Investigation on the Compressive Behavior of Waste Rock Backfill Materials with Different Specimen Sizes for Roof Control

Abstract

Waste rock backfilled into a goaf can function as the main load-bearing carrier to support the overlying strata, so the compressive behavior of backfill materials plays a critical role in the effectiveness of strata control. However, in the laboratory, the specimen size also significantly influences on the accurate prediction of compressive deformation in waste rock backfill materials. To assess the influence of the specimen size on compressive behavior in waste rock backfill materials, a WAW-1000D (Changchun Xinte Testing Machine Co., Ltd., Changchun, Jilin Province, China) electric servo-motor testing machine and self-made compressors of different sizes were used to characterize the compressive deformation of waste rock backfill materials with different specimen sizes. The stress–strain relationships and changes in the void ratio of specimens were analyzed, revealing the influence of the specimen size on the compressive behavior. The research found that when the ratio of the inner diameter of compressors to the maximum particle size of specimens is 15:1 and above, the inner diameter of compressors only has a slight influence. Taking a backfill panel in Xinjulong Coal Mine as the engineering context, waste rock with particle sizes in the range of 0~20 mm was backfilled. The measured roof subsidence was 568 mm, matching the measured experimental value. The results provide data to support roof subsidence predictions following waste rock backfill mining.

1. Introduction

Large quantities of waste rock are generated during coal mining, roadway driving, and coal separation [1], the production of which accounts for 15%~20% of total coal production [2]. The main method used to dispose of this waste rock is to stockpile it on the ground. However, stacking lots of waste rock on the ground (Figure 1a) not only occupies land resources, impairs the atmospheric environment, and damages the air environment and water resources, but may also cause potential disasters including landslides, debris flow, and spontaneous combustion [3,4,5]. In the meantime, the roof loses support from the lower coal seam with the mining of a coal seam. As a result, the roof subsides, breaks, and collapses under the dead load of strata and compression of the overlying strata [6,7]. This process affects the overlying strata (Figure 1b) and ultimately causes surface subsidence, giving rise to problems such as surface breaks, water and soil erosion, and vegetation dieback [8,9,10].

To solve this series of problems, a disposal method involving the crushing and backfilling of solid waste rock into the goaf has been proposed [11,12]. As shown in Figure 2, waste rock is crushed to the required particle size at ground level and then transported underground through a vertical feeding system. It is then conveyed to the backfill panel on conveyor belts, where it is compacted by the compactor of the backfill support to form a backfill body, which is used to support the overlying strata. This disposal method prevents a series of geological disasters and addresses environmental issues arising from intensive coal mining and the accumulation of solid waste rock. Meanwhile, solid waste rock functions as the main load-bearing carrier to support overlying strata after being backfilled in the goaf, and the compressive behavior of waste rock backfill materials (WRBM) plays a decisive role in roof control [13]. To predict the control effect on strata movement, it is necessary to test the compressive behaviors of backfill materials [14,15]. However, specimen size also significantly influences the compressive deformation of WRBM [16,17,18]. Therefore, it is necessary to investigate the compressive deformation properties of WRBM with different specimen sizes.

Scholars have studied the compressive behaviors of WRBM, focusing mainly on experimental tests and numerical simulation. Pappas and Mark [19] investigated the mechanical behavior of rock blocks caved in the goaf and revealed the relationships between the tangent and secant moduli and stress in the compaction process of rock blocks. They also used Salamon’s and Terzaghi’s formulas to describe the stress–strain relationship. By conducting compaction tests on broken rock blocks, Zhang et al. [20] obtained the relationships between the compressive modulus, axial stress, and axial strain and provided expressions linking the compressive modulus to the strength and porosity of rock blocks. Yadav et al. [21] used Salamon’s formula to express the stress–strain relationship of caved rock and proposed a numerical method to simulate the compaction of caved rock in the goaf based on the double-yield model of FLAC^3D software (ITASCA, Minneapolis, MN, USA, version V5.0, 2012). Li et al. [22] proposed an energy calculation method for broken waste rock and utilized a self-designed compactor and a SANS-CMT5305 (Shenzhen Sansi Test Instrument Co., Ltd., Shenzhen, Guangdong Province, China) test system to explore the influences of particle size on the energy evolution of broken waste rock. Karacan [23] demonstrated a predictive approach that combines fractal scaling in a porous medium with principles of fluid flow to calculate the porosity and permeability distribution of caved rock in the goaf in the compression process. Based on the numerical software PFC^3D (ITASCA, Minneapolis, MN, USA, version V6.0, 2020), Yang et al. [24] established a PFC model that considers the shape and particle size distribution of waste rock and discussed the energy dissipation and force chain evolution in the load-bearing process of waste rock backfill materials. Meng et al. [25] measured the flow properties of broken rock with different particle size distributions and established a fractional flow model for broken rock. Regarding broken rock in the goaf as granular media, Arasteh et al. [26] studied the porosity–stress and permeability–stress curves in the compression process of broken rock in the goaf. Moreover, some scholars also tested the influence of water content and the groundwater environment on the compressive deformation of broken waste rock, analyzing seepage pattern of broken rock during the compression process [27,28]. In summary, the aforementioned scholars have effectively measured the compressive behavior of broken rock, primarily focusing on the influence of material particle size, applied stress, and loading mode in tests on the compressive behavior of WRBM. However, specimen size also has a significant influence on the accurate prediction of compressive deformation of backfill materials in laboratory measurements of the compressive behavior of WRBM.

