In order to investigate the distribution patterns of in situ stress in the main coal seams (3# and 15#) of the Qinshui coalfield, an in-depth analysis was conducted on the in situ stress measurement results obtained from 139 measurement points across 46 mines within the mining area. The findings indicate that the maximum horizontal principal stress in the coal mining area of both seams is generally higher than the vertical principal stress. The stress field exhibits characteristics of a tectonic stress field, while deeper regions display features of a vertical stress field. The in situ stress values in the mining area of coal seam 3# are predominantly characterized by moderate stress field zones, while those in the mining area of coal seam 15# are mainly composed of low to moderate stress field zones. The maximum horizontal principal stress in the Yangquan and Changzhi mining areas for both coal Seams 3# and 15# is concentrated in the NE direction, whereas in the Jincheng mining area, it is predominantly concentrated in the NW direction, indicating a clear directionality. With increasing depth, the following trends can be observed approximately: the maximum and minimum horizontal principal stress values generally exhibit an increasing trend, and the geological structures throughout the mining area are primarily dominated by horizontal tectonic movements; the lateral pressure ratio gradually decreases and tends to concentrate near the value of 1; the relative difference between the maximum and minimum principal stresses tends to increase, with the horizontal principal stress difference ratio concentrating near 0.5. The relationship between the average horizontal principal stress ratio (k) and vertical principal stress at different depths within the measured area follows Hawke-Brown’s general law for this relationship curve. The research results have important guiding significance for the design of coal mining engineering in this area.

Coal and rock masses are highly complex geological bodies. In comparison to other engineering materials, coal and rock masses possess an internal stress field that significantly influences the deformation and failure of the surrounding rock masses in terms of both size and direction. This stress field serves as the foundation for all theoretical research, engineering design, and construction related to rock mass mechanics. The primary methods employed to obtain ground stress data for coal mine roadway surrounding rock include hydraulic fracturing, stress relief, and stress recovery [1].

Hongpu et al. [2-6] conducted extensive underground measurements in multiple mining areas using self-developed small-aperture hydraulic fracturing geo-stress measuring devices. Simultaneously, they collected geo-stress data of coal mine and relevant stress relief methods from specialized literature for establishing the “Chinese coal mine underground geo-stress database,” drawing the geo-stress distribution map of coal mine areas in China and analyzing the characteristics and main influencing factors of the geo-stress distribution. Qiangling et al. [7] developed an in situ testing system for geo-mechanical parameters of coal and rock masses, which includes borehole imager, rock borehole elastic modulus instrument, rock borehole strength instrument, rock borehole shear instrument, and hydraulic fracturing in situ stress testing device. This system was successfully applied in some coal mines to accurately, quickly, conveniently, and cost-effectively obtain geo-mechanical parameters of coal and rock masses. Meifeng et al. [8-11] improved a traditional stress relief method and conducted in situ stress measurement in numerous coal and metal mining areas in China. They revealed the distribution patterns of in situ stress while analyzing the influencing factors to guide relevant engineering practices. In order to address the challenges related to weak and broken surrounding rocks found predominantly in deep coal mines, where it is difficult to implement traditional ground stress testing methods, Quansheng et al. [12, 13] utilized a three-dimensional test system based on the flow stress recovery theory. This approach enabled them to obtain the ground stress data from deep weak broken surrounding rocks, which could effectively meet the requirements of the deep soft rock mining engineering. The hydraulic fracturing method is currently widely employed in the mining industry due to its ability to adapt to the complex and diverse mining environments found in coal mines, as well as its convenient operation. Additionally, a significant amount of geo-stress test data samples are obtained using this technique.

The Qinshui coal field is one of the five major coal production bases in China, situated in its central and southern Shanxi Province. The primary mining areas of the Qinshui coal field are concentrated in Yangquan, Lu'an, Jincheng, and several other regions. The main focus of its mining operations lies on the 3# and 15# coal seams having complex geological structures from south to north. As the mining scope and depth increase, the deep mining becomes more prevalent in this area. Consequently, various factors, such as connection tension and underground excavation along the goaf, lead to strong deformation. Additionally, secondary reuse of coal pillars is employed for protection purposes when dynamic pressure roadways, like no-coal-pillar stay lanes, are utilized. Furthermore, a long-term gas extraction process has damaged the mechanical properties and structure of the coal body due to the Coal Bed Methane enrichment in the Qinshui coalfield. Under these geological and production influences, a new pattern of stress distribution has emerged within underground roadways. Therefore, the study of the stress distribution law in the main coal seam of the Qinshui coalfield holds significant importance as it aids in understanding the roadway deformation mechanisms and failures while optimizing the mining engineering layouts and controlling the stability of the surrounding rocks [14-16].

