1 Introduction

Steeply dipping coal seam refer to coal seams with burial angles ranging from 35 to 55°, widely distributed in major mining areas in China. Their reserves are approximately 180–360 billion tons and production is approximately 150–300 million tons, accounting for 10% to 20% and 5% to 8% of the national coal reserves and production, respectively. More than 50% of steeply dipping coal seams are high-quality coking coal and anthracite coal (Wu et al. 2023, 2020), which are rare coal types for protective mining in China, and most of them are thick and extra thick coal seams, The full height method of comprehensive mining can improve the extraction efficiency of thick coal seam resources with steeply dipping angles. With the increase of mining height, the migration space of surrounding rock in stope increases, the characteristics of roof failure and migration are more active, and the phenomenon of roof caving and impact increases obviously. The essence of this process is the coupling process of surrounding rock stress and overburden rock migration. The change of surrounding rock stress causes overburden rock migration, and overburden rock migration leads to the evolution of surrounding rock stress. Therefore, it is particularly important to reveal the mechanical mechanism and motion law of overlying strata fracture with steeply dipping and large mining height.

In the mining of steeply dipping coal seams, due to the gravity dip effect, the roof strata not only move in the direction of vertical rock layers (similar to horizontal coal seam mining), but also move in the direction of parallel rock layers, resulting in a “temporal” and “asymmetric” deformation and failure process of the roof (Xie 2023; Xie et al. 2018; Wu 2024; Wang et al. 2015). Numerous scholars have adopted methods such as physical simulation experiments, theoretical analysis, numerical calculations, and on-site measurements to study the asymmetric deformation and failure motion laws of overlying strata with steeply dipping and high mining heights from different perspectives (Tu 2014; Xie et al. 2023a, b, c, d; Wang 2021; Chai et al. 2019; Zhen et al. 2023), the distribution characteristics and distribution patterns of surrounding rock stress (Xie 2023; Luo et al. 2022a, b; Pang 2020), and the stability control mechanism of the “support surrounding rock” system (Xie 2021; Yang et al. 2020; Wang 2017; Xie et al. 2023a, b, c, d) Research and exploration have been carried out on the formation mechanism of surrounding rock disasters in working faces such as coal wall fragmentation (Zhang 2019; Yang et al. 2019) and floor sliding (Luo 2018), and targeted prevention and control measures have been proposed, which has promoted the continuous progress of theory and technology in mining steeply dipping coal seams and laid the foundation for further research. However, the spatial fracture evolution characteristics and fracture mechanism of overlying strata in steeply dipping and high mining areas are not yet clear.

Therefore, based on existing research work, this article takes the steeply dipping and large mining height working face as the engineering background. Based on using similar simulation experiments to study the evolution law of the surrounding rock structure in the steeply dipping and large mining height mining area, a combination of numerical calculation and theoretical analysis research methods is used to analyze the characteristics of the overlying rock migration fracture and mining stress field evolution under the dip angle effect in the large mining height mining area. The mechanical analysis method was used to elucidate the stress transmission path caused by mining and the influence of thick and hard rock layers represented by the key layer of the staircase on the stress distribution and fracture process of the overlying rock group. The research results have a certain theoretical reference value for the study of the mechanism of instability and disaster caused by surrounding rock in steeply dipping mining areas and the control of roof stability.

2 Engineering background

The 2130 coal mine of Xinjiang Jiaomei Group is located in the western part of the Aiweiergou mining area, and its administrative division belongs to the Daban urban area of Urumqi City. The area of the well field is about 10.5km2, with a designed production capacity of 900,000 t/year. The working face is located in the 5th coal seam of the second mining area, with high mountains and gullies on the surface, distributed in a narrow and elongated pattern from east to west, high in the west and low in the east. The design of the working face has a length of 2098 m and a dip length of 100 m. The geographical location of the mining area is shown in Fig. 1.

Fig. 1
figure 1

Geographical location of mining area

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The average thickness of the 5# coal seam is 5 m, the local maximum thickness is 7 m, and the coal seam dip is 42–51°, with an average of 45°. The coal seam is weak and loose, and the hardness coefficient of coal f = 0.3–0.5. Unit weight 1.35t/m3. The immediate roof is grey-white gravelly coarse sandstone with a thickness of 2.4 m. It is mainly quartz, with strong weathering resistance but layer development of grey-white medium sandstone, a thickness of 16.2 m, which is a hard roof. The floor is coarse sandstone with a thickness of 17 m. The comprehensive mechanized large mining height mining method is adopted, the roof is managed by all caving methods, and the mining height is 4.5 m. The comprehensive column of the coal seam roof and floor is shown in Fig. 2.

