Introduction

Coal mining has an indispensable role in the rapid economic development of China. Conversely, the solid waste generated by mining piles poses a series of threats to the surrounding environment. For instance, the massive accumulation of coal gangue waste causes a waste of land resources, while sulfide spillage or leaching in coal gangue will seriously pollute land resources and water resources (Yang et al. 2021; Ran et al. 2022; Wang et al. 2021). In addition, coal seam mining will cause a certain deformation fracture of the overburden during the mining process. As shown in Fig. 1, a large amount of groundwater will flow into the coal mining area when the fractures generated by the overburden fracture extend to the aquifer (Yan et al. 2021), causing secondary ecological environment damage, such as groundwater level drop and surface subsidence (Zhu et al. 2019).

Fig. 1
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Ecological harm caused by coal mining

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To alleviate the ecological environmental problems caused by coal gangue accumulation and fracture of the water-bearing layer, backfill mining technology was proposed (Liu et al. 2021; Zhang and Cao 2021; Chen et al. 2022). Specifically, certain solid wastes, such as tailings, rock piles, and coal gangue, are selected as filling materials to backfill directly to the coal mine extraction area through filling equipment. The filling materials alleviate the fracture problem of the overlying water-bearing layer and subsequent series of hazards (Ding et al. 2016; Ma et al. 2020). However, the coal gangue filling material in the mined area may be repeatedly fractured due to the pressure of the overburden layer. Moreover, the strength and cementation of the backfill material may also be affected by the infiltration of water from the fracture of the water-bearing layer. Accordingly, studying the issues of load-bearing compression and hydraulic properties of fractured rock masses of filled bulk materials in the compacted gateway will provide guidance to mining practitioners who use solid materials as backfill.

Scholars have conducted a set of studies on the load-bearing compressive properties of filling materials using numerical simulations, laboratory studies, and engineering practice. Yu et al. (2021) constructed irregular particle clusters by using particle element theory and PFC numerical simulation software, and found that the irregular particle morphology can more accurately reflect the permeability characteristics of small particles in collapse rock. Wang et al. (2014) utilized granular flow simulation software to study the compressive mechanical properties of coarse-grained soils and the stress–strain problems of gravel aggregates with different particle sizes, and obtained the degree of influence of cyclic loading on the compressive bearing. Yu et al. (2016) and Wang et al. (2016) conducted compression experiments on saturated crushed rock masses, crushed sandstone, and coal gangue with different grain size gradations, and obtained different cases of stress–strain exponential growth relationships and damage characteristics of compressive deformation. To better solve the actual engineering seepage collapse problem, the hydraulic properties of fractured rock masses were studied. After the famous Darcy law (Wahyudi et al. 2002) was proposed, conversely, it was determined that actual engineering did not conform to Darcy’s law for fractured rock masses. The pressure gradient and seepage velocity have obvious nonlinear characteristics; hence, the non-Darcy law formula (Chen et al. 2015) was proposed by Forchheimer through numerous experimental studies. Since then, the research of scholars worldwide has rapidly developed in the field of seepage testing of fractured rock. Li et al. (2008) and Cao (2017) employed the transient permeability method to test the permeability of different coal samples and granite. It is found that the relationship between permeability and stress–strain and the air inclusions delay the attenuation of hydraulic pulse, which leads to the underestimation of permeability. Sinha et al. (2012) employed the steady-state method to obtain the permeability values of test samples by Darcy’s formula. The results showed that the steady-state method was more accurate for accurately measuring the permeability of slightly compact specimens. Ma et al. (2018) and Lv et al. (2022) conducted tests with a homemade percolation experimental apparatus and discovered that the variation in permeability was directly related to the hydraulic gradient and the amount of filtered sand.

To analyze the compressive bearing of filling materials and the percolation of complex internal pores, the fractal dimension was introduced to characterize the degree of fragmentation of filling materials and spatial distribution characteristics, and a relationship with the permeability and other parameters was established. Yang et al. (2017) and Yu (2016) obtained the variable relationship among several physical parameters, such as the fractal dimension of multiscale pores and tortuosity. Based on fractal geometry theory and techniques for laminar flow through tree-like branching networks with roughened channels, the relationships among pressure drops and permeability are investigated. Ma et al. (2019) established an improved model for predicting permeability evolution based on fractal dimension and determined that the loss of large particles and the change in fractal dimension were more significant at lower stress rates.

