Study on Fractal Characteristics of Evolution of Mining-Induced Fissures in Karst Landform

Abstract

The karst landscape is widespread in the southern region of China. As a result of underground mining activities, the original stress equilibrium is disrupted, causing the redistribution of stress in the overlying rock layer, inducing the longitudinal fracture of mining to expand and penetrate upwards, resulting in the rupture and destabilization of the karst cave roof, thus triggering a series of engineering problems such as karst cave collapse, landslide, the discontinuous deformation of the ground surface, and soil erosion. In order to study the evolutionary characteristics of buried rock fissures in shallow coal seam mining under the karst landform, taking the shallow coal seam with the typical karst cave development landform in Guizhou as the engineering background, based on the similarity simulation experiment and fractal theory, the evolution law of buried rock fissures and network fractal characteristics under the disturbance of the karst landform mining are analyzed. The research shows that the mining-induced fracture reaches the maximum development height of 61 m on the left side of the cave, and the two sides of the cave produce uncoordinated deformation. The separation fracture below the cave is relatively developed, and the overall distribution pattern of the cave rock fracture network presents a “ladder” shape. The correlation coefficient of the fractal dimension of the rock fractures under different advancing distances is more than 0.90, and the rock fracture network under the karst landform has high self-similarity. The variation of fractal dimension with the advancing degree of the working face can be divided into four stages. The first and second stages show an exponential growth trend, and the third and fourth stages show linear changes with slopes of 0.0007 and 0.0014, respectively. The fluctuation of the fractal dimension is small. The periodic weighting of the upper roof in the cave-affected zone is frequent, the fragmentation of the fractured rock mass becomes larger, and the fractures of the upper rock mass are relatively developed. The research results can provide a reference for the study on the evolution law of mining-induced rock fissures under similar karst landforms.

1. Introduction

Coal seams in the Guizhou mining area are generally characterized by shallow burial, thin bedrock, small spacing, and strong karst development. Due to the comprehensive effects of natural climate, geological structure, and water erosion, Guizhou has created a unique karst cave landform. Guizhou Province is one of the most typical karst landform areas in the world. Compared with non-karst mining areas, the ecological environment of the Guizhou mining area is fragile, and the bearing structure and stress environment of the surrounding rock are more complex [1,2]. Underground mining activities redistribute the original rock stress, induce the upward expansion and coalescence of the mining-induced longitudinal fracture cracks, and cause the roof failure and instability of the karst cave, which leads to a series of disasters such as karst cave collapse, mountain landslide, surface discontinuous deformation, and soil and water loss. The original ecosystem of the mining area is greatly damaged, and the environmental impact is extremely bad. Therefore, it is of great scientific significance to study the evolution law of rock fractures in the shallow seam mining under the karst landform.

In recent years, increasing attention has been focused on the combined application of fractal theory and similar simulation experiments, by which considerable progress has been made in the quantitative description of the evolution law of mining-induced fractures, such as: Xie et al.’s [3,4,5,6,7] fractal geometry theory, which is widely used in the study of underground coal seam mining, and which provides new ideas and ways for micro, complex, and disordered mining fracture evolution law. A large number of research results show that the distribution of mining fractures in geometric space has high self-similarity [8,9,10,11,12]. Scholz, Walsh, and Jackson [13,14,15] explored the evolution law of rock fractures under different coal seam spacing and analyzed the spatial occupancy of fracture networks by introducing fractal dimension. Li et al. [16] introduced the fractal theory to quantitatively describe the trend and extent of several important stages of rock fracture evolution affected by mining. Yin et al. [17] obtained the spatial evolution law of fracture networks under three-dimensional stress conditions according to the fractal geometry theory. Wei et al. [18] used fractal geometry theory and damage mechanics to quantitatively describe the overall characteristics of the fracture system in the fracturing process of large coal samples. Based on the laboratory similarity simulation, Li et al. [19] used the similarity simulation experiment to simulate the development and evolution process of overlying strata fracture in close-distance coal seam under repeated mining and used the fractal geometry theory to study the fractal characteristics of the overlying strata fracture network under repeated mining conditions. Liu et al. [20] used similar material simulation experiment to simulate the formation process and distribution state of fissure in a mined-out area and used fractal geometry theory to study the fractal law of fissure in mined-out area’s three zones’ rock mass. Wei et al. [21] used the three-dimensional physical similarity simulation method to study the evolution characteristics of fissures in fully mechanized overlying strata with a large mining height. Lin et al. [22] analyzed a simplified model, the main parameters, and the influencing factors of the spatial structure of a mining-fractured zone based on a similar material simulation experiment. Based on a similar simulation test and fractal theory, Liang et al. [23] obtained the fractal variation law of mining fracture, along with the mining process, and in different subregions of the mining face. Guo et al. [24] studied the fractal characteristics of the fracture networks and subsidence in the mining process by using a similar material simulation test and fractal method.

