Sage Journals: Discover world-class research

Abstract

Mine water disaster is closely related to the geological structure of the mine. A scientific evaluation of the complexity of the minefield structure can greatly contribute to mining safety. In this study, we optimized the fault impact index in the study area and proposed an improved local linear embedding (LLE) algorithm by investigating the Shengquan coal mine. We analyzed the fault formation age and connectivity between faults in the study area, combined with topology theory, and based on previous studies. The mechanical properties of faults and the influence of small faults on the strata can be combined to derive a quantitative evaluation model of the structural complexity of mines. Based on the evaluation model, the study area was divided into a simple structural area, a medium structural area, and a complex structural area. By comparing the location of water inrush points in recent years with the three-dimensional high-density electrical exploration of the 21,304 working face, the effectiveness and rationality of structural complexity zoning were determined.

Keywords

Construction complexity coal mine water prevention and control spatial local interpolation local linear embedding algorithm

Introduction

North China-type coalfields are one of the key coal-producing areas in China (Kang et al., 2014; Ma et al., 2020). The geological structure in this area is complex, and the fault structures are well-developed. According to incomplete statistics, more than 75% of water disasters associated with the mining of North China-type coalfields are closely related to fault structures (Wang, 2016). The complexity of fault structures can reflect the extent to which a region is cut and destroyed by faults (Zhou, 2013). Therefore, evaluating the complexity of fault structures (Fu et al., 2022a, 2022b) can contribute to guiding mine safety production (Singh, 1986).

The core of the quantitative evaluation of the structural complexity of a mine lies in two aspects, i.e. evaluation index and evaluation model (Mohamed et al., 2021). Studies on the quantitative assessment of the structural complexity of mines have found excellent results. Xu Zhibin (Xu et al., 1996) used fractal dimensions to quantitatively evaluate the complexity of coal mine fault networks. Shi Longqing (Shi et al., 2018) introduced the fault influence factor based on the fault strength index. To quantitatively evaluate the structural complexity, Chen and Yao (Chen et al., 2010) used the grey fuzzy comprehensive evaluation method. Shu Jiansheng (Shu et al., 2010) used the grey correlation analysis method and the equal block complete index evaluation method to quantitatively assess and classify the complexity of the structure of mines. However, in these studies, the evaluation indices often disregard the basic nature of the formation age of the fault. The water-bearing capacity and conducting capacity of the fault are very different in different formation ages.

This study was conducted in the west of the Tanlu fault zone, which is a part of the Luxi block. After deposition ended in the early Permian, it was compressed in the near north-south direction and subjected to uplift and denudation in the Triassic. The nearly east-west and northwest thrust fold system was formed, and the intermountain compression depression basin was developed. During the early Jurassic, the crust and lithosphere thickened as the north-south compression in the early stage expanded laterally due to gravitational instability, resulting in North-South extensional activities and many low and medium-angle shovel normal faults. Since the Paleogene, the Pacific plate has been obliquely subducted to the northwest, giving rise to many high-angle normal faults, which are widely developed in this region. Among them, NE trending faults started moving, which together with NW trending faults near EW trending faults, controlled the crustal extension of the Luxi block in this period. The direction of extension changed from early near SN to NW-SE. Rift basins developed with high-angle normal faults as basin-controlling structures.

Taking the Shengquan coal mine as an example, we used the feature vector weighting method based on nonlinear correlation in this study to comprehensively determine the weight of each main control factor of the structural complexity of mines. Our findings might help in quantitatively evaluating the structural complexity of mines and provide a theoretical basis for predicting the risk of fault water inrush in mines.

Overview and methods

Overview of the study area

Shengquan coal mine is located in the north wing of Xinwen coalfield Syncline in Quangou Town, Xintai City, Shandong Province. The mine is a wide and gentle anticline structure dipping to the south. The anticline axis is close to the north-south, and the coal seam is curved to the south, with a strike of N30°W to N30°E. The fault structure is well-developed in the minefield, cutting the anticline into several fault blocks of different sizes (Figure 1).

Figure 1.

Outline of the regional structure of the Shengquan coal mine.

From top to bottom, the strata in the area comprise the Quaternary system, lower Tertiary system, Cretaceous system, Jurassic system, Permian system, Carboniferous system, and Ordovician system. Shanxi formation of the Lower-Permian system and Taiyuan Formation of the Upper Carboniferous system are the primary coal-bearing strata. The Shanxi formation is 65.31–91.80 m thick, with an average of 77.59 m. The Taiyuan formation is bounded by fine sandstone about 10 m below the floor of coal seam 4. The lithology consists of gray-white medium-fine sandstone, light gray siltstone, gray and dark gray mudstone, and coal seam. Four coal-bearing layers and two minable layers are present; Taiyuan formation, 162.00–192.80 m thick, with an average thickness of 183.61 m.

