration [26] was adopted to test the compaction characteristics of crushed waste rocks used for backfilling.The specific test steps are as follows: (1) Preparation of CWR samples The preparation scheme of samples is summarised in Section 2.1.
(2) Placing the prepared CWR samples into the loading box layer-by-layer The loading box needed to be assembled before loading the samples and also the displacement and pressure sensors were reset to zero.Afterwards, the prepared samples were packed into the loading box after being divided into 3~6 layers.The samples were subjected to pre-compaction after packing each layer of samples until all layers were loaded.The total height of loaded samples of Energies 2019, 12, 17 6 of 13 each group was 200 mm, and then the mass of loaded samples of each group in the box was further recorded.After filling the whole loading box, the upper cover plate was connected and fixed by applying bolts and the loading box was placed on the test bench of the WAW-1000D electro-hydraulic servo-controlled universal testing machine.
(3) Lateral loading of CWR samples The power supplies to some devices (including the motor of the hydraulic pump unit, sensors, and PLC) were switched on and then MCGS software was used to monitor the pressure and displacement.According to the lateral stress pre-set in the test scheme, the corresponding oil pressure was calculated.Afterwards, the oil pressure in the pressure gauge was adjusted to the corresponding value.Furthermore, the samples were laterally compacted.Additionally, the lateral pressure and displacement during lateral loading were monitored and recorded in real time.
(4) Axial loading of CWR samples After completing the lateral loading stage, the upper cover plate needed to be removed.In this case, due to elastic rebound, the height of the samples was slightly greater than 200 mm (the height of loaded samples).Therefore, the upper press plate was placed on the samples so that the height thereof could be restored to 200 mm via pre-compaction in the testing machine.Afterwards, the pressure during axial loading was set and then axial loading applied (Figure 6).The lateral pressure, axial pressure, and axial displacement were monitored and recorded in real time.
Energies 2018, 7, x FOR PEER REVIEW 6 of 14 packing each layer of samples until all layers were loaded.The total height of loaded samples of each group was 200 mm, and then the mass of loaded samples of each group in the box was further recorded.After filling the whole loading box, the upper cover plate was connected and fixed by applying bolts and the loading box was placed on the test bench of the WAW-1000D electro-hydraulic servo-controlled universal testing machine.
(3) Lateral loading of CWR samples The power supplies to some devices (including the motor of the hydraulic pump unit, sensors, and PLC) were switched on and then MCGS software was used to monitor the pressure and displacement.According to the lateral stress pre-set in the test scheme, the corresponding oil pressure was calculated.Afterwards, the oil pressure in the pressure gauge was adjusted to the corresponding value.Furthermore, the samples were laterally compacted.Additionally, the lateral pressure and displacement during lateral loading were monitored and recorded in real time.
(4) Axial loading of CWR samples After completing the lateral loading stage, the upper cover plate needed to be removed.In this case, due to elastic rebound, the height of the samples was slightly greater than 200 mm (the height of loaded samples).Therefore, the upper press plate was placed on the samples so that the height thereof could be restored to 200 mm via pre-compaction in the testing machine.Afterwards, the pressure during axial loading was set and then axial loading applied (Figure 6).The lateral pressure, axial pressure, and axial displacement were monitored and recorded in real time.(5) Screening the CWR samples after loading After loading, the samples were graded (Figure 7).

Lateral Strain and Porosity
The loading direction and the dimensions of specimen are shown in Figure 8. (5) Screening the CWR samples after loading After loading, the samples were graded (Figure 7).
Energies 2018, 7, x FOR PEER REVIEW 6 of 14 packing each layer of samples until all layers were loaded.The total height of loaded samples of each group was 200 mm, and then the mass of loaded samples of each group in the box was further recorded.After filling the whole loading box, the upper cover plate was connected and fixed by applying bolts and the loading box was placed on the test bench of the WAW-1000D electro-hydraulic servo-controlled universal testing machine.
(3) Lateral loading of CWR samples The power supplies to some devices (including the motor of the hydraulic pump unit, sensors, and PLC) were switched on and then MCGS software was used to monitor the pressure and displacement.According to the lateral stress pre-set in the test scheme, the corresponding oil pressure was calculated.Afterwards, the oil pressure in the pressure gauge was adjusted to the corresponding value.Furthermore, the samples were laterally compacted.Additionally, the lateral pressure and displacement during lateral loading were monitored and recorded in real time.
(4) Axial loading of CWR samples After completing the lateral loading stage, the upper cover plate needed to be removed.In this case, due to elastic rebound, the height of the samples was slightly greater than 200 mm (the height of loaded samples).Therefore, the upper press plate was placed on the samples so that the height thereof could be restored to 200 mm via pre-compaction in the testing machine.Afterwards, the pressure during axial loading was set and then axial loading applied (Figure 6).The lateral pressure, axial pressure, and axial displacement were monitored and recorded in real time.(5) Screening the CWR samples after loading After loading, the samples were graded (Figure 7).