Fig. 2
figure 2

Coal seam roof and floor histogram

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3 Rock mechanics test and physical simulation experiment

3.1 Rock mechanics test

The roof and floor rock blocks obtained from field exploration were processed into a cylindrical standard sample with a diameter of 50 mm and a height of 100 mm. The uniaxial compression test and splitting test are carried out by using the HCT605A electronic universal test system. The mechanical parameters such as uniaxial compressive strength, elastic modulus, Poisson's ratio and tensile strength of the sample can be obtained. The failure mode of the main roof specimen in the uniaxial compression test is shown in Fig. 3. The stress–strain curve of the main roof specimen in the uniaxial compression test is shown in Fig. 4. Under the action of axial compressive stress, the specimen produces transverse tensile stress. When the transverse tensile stress exceeds its tensile limit, the specimen is destroyed. The uniaxial compressive strength of the main roof specimen is 79.9–100.2 MPa, the average elastic modulus is 1.2GPa, and the average Poisson’s ratio is 0.31. The specific physical and mechanical parameters of coal rock are shown in Table 2.

Fig. 3
figure 3

Failure mode of main roof specimen in uniaxial compression test

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Fig. 4
figure 4

Stress–strain curve of main roof specimen under uniaxial compression test

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3.2 Physical simulation experiment of similar materials

To investigate the spatiotemporal evolution of surrounding rock deformation and failure during mining with steeply dipping, physical similarity simulation experiments were carried out. The experimental model was selected as a vertical combined model frame independently designed and developed by Xi 'an University of Science and Technology. The size of the experimental model was as follows: length × width × height = 1500 mm × 600 mm × 1500 mm. According to the geological conditions of the mining area and the size of the experimental model, the geometric similarity ratio of the model was determined to be 1:20, the stress similarity constant was 32, and the bulk weight similarity constant was 1.6. River sand was selected as aggregate, gypsum and calcium carbonate as cementing materials, mica was used to simulate stratification, and the ratio of similar materials in the physical model was shown in Table 1. The high-precision sensor was installed on the hydraulic support to monitor the load of the pillar, and the fracture shape and evolution process of the roof were recorded by taking photos. The experimental model is shown in Fig. 5.

Table 1 Ratio of similar materials
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Fig. 5
figure 5

Physical similar material model

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3.3 Failure and migration characteristics of surrounding rock

The experiment adopts the method of internal mining of the model. The bearing plate is pushed inward by the jacks on the top and both sides of the test bench, and the vertical and horizontal directions of the model are continuously loaded. The average bulk density of the surrounding rock is γ = 25kN/m3, and the lateral pressure coefficient is 0.5. The vertical stress load of 0.06 MPa is applied on the top of the model, and the horizontal stress is 0.03 MP. The simulated formation depth is 80 m. The characteristics of surrounding rock failure and migration under the influence of mining in steeply dipping angle working face are studied.

Figure 6 shows the fracture evolution characteristics of the roof structure of the stope with steeply dipping and large mining height. The open-off cut is excavated from top to bottom, and the supports are installed in turn, as shown in Fig. 6a. It can be seen from the figure that during the initial mining of the working face, the immediate roof caving, the caving gangue sliding filling, forming a non-uniform filling belt behind the support. The main roof of the middle and upper part of the region has a split layer crack, and the crack does not have the bearing capacity, forming a roof bearing arch, the arch is in the middle and upper part of the dip, the upper arch foot is on the side of the return airway, and the lower arch foot is on the side of the transport roadway, as shown in Fig. 6a,b.

Fig. 6
figure 6

Fracture evolution characteristics of surrounding rock; a Advance 5 cm; b Advance 15 cm; c Advance 40 cm; d Advance 60 cm

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As the working face continues to advance, the main roof rock formation breaks down. The gangue filling in the lower area is dense, which supports the overlying strata, and the main roof of this area is stable. The cracks in the middle and upper part continue to expand and extend, the roof collapses in a large area, and the collapsed rock blocks completely separate from the unfractured rock mass, forming a large-scale cavity. The lower roof forms a triangular overhanging roof structure, the middle fault line develops parallel to the rock layer, the upper fault line develops horizontally, and finally forms a multi-step key layer, the lower layer is lower, and the middle and upper layer is higher. The broken rock blocks are stacked and hinged with each other to form an inclined masonry structure, which forms a collaborative bearing structure with the roof of the multi-step key layer, and jointly controls the overall stability of the stope, as shown in Fig. 6c.

Along the trend from bottom to up, the stability of the multi-step roof decreases, and the middle and upper areas form an unstable anti-trend stacking structure, which is easy to have impact of hanging roof. The arch of the roof bearing arch evolved toward the high rock layer, and the upper arch foot and lower arch foot further shifted toward both sides of the roadway, as shown in Fig. 6d.

At the position 10 cm above the coal seam on the surface of the model, a survey line is arranged along the inclined parallel direction of the coal seam, and the evolution law of surface displacement of surrounding rock under different advancing distances can be obtained, as shown in Fig. 7.

Fig. 7
figure 7

Displacement evolution law of surrounding rock

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With the increasing of the advancing distance, the displacement of surrounding rock increases gradually, and the peak position migrates from the middle and upper part of the dip to the middle area. When the advancing distance of the working face is 20 cm, 35 cm and 50 cm, the peak displacement value is 1.08 cm, 5.72 cm and 7.21 cm respectively, and the peak position distance from the upper-end position is 15 cm, 49 cm and 45 cm respectively. When advancing 20 cm, the roof is damaged in the upper area, the degree of damage is small, and only the separation cracks are produced. When advancing 35 cm, the breaking range extends to the middle, the main roof breaks for the first time, and the peak displacement of the roof is in the middle of the working face. When advancing 50 cm, the main roof breaks again, and the breaking range becomes larger. Under the action of the lower filling gangue, a multi-stage stepped roof structure is formed, and the damage range migrates to the middle and upper parts.