The researchers have explored the load-bearing compressive properties and hydraulic properties of these fill body materials through laboratory tests and numerical simulations, revealing insights for practical mining applications. However, there is a lack of in-depth investigation into the compressive and hydraulic properties of mixed fill materials with varying proportions. In this study, variations in the permeability coefficient and acceleration factor of crushed coal gangue specimens were mainly investigated using a homemade percolation test system and fractal theory. The fractal characteristics of crushed coal gangue particles were also revealed.

Materials and methods

Preparation and proportioning of test materials

The filling materials selected for this test were coal gangue and coal fly ash samples. The tested coal gangue was collected from Xiaojihan Coal Mine in Yulin, Shanxi. X-ray diffraction spectra of coal gangue powder and fly ash were measured by X-ray powder diffractometer (model: D2 Advance), as shown in Fig. 2.

Fig. 2
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The diffraction spectrum of samples and the content of main components: a coal gangue samples; b coal fly ash

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Coal gangue and fly ash are mostly composed of SiO2 and Al2O3, and the content of other components was slightly different. Large pieces of coal gangue were broken with the crusher; the four particle sizes required for the test were screened by a standard vibrating sieve and then mixed with different concentrations of coal fly ash. Among them, the particle size ranges of coal gangue are 2.5–5 mm, 5–8 mm, 8–12 mm, and 12–15 mm, as shown in Fig. 3.

Fig. 3
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Broken samples of different particle sizes

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Test system and operating procedure

Through extensive experimentation and testing, the seepage test was conducted using an independently designed test system, as shown in Fig. 4. The system is mainly composed of a seepage instrument, an electronic tension–torsion testing machine, a flow meter, pressure sensors, an oil pump, a water tank, an acquisition card, and a computer. The seepage instrument is the core device of this test system. The upper tray (6) of the seepage instrument is fixed with bolts (7), and the lower tray is fixed and sealed with an O-shaped rubber seal (9) and bolts (4). The outside of the seepage instrument is the cylinder tube (1), and five pressure sensors are arranged on the left side of the cylinder tube to record the pressure data. Water flows upwards through the cylindrical tube via a barrel pipe (8) and flows out the device from a water pipe (3). The function of the flow piston (2) is to regulate the experimental flow rate, while the overflow groove cover (5) prevents water from escaping from the top. The electronic tension–torsion testing machine can provide a maximum axial load of 150 kN, and its model is WDD-LCJ-150. The water in the water tank can be injected from the bottom of the seepage instrument through the water pump. Flow meter and pressure sensors record data to the data acquisition card, which is subsequently processed by the computer for analysis of the stored experimental data.

Fig. 4
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Percolation experimental system

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Test protocol and procedure

The hydraulic and deformation tests of mixed samples of broken coal gangue and fly ash strictly followed the steps:

  • Step 1: The samples were prepared and mixed with fly ash according to the matching stages

    The coal gangue was washed with water to remove the fine particles and soil left during the grading. The coal gangue can also be initially saturated. According to the volume of the cylinder, the mass of each group of samples was set to 1500 g. After removing 450 g of fly ash with a maximum mixing percentage of 30%, the remaining weight of coal gangue samples was graded. The sample quality of each particle size interval was matched according to Talbol Eq. (1) (Kong and Wang 2018). The mass distribution of each initial graded sample is shown in Table 1.

    $$P={\left(\frac{{d}_{r}}{{D}_{r}}\right)}^{n}\times 100\%$$
    (1)

    where P is the proportion of the mass of broken coal gangue with a diameter less than dr and the total mass, dr is the diameter of the broken coal gangue, Dr is the maximum diameter of the coal gangue, and n is the value of the Talbol power index.

    The four graded coal gangue samples were mixed with 10%, 20%, and 30% fly ash, respectively, and left for 12 h at room temperature with ventilation.

  • Step 2: Conduct equipment assembly and sample preliminary processing

    The mixed samples of coal gangue and fly ash were put into the cylindrical seepage vessel, and the whole seepage system was assembled. To eliminate the influence of the unsaturated state on the seepage test, the samples were saturated by low-pressure water injection until the flow rate was stable. Among them, the percolating fluid was water with mass density ρ = 1000 kg/m3, dynamic viscosity μ = 1.01 × 10–3 Pa·s, and coefficient of compressibility Cf = 0.556 × 10–9 Pa−1. The experimental temperature (T) was 25 °C.