At this stage, research on the evolution of fissures in the overburden of shallowly buried coal seam mining focuses more on methodological and experimental innovations, and less on mining research involving the special geological environment in the typical karst landscape of Guizhou mines. Therefore, this paper takes the mining of shallow coal seam under typical karst landform in the Guizhou mining area as the engineering background, using a similar simulation experiment and fractal theory to quantitatively study the evolution law and fractal characteristics of rock fractures in shallow coal seam mining under the karst landform, and reveals the influence of the karst cave structure on the evolution of rock fractures in mining.

2. Similar Simulation Study on Fracture Evolution Law of Mining Disturbed Rock

2.1. Project Overview and Experimental Design

In this paper, M18 coal seam of a mine in Guizhou is taken as the research background, which is located in the northwest of Guizhou Province, as shown in Figure 1a. The coal seam level is stable, and the roof and floor of the coal seam are mudstone. The thickness of the whole coal seam is 0.86~2.16 m, and the average burial depth is 103.4 m. The thickness is 0.86~2.02 m. Generally, there is no or occasionally 0~2 layer of rock, and the thickness of the rock is less than 0.38 m. The coal seam is mainly thin coal seam, and the part is medium-thick coal seam, which is relatively stable. The Changxing limestone cave above the coal seam is more developed, and the comprehensive histogram of the coal-bearing strata in the mine is shown in Figure 1b.

This paper presents a quantitative study on the evolution of overburden fractures and their fractal characteristics in shallowly buried coal seam mining under karst terrain in a typical mining area of Guizhou, using field research, similar simulation experiments, and fractal theory to reveal the influence of the karst cave structure on the evolution of overburden fractures in mining at the microscale level. An overview of the methodology in this study is shown in Figure 2.

2.1.1. Similar Materials and Ratio

To objectively reflect the development and fracture of intrusive rock fracture caused by underground coal seam mining, according to the actual engineering conditions, the test model is required to have a certain similar relationship in various physical quantities such as geometric shape, bulk density, and stress according to the similarity law. The geometric similarity ratio is $a_l=100$; the similar constant of bulk density: $a_r=1.6$; the time scale can be obtained according to the conversion relationship between the time similarity ratio and the geometric similarity ratio: $a_t=\sqrt{a_l}=10$ [25,26].

In this experiment, sand was selected as aggregate, and gypsum and lime as cement. Based on multiple ratio tests, and referring to References [19,20,21,22], the ratio of coal and rock strata was finally determined. As shown in

Table 1. Basic physical and mechanical parameters of coal and rock mass.

Number	Lithology	Thickness	Density	Elastic Modulus	Tensile Strength	Poisson Ratio
		(m)	(kg/m3)	(GPa)	(MPa)	(GPa)
15	Topsoil layer	8.9	1750	0.1	0.1	0.32
14	Changxing Formation	31.9	2430	19.9	4.4	0.20
13	Mudstone	8	2450	7	1.8	0.31
12	Sandy mudstone	19.6	2595	15.3	2.54	0.22
11	Mudstone	5.3	2450	7.34	2	0.31
10	Muddy siltstone	2.4	2520	14.2	1.7	0.21
9	Fine sandstone	5	2550	11.5	2.5	0.2
8	Muddy siltstone	6	2520	14.2	1.7	0.21
7	Mudstone	4.3	2550	7.34	2	0.31
6	Muddy siltstone	7.2	2600	15.6	3.9	0.23
5	Mudstone	2.8	2420	8.49	1.5	0.22
4	Coal M18	2	1400	2.5	0.6	0.25
3	Mudstone	2.7	2560	8.79	2.02	0.29
2	Limestone	0.5	2700	30	4.9	0.28
1	Mudstone	8.3	2640	7.87	2.37	0.29

, similar materials of each rock layer and their dosage are shown in

Table 2. Proportion and dosage of similar materials in each rock stratum.