3.4 Dynamic load characteristics of the support

In the process of roof separation, breaking and caving, the support resistance of the support reflects the instability characteristics of the roof well. Figure 8 shows the relation between support resistance and advancing distance of working face support.

Fig. 8
figure 8

Relationship between support resistance and advancing distance

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It can be seen that when advancing 5 cm, the resistance of 4 #, 5 #, 6 #, 7 # and 8 # supports in the middle and upper parts of the working face increases, and the resistance of 5 # support is the largest, indicating that the middle and upper roof is separated. The load of the roof is transmitted to the support, and the support resistance is increased. When advancing 10 cm, the resistance of the upper support decreases, while the resistance of the lower support increases, and the resistance of the lower support is the highest. It shows that the upper part of the roof has caved, but the lower part of the roof has not caved, but the range of separation is larger than the middle and upper part of the working face. When advancing 20 cm, the immediate roof is broken, the resistance of the middle support increases, and the lower part decreases. It shows that the collapse of the lower roof lags behind the upper roof. After advancing 30 cm, pressure occurs on the working face, and the pressure range is mainly inclined in the middle and upper part. After pressure, the resistance of the middle support decreases the most, followed by the upper support, and the lower support is unchanged. When advancing 40 cm, the resistance of the upper support decreases and the upper roof becomes unstable to pressure. When advancing 50 cm, the resistance of the middle support began to increase, and the resistance of the lower support decreased. It indicates that the lower roof is unstable and the middle roof begins to separate. When advancing 55 cm, the resistance of the middle support decreases, and the resistance of the lower and upper supports increases, indicating that the upper and lower roof of the working face forms a ladder overhanging roof structure.

Based on the relationship between the resistance of working face support and the advancing distance, it can be seen that the immediate roof and main roof fracture of the stope with steeply dipping and large mining height are both unbalanced and sequential. Due to the dip angle effect, the flexural deformation of rock strata in the middle and upper region is the largest, while the lower part is smaller than the upper part. With the advance of the working face, the gangue along the trend of non-uniform filling, roof failure presents a “middle-upper—lower” instability pressure sequence, and the middle and upper mine pressure development more severe than the lower part, and finally forms a multi-stage “step key layers” in the trend, and the pressure characteristics of different step ranges are obvious regionally.

4 Failure characteristics of surrounding rock and evolution law of stress field

4.1 Numerical calculation model

According to the geological data of the working face (Table 2), the 3DEC numerical calculation model of length × width × height = 200 m × 180 m × 200 m was established (Fig. 9). The working face length was 100 m.

Table 2 Mechanical parameters of coal rocks
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Fig. 9
figure 9

Numerical analysis model

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Vertical displacement constraints are applied at the bottom of the model, and horizontal displacement constraints are applied on the front, back, left and right sides of the model. A vertical load of 2 MPa was applied to the top of the model to simulate the formation depth of 80 m. The Mohr–Coulomb constitutive model is used, and the number of blocks and elements generated by the model is 22,512 and 249,501, respectively. According to the results of the field geological survey and rock mechanics test, the mechanical parameters of coal rock are determined. The working face is advancing along the positive direction of the y-axis, and the deformation failure and stress evolution characteristics of the roof of the large mining height working face are analyzed when the dip angles are 35°, 45° and 55° respectively.

4.2 Roof deformation and failure characteristics

It can be seen from Fig. 10a,b,c that in a stope with steeply dipping and large mining height, the broken roof forms a “multi-step key layer” roof structure with cross-horizon, large-scale and asymmetrical steps. The lower ladder structure is in the lower part, the level is low and stable; In the middle and upper part of the working face, the upper level of the ladder structure is higher, and the vertical distance from the floor is the largest. Inside the failure envelope, the roof-broken rock blocks are stacked and hinged to form an inclined masonry structure, see Fig. 10a.

Fig. 10
figure 10

Evolution characteristics of inclined roof failure; a 35°; b 45°; c 55°

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From the lower to the upper area along the tendency, the cambium level of the masonry structure gradually increases, but its stability and supporting effect on the undamaged overlying rock layer gradually weaken. Especially in the middle and upper part of the tendency, the masonry structure is hinged across layers and staggered layers, forming a reverse inclined stacking structure, and forming a void between the undamaged overlying rock layer. The inclined masonry structure and the multi-step key roof form a cooperative bearing structure, which jointly controls the overall stability of the stope, see Fig. 10b.

Affected by the failure migration and unloading effect of the roof rock mass, the roof strata outside the failure envelope surface formed an asymmetric arch shell rock mass structure. Along the trend from bottom to top, the cambium level of the roof arch shell structure gradually increases and its stability gradually weakens. When the dip angle is 35°, 45°, and 55°, the caving zone height is 29.6 m, 23.2 m, and 17.4 m; With the increase of dip angle, the stability of the inclined masonry structure and the high ladder rock layer in the middle and upper areas decreases, and the instability of the “high ladder rock layer” is easy to induce the “inclined masonry structure” to fracture at the same time, forming impact pressure, as shown in Fig. 10c.