2.1 Geological Structure

The folds in the Yangquan mining area are highly developed, which primarily consist of open folds with relatively weak deformation. Based on the direction and scale of their distribution, they can be classified into three main groups. The NNE-NE folds exhibit the highest level of development and exert significant control over the overall shape of the mine. They are followed by the near EW folds, while the NW folds display comparatively weaker development. In terms of the fault structures, the Yangquan mining area demonstrates a low degree of development characterized by clusters of small faults with limited drop and extension distances. Faults with drops exceeding 20 m can only be observed in the second and Minmetals mines. There is a noticeable difference between the faults occurred in 3# and 15# coals in the mining area. While 3# coal exhibits a higher number of faults compared to 15# coal, it is noteworthy that 15# coal has a higher proportion of faults with drops exceeding 5 m, indicating more pronounced development of larger faults. Regarding the types of faults, approximately 85% faults occurred in 3# coal are normal faults, whereas there is no significant variation in normal faults occurred in 15# coal. Different faults exhibit variations in their distribution directions also: the faults occurred in 3# coal are dispersed across all directions but show greater concentration and development toward NE and NW directions. Conversely, the faults occurred in 15# coal are more concentrated along the NNE direction. In regard of the dip distribution of faults among all the studied mines, no notable differences were observed as most dips fall within the range between 30° and 60° [17].

The Changzhi mining area is situated between the Taihang and Luliangshan uplift belts in the eastern part of the Qinshui Basin. It is bounded to the east by the Jinhuo fold fault belt and to the west by the Wuxiang-Yangcheng fold belt in the core of Qinshui Depression. Overall, this mining area exhibits a westward inclined monoclinal structure, accompanied by significant folds and faults of certain scales. The east-west boundary of this mining area plays a crucial role in determining its structural form. The Jinhuo fold fault belt exhibits a general strike of N25°E, and it is characterized by the presence of the Changzhi normal fault and Laodingshan anticline to the east in the Changzhi area. It demonstrates a pronounced strength gradient from north to south. Notably, there are distinct thrust faults in the Heshun and Zuoquan areas, and a central normal fault near Changzhi, as well as a series of folds located toward the southern region near Gaoping. The Wuxiang-Yangcheng fold belt is situated at the core of the Qinshui Basin. Its northern section trends to the NNE direction, while its midsouthern section aligns closely with the SN direction, forming a compound synclinal tectonic belt. A sequence of major faults within this area divides it into graben and horst structures. These faults have an average strike orientation ranging between NE50° and 80°, and an intersection angle with the Changzhi major fault between 30° and 50°. Furthermore, these faults exhibit considerable extensional displacement over long distances, resulting in fault drops exceeding 100 m with the maximum drop reaching up to 600 m. Importantly, they display clear genetic associations with the Jinhuo zone [18].

The geological structure of the Jincheng mining area is predominantly composed of a neocathaysian fold fault tectonic system in the NNE direction, followed by meridional and mountain font structures. The primary neocathayian structure is located at the southern end of the Jinhuo fold fault belt, which mainly consists of gently open folds trending to the NNE direction with limited development of faults and some secondary fault structures. The axial direction measures NNE20°–25°, with the occurrence of steeper strata in the inner inclined trough and slower asymmetrical wings. In this section, the main secondary faults are the Zhuangtou faults, which intersect with the fold fault belt from GaopingDuzhai to Qujiashan through Zhuangtou in Changzhi. In the Duzhai-Zhuangtou area, these faults strike NNE and have a drop of 170 m that decreases toward the south, reducing to 30 m in Bofang before gradually disappearing southwards from Duzhai. In the Zhuangtou-Qujiashan area, there is a change in strike to NEE for these faults along with an increased drop reaching 200 m. In addition, there are several smaller secondary faults, such as the Sanjiadian fault, Niushan fault, Sanjia fault, and Yincheng fault, which exhibit tensile behavior of normal faults. The meridional tectonic system is generally characterized by a north-south compressive tectonic belt comprising north-south uplifted fold belt, compressive faults, and depression zones. It forms a compound syncline with gentle and open morphology and undeveloped faults. However, high-angle normal faults dominate the region. This tectonic system is situated on the inner side of the eastern wing of the frontal arc of the Shanzi structure in the southeastern Jin province and extends to the shield site at its southern end along with part of its eastern side. Since the geological forces are balanced in this area, the strata display relatively gentle characteristics with a north-south overturned synclinal distribution. Coal-bearing formations are well-preserved, while coal-bearing rocks remain stable and consistently trend toward the north and south directions without significant structural complexities except for major structures like the Duantou Mountain anticline, Jincheng syncline, and Baima Si faults. Most of other structures within this region mainly consist of closed brachyanticlines. On the eastern side of the mining area where late tectonic movements occurred, there has been a transformation resulting in changes to the main coal rock formation toward the northeast direction [19].