The internal structure of the coalfield is relatively complex, and overall, it has a wide and gentle anticline structure dipping to the south. There are 23 main faults, divided into the near East-West strike fault group, northeast oblique fault group, and northwest oblique fault group. The near East-West trending fault group controls the minefield, followed by the NE fault group. The NW trending fault group has a negligible impact on the minefield. Due to the difference in formation time, the primary faults in the study area are staggered, and the small faults are distributed around the large faults. This breaks the stratum and increases structural complexity and the possibility of interconnection between faults. The minefield structure type is complex.

Grey correlation algorithm

The grey correlation algorithm (GRA) was proposed by Professor Deng Julong. It is a mathematical method for evaluating the nonlinear correlation between variables (Yazdani et al., 2019). This method uses the grey system theory and grey-weighted correlation degree to evaluate the geometric similarity between different variable curves. The specific steps for analyzing the data are as follows:

Step 1: Determining the sequence of grey correlation analysis.

There are two different types of grey correlation analysis series. One is the reference series, which is the data sequence reflecting the behavioral characteristics of the system and the evaluation standard of the grey correlation system; the second is the comparison sequence, which is the data sequence of factors affecting the behavioral characteristics of the system and the evaluation object of the grey correlation system. The reference sequence can be expressed as $x_{j} = {x_{j} (1), x_{j} (2) \dots x_{j} (n)}$ and the comparison sequence can be expressed as $x_{i} = {x_{i} (1), x_{i} (2) \dots x_{i} (n)}$ .

Step 2: Establishing the comparison matrix of evaluation objects.

To ensure that the results of the comprehensive evaluation are reliable, the evaluation object needs to be dimensionless before the analysis, and then, the evaluation object discrimination matrix is established.

The comparison sequence $x_{i} = {x_{i} (1), x_{i} (2) \dots x_{i} (n)}$ is normalized as follows:

y_{i} = \frac{x_{i} - (1 / n) \sum_{i = 1}^{n} x_{i}}{\sqrt{(1 / (n - 1)) \sum_{i = 1}^{n} {(x_{i} - \frac{1}{n} \sum_{i = 1}^{n} x_{i})}^{2}}}

(1)

The comparison matrix of evaluation objects is as follows:

Y = [\begin{matrix} y_{11} & y_{12} & \dots & y_{\ln} \\ y_{21} & y_{22} & \dots & y_{2 n} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ y_{n 1} & y_{n 2} & \dots & y_{m n} \end{matrix}]

(2)

Step 3: Determining the grey correlation degree

The grey correlation degree indicates the mean value of the correlation coefficient between each evaluation object and the corresponding elements of the reference sequence to reflect the correlation between each evaluation object and the reference sequence. The value of the correlation degree between the comparison series and the reference series at different positions is indicated by the grey correlation coefficient. The grey correlation degree can be calculated using the following equations:

G (i, k) = \sum_{k = 1}^{n} ξ_{i} (\hat{k})

(3)

ξ_{i} (k) = \frac{{min}_{i} {min}_{k} | y_{i} (k) - x_{j} (k) + ρ {max}_{i} {max}_{k} | y_{i} (k) - x_{j} (k)}{| y_{i} (k) - x_{j} (k) | + ρ {max}_{i} {max}_{k} | y_{i} (k) - x_{j} (k) |}

(4)

Here,

G (i, k)

denotes the grey correlation degree of the k index in the i evaluation object;

ξ_{i} (k)

denotes the grey correlation coefficient of the k index in the i evaluation object;

k = 1, 2, 3, \dots, n

;

i = 1, 2, 3, \dots, m

;

ρ

represents the resolution coefficient,

ρ \in (0, \infty)

, when

ρ \leq 0.5463

the resolution is the best. Generally,

ρ = 0.5

Local spatial difference algorithm

The local spatial difference algorithm uses the existing original data as the basis and the covariance function as the tool to perform linear unbiased (the expectation of deviation is zero) optimal prediction (the sum of squares between the predicted value and the measured value is the smallest) (Castaing et al., 1996). The size, shape, and spatial orientation of known points and the spatial relationship between them are considered. It is suitable for the datasets of the spatial correlation of regional variables.

Assuming that there is a discrete point $(x_{i}, y_{i}) \in W (i = 1, 2, \dots, n)$ in the study area space W, and $z_{i}$ is the attribute value at $(x_{i}, y_{i})$ , the predicted value ${\hat{z}}_{o}$ at the unknown point $(x_{o}, y_{o}) \in W (i = 1, 2, \dots, n)$ is the weighted sum of $z_{i}$ , i.e.:

{\hat{z}}_{o} = \sum_{i = 1}^{n} λ_{i} z_{i}

(5)

Here,

λ_{i}

represents the undetermined weight coefficient. According to the first law of geography, the attribute values

z_{i}

of different coordinates are related and associated with the change in distance and direction between different discrete data points. To predict the unknown point data, the linear unbiased prediction method is used. It can be inferred that the weight coefficient

λ_{i}

is a set of optimal coefficients that meet the minimum deviation between the estimated value (

{\hat{z}}_{o}

) and the real value (

z_{o}

) at the point

(x_{o}, y_{o})

. The expectation of deviation is 0, which suggests that the weight coefficient

λ_{i}

meets the following condition:

E ({\hat{z}}_{o} - z_{o}) = 0

(6)

min_{λ_{i}} V a r ({\hat{z}}_{o} - z_{o})

(7)

Assuming that for any discrete point

w_{x_{i}, y_{i}}

in W, the attribute value

z_{w}

has the same expectation c and variance

σ^{2}

, i.e. for any point

w_{x_{i}, y_{i}}

, there is:

E [z (x, y)] = E [z] = c

(8)

V a r [z (x, y)] = σ^{2}

(9)

Assuming that

λ_{i}

satisfies equation (6), the satisfaction relationship of

λ_{i}

can be derived by substituting equations (5) and (8) into equation (6):

c \sum_{i = 1}^{n} λ_{i} - c = 0 \Rightarrow \sum_{i = 1}^{n} λ_{i} = 1

(10)

Assuming that

λ_{i}

satisfies equation (7), the satisfaction relationship of

λ_{i}

can be derived by substituting equation (5) and equation (9) into equation (7):

\begin{aligned} σ^{2} = & V a r (\sum_{i = 1}^{n} λ_{i} z_{i} - z_{o}) \\ = & \sum_{i = 1}^{n} \sum_{j = 0}^{n} λ_{i} λ_{j} Cov (z_{i}, z_{j}) - 2 \sum_{i = 1}^{n} λ_{i} Cov (z_{i}, z_{o}) + Cov (z_{o}, z_{o}) \end{aligned}

(11)

After computing the weight coefficient

λ_{i}

, the attribute values

z_{i}

of all known discrete points

(x_{i}, y_{i})

are weighted and summed to obtain the estimated value

{\hat{z}}_{o}

of the unknown point

(x_{o}, y_{o})

Local linear embedding algorithm

The LLE algorithm is a nonlinear dimensionality reduction algorithm used for optimizing the dimension of the nonlinear index feature vector. This algorithm can extract the eigenvalues of the data twice, map the high-dimensional data to the low-dimensional space, and maintain the original topology of the data after dimensionality reduction (Gong et al., 2020). LLE algorithm assumes a neighborhood $P (x_{i}) = {x_{i} | a - δ < x_{i} < a - δ}$ in the data space $X (x)$ so that the data in $P (x_{i}) \subseteq U (x)$ and $P (x_{i})$ can maintain a linear relationship $x_{i} = w_{i j} x_{j} + w_{i k} x_{k} + w_{i l} x_{l}$ . Additionally, the local optimal weight matrix is established using the local covariance matrix and the Lagrange multiplier algorithm, and the output value of the $x_{i}$ sample is calculated based on the weight matrix and the sample attributes in the $x_{i}$ neighborhood. The specific steps for evaluating the locally linear embedding algorithm are as follows:

Step 1: To calculate the neighborhood $P (x_{i})$ of $x_{i}$ , the K-nearest neighbors (KNN) algorithm is used:

X = | \begin{matrix} x_{11} & x_{12} & \dots & x_{1 n} \\ x_{21} & x_{22} & \dots & x_{2 n} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ x_{m 1} & x_{m 2} & \dots & x_{m n} \end{matrix} |, \forall x_{i} \in X

(12)

P (x_{i}) = K N N (x_{i}, k)

(13)

Step 2: The weight matrix is defined as

w = [w_{1}, w_{2}, \dots w_{m}]

and the local optimal weight matrix is solved using equation (15):

min_{w_{1}, \dots w_{m}} \sum_{i = 1}^{m} {‖ x_{i} - \sum_{j \in P (x_{i})} w_{i j} x_{j} ‖}_{2}^{2}

(14)

Let

C_{j k} = (x_{i} - x_{j})^{T} (x_{i} - x_{k})

, then

w_{i j}

has a closed-form solution:

w_{i j} = \frac{\sum_{k \in P (x_{i})} C_{j k}^{- 1}}{\sum_{l, s \in P (x_{i})} C_{l s}^{- 1}}

(15)

Step 3: Solve the low-dimensional vector

z_{i}

through

w_{i}

min_{z_{1}, \dots z_{m}} \sum_{i = 1}^{m} {‖ z_{i} - \sum_{j \in P (x_{i})} w_{i j} z_{j} ‖}_{2}^{2}

(16)

Let

Z = [z_{1}, \dots z_{m}], W_{i j} = w_{i j}

, then equation (17) can be expressed as:

\begin{aligned} min_{Z} ‖ Z - Z W^{T} ‖_{2}^{2} = & min_{Z} t r ((Z - Z W^{T}) (Z - Z W^{T})^{T}) \\ = & min_{Z} t r (Z (I - W^{T}) (Z (I - W^{T})^{T}) \\ = & min_{Z} t r (Z (I - W)^{T} (I - W) Z^{T}) \\ = & min_{Z} t r (Z M Z^{T}) \\ s . t . Z Z^{T} = & I \end{aligned}

(17)

Here,

M = (I - W)^{T} (I - W)

. After determining the reconstructed dimension and solving the first

d + 1

eigenvalues and their corresponding eigenvectors of M, the eigenvector corresponding to the smallest

d^{'}

eigenvalues composed of the second eigenvector

d + 1

is the output sample set.