Number	Lithology	Thickness	Density	Elastic Modulus	Proportion Number	Sand	Lime	Gypsum	Total Material Weight	Water
		(cm)	(kg/m3)	(GPa)		(kg)	(kg)	(kg)	(kg)	(kg)
15	Topsoil layer	8.9	1094	0.00	-	127.57	9.11	9.11	145.79	16.20
14	Changxing Formation	31.9	1519	0.12	537	457.23	27.43	64.01	548.68	60.96
13	Mudstone	8	1531	0.04	773	114.67	11.47	4.91	131.05	14.56
12	Sandy mudstone	19.6	1622	0.10	737	280.93	12.04	28.09	321.07	35.67
11	Mudstone	5.3	1531	0.05	755	75.97	5.43	5.43	86.82	9.65
10	Muddy siltstone	2.4	1575	0.09	773	34.40	3.44	1.47	39.31	4.37
9	Fine sandstone	5	1594	0.07	737	71.67	3.07	7.17	81.90	9.10
8	Muddy siltstone	6	1575	0.09	773	86.00	8.60	3.69	98.29	10.92
7	Mudstone	4.3	1594	0.05	755	61.63	4.40	4.40	70.44	7.83
6	Muddy siltstone	7.2	1625	0.10	637	103.20	5.16	12.04	120.40	13.38
5	Mudstone	2.8	1513	0.05	773	40.13	4.01	1.72	45.87	5.10
4	Coal M18	2	875	0.02	873	18.63	1.63	0.70	20.96	2.33
3	Mudstone	2.7	1600	0.05	755	38.70	2.76	2.76	44.23	4.91
2	Limestone	0.5	1688	0.19	537	7.17	0.43	1.00	8.60	0.96
1	Mudstone	8.3	1650	0.05	737	118.97	5.10	11.90	135.96	15.11

. In the process of model laying, mica powder was used to stratify each rock strata. After the model laying, it was closed and fixed with high-strength channel steel.

2.1.2. Simulation Test Platform

The geometric size of this similar simulation test platform is 3 m long, 0.3 m wide, and 1.8 m high. The first coal seam 18 # is taken as the research object, and the height of the simulation prototype is 114 cm. The schematic diagram of the model is shown in Figure 3. Because the dissolution space is mostly irregular, in order to facilitate the study, the dissolution space is equivalent to a circular karst cave for analysis. Therefore, a circular karst cave is constructed in Changxing limestone above the coal seam. The radius of the rock cave is 8 m, which is located in the middle of the model. On both sides of the model, 30 cm boundary coal pillars are left, and the whole mining height is one time. The model is promoted from left to right [27,28,29].

2.1.3. Model Measuring Point Layout

In order to facilitate the analysis of the law of fracture development and the caving of overlying strata, the displacement monitoring line is arranged above the coal seam, and two lines are arranged at the upper and lower boundaries of the upper roof. The grid spacing of the monitoring line is 10 cm × 10 cm, and eight lines are arranged, a total of ten lines. The layout of the displacement monitoring line is shown in Figure 4 The high-precision total station is used to observe the coordinates of monitoring points in the process of advancing the working face so as to obtain the displacement of each monitoring point, and the high-definition camera is used to record the test phenomenon in real time [30,31].

2.2. Evolution Law of Weathered Rock Fissures under Mining Disturbance

2.2.1. Analysis of Dynamic Evolution Process of Fracture Propagation in Rock

The fissure development and expansion are closely related to the rock activity, the mining overburden breaking, and fissure development part during the working face advance is shown in Figure 5.

(1)

When the working face advances 24 m, the immediate roof collapses completely, and the caving block is broken, while the upper roof maintains high stability and does not produce obvious cracks; when the working face advances 43 m, the upper roof reaches the ultimate span, and its stability is completely destroyed, resulting in the initial weighting. At this time, a small number of transverse separation cracks are bred above the upper roof. Later, with the periodic instability weighting of the upper roof, the mining-induced cracks continue to expand upward.