Along the strike direction, the overall outline of the broken rock stratum presents a trapezoidal symmetry on both sides, see Fig. 11a. And the unbroken rock block on the side of the working face and the side of the cut eye is in the shape of a ladder, forming a cantilever beam structure, which is hinged and extruded with the broken block to form an unstable masonry structure, as shown in Fig. 11b. When the dip angle is 35°, 45° and 55°, the caving heights are 35.5 m, 31.3 m and 27.6 m, respectively. With the increase of dip angle, the caving height of the roof decreases gradually, the stability of the low-layer masonry structure decreases, the high-layer roof is prone to shear fall, and the probability of instability increases, see Fig. 11c.

Fig. 11
figure 11

Evolution characteristics of strike roof failure; a 35°; b 45°; c 55°

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Under the influence of the gravity dip effect, asymmetric fracture occurs in the main roof strata of steeply dipping stope. The roof caving in the upper area is obvious, forming a large number of shear and tensile failure zones, the roof displacement is the largest, and the caving range extends to the outside of the goaf. A V-shaped fracture track was formed in the middle, which was in the shape of the ladder and migrated from the middle to the lower part, see Fig. 12a. In the lower area, the rock strata have the smallest tensile failure, the roof is relatively complete, and a triangular overhanging roof structure is formed, extending from the lower part to the middle and upper part, forming a constraint effect on the overlying rock strata. With the continuous advance of the working face, the triangular area of the overhanging roof is increased, and the overhanging roof structure is broken in the next cycle, which also leads to the timing of pressure in the steeply dipping stope, as shown in Fig 12b.

There are a lot of cracks between the roof, and criss-crossing. The broken main roof is hinged with the unbroken rock block to form the inclined masonry structure along the dip and strike. With the increase of the dip angle, the damage degree of the main roof increases, the movement amplitude and activity of the broken rock block in the middle and upper part increase significantly, the local “X” shape cracks increase, and the breaking range has exceeded the goaf range and expanded to the side of the return airway. The regional characteristics of the three-dimensional stacking and hinged structure formed by the broken roof become more and more obvious, the stability decreases, and regional unbalanced instability is easy to occur, see Fig. 12c.

Fig. 12
figure 12

Evolution characteristics of main roof failure; a 35°; b 45°; c 55°

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4.3 Evolution characteristics of stress field of surrounding rock of stope

After coal seam excavation, the stress of the roof strata changes obviously, and the trend distribution characteristics of the maximum principal stress field of the roof strata under different dip angles are shown in Fig. 13. The trace line of maximum principal stress in the roof strata is asymmetrically arched, and stress release occurs in the roof strata above, see Fig. 13a, the minimum principal stress is 0.18–0.23MPa. The upper and lower arch feet form stress concentration, and the maximum principal stress is 13.1–13.9MPa. Under the influence of the dip angle effect, roof caving gangue tends to fill the goaf along a non-uniform trend, resulting in full roof caving in the middle and upper areas, and the isocontour of roof stress shifts to the middle and upper areas, and the roof stress release area in the middle and upper areas is larger than that in the lower areas, as shown in Fig. 13b. The centre axis of the stress contour of the floor is offset, and the floor is prone to slip failure in the lower part of the working face. With the increase of dip angle, the height of the stress arch decreases gradually, the stress vault is tilted upward, and the asymmetry of the stress arch becomes more and more obvious, see Fig. 13c.

Fig. 13
figure 13

Distribution characteristics of inclined principal stress field (Unit: Pa); a 35°; b 45°; c 55°

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Along the strike, the principal stress field of the wall rock of the stope presents a symmetrical arch distribution, see Fig. 14a, and the stress release range of the roof is larger than that of the floor, which forms a stress concentration in the front and rear coal walls, see Fig. 14b. With the increase of dip angle, the range of the stress release zone of roof and floor shrinks, the height of stress arch decreases gradually, and the stress release degree of low rock strata increases, as shown in Fig. 14c.

Fig. 14
figure 14

Distribution characteristics of strike principal stress field (Unit: Pa); a 35°; b 45°; c 55°

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As can be seen from Fig. 15, the stress value is the lowest in the middle and upper part of the main roof, and the width of the low-stress zone decreases from top to bottom, forming a low-stress zone with wide upper and narrow lower. When the middle and upper main roof reaches the ultimate strength, it collapses. According to the stress trace in the low-stress zone, the fracture trace of the roof can be obtained, and a stepped V-shaped fracture line can be formed. The stress trace extends from the upper to the middle and lower areas, as well as the leading roof area.

Fig. 15
figure 15

Distribution of the main roof principal stress field (Unit: Pa); a 35°; b 45°; c 55°

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After the fracture of the middle and upper roof, the stress is transferred to the non-caving area, forming a high-stress concentration area around it. The main roof of the lower part forms a triangular overhanging roof, and the high stress in the overhanging roof area is transferred to the leading roof of the working face. The larger the area of the overhanging roof, the higher the elastic energy of accumulation and the dynamic pressure of energy accumulation is easy to appear. With the increase of the dip angle, the length and width of the stress release zone shorten, the asymmetric characteristics of the stress track become more obvious, the stress release zone gradually moves upward, the stress concentration range gradually shrinks, but the stress concentration value gradually increases, up to 12 MPa.