Lateral Strain and Porosity
The loading direction and the dimensions of specimen are shown in Figure 8.

Lateral Strain and Porosity
The loading direction and the dimensions of specimen are shown in Figure 8. (1) Transformation from lateral loading stress to oil pressure during lateral loading By applying a hydraulic oil pressure, the WRB samples were subjected to lateral loading, and the lateral stress mentioned in the test scheme was referred to the compressive stress applied on WRB samples.Therefore, it is necessary to transform the lateral stress into oil pressure and then perform lateral loading on WRB samples under different lateral stresses by setting the oil pressure in the system.The relationship between the oil pressure σo and lateral stress σh can be expressed as follows: where, Ah, Lh, and hh refer to the area, length (200 mm), and height (200 mm) of the side-push plate, respectively.Ao and ro represent the cross-sectional area and the radius (62.5 mm) of the oil cylinder used for loading, respectively.By substituting the known parameters (including length of side-push plate, the height of side-push plate, and the radius of the oil cylinder) into Formula (1), the oil pressure corresponding to the lateral stress of 2 MPa can be calculated as 6.5 MPa.
(2) Calculating lateral strain on samples during lateral loading The lateral stress (σh) on the samples during lateral loading denotes the ratio of the lateral loading pressure to the area of the side-push plate.And by transforming Formula, the lateral stress (σh) can be calculated and obtained.
The lateral strain εh on the samples during lateral loading represents the ratio of the lateral loading displacement of the samples to the length of the loaded region: where, ΔLh and Ls represent the lateral loading displacement of the samples and the length (250mm) of loaded region, respectively.
(3) Calculating the lateral porosity of samples during lateral loading When carrying out lateral loading of WRB samples, the porosity of the samples changed constantly.The lateral porosity ϕh of the samples during lateral loading is expressed as follows: where, Vh, V0, and ms denote the volume of samples during lateral loading, the volume of the (1) Transformation from lateral loading stress to oil pressure during lateral loading By applying a hydraulic oil pressure, the WRB samples were subjected to lateral loading, and the lateral stress mentioned in the test scheme was referred to the compressive stress applied on WRB samples.Therefore, it is necessary to transform the lateral stress into oil pressure and then perform lateral loading on WRB samples under different lateral stresses by setting the oil pressure in the system.The relationship between the oil pressure σ o and lateral stress σ h can be expressed as follows: where, A h , L h , and h h refer to the area, length (200 mm), and height (200 mm) of the side-push plate, respectively.A o and r o represent the cross-sectional area and the radius (62.5 mm) of the oil cylinder used for loading, respectively.By substituting the known parameters (including length of side-push plate, the height of side-push plate, and the radius of the oil cylinder) into Formula (1), the oil pressure corresponding to the lateral stress of 2 MPa can be calculated as 6.5 MPa.
(2) Calculating lateral strain on samples during lateral loading The lateral stress (σ h ) on the samples during lateral loading denotes the ratio of the lateral loading pressure to the area of the side-push plate.And by transforming Formula, the lateral stress (σ h ) can be calculated and obtained.
The lateral strain ε h on the samples during lateral loading represents the ratio of the lateral loading displacement of the samples to the length of the loaded region: where, ∆L h and L s represent the lateral loading displacement of the samples and the length (250mm) of loaded region, respectively.
(3) Calculating the lateral porosity of samples during lateral loading When carrying out lateral loading of WRB samples, the porosity of the samples changed constantly.The lateral porosity φ h of the samples during lateral loading is expressed as follows: where, V h , V 0 , and m s denote the volume of samples during lateral loading, the volume of the samples before being crushed, and the mass thereof, respectively.Moreover, ρ s , l s , and h s denote the mass density of the samples, the width (200 mm) of the loaded region, and the height (200 mm) of the loaded samples, respectively.