2.2. Measures of Ground Stress in Main Coal Seam

The ground stress in Qinshui coalfield is measured by hydraulic fracturing method Figure 1 [20]. Hydraulic fracturing for geo-stress testing is a widely applied technique in various fields such as rock mass engineering, oil drilling, and seismic research. The fundamental principles of this technique are outlined below:

Testing Procedure: A section within a vertical borehole is isolated, and high-pressure water is injected into it. Once the pressure reaches its maximum value, Pb, the rock wall fractures, causing the pressure to decrease and eventually stabilize at a constant level to maintain the fracture opening.

Shutdown Pressure (Ps): Upon deactivating the injection pump, the pressure rapidly decreases due to fluid loss, causing the fracture to close. The rate of pressure reduction then slows down, and the critical value at this point is defined as the instantaneous shutdown pressure, Ps.

Re-opening Pressure (Pr): After fully depressurizing and then reinitiating fluid injection, the re-opening pressure of the fracture, denoted as Pr, and the instantaneous shutdown pressure, Ps, are obtained.

Recording Fracture Orientation: The direction of the fracture is recorded using an impression tool or borehole television to ascertain the orientation of the geo-stress.

Analysis of Measurement Results: Through actual underground measurements, the geo-stress state and its distribution patterns within the measured area are determined.

(1a)
(1b)
(1c)

In the equation, ρ represents the density of the overlying rock formations, with units of kg/m3; g denotes the gravitational acceleration, with units of m/s²; and h stands for the burial depth of the measurement point.

The small-borehole hydraulic fracturing method for geo-stress measurement offers an effective and rapid means of measuring geo-stress in deep mines. It provides reliable fundamental parameters for the layout of deep tunnels and the optimization of support designs, thus furnishing vital data support for mine safety and engineering design.

All collected data were compiled as presented in Table 1,1, where H represents the depth of each measuring point, σv denotes the vertical principal stress, σH indicates the maximum horizontal principal stress, and σh represents the minimum horizontal principal stress.

The in situ stress parameters of coal seams 3# and 15# were examined at a total of thirty-nine measuring points across fifteen mines in the Yangquan mining area, sixty-five measuring points across twenty mines in the Changzhi mining area, and thirty-five measuring points across eleven mines in the Jincheng mining area.

The type, magnitude, direction, size, and difference of the horizontal principal stress, lateral pressure ratio, and so on, of the ground stress fields of the 3# and 15# coal seams in different mining areas were analyzed in depth, where from it was found that the distribution of the ground stress shows the following regularities.

3.1. Types of Ground Stress Field

(1) 3# coal seams

According to the arrangement of the three principal stresses, the types of the stress field at five measuring points in the 3# coal seam of the Yangquan mining area can be classified into two categories. One category is characterized by a stress field dominated by the gravity stress (σv>σH>σh), which involves a total of 2 measuring points accounting for 40% of the overall measurement locations. The other category represents a dominant stress field influenced by the tectonic stress (σH>σv>σh), which involves a total of 3 measuring points accounting for the rest 60% of the total measurement locations. The depth range of these measuring points falls between 310 m and 595 m. The stress fields at 50 measurement points in the 3# coal seam of the Changzhi mining area can be classified into three types. First, there are a total of 13 measuring points (26% of the total points) dominated by the gravity stress (σv>σH>σh). Second, there are a total of 5 measuring points (10% of the total points) dominated by the structural stress, with the minimum horizontal principal stress acting as the intermediate principal stress (σH>σh>σv). Third, there are a total of 32 measuring points (64% of the total points) dominating the structural stress, where the vertical principal stress serves as the intermediate principal stress (σH>σv>σh). The depth range for these measurements falls between 165 m and 729.1 m. The types of the stress field at 27 measuring points in the 3# coal seam in the Jincheng mining area are primarily classified into three categories. First, there is a stress field dominated by the gravity stress (σv>σH>σh), which accounts for a total of 4 measuring points representing 14.8% of the overall measurements. Second, there is a dominant stress field of the structural stress (σH>σh>σv), where the minimum horizontal principal stress serves as the intermediate principal stress. This category comprises 6 measuring points accounting for 22.2% of the total measurements. Third, there is another dominant stress field of the structural stress (σH>σv>σh), where the vertical principal stress acts as the intermediate principal stress. This type encompasses a total of 17 measuring points, making up approximately 63% of the considered total measurements. The depth range for these measuring points falls between 77.4 m and 757 m. It is further illustrated by the vector-calibrated values as presented in Table 1 for both maximum and minimum horizontal stresses at each measuring point to draw an accurate ground stress distribution diagram for the 3# coal seam in the main mining area of the Qinshui coalfield Figure 2(a). The maximum horizontal principal stress in the 3# coal seam in the coal mining area of the Qinshui coalfield is generally greater than its vertical principal stress. The ground stress is entirely dominated by the horizontal stress, and its type is characterized by that of the tectonic stress field. But the local ground stress at the burial depth more than 500 m is characterized by the vertical stress field.