5 Overburden fracture mechanism

5.1 Stress transfer path and rock fracture track

Combined with physical simulation and numerical calculation, it can be seen that the non-equilibrium fracture migration of the broken rock in the roof of the steeply dipping stope leads to the change of the stress transfer characteristics of the roof, and the stability of the spatial ladder roof structure decreases from the bottom to the top. According to the first strength theory, the main reason for the fracture of brittle materials such as rocks is the maximum principal tensile stress, and the rock layer will break along the direction perpendicular to the principal tensile stress. Therefore, analyzing the arch distribution mechanism of mining stress field in steeply dipping stope can reveal the relationship between rock principal stress and rock fracture, and has an important guiding role in analyzing the crack propagation and fracture track of roof rock beam in steeply dipping stope.

Based on the results obtained from the numerical calculation, Fish language was used to post-process the numerical calculation model (Luo 2022). In the model, along the middle area of the working face tendency, the middle area of the strike, and the middle area of the normal main roof, the survey surfaces are arranged respectively, the calculation results were post-processed in combination with the elastic–plastic theory, the spatial distribution form of the principal stress trace was extracted, and the envelope diagram of the stress trace was drawn. The evolution characteristics of the mining stress transfer path and the fracture path of rock strata in the surrounding rock of the stope with steeply dipping and large mining height are comprehensively analyzed.

According to the elastic theory, the stress characteristic equation of coal rock mass is as follows:

$$\left| {\begin{array}{*{20}c} {\sigma_{{\text{x}}} - \sigma_{i} } & {\tau_{xy} } & {\tau_{xz} } \\ {\tau_{yx} } & {\sigma_{y} - \sigma_{i} } & {\tau_{yz} } \\ {\tau_{zx} } & {\tau_{zy} } & {\sigma_{z} - \sigma_{i} } \\ \end{array} } \right| = 0$$
(1)
$$\sigma_{i}^{3} - {\text{K}}_{1} \sigma_{i}^{2} + {\text{K}}_{2} \sigma_{i} - {\text{K}}_{3} = 0$$
(2)

Parameters K1, K2 and K3 in the above formula are respectively:

$$\begin{gathered} {\text{K}}_{1} = \sigma_{{\text{x}}} + \sigma_{y} + \sigma_{z} \hfill \\ {\text{K}}_{2} = \sigma_{{\text{x}}} \sigma_{y} + \sigma_{y} \sigma_{z} + \sigma_{z} \sigma_{{\text{x}}} - \tau_{xy}^{2} - \tau_{yz}^{2} - \tau_{zx}^{2} \hfill \\ {\text{K}}_{3} = \sigma_{{\text{x}}} \sigma_{y} \sigma_{z} - \sigma_{{\text{x}}} \tau_{yz}^{2} - \sigma_{y} \tau_{zx}^{2} - \sigma_{z} \tau_{xy}^{2} + 2\tau_{xy} \tau_{yz} \tau_{zx} \hfill \\ \end{gathered}$$
(3)

Combined with the above formula and parametric equation, three principal stresses s1、s2 and s3 of coal and rock mass can be obtained, and the results are as follows:

$$\sigma_{i} = \frac{{{\text{K}}_{1} }}{3} + \sqrt {\frac{ - 4}{3}\left( {{\text{K}}_{2} - \frac{1}{3}{\text{K}}_{1} } \right)} \cos \left( {\frac{\varphi + 2k\pi }{3}} \right),k = 0,1,2$$
(4)
$$\varphi = \arccos \{ \frac{{{\text{K}}_{3} + 2\left( {\frac{{{\text{K}}_{1} }}{3}} \right)^{2} - \frac{{K_{1} K_{2} }}{3}}}{{2\sqrt { - \left[ {\frac{{\left( {K_{2} - \frac{1}{3}K_{1} } \right)}}{3}} \right]^{8} } }}\}$$
(5)

Stress arch is the deflection of stress transfer to resist deformation after the rock is stressed and deformed. It is a phenomenon that the rock is self-regulated to achieve self-stability under the action of load. Along the dip, after coal seam mining, the track line of the maximum principal stress s1 (compressive stress) in the rock layer presents an asymmetric arch distribution along the dip, the track line of the minimum principal stress s3 (tensile stress) presents an asymmetric reverse arch shape, and the track line of the rock layer breaking presents an asymmetric step shape, but the range is smaller than the maximum principal stress arch.