Axial Strain and Porosity
(1) Calculating the axial strain on the samples during axial loading The axial stress σ v on the samples during axial loading refers to the ratio of the axial pressure on the samples to the area of the upper press plate.The area of upper press plate can be determined based on the lateral displacement.The specific calculation is as follows: where, P v and A v denote the axial loading pressure on the samples and the area of the upper press plate, respectively.Additionally, L v represents the length of the upper press plate, which depends on the lateral loading displacement of the samples, and l v denotes the width of the upper press plate (200 mm).Axial strain ε v in the samples under axial load is the ratio of axial loading displacement to the height of the loaded samples: where, ∆h v denotes the axial loading displacement of the samples.
(2) Calculating the axial porosity of the samples during axial loading When applying axial load to WRB samples, the porosity of the samples changes constantly and the axial porosity φ v of samples during axial loading is expressed as follows: where, V v denotes the volume of the samples during axial loading.

Influence of Number of Lateral Loading Cycles on Lateral Strain and Porosity
Based on the experimental data from samples recorded during lateral loading and results calculated by use of Formulae ( 1) to (3), the changes in strain and porosity of WRB samples after different numbers of cycles of lateral loading can be acquired (Figure 9).

Influence of Number of Lateral Loading Cycles on Lateral Strain and Porosity
Based on the experimental data from samples recorded during lateral loading and results calculated by use of Formulae (1) to (3), the changes in strain and porosity of WRB samples after different numbers of cycles of lateral loading can be acquired (Figure 9).Through analysis of the data shown in Figure 9, it can be seen that: Through analysis of the data shown in Figure 9, it can be seen that: (1) The lateral porosity of samples subjected to more lateral load cycles showed a greater reduction.For example, the lateral porosity of samples subjected to 7 cycles of lateral load decreased from 0.435 to 0.378.In contrast, the reduction in lateral porosity of samples undergoing 1, 3, and 5 cycles of lateral loading were 0.043, 0.047, and 0.053, respectively.This indicated that, during lateral loading, the lateral deformation of the sample subjected to 1 cycle of lateral loading was insignificant while significant lateral deformation was found in samples subjected to 7 lateral loading cycles.
(2) The lateral strain in the samples subjected to few lateral loading cycles was lower.The WRB samples were ranked, in a descending order, as those subjected to 7, 5, 3, and 1 lateral load cycles in terms of the lateral strain therein, respectively.For example, the lateral strain on a sample subjected to one lateral load cycle was only 0.072 while that undergoing 7 lateral loading cycles reached 0.093.This was because the larger the number of cycles of lateral load, the greater the work done by the test system on the samples.Therefore, during lateral loading, the particles of samples undergoing 7 lateral loading cycles were more likely to be subjected to crushing, slippage, and rotation.As a result, significant lateral deformation occurred, thus reducing the porosity of WRBs.

The Influence of Number of Lateral Loading Cycles on Axial Strain and Porosity
According to experimental data from samples under axial load and results calculated by use of Formulae (4) to (6), the changes in strain and porosity of WRB samples during axial loading are obtained after different numbers of cycles of lateral loading (Figure 10).
Energies 2018, 7, x FOR PEER REVIEW 9 of 14 (1) The lateral porosity of samples subjected to more lateral load cycles showed a greater reduction.For example, the lateral porosity of samples subjected to 7 cycles of lateral load decreased from 0.435 to 0.378.In contrast, the reduction in lateral porosity of samples undergoing 1, 3, and 5 cycles of lateral loading were 0.043, 0.047, and 0.053, respectively.This indicated that, during lateral loading, the lateral deformation of the sample subjected to 1 cycle of lateral loading was insignificant while significant lateral deformation was found in samples subjected to 7 lateral loading cycles.
(2) The lateral strain in the samples subjected to few lateral loading cycles was lower.The WRB samples were ranked, in a descending order, as those subjected to 7, 5, 3, and 1 lateral load cycles in terms of the lateral strain therein, respectively.For example, the lateral strain on a sample subjected to one lateral load cycle was only 0.072 while that undergoing 7 lateral loading cycles reached 0.093.This was because the larger the number of cycles of lateral load, the greater the work done by the test system on the samples.Therefore, during lateral loading, the particles of samples undergoing 7 lateral loading cycles were more likely to be subjected to crushing, slippage, and rotation.As a result, significant lateral deformation occurred, thus reducing the porosity of WRBs.

