Abstract
In this paper, the relative complexity of the tectonics in the Sangshuping coal mine was studied. On the basis of the assumption of equal blocks, using entropy function analysis and stepwise regression analysis, an empirical formula for quantitatively evaluating structural relative complexity was established from the structural characteristics in the exposed area, and then the formula was applied to the prediction of relative tectonic complexity in the unexposed area. The results are as follows. First, the main factors affecting the structural relative complexity of the No. 3 coal seam were the number of contour lines, the thickness of the overlying sandstone, the abnormality index of the coal seam thickness, and the lithology of the coal seam roof. Second, the complexity level in the exposed area of the No. 3 coal seam was mainly medium, and the level in the unexposed area was simple. The tectonics in the southern part of the coal mine were more complex than those in the north, and those in the east were more complex than those in the west. Finally, the relative complexity level of the No. 11 coal seam was simple; the tectonics of the northern part were relatively simple, and those of the central and southern parts were moderate.
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Introduction
An evaluation and prediction of the relative complexity of geological tectonics can be performed via a quantitative evaluation of the relative complexity of different blocks in a mining area or mine field. The purpose of this study was to find relatively simple blocks in mining areas where the geological tectonic type is complex or more complex. The results could provide a geological basis for the coal mine to select the most favorable mining block and arrange the working face, which could provide important guidance for safe and efficient production in coal mines.
The evaluation and prediction of the relative tectonic complexity were based on the analysis of the structural regularity and the condition of the deformed medium. On the basis of the assumption of equal blocks1,2,3,4,5 and taking the evaluation index as the basis and mathematical theory and computer technology as the means, an empirical formula for quantitatively evaluating the structural relative complexity was established in the exposed area; then, the formula was applied to predict the structural relative complexity in the unexposed area. Through preliminary exploration, many mathematical theories and computer technologies, such as multivariate statistics6,7,8, gray system theory9,10,11,12,13, fuzzy comprehensive evaluation14,15,16,17, fractal geometry18,19,20,21,22,23,24,25, artificial neural networks26,27,28,29,30, the analytic hierarchy process31,32,33,34, the entropy function method35,36, the independent weight coefficient method37,38, the maximum entropy machine learning technique39, remote sensing40, the folding catastrophe model41, numerical simulation42, and the deterministic and empirical approaches43,44, have been successfully applied to quantitatively evaluate and predict the relative tectonic complexity.
The Hancheng mining area is an important coal base in Shaanxi Province, and there are three coal mines. Large-scale geological exploration of the coalfield was completed mainly in the 1960s and 1970s. Limited by the economic and technological conditions at that time, the limited exploration work was concentrated mainly in shallow peripheral areas, resulting in insufficient geological data during mine construction. All the mines were designed on the basis of the assumption of low gas emissions and simple geological tectonics. After several years of mining, the current three coal mines entered the middle and deep mining stages. The geological conditions here differ significantly from those in shallow peripheral areas, with increasing influential factors. The Sangshuping coal mine is one of these mines. This coal mine is a double-outburst mine and has extremely complex hydrogeological conditions. With the increase in mine production capacity and the extension of the mining area and working face, the influence of tectonics has become increasingly prominent. The existing research on geological tectonics could no longer meet the requirements of efficient coal mining for geological work. Moreover, mine disaster sources, such as gas and mine water, pose an escalating threat to the safety of coal mining, which has become a major factor restricting company development. Therefore, in this study, the Sangshuping coal mine was selected as the research object. To scientifically prevent mine geological disasters and ensure safe and efficient mining, it is necessary to analyze and summarize the characteristics of geological tectonics systematically. This evaluation elucidates the controlling effect and degree of influence of the geological tectonics of coal mines.
Study area
The Hancheng mining area is part of the northern section of the Shaanxi Weibei Carboniferous–Permian coalfield and is part of the Weibei Coalfield of the Huanglong Base, one of the 13 large-scale coal bases planned in the country. The mining area is bounded by the outcropping No. 11 coal seam and the Fl fault in the southeast and by the vertical depth of 1500 m at the bottom boundary of the No. 5 coal seam in the northwest. It extends to the Yellow River in the northeast and is adjacent to the Chenghe mining area in the southwest, which is separated by Longting and Luojiahe. The mining area is approximately 56 km long and 20 km wide, covering an area of 1100 km2. The coal resources amount to more than 9.3 billion tons. Currently, three mine shafts, namely, the Sangshuping Mine, Xiayukou Mine, and Xiangshan Mine, have been built in the mining area, as shown in Figure 1.
