Backfill materials in working faces of SWBM are confined horizontally by sidewalls and the internal friction between themselves. A compacting device was designed to simulate the compaction of backfill materials in SWBM and characterize their energy dissipation properties. As shown in Figure 1, the compacting device consisted of three main parts: a piston, a cylinder tube, and a pedestal. The piston was employed to apply axial load to the test backfill materials. The cylinder tube was fabricated from fully quenched 45# steel, of which the elastic modulus was 210 GPa. The inner diameter and the wall thickness of this steel cylinder were 100 and 10 mm, respectively. The test accuracy of the pressing machine were axial force 20 N and axial stress 0.001 mm.

The gangue specimens used as backfill materials in this research were collected from the −592 m deep strata of Xiaojihan coal mine in Shanxi province of China. The main mineral composition of the tested gangue was determined through experimental analysis, showing that the gaugue specimens consist of 32% feldspar, 28% quartz, 12% kaolinite, 9% illite, 7% chlorite, 4% calcite, 3% siderite, and 5% other minerals. The average dry density was 2,562 kg/m³. The uniaxial compressive strength, tensile strength, cohesion, internal friction angle, elasticity modulus, and fracture toughness were 58.61 MPa, 7.65 MPa, 10.32 MPa, 34.08°, 30.40 GPa and 0.44 MPa m^1/2, respectively.

The test specimens were prepared in the laboratory following the procedure below: (1.) The gangue blocks were initially crushed into particles; (2.) The particles were separated by separation screens into five groups by their sizes, with diameters ranging from 2.5 to 5 mm (group A), 5∼8 mm (group B), 8∼10 mm (group C), 10–12 mm (group D), and 12∼15 mm (group E), as shown in Figure 2; and (3.) Specimens were prepared by mixing particles from groups A∼E, with a total mass of 2000 g. To account for the diverse size distribution of backfill materials and overcome the dimension disaster, each specimen was created using a combination of particles from different diameter ranges, according to Talbot theory (Yu et al., 2020). The Talbot formula is written in the following form P = d d max n × 100 % (1) where P is the passing rate of each diameter size in gangue particles, d is the particle diameter, d max is the maximum particle diameter, and n is the Talbot exponent. Based on Equation 1, the mass amount in each diameter range of the gangue specimens for four different cases (n = 0.2, n = 0.4, n = 0.6, and n = 0.8) are provided in Table 1.

Due to the movement of the overlying strata, the backfill materials in the working face are subjected to varying levels of loading over time. The compaction level increases gradually from beginning to end. Therefore, the impact of the compaction level (axial stress) on the energy dissipation of the backfill materials need to be considered. Given the working face depth (−592 m) and the in-situ strata stress (average bulk density of 0.024 MN/m³), a maximum axial stress of 16 MPa was prescribed for the compacting test. In this test, the axial stress was set to five different levels (2, 4, 8, 12, and 16 MPa). Thus, the energy dissipation properties of the four specimens were tested under six different conditions (including the initial state). A total of 24 sets of experiments were conducted.

To obtain the energy dissipation properties under different axial stresses, an axial force control mode was applied and the specimens were separated after the test. Each set of experiments was repeated three times, and the average test results were used in the analysis. Figure 3 illustrates the testing procedure.

In this research, particle flatness, f , was employed to quantify the evolution of particle morphology. It was expressed by the following equation. f = d f ⁡ max / d f ⁡ min (2) where d f ⁡ max and d f ⁡ min are the maximum and minimum Feret’s diameters of the particles, respectively. The specific notation for the two diameters is shown in Figure 4. Based on Equation 2, this value is always greater than or equal to 1. Particle flatness characterizes the elongation of particles; the closer a particle is to a spherical shape, the closer this value is to 1. Conversely, the more flattened and elongated the particle, the higher the value.