The Influence of Number of Lateral Loading Cycles on Axial Strain and Porosity
According to experimental data from samples under axial load and results calculated by use of Formulae (4) to (6), the changes in strain and porosity of WRB samples during axial loading are obtained after different numbers of cycles of lateral loading (Figure 10).It can be seen from Figure 10 that: (1) The axial porosity of samples subjected to fewer lateral loading cycles decreased more.For example, the axial porosity of a sample undergoing one lateral loading cycle decreased from 0.401 to 0.186.In contrast, the reductions in the porosities of samples subjected to 3, 5, and 7 lateral loading cycles were 0.212, 0.209, and 0.202, respectively.It implied that, during axial loading, the sample undergoing one cycle of lateral loading exhibited significant axial deformation while the axial It can be seen from Figure 10 that: (1) The axial porosity of samples subjected to fewer lateral loading cycles decreased more.For example, the axial porosity of a sample undergoing one lateral loading cycle decreased from 0.401 to 0.186.In contrast, the reductions in the porosities of samples subjected to 3, 5, and 7 lateral loading cycles were 0.212, 0.209, and 0.202, respectively.It implied that, during axial loading, the sample undergoing one cycle of lateral loading exhibited significant axial deformation while the axial deformation of the sample subjected to7 cycles of lateral loading was insignificant.
(2) The samples subjected to more cycles of lateral loading underwent less axial strain.The WRB samples were listed in a descending order as those samples undergoing 1, 3, 5, and 7 cycles of lateral load with regard to axial strain, respectively.For example, the axial strain in sample subjected to seven cycles of lateral loading was 0.229 while that undergoing one reached 0.253.The reason was that, when conducting lateral loading in advance, the greater the number of lateral loading cycles, the larger the reduction in porosity, thus improving the density of WRBs.Therefore, during the axial loading, the sample subjected to seven cycles of lateral load showed the greatest stiffness, thus resulting in an insignificant axial deformation.

Changes in Lateral Stress and Lateral Pressure Coefficient of Samples During Axial Loading
According to the experimental data from samples under axial load, and results calculated by using Formula (1), the changes in lateral stress on, and lateral pressure coefficient of, WRB samples during axial loading after different numbers of cycles thereof are attained (Figure 11).According to the experimental data from samples under axial load, and results calculated by using Formula (1), the changes in lateral stress on, and lateral pressure coefficient of, WRB samples during axial loading after different numbers of cycles thereof are attained (Figure 11).It can be seen from Figure 11 that: (1) Samples subjected to more lateral loading cycles exhibited a higher lateral stress.The WRBs were ranked in descending order as those subjected to seven, five, three, and one lateral loading cycle according to the lateral loading stresses therein.For example, the lateral stress on samples undergoing seven cycles of lateral loading reached 4.11 MPa while that after 1 cycle was 3.27 MPa.The reason for this was that the samples subjected to seven cycles of lateral loading underwent greater lateral deformation, consequently leading to a reduction in porosity and an improved density.Therefore, under axial load, it is unnecessary to continue to apply axial stress to decrease the porosity, thus meaning that samples subjected to seven cycles of lateral loading can transfer a higher stress to the lateral direction compared with samples undergoing one cycle of lateral loading.
(2) The lateral pressure coefficient of samples undergoing more cycles of lateral loading was larger.For example, the lateral pressure coefficient of samples subjected to seven cycles of lateral loading was 0.203 while those of the samples undergoing one, three, and five cycles of lateral loading were 0.163, 0.171, and 0.177, respectively.This indicated that, during axial loading, a higher stress was applied on the lateral direction of samples subjected to seven cycles of lateral loading while the stress applied in the lateral direction of samples which underwent one cycle of lateral loading was lower.It can be seen from Figure 11 that: (1) Samples subjected to more lateral loading cycles exhibited a higher lateral stress.The WRBs were ranked in descending order as those subjected to seven, five, three, and one lateral loading cycle according to the lateral loading stresses therein.For example, the lateral stress on samples undergoing seven cycles of lateral loading reached 4.11 MPa while that after 1 cycle was 3.27 MPa.The reason for this was that the samples subjected to seven cycles of lateral loading underwent greater lateral deformation, consequently leading to a reduction in porosity and an improved density.Therefore, under axial load, it is unnecessary to continue to apply axial stress to decrease the porosity, thus meaning that samples subjected to seven cycles of lateral loading can transfer a higher stress to the lateral direction compared with samples undergoing one cycle of lateral loading.