Tectonic map of the Hancheng area45. (I: Shallow steep-dip fault zone on the southeast side; II: Mid-deep slow-dip fault-and-fold zone; II-1: Sangbei fault-and-fold zone; II-2: North fold-and-slide zone; II-3: South fault-and-fold zone; II-2–1: Longguling fault zone; II-3–1: Baimaoling monoclinic zone; II-3–2: Dongzecun anticline and fault zone; II-3–3: Yingshangou syncline).
Stratigraphic sequence and its main characteristics
The stratigraphic division of the Hancheng mining area is part of the Erdos Basin subregion of the North China stratigraphic region. Large areas of bedrock are exposed in the mining area, and the strata are exposed from old to new as follows: the Neoarchean Sushui Group; the Neoproterozoic Huoshan Formation of the Sinitic System; the Paleozoic Cambrian, Ordovician, Carboniferous, and Permian Systems; the Mesozoic Triassic System; and the Cenozoic Quaternary System. The coal seams in the mining area are hosted mainly in the Taiyuan Formation and Shanxi Formation of Carboniferous–Permian Systems.
Coal measures and coal seams
Main coal-bearing strata and their coal-bearing properties
The coal-bearing strata in this area are the Taiyuan Formation and Shanxi Formation. The Benxi Formation generally does not contain coal, with only occasional coal seams or thin coal layers appearing at individual points. The Taiyuan Formation is part of interbedded marine and terrestrial sedimentation and contains three to nine coal seams, which are numbered 5-1, 5-2, 6, 7, 8, 9, 10, 11, and 12. The Shanxi Formation resulted from continental sedimentation and contains one to four coal seams, which are numbered 1, 2, 3, and 4. Among these coal seams, the No. 3, No. 5, and No. 11 coal seams are the main minable coal seams, whereas the No. 2 coal seam is locally minable. The remaining coal seams are unstable and thin, with very few minable points and no mining value.
Characteristics of minable coal seams
The No. 2 coal seam is a locally minable seam within the Shanxi Formation, whereas the No. 3 coal seam is the primary minable seam within the same formation. The No. 5-1 and No. 11 coal seams are the main minable seams within the Taiyuan Formation. The characteristics of each coal seam in the mining area are summarized in Table 1.
Tectonic location and basic structural framework of the region
Tectonic location
The Hancheng mining area is located in the eastern part of the Weibei Carboniferous–Permian coalfield, which is situated on the southeastern margin of the Ordos Block. The tectonic location of the Weibei coalfield changed over different geological time periods, evolving with the regional tectonic background. During the Paleozoic era, the Weibei coalfield was located on the southwestern margin of North China paleoplate, and it was part of the unified North China Carboniferous–Permian coal-accumulating basin and adjacent to the Qinling tectonic belt in southern China. During the Mesozoic era, the North China giant basin disintegrated, with the western depression evolving into the Ordos Basin and the eastern part becoming a giant uplift area. In the late Mesozoic era, the Weibei coalfield became the uplift area on the southern margin of the basin, known as the Weibei uplift. Since the beginning of the Cenozoic era, with the uplift of the Ordos Basin into a plateau, rift basins have developed around it, and the Weibei coalfield is located on the northern edge of the Fenwei Rift System. Currently, the Hancheng mining area is situated at the intersection of the Luliang Uplift and the Weibei Uplift on the southeastern margin of the Ordos Block.
Basic structural framework
The basic tectonic morphology of the Hancheng mining area is defined by monoclinic tectonics with a strike to the northeast and a tendency to the northwest, with a gentle occurrence and stratigraphic dip angles ranging from 3° to 20°, generally 3° to 8°.
Both compressive–contractive tectonics and tensile–extensional tectonics developed within the mining area. The compressive–contractive tectonics consist of folds and compression–shear faults, primarily trending NE, followed by ENE, with predominantly SE dips and fewer NW dips. The tensile–extensional tectonics manifested mainly as tensile–shear faults, with the Hancheng Fault F1 as the main trunk. On the northwest side, secondary faults exhibit a penniform distribution pattern with the Hancheng Fault, primarily trending NE and ENE.
The general structural characteristics of the mining area can be summarized as zonal distributions from east to west and segmented distributions from south to north, with stronger tectonics in southern and eastern China and weaker tectonics in northern and western China. The shallow and peripheral areas are more complex, whereas the central and deeper parts are simple. The northern region exhibits more traces of compressive tectonics, whereas the southern region is dominated by extensional structural traces. The major structural deformation zones are concentrated in the southeastern marginal zone of the mining area.