(2) 15# coal seam

According to the arrangement of the three principal stresses, the stress fields at 34 measuring points in the 15# coal seams of the Yangquan mining area are primarily classified into three types. The first type is a stress field dominated by the gravity stress (σv>σH>σh), which comprises a total of 4 measuring points accounting for 11.8% of the total number of measuring points. The second type is dominated by the structural stress with the minimum horizontal principal stress as the intermediate principal stress (σH>σh>σv), which consists of one measuring point accounting for 2.9% of the total number of measuring points. The third type is another stress field dominated by the structural stress with the vertical principal stress as the intermediate principal stress (σH>σv>σh), which encompasses a total of 29 measuring points accounting for 85.3% of the total measured points. The depths range from 195 m to 876.3 m.

The types of the stress field of 15 measuring points in 15# coal seam of the Changzhi mining area are primarily categorized into two types. The first type is dominated by the structural stress, where the minimum horizontal principal stress serves as the intermediate principal stress (σH>σh>σv). There are a total of 8 measuring points, accounting for 53.3% of the overall count. The second type is the structural stress, with the vertical principal stress acting as the intermediate principal stress (σH>σv>σh). This category comprises 7 measuring points, covering 46.7% of the total measuring points. The depth for these measurements falls between 49.5 m and 540.3 m. Similarly, in the 15# coal seam of the Jincheng mining area also, two main categories of stress fields were observed at 8 distinct measuring points. One is dominated by the structural stress with the minimum horizontal principal stress being the intermediate principal stress. There are 4 measuring points in total, accounting for 50% of the total number of measuring points (σH>σh>σv). The second category is dominated by the structural stress with the middle principal stress as the vertical principal stress (σH>σV>σh), accounting for 50% of the total number of measuring points. The depth of the measuring points falls between 101 m and 274 m. The maximum and minimum horizontal stresses of each measuring point, as presented in Table 1, were vector calibrated to generate the ground stress distribution map of coal seam 15# in the main mining area of the Qinshui coalfield, as depicted in Figure 2(b). In general, the maximum horizontal principal stress in the 15# coal seam of the coal mining area of the Qinshui coalfield exceeds the vertical principal stress. The prevailing ground stress is predominantly characterized by horizontal stresses, reflecting a type of tectonic stress field. Conversely, the local region in Yangquan coalfield with significant burial depth exhibits a vertical stress field.

3.2. Magnitude of In Situ Stress

The results of the stress in coal seam 3# of the Qinshui coalfield are presented in Table 1. It can be observed that the maximum horizontal principal stress in the mining area 3# of the Yangquan mining area ranges from 11.45 to 16.03 MPa. There are 5 measuring points with values greater than 10 MPa and less than 18 MPa, accounting for 100%. The highest value of the maximum horizontal principal stress is recorded as 16.03 MPa, which occurs in Xinyuan coal mine. In the Changzhi mining area, the maximum horizontal principal stress within the coal mining area 3# varies between 6.41 and 29.67 MPa. Eight measuring points have values below 10 MPa, representing approximately 16% of the considered total measurements. There are 34 measuring points with values greater than 10 MPa and less than 18 MPa, accounting for about 68%; and 8 measuring points with values exceeding 18 MPa but lower than 30 MPa which accounts for around 16%. Wuyang coal mine records the highest value of 29.67 MPa. The maximum horizontal principal stress in the coal mining area 3# of the Jincheng mining area ranges from 6.02 MPa to 22.08 MPa. There are a total of 7 measuring points with stress values below 10 MPa, accounting for approximately 25.9% of the total measurements. Additionally, there are 13 measuring points with stress values between 10 MPa and 18 MPa, accounting for approximately 48.1%. Furthermore, there are another set of measurements consisting of 7 points with stress values greater than 18 MPa and less than 30 MPa, which accounts for approximately 25.9%. The maximum value of the horizontal principal stress is 22.08 MPa, which occurs in Wangpo coal mine.