  • Step 3: Load axial stress and pass through different water pressure

Table 1 Initial quality of crushing samples in different particle size intervals
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In this step, the sample was first subjected to constant axial loadings, which were 40 kN, 60 kN, 80 kN, 80 kN, 100 kN, and 120 kN, each time a constant axial loading of 20 min, and then under an axial loading every 5 min into gradient water pressures. These were 1 MPa, 2 MPa, 3 MPa, and 4 MPa in sequence. The water pressure rose in a gradient over time and the changes between the four water pressures are synchronized. Each layer between the gradient changes is almost a horizontal line, as shown in Fig. 5.

Fig. 5
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Changes in water pressure over time

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Both a flow meter and a pressure sensor were used to record flow and pressure data. When the experiment was done, the sample was removed from the cylinder, and then particles of different particle sizes were selected with a standard vibrating screen. The samples were weighed and recorded with a high-precision electronic scale.

Principle of calculation of test parameters

According to the momentum equation, we employed the non-Darcy law formula of the porous medium (Zhang and Zhang 2019):

$${\rho c}_{a}\frac{dV}{dt}=-\frac{{\Delta p}_{i}}{H}-\frac{\mu }{k}V-{\rho \beta V}^{2}$$
(2)

where V = q/Q, q is the flow rate at steady state, Q = πφ2/4, φ is the inner diameter of the cylindrical tube, μ is the viscosity, ρ is the mass density of percolating fluid, ∆pi is the pore pressure difference, and H is the sample height.

According to previous studies of fractals (Li et al. 2019; Wu et al. 2021), the fractal dimension can be calculated:

$$\frac{{M}_{d}(x<d)}{{M}_{t}}=\frac{{d}^{3-D}-{{d}_{\mathrm{min}}}^{3-D}}{{{d}_{\mathrm{max}}}^{3-D}-{{d}_{\mathrm{min}}}^{3-D}}$$
(3)

where Md is the particle mass with a particle size less than d; Mt is the sum of the particles; d is the particle size of the broken rock mass particle; dmax is the particle size of the largest particle; dmin is the particle size of the smallest particle; and D is the fractal dimension of the particle.

Under the action of axial loading in this test, the minimum particle size dmin is 0 compared with the larger particles in the sample, and the listing can then be expressed as:

$$\frac{{M}_{d}\left(x<d\right)}{{M}_{t}}={\left(\frac{d}{{d}_{\mathrm{max}}}\right)}^{3-D}$$
(4)

Equation (4) takes the same log on both sides of the equation:

$$\mathrm{lg}\left({M}_{d}/{M}_{t}\right)=(3-D)\mathrm{lg}\left(d/{d}_{max}\right)$$
(5)

According to Eq. (5), a straight line is fitted in the double-log coordinate axis with a slope of 3-D, and then the fractal dimension D of the broken coal gangue sample is obtained.

Results and discussion

Influence law of axial loading on fractal dimension

Different axial loadings have a certain influence on the fractal dimension of the broken coal gangue test samples, as shown in Fig. 6.

Fig. 6
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Relations between axial loading and fractal dimension

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Figure 6 shows that the fractal dimension increases with increasing axial loading. The fractal dimensions of the three kinds of coal fly ash concentrations of the coal gangue specimens rapidly increase from 0 to 60 kN as the initially broken coal gangue large particle sample has the characteristics of the clear diamond and a small contact area. Hence, coal gangue specimens are very susceptible to fragmentation and cause a sharp increase in their fractal dimension under the action of axial loading. The fractal dimension rising trend slows with an increase in axial loading; when the particle is broken to a certain extent, increased contact between particles and particle migration is difficult. The broken coal gangue particles are fully in contact with each other and are further compacted. In addition, the change in the particle shape after fracture suppresses further fracture of the particles, and the close contact among the particles hinders their rearrangement. This is consistent with the findings by Wen et al. (2019): the overall deformation of the samples slowly increases, and the coal gangue samples rarely break. Consequently, the fractal dimension eventually gradually increases.

Simultaneously, the fractal dimension decreases with increasing coal fly ash concentration under the same axial loading. With the same initial particle size classification and stress conditions, the concentration of coal fly ash directly affects the strength of the crushing sample. Broken particles are less likely as the concentration increases, leading to a further decrease in the fractal dimension.

Analysis of factors influencing the seepage acceleration coefficient

By increasing the axial loading, the seepage characteristics of non-Darcy flow are calculated according to the collected time series. Table 2 represents the flow rate and pressure data. The acceleration coefficient (Ca) changes of four different grain grading and three different coal fly ash concentrations are shown in Fig. 7.