Tectonic development characteristics of the Sangshuping coal mine
The Sangshuping coal mine is characterized mainly by extensional tectonics. The basic tectonic form of the mine is monoclinal tectonics with a NNE strike and a tendency toward the WNW, with wavy undulations along the strike and dip. The dip angle of the strata is generally approximately 8 degrees. Large- and medium-sized faults have not developed in the mine. Since the mine was established and explored, no fault with a fault intercept greater than 10 m has been found. The faults exposed in the coal seam are all small faults.
Faults
According to statistics, a total of 146 faults have been exposed in the coal mine, including 16 faults in the No. 2 coal seam and 130 faults in the No. 3 coal seam.
There are relatively few faults exposed in the No. 2 coal seam, only 16 of which are normal faults with fault throws mostly less than 2 m. Therefore, no research has been conducted on the fault development patterns in the No. 2 coal seam, and the main focus has been on the exposed faults in the No. 3 coal seam. Most of the faults in the No. 3 coal seam are normal faults, whereas reverse faults are relatively rare, accounting for only 12.3% of the total number of faults. Fault strikes developed in all directions (Figure 2). The fault throws were mostly less than 2 m.
On the basis of the tectonic distribution map of the No. 3 coal seam (Figure 3), the fault density in the exposed area was 13 faults per km2, which were distributed mainly in the southern part of the mining area. There were fewer faults in the northern part of the mining area, and the geological tectonics were simple, with faults mostly concentrated on the two wings of the f3–6 anticline and the southern wing of the f3–7 syncline. Owing to the influence of large- and medium-sized tectonics, the moderate conditions of coal measure strata and corresponding tectonic stresses and the development of small faults exhibited a zonal pattern. To date, three groups of small fault-dense zones were identified, and these zones were nearly E–W-trending, NW-trending, and nearly N–S-trending. These three groups of fault-dense zones intersected obliquely with each other, and relatively few faults developed between these zones. Among these faults, the NW-trending small fault-dense zones consisted of a total of 7 groups, numbered A1–A7. These features were distributed mostly to the south of the f3–7 syncline and were arranged nearly equidistantly and in parallel, with widths ranging from 100 to 180 m. The nearly E–W-trending zone consisted of a total of five groups, numbered B1–B5. These areas were distributed in the f3-6 anticline and the southernmost end of the mining area, and they were arranged nearly equidistantly and in parallel, with zone widths ranging from 110 to 180 m. The nearly N–S-trending zone consisted of a total of three groups, numbered C1–C3, all located at the f3–6 anticline, with zone widths ranging from 110 to 140 m.
Folds
f3-3 Majiata north syncline
This syncline is located at the northern edge of the mine and is parallel to the Majiata anticline. The dip angles of its two wings are 5° to 12°, plunging toward the west‒northwest. Owing to the superposition of a more subordinate NE-trending anticline, the two wings exhibit undulation in the northwest direction. The amplitude of the syncline is approximately 30 m.
f3-4 Majiata anticline
This anticline has prominent fold tectonics in both the Sangshuping coal mine and the Hancheng mining area. This phenomenon is clearly reflected in the contour and trend maps of the coal seam floor. It extends from the north of the Sangshuping coal mine to the Majiata-Sanlangmiao line, with an axis trending west–northwest, plunging toward the northwest end, and an extended length of approximately 5 km, disappearing to the south of Sanlangmiao. The dip angles of its two wings are 5° to 7°. The maximum amplitude of the anticline could exceed 40 m.
f3-5 syncline
This syncline is located north of the f3-6 anticline. The northern limb has a relatively stable occurrence, whereas the southern limb has significant variations in dip angles, with a subordinate fold superimposed on the axis trending northeast. The amplitude of the syncline could exceed 30 m in the east, decreasing to approximately 10 m in the west.
f3-6 anticline
This anticline is located north of the f3-7 syncline. This is reflected in the contour map of the coal seam floor, with an axis trending west‒northwest. The maximum amplitude of the anticline is greater than 20 m, decreasing westward, and the anticline plunges.
f3-7 syncline
This syncline is located at the southern edge of the mine. The axis of the syncline extends approximately west‒northwest along the Zaokai River. It is faintly reflected in the contour map of the coal seam floor. The maximum amplitude of the syncline is approximately 10 m, with an extended length of approximately 4 km.