Changes in Particle Sizes before, and after, Compaction
(2) The lateral pressure coefficient of samples undergoing more cycles of lateral loading was larger.For example, the lateral pressure coefficient of samples subjected to seven cycles of lateral loading was 0.203 while those of the samples undergoing one, three, and five cycles of lateral loading were 0.163, 0.171, and 0.177, respectively.This indicated that, during axial loading, a higher stress was applied on the lateral direction of samples subjected to seven cycles of lateral loading while the stress applied in the lateral direction of samples which underwent one cycle of lateral loading was lower.

Changes in Particle Sizes before, and after, Compaction
After compaction testing, the samples were graded and particle size distributions of samples before, and after, compaction are as shown in Figure 12.It can be seen from Figure 12 that, after compaction, the particle size distributions of WRB samples after four different numbers of cycles of lateral loading all shifted upwards compared with those before compaction.This indicated that particles were crushed and therefore small particles accounted for an increasing proportion of the total, however, the lateral stresses were all low and did not reach the crushing strength of the particles.Thus, the increase in number of lateral loading cycles can decrease the porosity to thus increase the density of WRBs while not significantly influencing the crushing of particles before, and after, compaction.

Conclusions
By using a self-designed apparatus for the compaction test of CWRs, the influence of lateral loading cycles on the compaction characteristics of WRBs was explored and the particle size distributions of samples before, and after, compaction were computed.The main conclusions are as follows: (1) A bidirectional loading test system for CWRs was developed and methods for calculating the compaction parameters (including lateral strain, lateral porosity, axial strain, axial porosity, and lateral pressure coefficient) of CWRs were proposed.
(2) The more cycles of lateral load applied to the samples, the higher the lateral strain therein and the greater the reduction in lateral porosity.The reason for this was that the more lateral loading cycles applied, the greater the work done by the test system on the samples, thus resulting in a greater lateral deformation and a lower porosity.So the lateral loading will improve the compactness of waste rock backfill materials, and, more waste rocks can be disposed and filled into goaf.Thus, the waste rock dumps can be reduced for protecting the coal mine environment.
(3) The more cycles of lateral loading applied to the samples, the lower the axial strain therein and the smaller the decrease in axial porosity.This was because, when conducting lateral loading in advance of testing, the more cycles of lateral loading applied, the greater the reduction in porosity, thus increasing the density of WRBs thus further leading to their increased stiffness.The improvement of non-deformability can guarantee the controlling effects of strata control and surface subsidence.
(4) During axial loading, the samples subjected to more lateral loading cycles showed a higher lateral loading stress and a larger lateral pressure coefficient.The reason for this was that during lateral loading, the samples subjected to more cycles of lateral load underwent greater lateral deformation, thus reducing the porosity of the WRBs.Therefore, during axial loading, there was no need to continue to apply axial stress to reduce the porosity of samples, consequently resulting in a larger stress being transferred to the lateral direction.
(5) With an increase in the number of cycles of lateral loading, the porosity of the samples Thus, the increase in number of lateral loading cycles can decrease the porosity to thus increase the density of WRBs while not significantly influencing the crushing of particles before, and after, compaction.