Influencing factors of fault hydraulic conductivity

Tectonic stress is the primary cause of the stratum’s uplift, deformation, fracture, and other movements. The faults formed by different tectonic movements are similar and have similar distribution laws and combination forms. The faults in the region have obvious zoning under the control of the tectonic stress field (Buttinelli et al., 2021). These faults also have certain randomness due to different conditions of the medium (rock stratum). Therefore, the most effective evaluation method involves dividing the large-scale study area into several small areas and blocks, evaluating the small sections, and then making a global evaluation from small and large. Considering the geological, structural, and hydrogeological data of the minefield, we comprehensively analyzed the water-bearing capacity of the structure in the minefield based on four aspects, including the age of fault formation, the relationship between fault-cutting, the nature of the fault, and the topological structure relationship between faults. We applied the algorithm to organically integrate them to evaluate the structural risk in the minefield.

Age of fault formation

A fault has its evolutionary history, and its activity characteristics are different at different stages. Faults that form earlier have better cementation degree on their surface but lower water-bearing (conducting) capacity. In contrast, faults that form later have a better personality and connectivity between faults, lesser filling, poorer cementation on their surface, and higher water-bearing (conducting) capacity. Faults in different formation periods are produced under the action of structural stress in different directions, and thus, they have distinct occurrences (Fu et al., 2022a, 2022b). In this study, the occurrence of all strata in the study area was recorded and counted; the fault rose map of the study area was made (Figure 2), and the age of formation of the fault was estimated and divided (Table 1). Among them, the faults formed by Mesozoic and pre-Mesozoic tectonic movements, such as the Indosinian movement and Yanshan movement, were defined as “old” faults, the faults formed by Himalayan movement from Cenozoic to Holocene were defined as “middle” faults, and the faults formed after Holocene were defined as “new” faults.

Figure 2.

Fault map of the study area.

Table 1.

Data of the fault formation period.

Fault name	Trend	Formation period	Fault name trend	Trend	Formation period
F16	EW		F2	NE
F16-1	EW	Indosinian movement	F3-3	NE
F14	NWW		F3-4	NE
F14-1	EW		F4	NE
F3	EW		F4-1	NE	Himalayan movement
F12	NW		F4-3	NE
F12-1	NWW		F4-4	NE
F13	NW	Yanshan movement	F14-8	NE
F13-1	NW		F2-1	NE
F5	NW		F14-9	NE

Owing to the differences in the water-bearing (conducting) capacity between the faults in different formation times, and based on the actual field experience and expert opinions, the water-bearing coefficient $ζ_{1} = 0.4$ of the “old” fault, the water-bearing coefficient $ζ_{2} = 0.6$ of the middle fault, and the water-bearing coefficient $ζ_{3} = 0.8$ of “new” fault were defined.

According to studies, fault density is the chief index to judge the complexity of faults in an area. It can intuitively reflect the number of faults within a certain range but cannot distinguish different water-bearing capacities and conductivity of the faults. In this study, the organic integration of the water-bearing (conductivity) coefficient and density of faults (equation 1) was performed to accurately determine the complexity of faults in a certain area.

D_{m} = ζ_{1} * m_{1} + ζ_{2} * m_{2} + ζ_{3} * m_{3}

(18)

Here,

D_{m}

represents the improved fault density and the number of faults in different formation periods in the same block indicated by

m_{1}, m_{2}, m_{3}

Fault-cutting relationship

Due to the influence of multi-stage tectonic movement in the study area, a cutting relationship between faults is often found, where the new fault cuts the old fault. New tectonic stress transforms the old fault formed under the original tectonic stress system in different directions, which activates the originally closed fault or further crushes the original fractured rock mass, forming excellent water-bearing space (Figure 3).

Figure 3.

Schematic representation of fault activation.

The staggered faults also strengthen the connection between different water conservancy units, which increases the ease of forming the dominant water inrush channel. The pinch-out fault of the stope roof communicates with the mining fracture, which also increases the ease of forming the dominant channel of mine water inrush. The fault pinch-out point and intersection density refer to the number of fault pinch points or intersections per unit area. It can be used to determine the connectivity between the faults, assess the influence of tectonic stress on the stratum when the fault is formed, and examine the fractured state of the stratum in a certain area. The fault pinch-out point can be calculated using equation (19).

D_{i} = \frac{I}{S}

(19)

Here, I denotes the number of fault intersections and pinch points per unit area and S indicates the unit block area in km².

Fault self-property

Structural faults control water but might not contain water. Only when the fault is tensile and has a certain scale extension length and depth (drop) can it have a certain reservoir space.

Due to the different nature of the stratum and the difference in tectonic stress during formation, the degree of damage to different strata is different, and significant differences occur in the water-bearing and hydraulic conductivity. The fall and extension length of the fault is determined by the physicochemical properties of the stratum and the strength of tectonic stress. It is also the specific manifestation of the impact of tectonic movement on the stratum. Therefore, based on the fall and extension length of the fault, the hydraulic conductivity of the fault and the degree of stratum fragmentation around the fault zone can be evaluated more accurately. The fault strength index is defined as the sum of the extension length of all faults in the unit area and their drop (equation (20)), which can objectively reflect the comprehensive complexity of fault drop and the horizontal extension length of the faults.

