The Seepage Evolution Mechanism of Variable Mass of Broken Rock in Karst Collapse Column under the Influence of Mining Stress

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Introduction
Collapse column is a special geological structure in the coal field of North China. Under the mining disturbance of the working face and overlying aquifer, collapse column tends to be activated, becoming a pathway between the overlying aquifer and stope, threatening the safety of coal mining [1]. With the extension in deep coal mines, water inrush disasters in the collapse column become more serious [2]. Water inrush reflects seepage stability and loss of water in a broken rock under the mining disturbance.
Many experts and scholars have done many research on this aspect. Yin et al. [3] established a thick-walled cylinder mechanical model of the collapse column and obtained a theoretical criterion of water inrush. Bai et al. [4] proposed a fluid structure "plug model," and the influence of multifield coupling should also be considered [5]. Zhu and Wei [6] and Yang et al. [7] studied the water inrush with the COMSOL Multiphysics and studied the formation process and evolution law of the water inrush channel of the working face. In terms of the research on permeability characteristics, Zhu et al. [8], Chen et al. [9], Ma et al. [10,11], and Wu et al. [12] carried out a laboratory research on the permeability characteristics of broken rock and achieved variation rule of this aspect with time. Zhang et al. [13,14] used the improved seepage test equipment to obtain grain change rule and distribution characteristics of filling material in the collapse column under the condition of graded loading and different water pressure. Yu et al. [15] analyzed the influence of factors such as salt content, cement content, and rock grain size distribution on permeability characteristics. Feng et al. [16] analyzed the permeability characteristics and water intrusion and obtained the change law of mass loss with permeability. Zhang et al. [17] studied the relationship of pressure gradient with permeability in coal mining.
However, the change law of confining pressure with seepage characteristics under triaxial stress is seldom consid-ered in previous permeability tests; besides, cementation in broken grains is not considered in most of them [18][19][20][21]. In practical engineering, collapse column is a cemented body formed by gradual compaction and filling cementation [22][23][24]. Therefore, this paper studies the seepage evolution law of the cemented broken rock mass under mining action, such as different confining pressures, degree of compaction and cementation, and grain size distribution of the broken rock mass.     (Figures 1 and 2) is adopted, which contains five main parts, namely, confining pressure loading system, composed of the hydraulic manual pump and hydraulic flow meter, providing stable and adjustable confining pressure; osmotic pressure control system; the penetrator is the core device of this experiment; the data acquisition; and the filling grain collection system is mainly composed of the filter screen, oven, and electronic scale.

Sample Preparation.
Before the test, standard screening machine is used to screen 6 kinds of broken rock grains with diameters according to actual conditions, and samples with different grain sizes are shown in Figure 3. According to the Talbol theoretical formula, the grain mass distribution of the rock grain size range of each size (Table 1) is obtained. Figure 4 reflects the evolution law of the mass rate of lost grains of each sample under the action of different coaxial displacements. This is mainly due to smaller n samples, and large grains in the sample quality percentage are small. The residual rock grains in the sample flowed out, and the change rate of mass lost decreases gradually. As can be seen in Figure 5, the mass loss of small grain size accounts for a large proportion in the grain migration process, and the mass loss of grains gradually decreases with the increase in the Talbol index n. Grain size range of 0~0.25 mm is the most obvious, and the mass of lost grains at all levels is 51.28, 38.71, 30.62, and 26.13 g, respectively. Figure 6 shows the porosity time curve in the osmotic process. Pore rate decreases with increasing axial displacement (axial displacement is small) and a low degree of compaction. The porosity of the samples decreases with the augmentation of axial displacement. Under the action of higher confined pressure, the deformation of rock samples is greater, the water inrush channel is blocked, and the fine grains need to overcome greater resistance to overcome.