Conclusions
By using a self-designed apparatus for the compaction test of CWRs, the influence of lateral loading cycles on the compaction characteristics of WRBs was explored and the particle size distributions of samples before, and after, compaction were computed.The main conclusions are as follows: (1) A bidirectional loading test system for CWRs was developed and methods for calculating the compaction parameters (including lateral strain, lateral porosity, axial strain, axial porosity, and lateral pressure coefficient) of CWRs were proposed.
(2) The more cycles of lateral load applied to the samples, the higher the lateral strain therein and the greater the reduction in lateral porosity.The reason for this was that the more lateral loading cycles applied, the greater the work done by the test system on the samples, thus resulting in a greater lateral deformation and a lower porosity.So the lateral loading will improve the compactness of waste rock backfill materials, and, more waste rocks can be disposed and filled into goaf.Thus, the waste rock dumps can be reduced for protecting the coal mine environment.
(3) The more cycles of lateral loading applied to the samples, the lower the axial strain therein and the smaller the decrease in axial porosity.This was because, when conducting lateral loading in advance of testing, the more cycles of lateral loading applied, the greater the reduction in porosity, thus increasing the density of WRBs thus further leading to their increased stiffness.The improvement of non-deformability can guarantee the controlling effects of strata control and surface subsidence.
(4) During axial loading, the samples subjected to more lateral loading cycles showed a higher lateral loading stress and a larger lateral pressure coefficient.The reason for this was that during lateral loading, the samples subjected to more cycles of lateral load underwent greater lateral deformation, thus reducing the porosity of the WRBs.Therefore, during axial loading, there was no need to continue to apply axial stress to reduce the porosity of samples, consequently resulting in a larger stress being transferred to the lateral direction.
(5) With an increase in the number of cycles of lateral loading, the porosity of the samples decreased: however, owing to the lateral stress failing to reach the crushing strength of the particles in the samples, the number of cycles of lateral load exerted no significant influence on the crushing of particles before, and after, compaction.
(6) By the method proposed in this paper, we can obtain the the effect of cyclic lateral loading on compaction behaviours of waste rock backfill materials.In order to get better backfill effects, lateral loading can be applied during backfilling.The lateral loading can improve the support ability for strata, while simultaneously protecting the coal mine environment.

Figure 1 .
Figure 1.Schematic diagram of lateral loading on CWRs.

Figure 1 .
Figure 1.Schematic diagram of lateral loading on CWRs.

Figure 2 .
Figure 2. Crushed sandstone samples with different particle size distributions.

Figure 2 .
Figure 2. Crushed sandstone samples with different particle size distributions.

Figure 2 .
Figure 2. Crushed sandstone samples with different particle size distributions.

Figure 3 .
Figure 3. Crushed sandstone samples with different particle size distributions.

Figure 3 .
Figure 3. Crushed sandstone samples with different particle size distributions.

Figure 4 .
Figure 4. Schematic diagram of the bidirectional loading system.

Figure 5 .
Figure 5.The bidirectional loading test system.

Figure 5 .
Figure 5.The bidirectional loading test system.

Figure 6 .
Figure 6.Axial loading of a sample.

Figure 6 .
Figure 6.Axial loading of a sample.

Figure 6 .
Figure 6.Axial loading of a sample.

Figure 8 .
Figure 8. Loading direction and dimensions of the specimen.

Figure 8 .
Figure 8. Loading direction and dimensions of the specimen.

Figure 9 .
Figure 9. Changes in lateral strain and porosity during lateral loading.

Figure 9 .
Figure 9. Changes in lateral strain and porosity during lateral loading.

Figure 10 .
Figure 10.Changes in axial strain and porosity of samples during axial loading.

Figure 10 .
Figure 10.Changes in axial strain and porosity of samples during axial loading.

Figure 11 .
Figure 11.Changes in lateral stress and lateral pressure coefficients of samples during axial loading.

Figure 11 .
Figure 11.Changes in lateral stress and lateral pressure coefficients of samples during axial loading.
LithologyParticle Size Distribution/mm Cycles of Lateral Load/Numeric Lateral Stress/MPa