D_{f} = \frac{\sum_{i = 1}^{n} H_{i} * L_{i}}{S}

(20)

Here,

D_{f}

is the fault strength index; i denotes the total number of faults in the statistical unit;

H_{i}

denotes the drop of the first fault in the statistical unit, in km;

L_{i}

indicates the horizontal extension length of the i fault in the statistical unit, in km;

i = 1, 2, \dots, n

; S represents the area of statistical unit, unit: km².

Topological relationship between the faults

According to the fractal theory in mathematics, the whole and part of all natural objects have statistical similarities in morphology, information, and space (Zhao et al., 2019). Assuming that a geometric object has D dimensions, N original geometries can be obtained by increasing each dimension P times.

P^{D} = N

(21)

By taking the logarithm on both sides of equation (21), it can be expressed as:

D = \frac{\ln (N)}{\ln (P)}

(22)

When P tends to 0, there is a limit of fractal dimension D, and the fractal dimension value (

D_{S}

) can be computed as follows:

D_{S} = lim_{p \to 0} \frac{\lg (N (r))}{- \lg (r)}

(23)

The movement track of complex spatial changes in faults represents the fractal characteristics. These characteristics can be used to reflect the complexity and maturity of structural development and distribution in space.

The fault fractal dimension value is a comprehensive index that reflects the degree of development of fault structures and their influence on the surrounding strata (Zhang et al., 2021). To calculate the fault fractal dimension of the mine area, the block classification method was used. First, the study area was divided into n square blocks with side length $r = r_{0}$ . Then, the number of blocks with faults in the study area was identified. This number was recorded as $N (r_{0})$ . Next, $r = 1 / 2 r_{0}, 1 / 4 r_{0}, 1 / 8 r_{0}, 1 / 16 r_{0}$ was evaluated, and the number $N (r_{i})$ of fault structures in blocks with different side lengths was counted. This was substituted into the $L o g_{10} N (r) - L o g_{10} r$ coordinate system for fitting, and the absolute value of the slope of the fitting line was the fault fractal dimension value of the block that was used to determine the fault complexity in different regions. The data were evaluated using equation (24).

D_{S} = | \frac{N * \sum_{i = 1}^{n} N (r_{i}) - \sum_{i = 1}^{n} N (r_{i}) * \sum_{i = 1}^{n} r_{i}}{n \sum_{i = 1}^{n} r_{i}^{2} - {(\sum_{i = 1}^{n} r_{i})}^{2}} |

(24)

Taking the side length

r_{0}

of the largest block in the study area as 400 m, the study area was divided into 198 square blocks, the number of grids

N (r_{i})

containing fault traces in each block was counted, and the fault fractal dimension in different blocks was evaluated using equation (13).

Discussion

Exploratory data analysis of the fault complexity impact Index

Exploratory data analysis was performed for constructing all other mathematical models. Exploratory analysis of quantitative fault indicators refers to the data-level analysis of different model indicators. It helps in evaluating the correlations and differences between indicators to facilitate the accurate evaluation of the overall goal.

Data correlation refers to the difference and connection between different kinds of data. Using mathematical geology, different indicators are selected to extract and collect information on the faults in the study area, perform correlation analysis, and understand the covariant trend between data, which is crucial for selecting an appropriate fusion algorithm.

The fluctuation intensity analysis diagram of all collected data in the study area is shown in Figure 4. Similar fluctuations can be seen among the indicators. Therefore, two correlation analysis methods, including Pearson's correlation coefficient (PCC) and GRA, were used to analyze different fault indicators.

Figure 4.

Fluctuation intensity analysis of the factors that influenced the faults in the Shengquan minefield.

In natural science, PCC method is the most widely used method to analyze the linear correlation between variables. The PCC between different X and Y variables is defined as the quotient of covariance and standard deviation between variables (equation (25)).

ρ_{x y} = \frac{cov (x, y)}{σ_{x} σ_{y}} = \frac{E [(X - μ_{x}) (Y - μ_{y})]}{σ_{x} σ_{y}}

(25)

Here,

σ_{x} σ_{y}

represents the standard deviation of variable x and variable y, and

cov (x, y)

represents the covariance of variables x and y. The value of

ρ_{x y}

lies between −1 and 1. The closer the value of

ρ_{x y}

is to 0, the weaker the linear correlation is. As the value of

ρ_{x y}

approaches −1 or 1, the linear correlation becomes stronger. PCC is independent of the variable unit and does not distinguish between independent and dependent variables.

| ρ_{x y} | \in (0.8, 1]

indicates a very strong correlation,

| ρ_{x y} | \in (0.6, 0.8]

indicates a strong correlation,

| ρ_{x y} | \in (0.4, 0.6]

indicates a medium correlation,

| ρ_{x y} | \in (0.2, 0.4]

indicates a weak correlation, and

| ρ_{x y} | \in [0, 0.2]

indicates a very weak correlation or no correlation.