Table 2 Seepage characteristics of the coal gangue sample test
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Fig. 7
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Change pattern of the acceleration coefficient (Ca) under different axial loadings: a Talbol power index 0.2; b Talbol power index 0.4; c Talbol power index 0.6; d Talbol power index 0.8

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It can be concluded that with the axial loading ranging from 40 to 80 kN, the acceleration coefficient is constantly increasing. This is consistent with the findings of Kan et al. (2021); it should be noted that when the axial loading is greater than 80 kN, the acceleration coefficient decreases and then has a small recovery. The internal structure of the coal gangue test sample is destroyed with increasing axial loading. The pores do not continue to increase, and the permeability exhibits a slight increase. Moreover, after the axial loading exceeds 100 kN, the acceleration coefficient slowly changes as the coal gangue test sample is basically in the full compaction state, and slide movement between two subtle particles produces slow changes in the acceleration coefficient.

Through a comparison of four sizes of coal gangue samples, the acceleration coefficient decreases with an increase in the broken sample size. The acceleration coefficient reflects the change process of the fluid viscosity force; when a large coal gangue sample enters the water pressure, the fluid viscosity force exhibits a small change. On the other hand, the acceleration coefficient is inversely proportional to the porosity of the broken coal gangue sample. The acceleration coefficient decreases as the Talbol power index increases. Different concentrations of coal fly ash for the acceleration coefficient also have a certain influence, as shown in Fig. 6. The acceleration coefficient is proportional to the coal fly ash concentration. The degree of cementation of broken coal gangue is greater with increasing coal fly ash concentration, which further causes an increase in the acceleration coefficient.

Permeability evolution pattern

Analogous to the change process of the gradient water pressure, the tube height is divided into four layers to analyze the compaction samples of different layers. By processing the sample data of different layers separately, the change rule of four-layer permeability is obtained.

Figure 8 shows the permeability trend diagram of the Talbol power index is 0.4 and coal fly ash concentrations of 20% as an example. Notably, the top half of the diagram depicts a thumbnail of the sample, and the bottom half of the diagram depicts the different degrees of compaction inside the sample. The specimen will have particularly obvious transition zones at the beginning of the seepage. The permeability in the transition zone substantially varies. The seepage flow is extremely unstable, and with increasing axial loading, the permeability of broken coal gangue samples will be reduced.

Fig. 8
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Trend diagram of the permeability of each layer under different axial loadings

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The least squares method is a statistical method for fitting data or estimating parameters. Its fundamental principle involves the search for one or more curves that minimize the sum of squared vertical distances between observed data points and corresponding points on these curves. Based on test data and Eq. (2), permeability was fitted using the least squares method and the objective function is obtained as follows:

$$f\left(i\right)={\rho c}_{a}dx\left(i\right)-\frac{\upmu v\left(i\right)}{k}+\beta\uprho v(i)-dp(i)$$
(6)

The permeability k, the non-Darcy factor β, and acceleration coefficient Ca can be obtained by Eq. (6).

Figure 9 shows the measured values and fitted curves of permeability changes of each layer; the change curves of permeability of each layer are basically the same. Under the same axial loading, the permeability of the test sample decreases layer by layer when the axial pressure increases to 100 kN. Figure 9d shows that the original configuration of the broken coal gangue test sample is destroyed, and the conductivity of the coal gangue test samples increases. If the pore pressure does not continue to increase, the penetration rate slightly recovers. Different from the conclusion of Feng et al. (2018), there was no significant change in the permeability after the axial loading exceeded 100 kN. When the sensitivity of the permeability to axial loading decreases, coal gangue particles squeeze against each other, and the sliding deformation eventually reaches the equilibrium state. The axial loading continuously reduces the porosity of the broken coal gangue samples, the particles are more uniform, and the permeability varies by two orders from 10–11 to 10–9 m2.