(2)

When the working face is mined to 138 m, there is a separation fracture below the main key layer. With the increase of the mining width, the fracture channel is expanding, and the separation fracture is more obvious; when the working face advances 156 m, two obvious cracks appear on the left side of the cave, and the mining-induced rock fractures reach the maximum development height of 61 m. However, the cracks do not penetrate the rock strata where the cave is located, indicating that the Changxing limestone-containing rock caves is the main key stratum, and the rock strata are relatively hard, which can effectively prevent the upward development and expansion of the fractures, and the bearing stability is high. At the same time, the mining-induced fractures in the left and lower sides of the cave begin to gradually close.

(3)

After the end of working face mining, the development of mining-induced rock fractures stops, the obvious separation zone is formed in the bending zone, and the compaction closed zone is formed below the cave. The vertical fracture fractures above the open cut hole and the coal wall side are more developed. The overall distribution of rock fractures is similar to the ‘platform ladder’ shape.

2.2.2. Law of Strata Movement

When the working face is finished, the development of mining-induced fractures stops. By monitoring the monitoring line of the model surface, the displacement and subsidence curves of rock strata are plotted as shown in Figure 6.

It can be seen from Figure 6 that the change curve of rock strata movement is generally symmetrically distributed, and the shape is similar to the “fishtail” shape. The maximum subsidence position of karst rock strata displacement occurs on the left side of the cave, and the two sides of the cave produce uncoordinated deformation, indicating that, when the working face advances from the open-off cut to the cave, due to the lack of structural integrity of the rock strata, the diffusion and transmission of mining-induced stress are blocked to a certain extent, and the mining-induced stress is easy to accumulate on the left side of the cave, resulting in local stress concentration. Therefore, the rock strata above the advancing side are strongly affected by mining, and the displacement and subsidence of the rock strata on the left side of the cave are large. When the working face is located below the cave, the upper rock layer reaches the fully mining state, and the maximum subsidence of the upper roof is 1.7 m. As the main key layer, the rock layer where the cave is located has the characteristics of large thickness and high strength, and the roof subsidence is small. After the mining of the working face, the dislocation momentum of the two sides of the cave decreases.

2.2.3. Variation of Development Height of Separated Fractures

By measuring and recording the height of the delaminated fissures at different advance distances for similar simulation experiments, and then plotting the height of the delaminated fissures development with the advance of the working face is shown in Figure 7.

It can be seen from Figure 7 that, before the periodic weighting of the upper roof, the development of mining-induced fissures is slow, and the amount of separation is small. With the frequent periodic weighting of the upper roof, the rock activity is strong, the mining-induced fissures continue to expand and extend upwards, and the height of fissure development increases rapidly. When the working face is directly below the cave, the development of separation fissures tends to be moderate, and the development height is maintained at 49 m. When the mining distance is 138 m, a separated layer fracture is generated below the main key layer, and the development of the separated layer fracture reaches the maximum height, with the maximum development height of 61 m, and the vertical distance from the bottom of the cave is about 4 m. Since then, with the continuous advancement of the working face, the development height of the separated layer fracture remains basically stable, and the separated layer fracture channel below the cave is gradually compacted and closed, forming a fracture closed area.

In summary, when the working face is close to the bottom of the karst cave, the mining-induced fissure is in the range of the fracture zone. When the working face advances the karst cave, the separation fissure is generated in the bending zone, and the separation fissure reaches the maximum development height. The results show that when the main key layer is a thick and hard rock layer, it is easy to form the separation zone in the bending zone.

3. Study on Fractal Characteristics of Rock Fracture Evolution under Karst Landform

The distribution of mining-induced fractures in time and space is anisotropic, with complexity and randomness. Especially under the condition of relatively complex spatial structure characteristics of intrusive rocks, it is difficult for the traditional research methods to comprehensively analyze the development degree and change trend of mining-induced fracture network of the rock mass. Based on the qualitative analysis, the fractal dimension is used to quantitatively characterize the fractal characteristics of the fractures of intrusive rocks under mining disturbance by introducing the fractal geometry theory, revealing the propagation and evolution law of the fractures of intrusive rocks from the microscale level, and revealing the influence law of rock cave structure on the fractal dimension of mining-induced fracture network [32,33,34,35,36].

3.1. Definition of Fractal Dimension

The concept of fractal geometry was first proposed by mathematician B.B. Mandelbrot [3,25], and, on this basis, F. Hausdorff extended the fractal dimension; fractal dimension, based on fractal theory, as an important mathematical method, can measure complex irregular things from the microscopic level and can better describe the self-similarity of mining rock mass [4,5,6].