Under the influence of the coal seam dip angle, the stress deflection boundary (the critical curve where the principal stress direction does not deflect) is generated in the roof stratum of the steeply dipping stope. With the reduction of the roof level, the stress deflection boundary migrates from the left side of the central axis to the right side, resulting in the asymmetric deflection of the roof stress transfer path. Then the inclined asymmetric stress arch is formed. Outside the maximum principal stress arch (compressive stress), the overlying rock load of the roof tends to transfer to the coal body on the upper and lower side of the working face, the principal stress value increases and the direction shifts to both sides of the stress deflection boundary, resulting in stress concentration phenomenon, as shown in regions B and C in Fig. 16a. In the interior of the stress arch, especially in the fracture track line, an obvious stress release zone is formed, the principal stress value is greatly reduced, and the roof of the low rock layer in the upper area changes from bidirectional compression to bidirectional tension, as shown in region A of Fig. 16a.

Fig. 16
figure 16

Stress transfer path and rock fracture track line

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Along the strike, the trace line of the maximum principal stress presents a symmetrical arch distribution, and the front and back arch feet are located on the coal body on both sides of the strike of the goaf. The trace line of minimum principal stress (tensile stress) is a symmetrical reverse arch, and the fracture trace line is asymmetric “八” shape, and the range is smaller than the maximum principal stress arch. The overlying rock load outside the maximum principal stress arch not only transfers to the coal body in front and behind the working face, but also transfers to the coal body on the upper and lower sides of the working face. The closer to the working face, the more loads transferred to the coal body in front and behind the working face, and the less transferred to the coal seam on the upper and lower sides of the tending. In other words, the closer to the working face, the greater the increase of the maximum principal stress and the direction deflection angle, as shown in regions B and C in Fig. 16b; In the interior of the stress arch, especially in the fracture track line, a stress release zone is formed, and the principal stress value decreases significantly and the direction changes obviously, as shown in region A in Fig. 16b.

Along the normal direction of the coal seam, in the roof stress release area above the goaf, the main roof rock changes from the original rock stress state of three-direction compression to single and bidirectional tension, and some areas even become three-direction tension state, the stress value is greatly reduced and the direction is deflated. In the stress concentration area around the stope, the three-direction stress state of the roof also changes obviously, the principal stress value increases greatly, and the direction deflection degree is obvious. From the centre of the goaf to the surrounding area, the principal stress increases first and then decreases, in which the first principal stress changes the most, and the third principal stress changes the second. Numerically, the first principal stress increases first and then decreases, the second principal stress continues to decrease, and the third principal stress slightly increases, as shown in Fig. 17.

Fig. 17
figure 17

Stress evolution characteristics of main roof

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When the coal seam dip angle is 35°, 45°and 55°, the arch height of the principal stress arch is 53.2 m, 45.9 m and 38.4 m respectively, and the distance between the projection position of the vault in the direction of the vertical coal seam and the coal body on the upper side of the dip is 12.7 m, 4.4 m and − 4.8 m respectively (negative values indicate that the projection position of the vault is on the coal body on the upper side of the working face). With the increase of coal seam dip angle, the stress transfer of surrounding rock is unbalanced, the range of stress release area of the asymmetric arch decreases obviously, and the position of the arch tends to move upward to the working face. The principal stress arch and the fracture path of rock strata also decrease, and at the same time, they tend to develop towards the upper part of the working face, as shown in Fig. 18.

Fig. 18
figure 18

Principal stress track evolution

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5.2 Mechanism of influence of key strata on mining stress field of overburden rock

According to the key layer theory, when there are multiple rock layers in the overlying rock layer of the stope, the rock layer that controls the activity of the rock mass completely or partially is called the key layer. Among them, the middle sandstone represented by the basic roof has a large thickness, large elastic modulus and high strength, and the overlying rock strata sink synchronously and harmonically, and exist in the form of plates or beams before breaking, as the main bearing body of the rock strata in the stope.

It is assumed that the overlying rock of stope contains m layers, and n layers are deformed (n ≤ m) during mining, and the thickness of each layer is hi(i = 1,2,3,… m). Considering that the shear resistance on the intermediate surface of layered rock mass is weak, according to the composite beam analysis theory (Qian et al. 2021), the following results are obtained:

$$M_{i} (x) = E_{i} I_{i} \frac{M(x)}{{\mathop \sum \limits_{i = 1}^{n} E_{i} I_{i} }}$$
(6)

According to the calculation formula of maximum normal bending stress (Lou 2019; James et al. 2009), it can be obtained:

$$\left( {\sigma_{\max } } \right)_{i} = \frac{{M_{i} (x)}}{{I_{i} }}\left( {y_{\max } } \right)_{i}$$
(7)

By substituting formula (6) into formula (7), we get:

$$\left( {\sigma_{\max } } \right)_{i} = \frac{{M_{i} (x)}}{{I_{i} }}\left( {y_{\max } } \right)_{i} = E_{i} I_{i} \frac{M(x)}{{\mathop \sum \limits_{j = 1}^{n} E_{j} I_{j} }}\frac{1}{{I_{i} }}\frac{{h_{i} }}{2} = \frac{1}{2}\frac{M(x)}{{\mathop \sum \limits_{j = 1}^{n} E_{j} I_{j} }}E_{i} h_{i}$$
(8)

As can be seen from the above formula, for the same stratum group, \(\frac{M(x)}{{\mathop \sum \limits_{j = 1}^{n} E_{j} I_{j} }}\) is a constant, and the maximum bending normal stress of each stratum is only related to the parameter \(E_{i} h_{i}\) of the stratum itself, namely:

$$\left( {\sigma_{\max } } \right)_{i} \propto E_{i} h_{i}$$
(9)

It can be seen that the maximum bending normal stress of each rock layer is directly proportional to the thickness hi and elastic modulus Ei of the rock layer itself. The greater the stiffness and thickness of the rock layer, the greater the maximum normal stress. Therefore, in the same stratum group, the thick hard stratum represented by the key stratum has higher stress in bending deformation than the stratum with small thickness and low elastic modulus. After the rock stratum is broken, the fracture track line is in the shape of asymmetric steps, and the multi-step key layer and the inclined masonry structure form a cooperative bearing structure, which continues to be the main bearing body of the stope.