Influence of Different Cementation Strengths on Seepage
Characteristics. Figure 7(a) shows the rate evolution of mass lost with various bonding strengths. The factor of the sample elevates greatly with the decrease of the bonding strength of the sample. The interaction between grains is small, and the pore structure of the sample has low stability. Figure 7(b) shows the porosity evolution of samples with different cementation strengths. The stability of the pore structure of the sample with low cementation strength decreases, and the porosity increases significantly.
The permeability tests show that grain migration is the reason for mass seepage and loss and also a key factor for water inrush. As the main water channel after a seepage disaster, the whole water inrush process contains initial seepage, seepage surge, and seepage stability, shown in Figure 8.
In the formula, q f represents the Darcy velocity of the fluid; η represents the dynamic viscosity of the fluid; p repre-sents the pore pressure; k represents the permeability; ∇z represents the direction of the gravity unit vector.

Conservation Equation of
Mass. The mass conservation of grains is In the formula, b represents the crack width, ϕ represents the porosity of the matrix block, c represents the volume concentration of suspended grains, and a represents the side length of the matrix block.

Conservation in Fluid Mass
In the formula, λ 1 is a constant, and jqj represents the seepage velocity absolute value. Figure 9 is the computational model. The model diameter is 8 m, the height is 40 m, and the bottom water pressure is 2 MPa; the seepage boundary conditions are set, namely, the lower boundary water pressure p = 2 MPa; the top boundary is the water outlet; the pressure is set to air pressure, p = 0:1 MPa; and the left and right boundaries are impermeable boundaries. Six time points of 0 s, 4000 s, 8000 s, 12000 s, 16000 s, and 20000 s are selected as monitoring time points for calculation, and a position is selected at the bottom, middle, and top as monitoring points, respectively-point 2 (4.5, 20) and domain point 3 (4.5, 34.5). For the migration of grains in the model, the corresponding boundary conditions are set, namely, the lower boundary is the Dirichlet boundary and the upper boundary is the Newman boundary. The initial conditions are the pore water pressure at the lower boundary is 2 MPa, the upper boundary is the air pressure 0.1 MPa, the initial volume fraction of grains filled in the model pores is c = 0:01, and the matrix porosity satisfies the Weber distribution m = 3. The main parameters are in Table 2. Figure 10 is a cloud map of porosity distribution at different times. It is obvious that the pore structure is relatively stable before 12000 s. With the elevation of seepage time, broken rock grains migrate  7 Geofluids gradually, and internal pore and skeleton structure are gradually damaged. Besides, the fine grains migrate, and seepage characteristics in broken rock are improved, thereby forming a potential water-conducting channel. According to the porosity change equation, mass migration is the main factor causing the porosity change, and the faster the mass migration, the faster the porosity change. Figure 11 is a cloud map of permeability change with time. It is obvious that the permeability increases slowly firstly. Before t = 12000 s, maximum permeability is only 7:21 × 10 −11 m 2 . After t = 12000 s, the permeability increases quickly, and the maximum permeability of the model is 1:45 × 10 −9 m 2 , and the increasing range is 20.1 times. The broken rock inside the collapse column is lost, and several discontinuous seepage channels are formed.

Conclusions
(1) The test samples based on the fractal theory and the Talbol gradation theory are prepared, and the selfdeveloped broken rock seepage equipment is employed to analyze the seepage evolution law of broken rock mass in the collapse column under triaxial stress. The grain mass loss rate is inversely proportional to n and axial displacement, and the grain mass loss rate increases as the value of n decreases (2) As n value increases, porosity increases as a whole. Grain loss becomes the internal factor for the stability of seepage in the collapse column. Under the influence of water corrosion, grains inside the collapse column are continuously migrated and lost, forming several discontinuous seepage channels

Geofluids
(3) Based on the fluid mechanics and the COMSOL Multiphysics, the mechanics model of the collapse column is established, which clarifies the developing process of the water-conducting channel. Under the action of water corrosion, broken rock mass inside the collapse column is lost, and several discontinuous seepage channels are formed

Data Availability
The data used to support the findings of this study are included within the article.

Conflicts of Interest
The authors declare that they have no conflicts of interest.