Basic principles and methods for evaluating and predicting the relative tectonic complexity
This study of the relative tectonic complexity generally followed the hypothesis of isotropic segments. On the basis of the division of isotropic segments in the coal mine, the evaluation index data of relative tectonic complexity for each block were statistically analyzed. The entropy function was used to quantitatively evaluate the relative tectonic complexity of the exposed areas, and stepwise regression analysis was employed to establish an empirical formula for predicting the relative tectonic complexity of the unexposed areas.
Isotropic segment
The isotropic segment was a coal seam block with an area that exhibited broadly similar major geological characteristics, serving as the fundamental unit for evaluating the relative tectonic complexity of coal seams. When delineating isotropic segments, the typical base map was the contour map of the coal seam floor. The study area was discretized into several square grid cells of the same size on the basis of the layout of the working faces. The index values of factors related to the relative tectonic complexity within each grid cell were then statistically analyzed.
When studying relative tectonic complexity, the long-axis direction, shape, and size of the grid blocks were the three essential elements in block division. The long-axis direction of the grid blocks was generally aligned with the strike of the working faces in the plan view of the mining and excavation of the coal seam. The width-to-length ratio of the grid blocks was approximately 1:1 to 1:2. The size of the grid blocks was a crucial factor in determining whether the tectonic characteristics of the study area could be adequately reflected.
Entropy function
Since its introduction by L. Boltzmann, the entropy function has been widely applied in various fields, such as biology, meteorology, astronomy, economics, and sociology.
The entropy function is commonly expressed as follows.
where S is the entropy of the system; Pi is the probability of the occurrence of state i in the system; and n is the number of states in the system.
Entropy possesses the following significant properties. First, the entropy is zero only when one of P1, P2,…,Pn equals 1 and the rest of the parameters are 0, and the entropy is always positive in other cases. Second, S attains its maximum value (lnn) when the occurrence probabilities of the n possible states are equal.
To eliminate the influence of different states of the system on the system’s entropy, the concept of relative entropy is introduced.
where S′ is the relative entropy of the system; Smax is the maximum entropy value of the system; and n is the number of states in the system.
The entropy of multiple systems is additive. In information theory, information entropy refers to the uncertainty in the transmission of information. A high content of information content exhibits low entropy, whereas a low information content exhibits high entropy. Therefore, in the evaluation of relative tectonic complexity, the smaller the entropy value of the entropy function is, the more complex the tectonics, and the larger the entropy value is, the simpler the tectonics.
Stepwise regression analysis
Stepwise regression analysis is a type of regression analysis. Regression analysis is a statistical method in which the interrelationship between one variable and one or more other variables is evaluated.
We assume that n sets of geological data are known and that each set includes p variables, which are denoted as x1, x2,…,xp, and assume that the random variable y has a linear relationship with these variables.
To predict y on the basis of these variables, a linear regression model with p variables can be established as follows.
where βi represents the unknown parameters and ε represents the random errors.
Since the random error ε is a normal random variable with a mathematical expectation of 0 and variance of σ2, the linear regression model in Equation 3 can be rewritten as follows.
By substituting the observed values of the variables into Equation (4), the coefficients βi (i=0,1,…,p) in the expression are determined on the basis of the principle of least squares.
After the expression is established, the significance test must be performed before it can be used for prediction.
In stepwise regression analysis, the contribution of each variable is considered, and the variables are gradually selected into the regression equation on the basis of their importance. During this process, variables are selected, including but not limited to the important variables, individually on the basis of their contribution. That said, we consider that some variables that were previously selected for the regression equation might lose their original significance as subsequent variables are introduced. Such variables should be promptly removed from the equation to ensure that only important variables remain in the regression equation. Conversely, if a previously removed variable becomes significant again due to the introduction of new variables, it should be reselected into the equation. This process continued until no further variables could be removed or introduced.
There were specified criteria for both introducing and eliminating variables. First, on the basis of the specific situation, the criteria Fl and F2 for selecting and eliminating variables were determined, with Fl ≥ F2 serving as the critical value of the F test for testing each variable contribution. Fl is the F test threshold value for determining when an independent variable should be included in the equation, whereas F2 is the F test threshold value for determining when an independent variable should be removed from the regression equation. Variables were introduced when F was greater than Fl and eliminated when F was less than F2. It is possible to set F1 equal to F2. Generally, to include more variables in the regression equation, Fl and F2 should not be set too high. Fl and F2 can be obtained by consulting the F-table on the basis of the significance level α and a preliminary estimate of the degrees of freedom of f. When it is impossible to predict Fl and F2, constants unrelated to degrees of freedom may be used.
In the regression analysis, the relative entropy value served as the dependent variable, whereas the other factors were independent variables. After the regression equation between the relative entropy values and independent variables in the exposed area was established, predictions could be made for the relative entropy values of the unexposed areas.