In view of this, taking WRBM as the research object, the study used a WAW-1000D electric servo-motor testing machine and self-made compressors with different sizes to test the compressive behavior of WRBM with different particle size distributions in compressors with different inner diameters. According to the test results, the stress–strain relationships and changes in the void ratio of specimens were analyzed to reveal the influencing mechanism of specimen size on the compressive behavior of WRBM. Additionally, the ratio of the inner diameter of the load-bearing compressors to the maximum particle size of the backfill materials was determined. Finally, a backfill panel in Xinjulong Coal Mine was taken as the engineering context to optimize tests according to the research results. WRBM with particle sizes of 0~20 mm were backfilled into the underground goaf, and the roof displacement of the panel was monitored many times, thereby verifying the effectiveness of the backfill materials in controlling strata movement.

2. Materials and Methods

2.1. Raw Materials and Specimen Preparation

The solid waste rock needed for the tests was collected from Xinjulong Coal Mine in Shandong Province, China. At first, a hammer was used to break the waste rock into particles smaller than 50 mm. Then, a crushing machine was used to crush the waste rock into particles smaller than 20 mm. In the end, stone screens were used to screen the waste rock to produce waste rock specimens with particle size distributions of 0~5, 5~10, 0~10, 10~15, 15~20, and 0~20 mm. After preparation, the mass density and the stacking density of the waste rock specimens were measured. The preparation process of the waste rock specimens is shown in Figure 3.

Using X-ray diffraction (XRD), the relative content of the mineral components was obtained by comparing and analyzing the measured patterns with the patterns in the database. The results of the XRD patterns of the waste rock are shown in Figure 4. It can be seen that the waste rock mainly consists of quartz (SiO₂) and Kaolinite (Al₂H₄O₉Si₂) and contains a small amount of minerals such as potassium feldspar (KAlSi₃O₈) and plagioclase (Na_1−xCa_x[(Al_1+xSi_3−x)O₈]), which is a typical sandstone.

Using scanning electron microscope (SEM), magnified images of the waste rock were obtained, the waste rock are shown in Figure 5a magnified 1000 times, Figure 5b magnified 2000 times, Figure 5c magnified 5000 times and Figure 5d magnified 10,000 times. The surfaces of the waste rock are shown to be rough, with some tiny pores and fractures. The widths of the fractures and pores separately reach 250 nm and 90~4700 nm, respectively. However, the pores and fractures do not coalesce to form complete fracture networks, so the waste rock is relatively intact. The waste rock contains space that can be filled by tiny particles, resulting in a skeleton structure.

2.2. Compression Tests

The test system comprises a WAW-1000D electric servo-motor testing machine and self-made compressors of backfill materials, as shown in Figure 6. The test machine could provide axial force from 0~1000 kN and had a stroke in the range of 0~780 mm. Furthermore, the data acquisition system of the testing machine could obtain mechanical parameters including load and displacement. To meet the test requirements, compressors with different internal diameters (50, 70, 100, 150, and 250 mm) were designed (Figure 7). The compressors consist of a removable steel cylinder, a dowel bar, and a sleeve. The removable steel cylinder was formed by fixing two steel slots on a base using screws. The dowel bar was composed of a base and a steel column, and the size of the base was slightly smaller than the inner diameter of the removable steel cylinder. The dowel bar was used to ensure uniform stress on the WRBM during the loading process. The sleeve was placed on the base of the dowel bar in the loading process to avoid deformation of the base due to stress concentration under load.