The results of the stress test for the 15# coal seam of the Qinshui coalfield are presented in Table 1. It can be observed that the maximum horizontal principal stress in the 15# coal mining region of the Yangquan mining area ranges from 6.04 MPa to 32.26 MPa. There are 7 measuring points with values below 10 MPa, accounting for 20.6% of the total. There are also 18 measuring points with values greater than 10 MPa and less than 18 MPa, accounting for 52.9%. Furthermore, there are another 7 measuring points with values greater than 18 MPa and less than 30 MPa, accounting for 20.6%. Additionally, there exist 2 measuring points exceeding 30 MPa with coverage of 5.9%. The highest value of maximum horizontal principal stress is recorded as 32.26 MPa, which occurred in Baoan coal mine. The maximum horizontal principal stress in the 15# coal mining area of the Changzhi mining area ranges from 4.3 MPa to 20.48 MPa. Among them, there are 6 measuring points with a stress less than 10 MPa, accounting for 40% of the total points. There are also 6 measuring points with a stress greater than 10 MPa and less than 18 MPa, accounting for another 40%. Further, there are 3 measuring points having stress greater than 18 MPa and less than 30 MPa, accounting for the remaining 20%. The highest value of the maximum horizontal principal stress is recorded in the Fusheng coal mine, reaching up to 20.48 MPa. The maximum horizontal principal stress in the 15# coal mining areas of the Jincheng mining area ranges from 3.23 MPa to 9.88 MPa. There are a total of 8 measuring points with values below 10 MPa, accounting for 100% of the considered measurements. The highest value of the horizontal principal stress, which is recorded as 9.88 MPa, occurs in Huayang coal mine.

According to the relevant criteria, the low stress zone is defined as 0–10 MPa, the medium stress zone is defined as 10–18 MPa, and the high stress zone is defined as 18–30 MPa. The ultra-high stress area refers to values exceeding 30 MPa [1].

The ground stress value in the 3# coal mining area of the Yangquan mining area is classified as belonging to the medium ground stress field. In the 3# coal mining area of the Changzhi mining area, there are distributions of low, medium, and high stress fields, with a predominant presence in the medium stress field. Similarly, in the 3# coal mining area of the Jincheng mining area, there are also distributions of low, medium, and high stress fields. However, nearly half of these areas fall under the category of the medium stress field. Conversely, no ultra-high ground stress field exists in the 3# coal mining area of the Qinshui coalfield. In the Yangquan mining area, which is known for its coal mining activities, the distributions of ground stress fields are categorized as low, medium, high, and ultra-high. Notably, the medium ground stress field accounts for more than half of the total distribution. Similarly, in the 15# coal mining area of the Changzhi mining area, we observe the presence of low and medium stress fields dominating the region. On the other hand, in 15# coal mining zone of the Jincheng mining area, we find it falling under the category of the low ground stress field.

3.3. Distribution Characteristics of Horizontal Principal Stress

According to the measured results related to the direction of the horizontal principal stress in the main coal seam of the Qinshui coalfield, a vector diagram illustrating the maximum value of this stress is depicted in Figure 3. The direction of the maximum horizontal principal stress at 5 measuring points in the 3# coal seam of the Yangquan mining area is concentrated in the range of N (36.7°–75.1°) E. Similarly, for 17 measuring points, the directions of the maximum horizontal principal stress are concentrated in the range of N (4.1°–74.0°) W; while for other 33 measuring points, it is concentrated in the range of N (13.6°~88.6°) E. In addition, within the mining area of the 3# coal seam in the Jincheng mining area, out of a total of 27 measuring points, the directions of the maximum horizontal principal stress at 17 points are concentrated in the range of N (21.3°–47°) W; while the same fall in the range of N (18.8°–67.6°) E at the remaining 10 measuring points.

The maximum orientations of the horizontal principal stress in 10 out of 34 measuring points in the 15# coal seam of the Yangquan mining area are concentrated in the range of N (30.6°–57.8°) W, while those at the remaining 24 measuring points are concentrated in the range of N (13.6°–80.8°) E. In the 15# coal seam of the Changzhi mining area, the maximum orientations of the horizontal principal stress at 6 out of 15 measuring points are concentrated in the range of N (26.7°–41.6°) W and is the same at other 9 measuring points are concentrated in the range of N (23° –81.6°) E. Finally, in the 15# coal seam of the Jincheng mining area, the maximum orientations of the horizontal principal stress at 5 out of 8 measuring points are concentrated in the range of N (21.7 °–88.4 °) W, and the same at the remaining 3 measuring points are concentrated in the range of N (20.1 °–72.8 °) E.