Indicators
Coal seam thickness, coded as x1
This indicator signifies the thickness values of coal seams, which can be obtained from boreholes in a coal mine.
Coal seam thickness abnormality index, coded as x2
This indicator signifies the ratio of the coal seam thickness to the arithmetic mean value. This indicator cannot be directly obtained from the borehole and requires calculation on the basis of the coal seam thickness.
Sandstone thickness within 50 m of the roof of the coal seam, coded as x3
This indicator signifies the thickness values of sandstone within 50 m above the roof of the coal seam, which can be obtained from boreholes in the coal mine.
Lithology of the coal seam roof, coded as x4
This indicator signifies the lithology of the direct roof above the main mining coal seam, which can be obtained from boreholes in the coal mine. To facilitate the assignment of values in the isotropic segments in a coal mine, the lithology first needs to be quantified. The results are shown in Table 2.
Elevation of the coal seam floor, coded as x5
This indicator signifies the altitude of the coal seam floor. To obtain this indicator, it was necessary to subtract the thicknesses of the overlying rock and the soil layer on the coal seam floor from the ground elevation of the borehole.
Abnormality index of the elevation of the coal seam floor, coded as x6
This indicator signifies the ratio of the elevation of the coal seam floor to its arithmetic mean value. This indicator could not be directly obtained from the borehole and needed to be calculated on the basis of the elevation of the coal seam floor.
Number of contour lines, coded as x7
This indicator was used mainly to reflect the changes in the dip angle of the coal seam floor in the mining field. The more contour lines there are within an isotropic segment, the larger the dip angle, and vice versa. This indicator can be obtained after the contour lines are drawn via the interpolation method, which is based on the elevation of the coal seam floor corresponding to each borehole.
Folds
This indicator signifies the folds revealed in the coal mine, including monoclinic, synclinal, and anticlinal folds.
If there was an axis of an anticline or syncline within an isotropic segment, the fold type within that block was defined as an anticline or syncline. Otherwise, it was defined as monoclinic.
Faults
This indicator signifies the faults revealed in the coal mine, including large-scale faults (with a drop larger than 5 m), medium-scale faults (with a drop between 1 and 5 m), and small-scale faults (with a drop less than 1 m).
The folds and faults were revealed mainly in the exposed areas, and the unexposed areas had not yet been arranged with working faces, making it impossible to reveal this information. Therefore, the indicators for exposed and unexposed areas should be treated differently, as shown in Table 3.
Relative entropy values were calculated primarily within the exposed areas. During this calculation, a total of five variables were involved: the total number of faults, the number of large-scale faults, the number of medium-scale faults, the number of small-scale faults, and the type of folds. Simply using the number of faults and folds cannot accurately reflect the complexity of geological tectonics. Therefore, the weights should be assigned to faults and folds before the entropy values are calculated. Since the entropy values need to be compared after calculation, the assignment of weights focuses only on their relative magnitudes, not their absolute magnitudes. However, to significantly reduce the impact of human assignment on the evaluation results, larger faults and folds should be assigned higher values, and vice versa. The weights for faults and folds in the study area are shown in Table 4. The process for quantitative evaluation and prediction is shown in Figure 4.
Key novelties of the work
The geological characteristics of the roof and floor strata of coal seams could influence the degree to which tectonics modify the coal seams. The coal seam thickness provides a direct indication of tectonic modification effects. On this basis, the above indicators were established. Among the indicators, the coal seam thickness (coded as x1), sandstone thickness within 50 m of the roof (coded as x3), lithology of the coal seam roof (coded as x4), and elevation of the coal seam floor (coded as x5) can be revealed through drilling and reflect the geological characteristics of the roof and floor strata. Additionally, the coal seam thickness abnormality index (coded as x2), abnormality index of the elevation of the coal seam floor (coded as x6), and number of contour lines (coded as x7) reflect the effects of tectonic modification. These indicators are easily obtainable and closely related to the relative complexity of tectonics; thus, the indicators established in this paper are more operable than other findings in the literature.
The main types of tectonics affecting coal mining are folds and faults. These tectonics could be revealed in already exposed areas but could not be directly obtained in unexposed areas. Therefore, it was necessary to distinguish between exposed and unexposed areas when considering the tectonic distribution. In the literature, the influences of folds and faults were generally considered from the scale of mining areas and mining sections. These tectonics were large in scale, had a wide range of influence, and may have constituted the main geological features, whereas tectonics within the working face scale were less frequently considered. In this work, the tectonics within the working face scale were also incorporated into the evaluation of relative complexity, and the characteristics of the exposed areas were used to predict the unexposed areas, thereby increasing the prediction accuracy.