The specific test steps are described as follows:

Step 1: Loading the waste rock specimen in the steel cylinder

After assembling the removable steel cylinder and placing waste rock with the corresponding particle size into it, the specimen was flattened, and the height of the specimen was back-calculated by measuring the remaining height of the removable steel cylinder using a steel ruler. The loading was stopped after the specimen height reached 150 mm. The particle size distributions and the sizes of removable steel cylinders in each group of specimens are summarized in

Table 1. Specific test schemes.

No.	Particle Size Distribution (mm)	Inner Diameter (mm)	Axial Compressive Stress (MPa)
y-1	0~5	150	20
y-2	5~10
y-3	0~10
y-4	10~15
y-5	15~20
y-6	0~20
y-7	0~10	50	20
y-8		70
y-9		100
y-3		150
y-10		250

.

Step 2: Assembling the compressor

The dowel bar was placed on the specimen and the sleeve was put on the dowel bar, during which it should ensure that the dowel bar and sleeve were placed horizontally at the center of the specimen. After assembly, the compressor was placed on the WAW-1000D electric servo-motor universal test system.

Step 3: Pre-compression of the specimen

The computer was turned on to run data acquisition and detect the software (16.5.10.2016.). The system was stopped automatically after applying an axial pre-pressure of 2 MPa [29].

To reduce the void ratio of, and strain in, the backfill materials, a certain lateral pressure was applied during field backfilling. To conform to prevailing engineering conditions, the backfill materials were also pre-compressed.

Step 4: Axial loading of the specimen

After running the data and detecting the software (16.5.10.2016), the corresponding program was set and run. The tester utilized a displacement transducer and a pressure transducer to obtain displacement and stress changes in the waste rock specimen. When the axial stress reached 20 MPa, the system stopped automatically.

The axial strain ε of the specimen is the ratio of the displacement during axial loading to the height of the specimen after pre-compression [30] as given by

$$\epsilon ={\displaystyle \frac{\Delta h}{h-h_1}}$$

(1)

where h is the loading height (150 mm); h₁ is the displacement of the specimen during pre-compression; and Δh is the displacement of the specimen during axial loading.

The void ratio of the waste rock specimen changes constantly throughout the loading process [31]. The void ratio P of the specimen is

$$P={\displaystyle \frac{V_V}{V_T}}=1-{\displaystyle \frac{\frac{m}{{\rho }_s}}{\left[(1-{\epsilon }_1)\frac{m}{{\rho }_b}\right](1-\epsilon )}}=1-{\displaystyle \frac{{\rho }_b}{(1-\epsilon )\left[(1-{\epsilon }_1){\rho }_s\right]}}$$

(2)

where V_V is the void volume in the waste rock specimen; V_T, m, ρ_s, and ρ_b are the total volume, mass, mass density, and stacking density of the waste rock specimen, respectively; ε is the strain in the waste rock specimen; and ε₁ is the strain in the waste rock specimen during pre-compression.

Step 5: Removal of the waste

The compressor was taken down and screws were removed to observe the appearance of the compressed specimen. After sweeping away the waste, the above steps were repeated to conduct the next group of tests. Figure 8 shows the appearance of the compressed backfill material specimen y-3.

3. Results and Discussion

3.1. Compressive Deformation Ccharacteristics

The stress–strain curves of waste rock specimens with various particle sizes under axial loading are illustrated in Figure 9.

Analysis of Figure 9 reveals that, under stress, the stress–strain curves of specimens with various particle sizes follow a similar trend with increasing axial stress. This can be divided into two stages: The first shows low concavity and entails quasi-linear deformation, which occurs because some voids present between waste rock particles are closed under the external force as the axial pressure grows. The second stage entails large concavity and is non-linear. At the beginning of the stage, some voids in the waste rock specimen are filled with pre-existing fine particles in the specimen, while other voids are not filled due to the support of the skeleton structure formed by waste rock particles and a small number of fine particles. As the axial pressure increases, large waste rock particles begin to break and form fine particles, the skeleton structure is broken, and voids are further filled.

The compressive deformation properties of specimens are strongly influenced by particle size distribution. The strain of specimens with continuous particle size distributions of 0~5, 0~10, and 0~20 mm containing fine particles is lower than that of specimens with single particle size distributions of 5~10, 10~15, and 15~20 mm. Moreover, the strain increases with particle size in both cases. This is because specimens with continuous particle size distributions under natural crushing contain pre-existing fine particles that can fill in voids. As a result, voids that can be filled in by these specimens during the deformation process are smaller than those in specimens with a uniform particle size.