Strain energy density is used to express the energy consumed by the deformation of specimens per unit volume under compaction. In this test, the elastic deformation of testing equipment (e.g., dowel bar, compacting head, piston, cylindrical tube, and pedestal) played a negligible role, and the work done by the pressure machine was mainly consumed by the deformation of specimens and friction between the gangue particles and cylindrical tube inner wall. The work done by compaction per unit volume of specimen W can be calculated by W = ∫ 0 ε σ 1 d ε (3)

Based on Equation 3, the unit energy dissipation of the friction between the gangue particles and the cylindrical tube’s inner wall W m can be calculated by W m = ∫ 0 ε μ λ σ 2 π r h 0 1 − ε h 0 2 d ε π r 2 h 0 1 − ε = λ μ h 0 r W (4) where μ , λ , r and h 0 are the friction coefficient, lateral pressure coefficient, radius of the cylindrical tube inner wall, and initial height of specimen, respectively. In Equation 4, the friction coefficient and lateral pressure coefficient were set at 0.25 and 0.43, respectively (Zhou et al., 2016).

Therefore, the strain energy density ν ε of the specimen can be expressed as ν ε = W − W m = 1 − 0.1075 h 0 r W (5)

Based on Equation 5, the energy consumption during the compaction process of a unit volume specimen includes particle crushing energy, ν b , frictional energy dissipation, ν f , between particles, particle deformation energy, ν d , and other forms of energy dissipation, ν e , which can be expressed by Equation 6 ν ε = ν b + ν f + ν d + ν e (6)

According to Griffith’s fracture mechanics theory, the energy consumption W b associated with the formation of new fracture surfaces during particle breakage can be expressed (Lawn, 1993) W b = 2 K I C 2 Δ A / E (7) where K I C is the fracture toughness of the particle material, Δ A is the area of the new fracture surfaces generated by particle breakage, and E is the elastic modulus of the particle material.

The relationship between the surface area, A S , of an individual gangue particle and its particle size, d s , can be expressed by Equation 8 A s ∝ d s 2 (8)

In this test, gangue particles of different size ranges were sieved using circular perforated sieves. Considering that gangue particles are irregular polyhedra and that their particle circularity decreases during compaction (Yu et al., 2020), in this research, spherical shapes were used to simulate gangue particles for volume calculation. For a single spherical particle with a diameter of d s , its volume, V s , is calculated as follows V s = π d s 3 / 6 (9)

For gangue particles within a certain size range, considering their irregular shape, the average of the upper and lower sieve apertures D i and D i + 1 was taken as the characteristic value, d i , of the particle size for that range, which can be expressed as d i = D i + D i + 1 / 2 (10)

By substituting d i in Equation 10 into Equation 9 instead of d s , Equation 9 can be rewritten as Equation 11. V s = π d i 3 / 6 (11)

Assuming the number of particles within this size range is N i , the total surface area, A i , of all particles can be expressed as A i = N i π d i 2 (12)

Thus, the total mass, m i , of particles within this size range can be expressed as m i = ρ N i π d i 3 / 6 (13) where ρ is the density of the gangue particles.

By combining Equations 12, 13, we obtain A i = 6 m i / ρ d i (14)

During the compaction process of the specimens, under a certain axial stress, σ 1 j , the mass, m i , of gangue particles in each size range can be obtained through sieving and weighing. Substituting these values into Equation 14, we obtain the total surface area, A i , of gangue particles for that size range. Summing the values calculated for each size range provides the total surface area of gangue particles, A j , in the entire specimen, which can be expressed by Equation 15. A j = ∑ 1 6 A i (15)

Using the data from the previous axial stress, σ 1 j − 1 , the increment, Δ A j , in the surface area of gangue particles can be obtained. Δ A j = A j − A j − 1 (16)

Substituting Equation 16 into Equation 7, the energy required to generate new surfaces during gangue particle breakage, W b j , can be calculated.

Therefore, under axial stress, σ 1 j , the particle crushing energy consumption, ν b j , per unit volume of the specimen can be expressed by Equation 17 ν b j = ∑ 1 j W b j / V j (17) where V j is the volume of the specimen under axial stress.