In this work, stepwise regression analysis was employed to consider the contribution of each variable; only the important variables could be selected for the regression equation, and these variables were the main factors influencing relative complexity. Therefore, the established predictive formula could be used to predict areas in similar sedimentary environments in adjacent mining areas. This method avoids the universal application of a single formula.
Quantitative evaluation and prediction of the relative tectonic complexity of the Sangshuping coal mine
The mineable coal seams in the Sangshuping coal mine include the No. 3 and No. 11 coal seams, with the No. 3 coal seam being the primary mining seam, whereas the No. 11 coal seam currently remains unmined. The quantitative evaluation of the relative tectonic complexity focused mainly on the No. 3 coal seam, and the quantitative prediction focused primarily on both the No. 3 and No. 11 coal seams.
Isotropic segment division
When the isotropic segments in the Sangshuping coal mine were divided, the direction of the segment was determined to be parallel and perpendicular to the advancing direction of the mining face. The shape of the block unit was determined to be square, which means that the length of the segment in both the parallel and perpendicular directions of the advancing direction of the mining face was the same. The size of the segment was determined to be 200 m by 200 m. The result of the division of the isotropic segments is shown in Fig. 5.
Spatial distribution characteristics of the evaluation indicators
No. 3 coal seam in the Sangshuping coal mine
The contour lines of the main indicators are shown in Fig. 6. The indicators used were the coal seam thickness, sandstone thickness within 50 m of the coal seam roof, lithology of the coal seam roof, and coal seam floor elevation. These data can be obtained from boreholes, and some of the data are shown in Table 5. Other indicators that could not be directly obtained from drilling were not specifically displayed here.
No. 11 coal seam in the Sangshuping coal mine
The contour lines of the main indicators are shown in Fig. 7. The indicators used were the coal seam thickness, sandstone thickness within 50 m of the coal seam roof, lithology of the coal seam roof, and coal seam floor elevation. These data can be obtained from boreholes, and some of the data are shown in Table 6. Other indicators that could not be directly obtained from drilling were not specifically displayed here.
Classification of the relative tectonic complexity
The level of the relative tectonic complexity was classified into three grades: complex, medium, and simple.
Within the mined area, the relative entropy value was calculated on the basis of tectonics, such as faults and folds, serving as the basis for classifying the relative complexity. The relative entropy values range between 0 and 1. According to the characteristics of entropy, in the evaluation of the relative tectonic complexity, a smaller relative entropy value indicates more complex tectonics, whereas a larger entropy value indicates a simpler structure. Therefore, the corresponding relationship between the relative entropy value and the grade of relative tectonic complexity is shown in Table 7.
Quantitative evaluation and prediction of the relative tectonic complexity of No. 3 coal seam
A total of 1321 isotropic segments were identified in the Sangshuping coal mine. Taking the relative entropy value as the dependent variable (y), the independent variables were as follows: coal seam thickness (x1), coal seam thickness anomaly index (x2), sandstone thickness within 50 m of the coal seam roof (x3), lithology of the coal seam roof (x4), elevation of the coal seam floor (x5), abnormality index of the elevation of the coal seam floor (x6), and number of contour lines (x7). Stepwise regression analysis was conducted. When determining criteria Fl and F2 for selecting and eliminating variables, the significance level α was set to 0.10, and the degrees of freedom f were initially estimated as 7 and ∞, respectively. Fl and F2 were determined to be 1.72. Through stepwise regression calculations, the regression equation for the No. 3 coal seam was established as follows.
The primary factors influencing the relative tectonic complexity of the No. 3 coal seam are the number of contour lines (x7), the sandstone thickness within 50 m of the coal seam roof (x3), the coal seam thickness anomaly index (x2), and the lithology of the coal seam roof (x4).
The test value of F for the regression equation was 11.57, whereas the critical value F0.1(4, 200) was 1.97, indicating that the regression equation was significant. On the basis of this regression equation, the prediction accuracy of the relative tectonic complexity in isotropic segments of the exposed area was 70%. Therefore, this regression equation could be used to predict the relative tectonic complexity in the unmined areas of the No. 3 coal seam.