The data on the factors that influence faults include a group of continuous fluctuation curves, but PCC can only represent the linear correlation between variables and cannot represent the nonlinear correlation of curves. Therefore, the grey correlation coefficient was used to determine the similarities between different types of logging curves for evaluating nonlinear correlations between curves.

As shown in Figure 7, the correlation between the data was calculated using equations (4) and (5), and a heat map was constructed for the correlation analysis of the factors that influenced the faults in the Shengquan minefield.

As shown in Figure 5, PCCS and the GRA between $D_{m}$ and $D_{i}$ were 0.86 and 0.936, i.e. they were highly correlated. This reflected the strong similarity between the two indicators, which contained similar information. The linear correlation between $D_{F}$ , $D_{i}$ , and $D_{s}$ was weak, and the maximum correlation was only 0.294. The linear correlation and nonlinear correlation $D_{s}$ for the other three factors were moderate and were different from other parameters. $D_{F}$ reflected different information from the other indicators, which must be considered. The strong nonlinear correlation between $D_{F}$ , $D_{i}$ , and $D_{s}$ indicated that they had similar wave shapes to a certain extent. Through careful consideration, we found that the index $D_{F}$ has different data fluctuation amplitude under the condition of keeping the shape of data fluctuation intact. The extension length, fall, and other self-property indices of the fault significantly affected $D_{F}$ .

Figure 5.

Correlation analysis of the factors that influenced the faults in the Shengquan minefield.

Single-factor analysis of fault complexity

Various methods are used to evaluate the fault complexity in the study area of data statistics. The values obtained by different index acquisition methods are distributed in different discrete points in the study area. According to the first law of geography, a spatial correlation occurs between various physical attributes in geography. Things that are located closer spatial have a higher similarity than those that are farther. To address this, the data of all known coordinate points in space are used to estimate the data of unknown coordinate points. To observe the overall fault development trend in the study area, the coordinates between different indicators are unified, and the information fusion analysis is performed. The spatial local interpolation method (Kriging) is used to optimally predict the changing trend of the overall fault complexity in the study area based on structural analysis and covariance function.

In this study, the discrete point $(x_{i}, y_{i})$ consisted of four attribute values: fault density ( $D_{m}$ ), fault annihilation point & intersection density ( $D_{i}$ ), fault strength index ( $D_{F}$ ), and fault fractal dimension ( $D_{s}$ ). The spatial local interpolation algorithm was used to calculate four different attributes to draw the distribution maps of different attributes.

The distribution map of the study area $D_{m}$ is shown in Figure 6(a). The structure of the mining area was complex, and there were many faults. The primary fault zone ran through the East and West in the middle of the minefield, which was associated with several small faults around, and the stratum was severely broken. After integrating the formation age and the number of faults, the index in the figure was comprehensively drawn. The density of faults in the north and middle of the minefield was large, which was an associated small fault formed by later tectonic movements, leading to stratum fragmentation, stratum fracture development, and excellent water storage capacity.

Figure 6.

Contour maps of the factors that influenced the faults of coal seam 13 in the Shengquan minefield.

The distribution map of the study area $D_{i}$ indicated that the distribution trend of fault pinch-out and intersection density in the study area was roughly the same as that of the fault density (Figure 6(b)), which matched the fact that the study area experienced multiple tectonic stress and also exhibited the complexity of fault structures in the study area. The key fault structure development area in the minefield and the key fault structure development area in the north of the minefield were affected by the tectonic movements in different periods. There were many fault intersections, and their distribution trend was relatively average. Distinguishing the degree of regional strata affected by the structure is a difficult task.

The distribution of $D_{s}$ in the study area is shown in Figure 6(c). The complexity of the fault showed a strong linear relationship with $D_{s}$ . A smaller value of $D_{s}$ indicated a simpler fault structure, while a larger value of $D_{s}$ indicated a more complex fault structure. Good linear fitting indicates that the distribution of faults has good statistical self-similarity under the adopted criteria. The complex fault area was chiefly distributed in the middle of the minefield in a herringbone shape. In the middle and north of the mining area, the tectonic stress was concentrated, with many small fault layers, mainly associated faults, with a large influence range, serious stratum fragmentation, and fracture development. The change in fault fractal dimension was regular, and the change in the direction of the isoline was close to the direction of the primary structural line.

The distribution of $D_{F}$ in the study area is shown in Figure 6(d). The value of $D_{F}$ was high in the three main structural development areas in the middle, north, and south of the minefield. The fault strike could be divided into two groups, i.e. the NEE fault group and the WE fault group. The development characteristics of the NEE fault group were consistent with the direction of a large fault structural line in the mining area. This group of fault drops was 40 m, and the extension length was long. Its generation period and genetic characteristics were related to the late Yanshan movement or the Himalayan period, with good water conductivity. The WE trending fault group was affected by large faults, distributed on both sides of the fault. It was formed earlier and was squeezed and cut by the epigenetic tectonic movement. Controlled by the large fault, it had poor water conductivity. However, because of the influence of multi-stage tectonic movements, the integrity of the rock stratum was poor, the fractures were relatively developed, and the fracture was serious.