Figure 10 shows the stress–strain curves of waste rock with particle size distributions of 0~10 mm placed in compressors with different inner diameters.

Analysis of Figure 10 shows that the inner diameter of compressors greatly affects the strain of waste rock specimens during axial loading. Under the axial stress of 20 MPa, the strain of specimens in the compressor with an inner diameter of 50 mm is only 0.13107, while that in the compressor with an inner diameter of 250 mm reaches 0.15781, increasing by 20.4%. The strain is positively correlated with the inner diameter of compressors. This is because, under a random distribution of waste rock particles, the larger the inner diameter of a compressor, the lower the probability that stable skeleton structures will form from hinged hard waste rock particles, and thus the weaker the overall compressive behavior of the structure. Moreover, due to the random distribution of defects in the specimens, the larger the inner diameter of a compressor, the higher the probability of low-strength waste rock particles occurring in the specimens, and therefore the weaker the overall compressive strength of the structure.

3.2. Changes in Void Ratio

Using Equation (2), change curves of the void ratio of waste rock specimens with various particle sizes are calculated, as illustrated in Figure 11.

Figure 11 shows that, as the compressive stress gradually increases, the void ratios of waste rock specimens decrease at a decreasing rate. This is because, under compression, the skeleton structure of waste rock particles prevents the further closure of voids. The initial void ratio of specimens with continuous particle size distributions is larger than that of specimens with uniform particle size distributions. However, the rate of decrease in the void ratio of specimens with continuous particle size distributions is greater than that of specimens with uniform particle size distributions after compressive deformation. This is because specimens with continuous particle size distributions contain pre-existing fine particles that can fill the voids, which results in an initial void ratio that is smaller than that of specimens with uniform particle size distributions. As the compression continues, pre-existing fine particles in the specimens with continuous particle size distributions do not readily slip and fill the voids due to the presence of the skeleton, while fine particles formed due to breakage of waste rock particles fill the voids more efficiently than pre-existing fine particles in the specimens.

Changes in the void ratio of waste rock specimens with particle size distributions of 0~10 mm in compressors with different inner diameters are obtained using Equation (2), as shown in Figure 12.

As shown in Figure 12, the waste rock specimens have the same initial void ratio. The void ratio changes after pre-compression, while it differs slightly in compressors with different inner diameters. With the application of axial pressure, the difference in void ratio gradually increases. The maximum and minimum void ratios are separately 0.25659 and 0.22281 under the compressive stress of 20 MPa, and the void ratio gradually decreases when increasing the inner diameter of the compressors. This is because the larger the inner diameter of compressors, the lower the probability of formation of stable skeleton structures, and the less numerous the voids that are maintained by stable skeleton structures.

3.3. Determination of the Specimen Size

To explore the influence of specimen size on the compressive behavior of waste rock specimens, the strain of specimens in compressors with different inner diameters under 5 MP, 10 MPa, 15 MPa, and 20 MPa was subjected to non-linear curve fitting with the inner diameter of corresponding compressors, then iteration to convergence. The fitted curves and their equations are shown in Figure 13.

Analysis of Figure 13 shows that the inner diameter Φ of compressors and the strain ε of waste rock specimens can be expressed by this function: $\epsilon =y_0+A_1{e}^{-\Phi /t_1}$. The curves change greatly in the initial stage while the variation of strain tends to stabilize when an inner diameter is 0.15 m. This means that the inner diameter of compressors influences the compressive behavior slightly when using circular load-bearing compressors with the inner diameter of 0.15 m to conduct tests on specimens with particle sizes of 0~10 mm. Similarly, the ratio of the inner diameter of load-bearing compressors to the maximum particle size of waste rock should be 15:1 (or above) in compression tests on specimens with other particle sizes, so as to reduce the influence of the inner diameter of compressors on the compressive behavior of waste rock specimens.

4. Backfill Performance Analysis

4.1. Site Conditions

Large quantities of waste rock are generated during the underground development and mining of Xinjulong Coal Mine. Lifting waste rock not only incurs high haulage costs but also decreases the efficiency of production. Meanwhile, the lifted waste rock is stacked on the ground, affecting the ecological environment in and around the mining area. To address these issues, operatives directly backfill the waste rock separated underground into the goaf, which not only solves the above problems, but also controls the movement and deformation of overlying strata. The 1303N-1# backfill panel was taken as an example (Figure 14), which was designed to mine the No. 3 coal seam. The stability occurs in coal seams with an average thickness of 3.19 m and a burial depth of 754.8~787.1 m. The backfill panel is 115 m long in the dip direction and is advanced by 911.6 m in the strike direction, corresponding to the farmland of Longmei Agricultural Development Company at ground level.