The result of the evaluation of the relative tectonic complexity of the No. 3 coal seam is shown in Fig. 8, with the exposed areas indicated by the dotted line. Currently, there are two main exposed areas. The level of relative tectonic complexity within the exposed areas was primarily moderate. In the northern exposed area, the moderate level of relative tectonic complexity held an absolute advantage, gradually weakening from north to south and gradually intensifying from east to west. In the southern exposed area, neither the moderate nor simple level held an absolute advantage, with moderate complexity extending in a banded pattern from east to west, alternating with simple complexity from north to south, and showing a tendency to increase in complexity from east to west.
The unexposed areas of the No. 3 coal seam primarily exhibited a simple level of tectonic complexity, with moderate complexity being scattered sporadically. Comparatively, the tectonics in the northern part are more complex than those in the southern part, and those in the east are more complex than those in the west, with the central part of the mine field being the most complex.
Overall, the relative tectonic complexity of the No. 3 coal seam in the Sangshuping coal mine is primarily simple, with moderate complexity occurring mainly in the central and southern parts of the coal mine. The most tectonically complex area is located in the center of the coal mine.
Prediction of the relative tectonic complexity of No. 11 coal seam
Since the No. 11 coal seam in the Sangshuping coal mine is currently not being mined and the No. 3 and No. 11 coal seams are part of the same coal-bearing rock series with similar geological conditions, the regression equation established using the No. 3 coal seam was used to predict the relative tectonic complexity of the No. 11 coal seam. The prediction results are shown in Fig. 9. The relative tectonic complexity level in the No. 11 coal seam is predominantly simple. The simple zones are distributed mainly in the northern part of the mine field, and the moderate zones are distributed primarily in the central and southern parts. The eastern part of the coal mine is more complex than the western part. In terms of distribution patterns, the moderate zones form a circular shape, mainly extending along the southern boundary of the coal mine, i.e., primarily in the NE–SW and NW–SE directions.
Discussion
Comparison of the quantitative and predictive evaluations of the relative tectonic complexity of No. 3 coal seam in the Sangshuping coal mine
On the basis of the entropy function, the zone of the quantitative evaluation of the exposed area of the No. 3 coal seam in the Sangshuping coal mine is shown in Figure 10. In the northern exposed area, the moderate level of relative tectonic complexity in the central region exhibited a nearly N–S-trending zone, corresponding to small fault-dense zones. In the eastern and western regions, the moderate level presented a clumped distribution. The complex level is solely distributed in the eastern part, corresponding to the nearly E–W-trending small fault-dense zones in this region. In the southern exposed area, the moderate level was distributed in the middle and southern regions, displaying a NW-trending zone that aligns with the fault-dense zones in this area. The complex level was exclusively distributed in the western part.
The regression equation for the No. 3 coal seam in the Sangshuping coal mine was applied to predict the relative tectonic complexity in the exposed area, as shown in Figure 11. In the northern exposed area, the moderate level exhibited a characteristic pattern of N–S banding and E–W blocking, which was similar to the distribution characteristics obtained from the entropy function. This distribution corresponds to the distribution of fault-dense zones in this region. In the southern exposed area, the moderate level was distributed in the southern part, and the distribution characteristics were also generally similar to the results of the entropy function.
The area percentages of the quantitative and predictive evaluation of the exposed area of the No. 3 coal seam in the Sangshuping coal mine are summarized in Table 8. In the northern exposed area, the predictive value decreased by approximately 0.69% in the complex level zone, decreased by approximately 11.49% in the moderate level zone, and increased by approximately 12.18% in the simple level zone. In the southern exposed area, the predictive evaluation revealed a decrease of approximately 1.33% in the complex level zone, a decrease of approximately 24.78% in the moderate level zone, and an increase of approximately 26.11% in the simple level zone. On average, the predictive evaluation of the exposed area revealed a decrease of approximately 1.01% in the complex level zone, a decrease of approximately 18.14% in the moderate level zone, and an increase of approximately 19.15% in the simple level zone.
On the basis of the comprehensive analysis of the significance of the test results of the regression equation, the assessed accuracy rate, and the comparison of the characteristics and percentage area of relative tectonic complexity, the empirical formula for predicting the tectonic entropy value of the No. 3 coal seam in the Sangshuping coal mine had a good effect.
Comparison of the quantitative and predictive evaluations of the relative tectonic complexity of No. 3 coal seam in the Xiayukou coal mine
Among the three coal mines in the Hancheng mining area, the Xiayukou coal mine is adjacent to the Sangshuping coal mine, and the primary mining seams in the Xiayukou coal mine are the No. 2 and No. 3 coal seams. Therefore, the empirical formula of the No. 3 coal seam in the Sangshuping coal mine was applied to evaluate the relative tectonic complexity in the exposed area of the No. 3 coal seam in the Xiayukou coal mine, as shown in Figure 12.