As a whole, the maximum horizontal principal stress of the 3# coal seam of the Yangquan mining area in the Qinshui coalfield is predominantly oriented toward the NE direction. The maximum horizontal principal stress of the 3# coal seam of the Changzhi mining area is primarily concentrated in the NE direction, with 33 out of 50 measuring points falling in this region, accounting for 66% of all measurements and exhibiting a clear directional trend. The maximum horizontal principal stress of the 3# coal seam in the Jincheng mining area is predominantly oriented toward the NW direction, with 17 out of 27 measuring points (63% of total) indicating significant directional preference. The maximum horizontal principal stress of the 15# coal seam in the Yangquan mine area is primarily concentrated in the NE direction, with 24 out of 34 measuring points (70.6% of total) demonstrating clear directionality. In the Changzhi mining area, the maximum horizontal principal stress of the 15# coal seam is mainly directed toward NE, as observed at 9 out of 15 measuring points (60%). Similarly, for the 15# coal seam in the Jincheng mining area, its maximum horizontal principal stress is predominantly oriented toward the NW direction, as identified at 5 out of 8 measuring points (62.5%), thus displaying evident of directionality. Research on in situ stresses in the coal mines in the Shanxi Province reveals that northern areas, such as Datong and Pingshuo, exhibit NNE orientation for the directions of their maximum horizontal principal stress. Whereas there are two primary orientations, NNE and NNW, near the Taiyuan to Jiexiu regions. The central Shanxi Province experiences various directions of its maximum horizontal principal stress, while that of the western Shanxi Province aligns with an NNE orientation. Through comparison, it can be concluded that the measured ground stress values align consistently with those obtained from comprehensive tests assessing the whole-horizontal principal stresses across the Shanxi Province.

3.4. Variation of Principal Stress with Burial Depth

The scatter diagram shown in Figure 4 depicts the depth-dependent variation of the principal stress at the measuring points, based on the ground stress test conducted specifically on the primary coal seam in the Qinshui coalfield.

Conducting linear regression analysis of the obtained data by using the least square method, the following relationships were obtained among the maximum and minimum horizontal principal stress and vertical stress and burial depth:

(2)
(3)

As depicted in Figure 4, the maximum and minimum horizontal principal stresses generally increase with the burial depth, indicating that the geological structure of the entire mining area is predominantly influenced by horizontal tectonic movements. A smaller R2 value indicates a poor linear correlation between the maximum/minimum horizontal principal stress and burial depth, implying greater discreteness of data. Moreover, the linear correlation between the maximum/minimum horizontal principal stress and burial depth is weaker for the 3# coal seam compared to that for the 15# coal seam due to the variations in mining ranges and inconsistent intensity of geological structural movements among different coal seams. In terms of coal seams, the overall horizontal tectonic movement is more pronounced in the 3# coal seam than in the 15# coal seam.

3.5. Variation in the Ratio of Maximum Horizontal Principal Stress to Vertical Stress with Burial Depth

The lateral pressure ratio primarily refers to the ratio of the maximum horizontal principal stress to the vertical stress (σH/σv). The changes in the states of the stresses at the measuring points with burial depths can be analyzed by measuring the lateral pressure ratio. The distribution of the lateral pressure ratios at different measuring points is illustrated in Figure 5.

It can be seen from Figure 5 that the side pressure ratio of the 3# coal seam in the Qinshui coalfield is mainly concentrated in the range of 0.49–3.82, and its maximum value at 82 measuring points is 3.82, and the burial depth of the corresponding measuring point is 78.3 m. The minimum measured pressure ratio is 0.49, and the burial depth of the corresponding measuring point is 518 m. The side pressure ratio of the coal seam is mainly concentrated in the range of 0.70–3.58, with its maximum value of 3.58 occurring at the measuring point 57 at the burial depth of 80 m. The minimum pressure ratio is 0.70 occurring at the burial depth of 456 m. As the burial depth increases, the lateral pressure ratio gradually decreases, and the lateral pressure ratio approaches 1. The maximum horizontal principal stress at the measuring point may become equal to or less than the vertical stress also, indicating that the type of the ground stress field at the measuring point changes, and the lateral pressure ratio at that point increases with increasing burial depth. The lateral pressure ratio changes regularly with burial depth, indicating that the stress state of the original rock at the deep measuring point changes gradually. This corresponds to the gradual change from horizontal stress to simultaneous horizontal stress and vertical stress in shallow areas.

As depicted in Figure 6, the pressure ratio of 82 measuring in the 3# coal seam is predominantly concentrated in the range of 1–2. Moreover, there are 63 measuring points exhibiting a pressure measurement ratio exceeding 1, accounting for approximately 76.8% of the total. These measurements correspond to the burial depths ranging from 246 m to 755 m, indicating that the dominant stress field in the 3# coal seam of the Qinshui coalfield is primarily horizontal in nature. In addition, there exist another set of measurements comprising 19 data points with pressure ratios falling between zero and one, constituting around 23.17% of the total observations. These specific measurements are mainly clustered within deeper regions at burial depths ranging approximately from 500.5 m to 757 m. This observation indicates that the horizontal ground stress tends to be lower than the vertical stress in most cases within these deep regions. Consequently, it can be inferred that the vertical stress field predominantly influences this particular area.