Fault complexity evaluation

In factor correlation analysis, the relationship between variables cannot be easily expressed through algorithms such as the PCC or GRC, especially in the field of high-dimensional data. Assuming that the linear correlation between the data was strong, and the principal component analysis and multi-dimensional scale analysis of classical algorithms had good results, a new algorithm was introduced to evaluate the spatial correlation of the four evaluation indices. This was used to extract the eigenvalues for a comprehensive evaluation that could perform information fusion while keeping the original amount of information intact. Based on the spatial correlation of different indicators, we used the LLE algorithm to fuse different indicators based on the data to evaluate the fault complexity in the study area.

In this section, NumPy and Skleran modules in Python were used for programming. Taking $D_{F}$ , $D_{m}$ , $D_{i}$ , and $D_{s}$ as input sample data, the nearest neighbors were selected, they were mapped into embedded coordinates after linear reconstruction, and the comprehensive index was normalized after LLE processing [0,1]. Thus, the fault complexity index $D_{l l e}$ was obtained. The complex contour map of the regional structure was constructed through $D_{l l e}$ (Figure 7).

Figure 7.

A comprehensive diagram of the evaluation of fault complexity.

Based on the principle that the higher complexity of the fault leads to a greater risk of water inrush (Chen et al., 2018) and along with Figure 7, complexity zoning was obtained.

When $D_{l l e} < 0.4$ , it indicates a simple structural area with a low risk of water inrush; when $D_{l l e} \in 0.4 \sim 0.6$ , it indicates a medium structural area with a medium risk of water inrush; when $D_{l l e} > 0.6$ , it indicates a complex structural area with a high risk of water inrush.

Engineering example verification

The Shengquan coal mine is a typical Carboniferous Permian coalfield. The chief water inrush threat faced by mining here is floor water, and the main water inrush channel is a fault. To determine the correctness and practicability of the fault complexity evaluation model, all water inrush events that occurred in the Shengquan coal mine from 2001 to 2021 were recorded and counted, and the positions of all water inrush points were marked in Figure 9 (points A–K). Our analysis showed that all water inrush points were located in the complex structural area highlighted in Figure 7, thus, the accuracy of the evaluation model is preliminarily verified.

The above process provided a preliminary idea of the correctness of the model from a statistical perspective. To further validate the correctness of the model, the three-dimensional high-density electrical method technology was adopted. It helped to detect the untapped area before mining in the 21,304 working face of coal seam 13 (see Figure 7).

The three-dimensional high-density electrical advance detection technology is an advanced method based on the DC electrical exploration technology. It is primarily used to detect the geological conditions of the strata in front of the underground roadway excavation. The specific content of this work was at 330 m × Within the working area of 330 m, 10 m (line distance) × 33 survey lines were arranged according to the rule of 3 m (point distance) × 330 m/piece, 10,890 m measuring line length, and 3630 physical points. WDID-1 digital DC IP instrument and three pole devices (MN-B or A-MN) were selected for detection. The data recorded by the instrument were imported in the wda format into the computer, the WDAFC software was used to convert it into res format, the RES software was used to process the data, and finally, a chart showing the results was obtained (Figures 8 and 9).

Figure 8.

The low-resistance anomaly of the 3D data volume of roof resistivity detected in advance in the mining area.

Figure 9.

The low-resistance anomaly of the 3D data volume of floor resistivity detected in advance in the mining area.

According to the basic principle of the 3D high-density electrical method, the water abundance in the low-resistance area is strong, and that in the high-resistance area is weak. Considering the detection results, we found that there were two large low-resistivity anomaly areas in the 21,304 working face, which were located at the two ends of the working face. The total height of the anomaly area in the west of the working face was about 80 m, and that in the west of the working face was about 120 m. The overall resistivity was similar. We concluded that the stratum caused by the structural movement was relatively broken, forming a water-rich area. According to the fault complexity model, there were also two high-risk areas in the 21,304 working face (Figure 7, L, M) that were consistent with the geophysical results. Therefore, we comprehensively inferred that the L and M areas of the 21,304 working face have strong water abundance and a high risk of water inrush.

To further validate the accuracy of the results, drilling verification was performed on the working face. Through the verification results, we found that a large quantity of water was discharged from the boreholes in L and M, the maximum water inflow of the boreholes in L was 500 m³/h, and the normal water inflow was 150 m³/h. The maximum water inflow of boreholes in area M was 550 m³/h, and the boreholes with a normal water inflow of 220 m³/h did not have water. These results further verified the effectiveness and rationality of the evaluation model.

Conclusion

Four main control factors were selected that affect the structural complexity, including fault fractal dimension value, fault strength index, the number of fault intersections, and pinch points per fault density. The weight of the main control factors of the complexity of the mine structure was comprehensively obtained using the improved local linear embedding (LLE) algorithm to calculate the index weight, and the quantitative evaluation model of mine structure complexity was established.