Based on the test data of axial stress and axial strain, the relationship between axial strain and axial stress was investigated (Figure 5). As observed, the axial strain increased with the increase in axial stress. The increase in axial strain consisted of three stages: the rapid increase (0∼2 MPa) stage, the slow increase (2∼8 MPa) stage, and the slight increase (8∼16 MPa) stage. During the rapid increase stage, the axial strain increased quickly by 45.87%–50.97% of the total increment (0∼16 MPa). During the slight increase stage, the axial strain increased slightly by 12.43%–13.51% of the total increment and tended to become stable.

The relationship between axial strain and axial stress was approximated by a negative exponential function, and the correlation coefficients were all above 0.99. The axial strain was expressed by Equation 18 ε = a 1 − e − b σ 1 (18) where ε is the axial strain, σ 1 is the axial stress, and a and b are fitting parameters.

To investigate the evolution of particle morphology, the particle morphology and size measurement method proposed by Yu et al. was applied (Yu et al., 2020). The “Analyze Particles” function of ImageJ was employed in this research to calculate the maximum and minimum Feret’s diameters of each particle. The particle flatness was then calculated using Equation 2.

Table 2 exhibits the calculated particle flatness (n = 0.4), and Figure 6 shows the relationship between particle flatness and axial stress. As seen, the particle flatness varied from 1.38 to 1.75 across different axial stress levels. With the increase of axial stress, the particle flatness decreased gradually with some fluctuations. This can be mainly explained by the constant particle breakage during compaction, leading to the detachment of particle edges and corners. Hence, the gangue particles became more and more regular in shape. Interestingly, the particle flatness of gangue particles in the 0∼2.5 mm range was relatively low and stable as compared to larger particles, ranging from 1.38 to 1.45. This is mainly because smaller particles are more regular in shape and less likely to break again. In contrast, for the gangue particles with diameters of 5∼8 mm, 8∼10 mm, and 10∼12 mm ranges, the particle flatness values fluctuated significantly, mainly due to random breakage of larger particles during compaction. Under 16 MPa axial stress, the particle flatness values ranged from 1.39 to 1.42. The flatness values of particles in the 0∼2.5 mm, 2.5∼5 mm, and 12∼15 mm ranges were relatively lower, while those in the 5∼8 mm, 8∼10 mm, and 10∼12 mm ranges were relatively higher.

Table 3 exhibits the calculated strain energy density values, which varied from 74.05 kJ/m³ to 614.87 kJ/m³. When the compaction started, the specimen structure was loose, with many voids, low friction between gangue particles, and many particle edges, making them prone to breakage. Consequently, the energy consumption for specimen deformation was low. Thus, the specimen was easily deformed, and the strain energy density increased slowly. During the 0∼4 MPa process, axial strain accounted for 69.41%∼73.48% of the total strain, while strain energy density accounted for only 31.43%∼34.88% of the total increment. As the compaction progressed, the specimen structure became dense, featuring close contact among gangue particles, higher friction, and reduced particle movement and breakage. As a result, significant energy was required for the specimen to deform.

Table 4 exhibits the calculated total surface area, and Figure 7 shows the relationship between total surface area and axial stress. As indicated in Figure 7, the total surface area varied from 0.688 m² to 2.092 m² and increased monotonically with the increase of the axial stress. When the axial stress was lower than 4 MPa, the total surface area increased rapidly, accounting for 54.44%–70.33% of the total increment. This was observed primarily due to the particle morphology in the initial stage of compaction, during which particles had numerous edges, and some were slender. When the specimen was compressed, stress concentration easily occurred, forming large new fracture surfaces. The total surface area increased slowly between 4 MPa and 16 MPa. However, the initial particle size distribution (Talbot exponent) had negligible influence on the total surface area.

Table 5 exhibits the calculated particle crushing energy, and Figure 8 shows how the particle crushing energy vary with axial stress. As illustrated in Figure 8, the particle crushing energy varied from 4.81 kJ/m³ to 14.35 kJ/m³ and increased monotonically with the increase of the axial stress. The trend in strain energy density is similar to that of the total surface area and can be divided into two stages, with 4 MPa as the inflection point: a rapid increase stage below 4 MPa and a slow increase stage above 4 MPa.