4.2. Application of Backfill Materials

To reduce the influence of the inner diameter of compressors on the compressive behavior of waste rock specimens, the waste rock separated underground in Xinjulong Coal Mine was crushed into particles smaller than 20 mm and then placed in a compressor with an inner diameter of 300 mm to conduct compression tests. Since the vertical stress in the goaf after the end of mining tends to be close to the in situ stress (20 MPa), the compressive stress of 20 MPa was applied in the test. The test results are displayed in Figure 15.

Figure 15 shows that when subjected to a compressive stress of 20 MPa (approximate to the in situ stress), the strain in the backfill materials is 0.183; that is, the compression ratio is 18.3%. Since the average coal thickness of the 1303N-1# backfill panel is 3.19 m, it is predicted that the compressive deformation of WRBM is 584 mm. The results were verified below in tandem with field measurement.

4.3. Deformation Monitoring

To evaluate the control effect of WRBM on roof subsidence after backfilling the backfill materials into the goaf, five displacement sensors for the roof of the goaf were set in the backfilling bodies at a location 450 m from the open-off cut of the backfill panel. Measuring point 1# was 15 m from the tail entry and measuring point 3# was arranged in the middle of the panel. The specific arrangement of the sensors is displayed in Figure 16.

Based on the monitoring data, measuring points 1# and 3# were selected to monitor and analyze the roof dynamic subsidence. The monitoring results of roof dynamic subsidence are shown in Figure 17.

Figure 17 shows that as the backfill panel advances, the changes in the roof dynamic subsidence of the goaf can be divided into three stages: the accelerated subsidence stage (where the backfill panel is 0~88 m from the measuring points), slow subsidence stage (88~188 m), and steady subsidence stage (longer than 188 m). When the distance from measuring points to the backfill panel is more than 188 m, it enters a stage entailing steady deformation. With the advance of the backfill panel, WRBM are gradually compressed and become the main load-bearing carrier to support the overlying strata. The interaction between the compressive deformation of WRBM and the overlying strata begins to be balanced and roof subsidence begins to stabilize. The maximum roof subsidence at measuring point 3# is 568 mm, based on which it is calculated that the compression ratio is 17.81%, similar to the predicted value in the tests. Therefore, the tests provide data to support compressive deformation predictions for WRBM in underground goafs.

5. Conclusions

The WAW-1000D electric servo-motor testing machine and compressors with different inner diameters were used to assess the influence of specimen size on the compressive behavior of WRBM based on the particle size distribution of specimens and inner diameter of compressors. The stress–strain relationship and changes in the void ratio of specimens were analyzed, and the influencing mechanism of the specimen size on the compressive behavior of WRBM was revealed. Moreover, the test method to reduce the influence of the size effect was determined and in situ monitoring was performed for verification. The main conclusions obtained are as follows:

(1) The particle size distribution of specimens affects their compressive deformation characteristics. Under natural crushing, waste rock specimens with continuous particle size distribution have pre-existing fine particles that can fill the voids, so their strain and initial void ratio are lower than those of specimens with uniform particle size distributions. As compression proceeds, pre-existing fine particles in specimens with continuous particle size distribution cannot slip to fill the voids due to the presence of the skeleton, while fine particles produced by broken waste rock particles are more efficiently filled in the voids. As a result, the void ratio of waste rock specimens with continuous particle size distribution is, on the contrary, slightly lower than that of specimens with uniform particle size distributions.

(2) The inner diameter of the compressors affects the compressive behavior of the specimens. Under random distribution of waste rock particles, the larger the inner diameter of the compressor, the lower the probability of formation of stable skeleton structures by hinged hard waste rock particles, and thus the lower the strain and void ratio. The relationship between the inner diameter Φ of compressors and strain ε is expressed by the function $\epsilon =y_0+A_1{e}^{-\varphi /t_1}$. When the ratio of the inner diameter of compressors to the maximum particle size of waste rock is 15:1 and above, the strain ε tends to stabilize and the specimen size exerts a slight influence on the compressive behaviors of the specimens.

(3) Taking the 1303N-1# backfill panel in Xinjulong Coal Mine as an example, the tests show that the strain of waste rock specimens with a particle size of 0~20 mm under 20 MPa is 0.183. Based on this result, it is predicted that the maximum roof subsidence is 583.77 mm. After stabilization of the backfill panel, the maximum in situ roof subsidence measurement is 568 mm, which differs slightly from the test results.