3.2. Calculation Method of Fractal Dimension

In the quantitative description and analysis of irregular and complex phenomena, the main characteristics of the research object should be fully grasped. Otherwise, the calculation results of the same phenomenon may vary greatly by using different fractal dimension calculation methods. Therefore, it is particularly important to reasonably select the fractal dimension calculation method. At present, the calculation of fractal dimension is mainly determined by experiments, and then the fractal dimension is calculated by changing the observation scale.

This method is a calculation method of fractal dimension based on the definition of information dimension and box-counting dimension [23,24,25]. That is, using the basic graphics with a characteristic length (such as circle or square, ball or cube, etc.) to cover fractal graphics. Let δ be the characteristic length of the basic graph, which is used to approximate or cover the fractal graph. The total number of basic graphs required to approximate the whole fractal graph is denoted as N (δ). Different N (δ) values can be measured by changing the characteristic length δ of the basic graph. Fractal figure satisfies: N (δ) ∝ δ^−D [37,38,39,40,41].

3.3. Fractal Characteristics of Mining-Induced Fissure Evolution

3.3.1. Fractal Dimension Calculation Program

In this paper, the calculation method of fractal dimension is based on the box-counting dimension method. The calculation program is written using advanced language. Finally, MATLAB (MATLAB v2014B, Mathworks Company, Minato, Tokyo) is used as the execution calculation platform to realize the calculation and fitting analysis of fractal dimension of the two-dimensional image of rock fracture under mining disturbance. This method has the characteristics of simple operation and batch processing. The basic process is as follows: the fracture distribution map of overlying strata in the advancing process of the similar simulation test working face is collected (Figure 8a), and the graph processor is used to binarize and reduce noise (Figure 8b). Then, the software is imported to perform the calculation program based on the box-counting dimensions. By using the graph surface of r small squares covered with different scales, the edge identification is automatically carried out, and the corresponding number of squares containing fractures N (r) is obtained by statistics. The logarithm values of r and N (r) are plotted in the rectangular coordinate system. Finally, the least square method is used for linear fitting, and the slope is the fractal dimension, as shown in Figure 8c [42,43,44].

3.3.2. Relationship between Fractal Dimension and Working Face Advancing

The high-definition digital camera was used to record the distribution map of the fissure development in each mining stage in the process of a similar simulation experiment, and the binarization processing was carried out by using MATLAB. Finally, the distribution map of the fissure in the eroded rock with different advancing degrees in the working face was obtained. Figure 9 shows the extraction part of the fissure network in the eroded rock in each periodic weighting period of the upper roof.

The two-dimensional space occupation of mining fractures is analyzed by introducing the classification dimension after the gray processing of the collapse morphology photographed by the test, and the spatial distribution law and fractal characteristics of shallow mining fractures under the karst landform are quantitatively revealed. Figure 10 is the double logarithmic fitting graph of fracture network corresponding to Figure 9, and its linear correlation is high, indicating that the mining-induced fracture network has good self-similarity.

According to the calculated value of the fractal dimension, the variation curves of the fractal dimension at different mining stages are shown in Figure 11. It can be seen from the figure that the fractal dimension generally shows an upward trend. According to the variation characteristics of the fractal dimension with the working face, it can be divided into four stages, and the fractal dimension of each stage is fitted. The fitting curve of the fractal dimension at each stage and the advancing distance of the working face is shown in Figure 12.

In the first dimension increasing stage, the immediate roof completely collapsed when the working face advanced 24 m. As the working face advanced to 63 m, the mining-induced rock fractures increased continuously, and the fractal dimension met the exponential growth. The correlation coefficient and its fitting formula are shown in Figure 12a; in the second dimension-raising stage, when the working face advances from 77 m to 116 m, the fractal dimension grows fastest, and the separated cracks and vertical fracture cracks continue to develop upwards. The fracture penetration increases with the increase of the working face advancing length, and the space occupation of the mining-induced fissures increases exponentially. The fissures begin to extend and progress to the bottom corner of the karst cave and the two sides, and the fractal dimension reaches the maximum, as shown in Figure 12b. In the third dimension reduction stage, when the working face was pushed from 116 m to 200 m, the development and expansion of the erosion rock fissures in this stage were relatively complex, and the erosion rock fissures began to close. The fractal dimension of the fracture network showed a linear downward trend, and the slope of the fitting curve was −0.007, as shown in Figure 12c. In the fourth linear dimension-raising stage, when the working face is pushed from 200 m to 240 m, the height of fracture development is basically unchanged. The separated fractures in the area below the cave are closed, and the space occupation of the fracture network is increased as a whole. The fractal dimension begins to increase again, and the growth rate is small. The variation trend of the fractal dimension of weathered rock fractures meets the linear growth relationship. The slope of the fitting curve is 0.0014, as shown in Figure 12d.