Based on the new index weighting algorithm, the structural complexity of the whole study area was quantitatively evaluated. The cluster analysis method was used to classify the complexity of the structure of the mine, and the study area was classified into a simple structural area, medium structural area, and complex structural area according to the complexity of the minefield.

The validity and rationality of the evaluation model were confirmed by comparing the location of water inrush points in the study area and the geophysical prospecting advance detection results of 21,304 working face in Coal Seam 13 in recent years. The water inrush points were located in the complex structural area of the evaluation model. The low resistivity anomaly area of geophysical prospecting in the 21,304 working face was consistent with the complex structural area in the evaluation model.

Footnotes

Acknowledgements

The authors thanks to all experts for their careful work and thoughtful suggestions.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Natural Science Foundation of Shandong Province, National Natural Science Foundation of China (grant number ZR2020KE023, 41807283, 51804184).

ORCID iD

Longqin Shi

References

Buttinelli

Petracchini

Maesano

, et al. (2021) The impact of structural complexity, fault segmentation, and reactivation on seismotectonics: Constraints from the upper crust of the 2016–2017 Central Italy seismic sequence area. Tectonophysics 810(2): 228861–228879.

Castaing

Halawani

Gervais

, et al. (1996) Scaling relationships in intraplate fracture systems related to Red Sea rifting. Tectonophysics 261: 291–314.

Chen

Feng

, et al. (2018) Prediction of water inrush areas under an unconsolidated, confined aquifer: The application of multi-information superposition based on GIS and AHP in the Qidong Coal Mine, China. Mine Water and the Environment 37: 786–795.

Chen

Yao

Tian

, et al. (2010) Quantitative assessment of geological structure comp licated degree of NO. 61 seam in Qidong mine. Coal Science and Technology 38(03): 101–103.

Fan

, et al. (2022a) Calculating the formation period of fault lateral sealing and its application. Energy Geoscience 3: 17–22.

Niu

Cui

, et al. (2022b) Evaluation of deep high-rank coal seam gas content and favorable area division based on GIS: A case study of the South Yanchuan block in Ordos Basin. Energy Exploration & Exploitation 40(4):1151–1172.

Gong

Nie

(2020) Geometrical and topological analysis of pore space in sandstones based on X-ray computed tomography. Energies 13(15): 3774–3792.

Kang

Zhao

Wang

, et al. (2014) Abundance and geological implication of rare earth elements and yttrium in coals from the Suhaitu Mine, Wuda Coalfield, Northern China. Energy Exploration & Exploitation 32(5): 873–889.

Liu

Zhang

, et al. (2020) Geochemical characteristics of No. 6 coal from Nanyangpo Mine, Datong coalfield, north China: Emphasis on the influence of hydrothermal solutions. Energy Exploration & Exploitation 38(5): 1367–1386.

10.

Mohamed

Yahya

Taoufik

, et al. (2021) A fuzzy mathematical model for evaluation of rock-fracture and structural complexity: Application for Southern Atlas in Tunisia. Acta Geodaetica et Geophysica 56: 579–604.

11.

Shi

Qiu

(2018) Statistical characteristics and analysis of fault properties of Zhaizhen minefield. Coal Technology 37(11): 128–130.

12.

Shu

Jia

Wang

, et al. (2010) Quantitative evaluation of geological structure complexity: With Guobei coal mine as example. Coal Geology & Exploration 38(6): 22–26.

13.

Singh

(1986) Mine inundations. International Journal of Mine Water 5: 1–28.

14.

Wang

(2016) Analysis on the law of coal mine death in the last ten years. Observation and Discovery 6: 68–70.

15.

Wang

Zhang

, et al. (1996) Fractal dimension description of complexity of fault network in coal mines. Journal of China Coal Society 4: 24–29.

16.

Yazdani

Kahraman

Zarate

, et al. (2019) A fuzzy multi attribute decision framework with integration of QFD and grey relational analysis. Expert Systems With Applications 115: 474–485.

17.

Zhang

Guo

, et al. (2021) Quantitative analysis and evaluation of coal mine geological structures based on fractal theory. Energies 14(7): 1–14.

18.

Zhao

Yang

Lin

, et al. (2019) Fractal study on pore structure of tight sandstone based on full-scale map. International Journal of Oil Gas and Coal Technology 22(2): 123.

19.

Zhou

(2013) Accumulation mechanism of complicated deep carbonate reservoir in the Tazhong Area, Tarim Basin. Energy Exploration & Exploitation 31(3): 429–457.

Quantitative evaluation of structural complexity in Shengquan minefield based on improved local linear embedding algorithm

Abstract

Keywords

Introduction

Overview and methods

Overview of the study area

Grey correlation algorithm

Local spatial difference algorithm

Local linear embedding algorithm

Influencing factors of fault hydraulic conductivity

Age of fault formation

Fault-cutting relationship

Fault self-property

Topological relationship between the faults

Discussion

Exploratory data analysis of the fault complexity impact Index

Single-factor analysis of fault complexity

Fault complexity evaluation

Engineering example verification

Conclusion

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

ORCID iD

References