Fig. 9
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Permeability of four layers varies with different axial loadings: a first layer sample; b second layer sample; c third layer sample; d fourth layer sample

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The results in Fig. 10 show that the rate of change of seepage rate decreases steadily with the axial loading firstly. When the axial loading is 100 kN, the rate of change of permeability is small and conforms to the fitted exponential function with an accuracy of 0.9913. As can be seen from the 95% confidence band, the change rate of permeability is included in it, and the change range is relatively large. At this time, the change rate of permeability ranges from –0.5 to 0.1. This is because the sample tends to be tightly compacted and the permeability does not change significantly, which is consistent with the permeability of the above four layers. Therefore, it is concluded that the broken coal gangue test sample has a strong deformation ability and can be used as a backfill mining material to prevent water failure caused by surface settlement and fracture of the water-bearing layer. The results of the influence of particle size grade on hydraulic performance were compared by Ma et al. (2021). The permeability value of the four samples when the compressive stress is greater than 4 MPa is less than 10 μm2, and the permeability decline rate is fast from 0 to 3 MPa, which is basically consistent with the permeability change in the early stage of this paper. Different from the investigated permeability method, the layered permeability method adopted in this paper can more directly obtain the internal connection between permeability and porosity and compaction state. The results show that adding a certain concentration of coal fly ash can improve the adhesion degree of the test sample of broken coal gangue to effectively control the mining settlement and protect the ecological environment.

Fig. 10
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Relationship between permeability change rate and axial loading

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Variation pattern of permeability and fractal dimension

Based on the mass of different particle sizes before and after the compaction of the broken coal gangue samples, the relationship between fractal dimension and permeability is obtained, as shown in Fig. 11.

Fig. 11
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Relation for permeability and fractal dimension

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The fractal dimension and permeability are fitted into a primary equation, and the specific equation expression is shown above, where the fractal dimension ranges from 2.15647 to 2.58933. Zhang et al. (2020) obtained the results of increasing the fractal dimension from 2.38 to 2.56 in the 95% humidity test, which is basically consistent with the results of this paper. However, different from the change in humidity, this paper explores the effect of fractal dimension on permeability by changing the coal fly ash concentration. The effect of fractal dimension on permeability was investigated by changing the coal fly ash concentration. The results show that permeability gradually decreases with increasing fractal dimension. As the fractal dimension increases, the fragmentation of the coal gangue specimen intensifies, resulting in an increase in the number of small particles produced. Consequently, this leads to a direct increase in the number of pores in the broken specimen. The average diameter of pores and pore volume are inversely proportional. At this time, the small particles of the coal gangue sample under axial loading are continuously displaced and compacted, and particle size distribution recombination causes pore blockage by small particles, which leads to a permeability decrease.

Conclusions

In this study, the basic mechanical properties of mixed specimens of coal gangue (obtained from a single mine source) and coal fly ash under different axial loading conditions were tested using a homemade percolation test system. The variance ratio of permeability between different axial loading levels and the relationship between axial loading and acceleration coefficient under different grain grading were obtained. The characteristic relationships between axial loading and permeability and particle fractal dimension for different coal fly ash concentrations were discussed. The following conclusions are made based on the experimental results.

  1. (1)

    The increasing rate of fractal dimension further increases when the axial loading ranges from 0 to 60 kN and decreases when the axial loading is greater than 60 kN. This rate is negatively correlated with the coal fly ash concentration, and in this study, the increasing range of fractal dimension is 2.15647 ~ 2.58933.

  2. (2)

    The axial loading and acceleration coefficients are positively proportional, and the grain grading of the crushed coal gangue specimen is inversely proportional to the acceleration. The higher the concentration of coal fly ash for the same stress and particle size, the greater the acceleration coefficient of the crushed specimen. The non-Darcy flow β factor changes in the range of 109 ~ 1012 m−1, and the acceleration factor Ca changes in the range of 105 ~ 109. The results show that the crushed coal gangue specimen is mixed under a smaller grain grading, and a higher coal fly ash concentration as filler material will yield better performance.

  3. (3)

    The water pressure rises in a gradient with creep time and is basically in a synchronized state as the axial loading reaches a preset value while maintaining a constant load to the corresponding creep time. This finding is helpful for the correctness and reliability of parameters such as permeability and fractal dimension. Porosity is a physical parameter that directly affects the permeability of crushed specimens, while the permeability varies with each layer of specimen; the magnitude range of permeability k is 10–11 ~ 10–9 m2. The results indicate that the specimens in the compaction process undergo asynchronous crushing and particle sliding displacement, which is directly related to the height of the test barrel diameter.

  4. (4)

    According to the correspondence between permeability and particle fractal dimension, it was determined that the broken coal gangue specimens have obvious fractal characteristics. It is suggested to compress the broken coal gangue specimens with axial loading at a lower rate to reduce the risk of overburden and avoid the destruction of water-bearing layers.