In summary, the variation curves of fractal dimension in each stage show that the shallow buried coal seam under the karst cave landform has a good self-similarity in the exploitation of weathered rock fissures. The fractal dimension is closely related to the advancing degree of working face, the structure of weathered rock, and the roofing activity of stope, which reflects the evolution law of the mining-induced weathered rock fissures from a quantitative perspective.

3.3.3. Fractal Characteristics of Three Zones

With the advance of the working face, the mining-induced fissure network is also in a dynamic change. The fissures continue to expand and develop upwards, and there are horizontal separation fissures and longitudinal fracture fissures, resulting in the loss of structural stability of the coating rock, and the roof is deformed and broken. After the advance of the working face, the coating rock in the goaf will move and deform to different degrees. According to the deformation and failure characteristics of coating rock, it can be divided into a falling zone, fracture zone, and bending zone from bottom to top, as shown in Figure 13. There are obvious differences in the development of fractures in the three zones. According to the fractal dimension calculation program, the corresponding fractal dimension values of the three zones are calculated, which are shown in Figure 14 to characterize the spatial occupancy of fractures in different regions.

It can be seen from Figure 13 that the distribution of the fracture network in the vertical three zones of rock also has a high self-similarity. The fractal dimensions of the fracture network in the falling zone, crack belt, and curving belt are 1.114, 1.343, and 0.874, respectively. With the advancement of the working face, the hanging space of the stope is increasing, resulting in the collapse of the immediate roof and the upper roof. After the roof is broken, the gap between the blocks is large, the fracture in the falling zone is mainly developed, and the space occupancy ratio is small. The overall fracture development degree of the fracture zone is high, and the transfixion degree of the separated fractures in this region is large. At the same time, the vertical fracture fractures near the working face and the side of the open-off cut are densely distributed, and the spatial occupancy is relatively high, so the fractal dimension of the crack belt is higher than that of the falling zone. The stability of Changxing limestone in the bending zone is good, and only a horizontal separation fracture is generated below the rock stratum. Local longitudinal fractures are generated in the sidewall and bottom corner of the cave. Therefore, the distribution of mining-induced fractures in this region is less, and the fractal dimension of the fracture network is the smallest.

4. Conclusions

(1)

The cave plays a guiding role in the development of mining fractures. Due to the existence of the cave, the integrity of the rock structure is missing, which hinders the transmission of mining stress in the horizontal direction to a certain extent and causes the two sides of the cave to show uncoordinated deformation. The periodic weighting of the upper roof in the cave-affected zone is frequent, and the fragmentation of the fault rock mass becomes larger. The fractures of the upper rock mass are relatively developed, and the fractal dimension of the erosion rock fractures in this region is large.

(2)

By calculating the fractal dimension of the two-dimensional image of similar simulated mining-induced fissures, the quantitative characterization and analysis of the mining-induced fissures are carried out. It is concluded that the correlation coefficient of the fractal dimension of the mining-induced fissures under different advancing distances is as high as 0.90, indicating that the mining-induced fissure network of shallow coal seam under karst cave topography has high self-similarity.

(3)

According to the variation characteristics of fractal dimension with working face, it can be divided into four stages. The first, second, and fourth stages are all ascending stages, and the fractal dimensions of the first and second stages increase exponentially with the correlation coefficients of 0.999 and 0.993, respectively, and the growth rate of the second stage is relatively fast. The fourth stage is linear growth, the slope is 0.0014, and the correlation coefficient is 0.923; the third stage is the dimension reduction stage, where the fractal dimension of fracture network decreases linearly, the slope is −0.0007, and the correlation coefficient is 0.968. The fitting curves of each stage are convergent, and the fitting correlation is high.