The pressure ratios at 57 measuring points in the 15# coal seam are primarily concentrated between 1 and 2, with 53 measuring points exhibiting the same greater than 1, accounting for approximately 93.0% of the total. The burial depth ranges from 123 to 876.3 m, indicating that the predominant stress field in the 15# coal seam of the Qinshui coalfield is horizontal. Additionally, there are four measuring points with pressure ratios ranging from 0 to 1, constituting approximately 7.02% of the total. These points are concentrated in the deep area between 447 and 501 m, indicating that the horizontal ground stress in the deep area is smaller than the vertical stress in most cases, and this area is dominated mainly by the vertical stress field.

3.6. Change in Maximum and Minimum Horizontal Stress with Burial Depth

The shear stress in the coal and rock mass is directly determined from the difference between the maximum and minimum horizontal principal stresses. A larger difference in the horizontal principal stresses creates favorable conditions for the formation of joints, cracks, and failure of the coal and rock mass. The deformation and failure of underground roadways are primarily influenced by the variation in the difference of the horizontal principal stresses. Figure 7 illustrates the relationship between the burial depth and difference in the horizontal principal stress for the main coal seam in the Qinshui coalfield. It can be observed from Figure 7 that the difference in the horizontal stress ranges from 2.63 MPa to 13.60 MPa for the 3# coal seam, with an increasing trend with increasing burial depth. Overall, there is a relatively discrete distribution of the difference in the principal stresses, ranging from the minimum 2.63 MPa at the burial depth of 518 m to the maximum of 13.60 MPa at the burial depth of 729.1 m. For the coal seam, the range of the difference in the horizontal stresses is from 1.28 MPa to 14.99 MPa with an increasing relative difference between the maximum and minimum principal stresses as the burial depth increases. The difference in the minimum principal stresses occurs at a burial depth of 123 m with a value of 1.28 MPa, while the difference in the maximum principal stresses occurs at a burial depth of 876.3 m with a value of 14.99 MPa. In comparison, the dispersion of the differences in the principal stresses for coal 15# is less than that for coal 3#.

The difference in the horizontal stress (i.e. shear stress) is the fundamental factor influencing the deformation and damage in underground roadways. The ratio of the difference in the maximum and minimum horizontal principal stresses to the maximum horizontal principal stress is referred to as the ratio of the difference in the principal stresses (σH− σh/σH). Figure 8 illustrates the variation in this ratio with burial depth. In the 3# seam, the ratio of the difference in the maximum principal stress in the horizontal stress field is 0.54, while that in the minimum principal stress is 0.36. In the vertical stress field, it ranges from a maximum of 0.49 to a minimum of 0.38. In the horizontal stress field of the 15# coal seam, this ratio in the maximum principal stress is 0.51 and that in the minimum principal stress is 0.40. In the vertical stress field, the same in the maximum principal stress is 0.49 and that in the minimum principal stress is 0.45.

The concentration of the ratio of the difference in the horizontal principal stress is around 0.5. Its stable distribution can be observed from Figure 8, which indicates significant variations in the horizontal principal stresses in both shallow and deep areas of the coal mine. It is evident that substantial shear stresses are experienced by both shallow and deep areas of the coal mine. The proximity of the difference in the horizontal stress to the uniaxial compressive strength of the coal body leads to pronounced shear failure and fragile integrity disparity within the coal body, resulting in extensive deformation of the surrounding rock due to the mining activities. This corresponds to the development of coal and rock joints in the Qinshui coalfield, as well as severe slope instability in roadways, and significant deformation and instability of the surrounding rock due to the mining activities.

3.7. Ratio of Average Horizontal Principal Stress and Vertical Principal Stress Varying with Depth

The mean horizontal principal stress is defined as the arithmetic average of the maximum and minimum horizontal principal stresses, that is (σH + σh) /2. Based on the measured data, Figure 9 illustrates the relationship between the ratio of the average horizontal principal stress to vertical principal stress and burial depth.

According to the research findings and analysis method of the Hoek-Brown’s global stress distribution, a regression analysis is conducted for the ratio between the average horizontal principal stress and vertical principal stress at all the measuring points.

The ratio of the mean horizontal and vertical principal stresses, denoted by k, can be expressed as follows:

(4)

where a and b are two undetermined constants.

The test data are analyzed by linear regression to obtain the following:

(1) 3# coal

a = 199.58, b = 0.5048. That is

(5)

(2) 15# coal

a = 113.23, b = 0.7902. That is

(6)

Hoek-Brown compiled and analyzed global earth stress data, presenting the proportional relationship between the average horizontal earth stress and vertical earth stress as follows [21]:

(7)
(8)

The relationship between ratio k of the average horizontal principal stress and vertical principal stress in the measured area to the burial depth conforms the Hoek-Brown’s general law of the relationship curve, with a value of k falling within the internal complex line. Hoek-Brown summarized that worldwide earth stress data encompass sedimentary rock, magmatic rock, and metamorphic rock. In the Qinshui coalfield, where the main roof of the coal seam primarily consists of weak and diverse sedimentary rock, involving significant variation in elastic modulus among different types of rock masses. Consequently, this leads to substantial differences in the accumulated stress characteristics and levels within the rock mass due to the varying tectonic movements across regions. These variations in stress field characteristics hold crucial significance for underground structural engineering design, specifically pertaining to sedimentary rock areas associated with the main coal seam in the Qinshui coalfield, particularly for coal mining engineering design.