To further study the influence of the step key layer on the evolution of mining stress field of overburdened rock, Fish language is used to extract the maximum principal stress σ1 of each zone element after mining, and compare it with the principal stress σ1 of the initial equilibrium state respectively, then obtain the maximum principal stress ratio of each zone element. By drawing the ratio σ1 cloud map, the zonal evolution characteristics of the principal stress field of overlying strata can be directly reflected, as well as the influence mechanism of the stepped key layers on the evolution of the macro stress field.

After the initial equilibrium of the model, the distribution of the principal stress field is shown in Fig. 19. In the range of z = {0, 320}, the maximum principal stress shows a non-equilibrium decreasing trend along the height direction, σ1 = 2–10 MPa, along the same height direction, the maximum principal stress is basically the same.

Fig. 19
figure 19

Initial principal stress distribution of the model

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Figure 20 shows the cloud map of the ratio of principal stress to the centre of the stope at 100 m advance. According to the lithology of the overlying rock and the characteristics of its location, the maximum principal stress field of the overlying rock shows the characteristics of zonal evolution:

Fig. 20
figure 20

Inclined principal stress ratio distribution

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In the goaf and the area near the roof and floor, ratio σ1 = {0, 1} belongs to the stress reduction zone. The ratio σ1 in the upper and lower end and its adjacent areas is greater than 1, which belongs to the stress rise zone.

The distribution of stress ratio in different regions of the stress reduction zone is obviously different, and the stress reduction in the caving area is the largest, the stress ratio is the smallest 0.1, and the stress ratio of the hard rock above the caving area is significantly higher than that of the former. To reflect this regional difference, according to the distribution pattern of the goaf range and stress ratio cloud map, the dividing line is ratio σ1 = 0.5 and 1, respectively. The overburden stress field can be divided into three regions from the inside out, namely, σ1 relief zone, ratio σ1 = {0, 0.5}, including the caving zone range. The area near the roof and floor is the σ1 reduction area, ratio σ1 = {0.5, 1}; The upper and lower ends and their adjacent areas are the areas where σ1 increases, and the ratio σ1 is greater than 1.

The rock mass in caving zone of goaf is broken, and the stress relief range is the largest. The multi-step key layers and the rock formations controlled by them are stress reduction zones. The thick hard rock layer represented by the key layer is the link connecting the relief zone with the stress reduction zone and the stress rise zone. Due to the control effect of the step key layer and the formation of the stress transfer structure after fracture, its own principal stress is obviously higher than that of the neighbouring layer, and the two ends transfer loads to the neighbouring area and the stress rise zone in the form of arch feet.

The maximum principal stress σ1 of each zone element is extracted from the section along the direction of the parallel coal seam, and the cloud map of the principal stress ratio of the thick and hard main roof can be obtained, as shown in Fig. 21. As can be seen from the figure, the stress at the upper area has the largest reduction, and the stress ratio is 0.1. From the upper area to the lower, the stress ratio gradually increases (0.1 → 0.2 → 0.3 → 0.5), and the isocontour of the stress ratio extends downward in a step-like track line. From inside the goaf to around the stope, the stress ratio first increases and then decreases (0.1 → 0.5 → 1 → 1.3 → 1).

Fig. 21
figure 21

Ratio distribution of the main roof principal stress

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The main roof stress field is divided into three areas from the inside out, namely, σ1 relief area, ratio σ1 = {0, 0.5}, including the middle and upper roof broken area. The lower overhang area and triangular overhang structure are σ1 reduction zone, ratio σ1 = {0.5, 1}; The area around the stope is an increasing area of σ1, with ratio σ1 > 1.

The triangular overhanging roof area in the lower part of the stope is used as a stress transfer structure, and the high stress is transferred to the leading roof. With the advance of the working face, the area of the overhanging roof increases gradually, and the structure of the overhanging roof breaks periodically.

From the above analysis, it can be seen that in steeply dipping and large mining height mining areas, asymmetric overlying rock stress arch shells are formed in the mining area due to the influence of the gravity dip angle effect. The top of the shell is in the middle and upper part of the inclination, and the base of the shell is in the surrounding coal bodies. In the stress arch shell, the rock layer produces a large number of separate layer-bending phenomena, resulting in the rock layer being in a state of tension, stress release and instability of the rock layer. In the stope, a multi-level “step key layer” structure with cross-layer migration is formed, and the step key layer and its controlled rock group form a stress transfer structure, which acts as the connection link between the broken inclined masonry structure and the stress arch shell. The triangular hanging area in the lower part of the thick and hard main roof serves as a stress transfer structure, transmitting the accumulated stress to the leading roof.