Comparison of the quantitative evaluation of the relative tectonic complexity and predictive evaluation of the exposed area of the No. 3 coal seam in the Xiayukou coal mine. (a) Quantitative evaluation of the zone of relative tectonic complexity based on the entropy function; (b) predictive evaluation of the zone of relative tectonic complexity based on the regression equation.
On the basis of the entropy function, in the quantitative evaluation of the relative tectonic complexity of the exposed area of the No. 3 coal seam in the Xiayukou coal mine, the complex level zone was located in the southeastern region, whereas the moderate -level zone was located mainly in the northern, eastern, and southern regions, extending along the nearly N–S-trending, NE-trending, and NW-trending zones, corresponding to the fault-dense zones.
For the predictive evaluation of the relative tectonic complexity of the exposed area of the No. 3 coal seam in the Xiayukou coal mine using the regression equation of the No. 3 coal seam in the Sangshuping coal mine, the moderate-level zone was distributed in the central and southern regions, primarily trending nearly N–S, NE, and NW. Compared with the results of the quantitative evaluation, the results of the predictive evaluation decreased by approximately 7.50% in the area of the complex-level zone, increased by approximately 14.60% in the moderate-level zone, and decreased by approximately 7.10% in the simple-level zone, as shown in Table 9. The distribution ranges and extension directions of the moderate-level zones in both evaluations showed similar patterns, indicating that this regression equation had a certain degree of applicability in the exposed area of the No. 3 coal seam in the Xiayukou coal mine.
In conclusion, the predictive performance of the regression equation of the tectonic entropy for the exposed area of the No. 3 coal seam in the Sangshuping coal mine exhibited a degree of deviation from the actual conditions, which was constrained primarily by its main influential factors. Nevertheless, the prediction errors remained within an acceptable margin. Furthermore, the evaluation indicators were readily accessible. Consequently, the methodology for assessing the relative tectonic complexity outlined in this article was deemed feasible and could offer a technical safeguard for safe mining operations in coal mines.
Conclusions
First, on the basis of the principle of the isotropic segment, an empirical formula for predicting the structural entropy value of the No. 3 coal seam in the Sangshuping coal mine was established using the entropy function analysis and stepwise regression analysis. The results revealed that the main factors influencing the relative complexity of coal seam tectonics were the number of contour lines (x7), the sandstone thickness within 50 m of the roof of the coal seam (x3), the coal seam thickness abnormality index (x2), and the lithology of the coal seam roof (x4). These factors were all negatively correlated with the relative complexity of the tectonics.
Second, the level of relative tectonic complexity of the No. 3 coal seam in the Sangshuping coal mine was simple, with moderate and complex zones appearing primarily in the central and southern parts of the mining field. The relative complexity level in the exposed areas was primarily moderate, exhibiting a striped distribution pattern trending nearly E–W, NW, and nearly N–S, similar to the distribution characteristics of the small fault-dense zones. In the unexposed areas, the relative complexity of the structure was simple, with the southern part being more complex than the northern part and the eastern part being more complex than the western part.
Finally, the prediction results for the relative complexity of the No. 11 coal seam revealed that the level was mainly simple, with moderate zones distributed primarily in the central and southern parts of the mining field forming a circular shape, mainly exhibiting a striped pattern trending nearly NE-SW and NW-SE.
Data availability
The data that support the findings of this study are available on request from the corresponding author, [31319284@qq.com (R.J. Du)], upon reasonable request.
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Authors sincerely appreciate all participants for their contributions.
Funding
This research was funded by the Natural Basic Research Program of Shaanxi Province, grant number 2014JQ5178; the Key Project of the Shaanxi Coal and Chemical Industry Group Company Limited, grant number 2015SMHKJ-B-J-08; and the Key Project of the Shaanxi Coal and Chemical Industry Group Company Limited, grant number 2019SMHKJ-B-J-15.
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All of the authors participated in the project and their contributions were as follows: Rongjun Du: conceptualization, data analysis and writing original draft. Yucheng Xia: conceptualization, writing review & editing. Xueyang Sun: methodology, data collection. Chen Guo: data analysis, formal analysis. Lintian Miao: investigation, formal analysis.
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Du, R., Xia, Y., Sun, X. et al. Quantitative evaluation and prediction of the relative complexity of Sangshuping coal mine tectonics in the Hancheng mining area. Sci Rep 15, 16402 (2025). https://doi.org/10.1038/s41598-025-01510-4
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DOI: https://doi.org/10.1038/s41598-025-01510-4