  1. The maximum horizontal principal stress in the 3# and 15# coal mining areas generally exceeds the vertical principal stress, indicating a dominance of the horizontal stress in the overall stress field. The stress field exhibits the characteristics of a tectonic stress field, with deeper areas displaying characteristics of a vertical stress field. In the Yangquan mining area, the geo-stress value in the 3# coal mining area falls within the medium range. In the Changzhi and Jincheng mining areas, there are distributions of low, medium, and high geo-stress fields in the 3# coal mining area, with medium geo-stress being predominant. In the 15# coal mining area of the Yangquan mining area, there are distributions of low, medium, high, and ultra-high ground stress fields, with more than half falling in the category of the medium ground stress field. The Changzhi’s 15# coal mining area is dominated by the distributions of low and medium ground stress fields; while the Jincheng’s 15# coal mining area belongs to the category of low ground stress field. The maximum horizontal principal stresses in both 3# and 15# coal seams in the Yangquan and Changzhi mining areas predominantly align along the NE direction; whereas for the same in the Jincheng mine mainly align along the NW direction with clear directional preference.

  2. With the increase in the burial depth, there is always an increasing tendency for both maximum and minimum horizontal principal stresses. The geological structure of the entire mining area is predominantly influenced by the horizontal tectonic movement. However, it should be noted that the linear correlation between the maximum and minimum horizontal principal stresses for the 3# coal seam and burial depth is weaker compared to that for the 15# coal seam. Additionally, the overall horizontal tectonic movement is stronger in the 3# coal seam than that in the 15# coal seam. As the burial depth increases, the lateral pressure ratio gradually decreases and tends to concentrate around 1. It is also observed that the maximum horizontal principal stress may become equal to or less than the vertical stress as well as changes occurring in ground stress field type. Furthermore, the lateral pressure ratio becomes more discrete while the deep original rock experiences a gradual transition in its stress state from shallow rock’s dominance of horizontal and vertical stresses.

  3. With the increase in the burial depth, the relative difference between the maximum and minimum principal stresses tends to escalate, while their overall dispersion is smaller in the 15# coal compared to that in the 3# coal. The ratio of the difference in the horizontal principal stress is concentrated around 0.5 and exhibits a stable distribution. The shallow and deep regions of the coal mine exhibit significant disparities in the horizontal principal stress, resulting in substantial shear stresses on coal and rock masses. This corresponds to the development of joints within these masses in the Qinshui coalfield, as well as severe slope instability in roadways due to excessive deformation caused by mining activities. The ratio between the average horizontal principal stress to vertical principal stress, k, in the measured areas of the main coal seam in the Qinshui coal field aligns with the Hoek-Brown’s general law for summarized relationship curve, with k falling within a complex internal range. These findings hold crucial reference values for underground structural engineering design, particularly for designs related to coal mining engineering.

Qinshui coalfield is one of China’s important coal production bases, with the main coal mining areas concentrated in Yangquan, Lu'an, Jincheng, and other regions of Shanxi Province, mainly mining the 3# and 15# coal seams. In recent years, with the expansion of mining scope and depth, geological and production conditions have been continuously changing, and the stress environment of the surrounding rock in the mine tunnels has shown new patterns. This study attempts to explore the type and magnitude of the in situ stress field in the main 3# and 15# coal seams of the Qinshui coalfield, the distribution characteristics of the horizontal principal stress direction, the variation laws of the principal stress values, the ratio of the maximum horizontal principal stress to the vertical stress, the horizontal stress difference, and the ratio of the average horizontal principal stress to the vertical principal stress with burial depth. This is of great significance for revealing the deformation and failure mechanism of the surrounding rock of the tunnel, optimizing the layout of mining and excavation projects, and guiding the control of the surrounding rock.

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy restrictions.

The author(s) declare(s) that there is no conflict of interest regarding the publication of this paper.

This work was supported by the Science and Technology Innovation Fund Project of CCTEG Coal Mining Research Institute(KCYJY-2023-MS-09, KCYJY-2025-MS-07) and National Natural Science Foundation of China (42372297,52174080).

Financial support for this work, provided by the Science and Technology Innovation Fund Project of CCTEG Coal Mining Research Institute(KCYJY-2023-MS-09, KCYJY-2025-MS-07) and National Natural Science Foundation of China (42372297,52174080). The authors would like to express their gratitude to EditSprings (https://www.editsprings.cn) for the expert linguistic services provided.