In the outer part of the stress arch shell, the load of overlying strata is transferred to the surrounding shell base, the principal stress of surrounding rock increases and the direction is deflected. The stress path of surrounding rock is not evenly transferred and evolves in stope space, resulting in different roof stress environments and load history in different regions. The deformation and failure of the roof have obvious regional characteristics, and the fracture and pressure characteristics of multi-step key layers also have temporal characteristics, resulting in extremely complex load and instability characteristics of support. And this phenomenon will be more serious with the increase of coal seam dip angle, mining height and other factors.

6 Field monitoring

To grasp the distribution characteristics of mine pressure in the working face, the test areas are arranged in the upper, middle and lower areas of the tendency, and the KJ377 mine pressure dynamic monitoring system is used to continuously record the load on the front and rear columns of the support. In addition, a CMS 3D laser scanner was used to conduct 3D scanning detection of goaf, master the basic data of the three-dimensional form of goaf and gangue filling, analyze the working resistance of supports in different regions, and reflect the fracture instability process of overlying rocks from the side based on the above stress evolution characteristics of overlying rock fracture instability, providing a basis for the prediction of roof pressure and dynamic disasters.

The monitoring results show that the regional characteristics of the support are obvious under the influence of the dip effect. The average working resistance of the support in the working face, upper middle and lower areas is 4985 kN, 6422 kN and 3505 kN, respectively, and the maximum working resistance is 6481 kN, 7546 kN and 5400 kN. The standard deviations of working resistance were 1088.07 kN, 1358.17 kN and 767.12 kN, respectively. The load ratio of the front column and the rear column in the inclined upper, middle and lower areas is 51.2%, 108.8% and 88.9%, respectively. The load state of the support is variable and the range is large, and the stability of the support is poor, as shown in Fig. 22.

Fig. 22
figure 22

Field measurement of support working resistance

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It can be seen that under the unbalanced load and constraint of the roof, the average working resistance and dispersion degree of the support show the basic characteristics of the largest in the middle, the second in the upper part and the smallest in the lower part, and the pressure strength in the middle and upper part is larger, which can also explain the stress characteristics and instability fracture process of the overburden rock in different areas of the stope space.

The pressure strength of the lower part of the working face is small and the step distance is large. The middle-pressure duration is long, and the support load exceeds the rated working resistance (6500kN) for a long time, resulting in the opening of the safety valve; The upper area is frequently pressured, the period is short, and there is an empty roof phenomenon, the support is easy to be affected by the impact of the roof, the tipping and extrusion between the supports, and the surrounding rock disaster is easy to occur. According to the field observation and goaf scanning cloud image, it can be seen that there are multi-step key layer structures in the middle and upper part of the mining tendency, and there are large-scale empty roof areas (Fig. 23), which verifies the regional distribution characteristics of overlying rock fracture structure and gangue filling in different areas of goaf in physical simulation and numerical calculation.

Fig. 23
figure 23

Field observation results

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7 Conclusion

  1. (1)

    Under the influence of gravity dip effect and increasing mining height, the stope with steeply dipping and large mining height forms a multi-step key layer roof structure with cross-layer migration, and the broken rock blocks are stacked and hinged with each other. A large scale cavity appeared in the upper region, and the peak displacement moved from the upper part of the dip to the middle part. The inclined masonry structure and the multi-step key layers form a cooperative bearing structure, which jointly controls the overall stability of the stope.

  2. (2)

    The principal stress field of overlying rock in steeply dipping stope presents the characteristics of zonal evolution, and the multi-step key layer is the stress transfer structure between the caving zone and the stress arch. The load of overlying strata tends to the upper and lower coal bodies and the front and rear coal bodies with the boundary of stress deflection, the track of tensile stress is inverted arch, and the fracture track of rock strata is asymmetrical ladder shape and “八” shape. With the increase of dip angle, the fracture range of the ladder and principal stress arch decreases, and the stress vault tends to shift upward.

  3. (3)

    In the upper area of the main roof, the fracture track extends to the outside of the goaf, the V-shaped ladder fracture track is formed in the middle, and the triangular overhanging roof structure is formed in the lower part. With the increase of dip angle, the height of the roof caving zone decreases, the movement amplitude and activity of the broken rock block in the middle and upper part increase, the local cracks increase, and the instability of the “high ladder rock layer:” is easy to induce the “inclined masonry structure” to fracture at the same time, resulting in regional unbalanced instability and forming impact pressure.

  4. (4)

    The non-equilibrium fracture in the three-dimensional space of the roof leads to obvious regional characteristics of the working resistance of the support and its dispersion degree and the load ratio of the front and rear columns, and the overall performance is inclined to the middle > upper > lower. The sliding, deformation and instability of the broken roof lead to the variable load of the support, the increased interaction between the supports, the stability of the “support-surrounding rock” system is reduced, and the surrounding rock disaster induced by dynamic instability is easy to occur.