Dip angle effect on the main roof first fracture and instability in a fully-mechanized workface of steeply dipping coal seams

The study of fracture and instability mechanism of the main roof in steeply dipping coal seams (SDCS) workface is crucial to the proper choice of support type and control of stability of surrounding rock, as well as the safe and effective mining in the coal seam. Based on the established SDCS main roof model, this study derived the stress distribution in the main roof under linear load, analyzed the dip angle effect associated with the evolving stress of SDCS workface, and elaborated the sequential characteristics of the ground pressure mechanism. Besides, an inclined unstable structure model of the main roof based on deformation, fracturing, and rotating of the main roof in the SDCS workface was also proposed here, which explained the impacts of overburden rock's key parameters on sliding and rotatory instability of rock mass. In light of the analysis of the movement rule of overburden rock and loading condition of support, it is found that, when the roof and floor in the workface are stable, the critical support resistance with the absence of sliding and rotating increases as the dip angle of coal seam increases, the roof is in the state of discontinuous movement due to its self-weight and overburden pressure. Support is affected by the discontinuous movement and moved along with the roof. The results of this study can be of theoretical reference to the control of SDCS.


Introduction
With a gradual reduction of coal resources and growing mining intensity, mining under complicated conditions has been increasing in recent years (Wu et al. 2014). In particular, steeply dipping coal seams (SDCS) are regarded as difficult for mining (Ye et al. 2017;Wu et al. 2010;Tu et al. 2019). However, with the development of fully-mechanized mining theories, advancing research of equipment, and improved management in the workface, SDCS with shallow depth has gradually become the main coal seam in western China's mining areas. For example, the Sichuan Coal Industry Group Ltd. has succeeded in the trial mining in the Lvshuidong coal seam with a dip angle of 70°. The rock pressure pattern in the SDCS workface is influenced by a dip angle, which results in a significant difference from coal seam with a low dip angle during mining (Kang et al. 2002;Shi et al. 2018). The available pressure control and technology theories focused on horizontal coal seams and coal seams with a shallow dip angle cannot guide the safe and efficient mining in SDCS. At present, roof falling, flying gangue in workface, and hydraulic support sliding are the major disasters in SDCS mining (Shan et al. 2020;Hu et al. 2017) and are all directly related to roof stability. Therefore, the study of roof failure and movement is the prerequisite for safe and efficient mining in SDCS (Zhang et al. 2018;Das et al. 2017).
Numerous field test results proved that mining in SDCS caused roof weighting in different zones in the workface, and the ground pressure became abnormal. Studies of fracturing in different zones in the roof of the SDCS workface were conducted by different researchers and were focused on the failure, migration, and evolution law of the workface roof (Wang et al. 2015b). Several studies performed the analysis of the fracturing pattern of the main roof in the workface and the relationship between the support-surrounding rock (Jiang et al. 2014). Establish a mechanical model of stope roof based on elastic theory, analyze the evolution characteristics of basic roof fracture, and obtain fracture forms in different periods (Wang et al. 2016;Cui et al. 2019). Based on the hinged rock block model, the limit position of the rotation instability of the hinged structure is studied, and the unique instability mode of the shallow-buried thin bedrock roof and the method for determining the working resistance of the support are proposed (Wang et al. 2015a). Based on the theoretical model of inclined coal seam stope, the stress distribution characteristics and fracture mechanism of basic roof strata during mining are analyzed (Zhang et al. 2010;Yang et al. 2013).
Based on beam and plate models, numerous researchers systematically investigated the fracture and evolution law of a roof in a fully-mechanized workface, improved the understanding of the main roof's first fracture, and refined the surrounding rock control theory. However, due to the complex characteristics of mines' geological conditions, it is difficult to fully and accurately reflect the fracture evolution law of the roof during mining in the coal seam and further study the dip angle effect on the kinematic movement law of overburden rock is highly demanded. Therefore, based on available findings, this study utilized a theoretical analysis method and elaborated a mechanical model of the main roof in SDCS to investigate the effect of dip angle on the first fracture of the main roof in a fully-mechanized workface. Thus, it determined the key factors controlling the surrounding rock stability. The results in this study provide theoretical reference for the effective preventive measures in mining.

Assumptions of the main roof mechanical model
According to the assumption of a thin plate (or a slender body) in the elasticity theory (Yang et al. 2013), an elastic plate can be treated as a thin plate if the ratio between its thickness h and length of its shortest side l satisfies the following conditions: Below the first-fracture mining pressure in the longwall workface in SDCS is reached, the main roof can be regarded as a thin plate since its thickness and length satisfy the above equation.
Hard hanging roof zone appears in the goaf rear area after mining in the workface. Usually, the narrow coal pillar side and fault side are treated as simple boundaries. The solid coal side is treated as a clamped boundary (Jiang et al. 2014), where deflection and rotation are zero.

Basic equations of thin plate
As mining advances from the open-off cut, the main roof's exposed area gradually increases, and fracturing happens when the stress reaches the stratum's ultimate strength. The main roof in the SDCS workface is supported by integrated coal before fracturing. Since the coal seam's dip angle is relatively large, the false and immediate roofs fall to the bottom of goaf as mining proceeds. Therefore, a mechanical model of the main roof in SDCS, as shown in Fig. 1, was elaborated in this study. Herein, the dip angle of the coal seam is α, the x-axis is directed along the workface strike with a length of a, the y-axis is along the workface dip with a length of b, and the z-axis is normal to the roof and has positive downward direction.
Due to the impact of dip angle, the load from overburden rock that acts on the roof can be simplified as P(y) that linearly changes along the dip (i.e., positive axis), which is expressed as: where γ is the average unit weight of the overburden rock and P0 is the overburden load in the roadway of workface. The later value, P0 , is decomposed into the force perpendicular to the roof denoted by 1 ( ) cos P P y   and the force parallel to the roof denoted by 2 ( ) sin P P y   . Since the latter force component P2 is much smaller than P1 within the dip angle range under study, its effect is neglected, and the deflection function of the main roof under the linear overburden load is written as: According to the principle of minimum potential energy (Yang et al. 2013), the total potential energy of a thin plate under the linear overburden load is: where P1 is the overburden load perpendicular to the roof, 1  is the deflection function of the main roof under linear overburden load, and μ is Poisson's ratio. 10 120 where D is the bending stiffness of the thin plate, Gangue filling in the goaf of SDCS is highly heterogeneous. Hence, the upper, middle, and bottom areas of the main roof have different stress states and kinematic movement patterns. It is assumed that falling gangue fills two-thirds of the total space of goaf of SDCS, the bottom area has good filling and is closer to the intact rock strength than the middle area, and the upper area has no filling, so a load of gangue filling on the main roof 3 P is derived as follows: According to the principle of minimum potential energy, the deflection function of the main roof under gangue filling is Using Eqs. (7) and (9)

Stress expression
Using the coefficient and the relation between deflection and stress in the theory of thin elastic plate, stresses in the SDCS main roof can be derived as follows:

Stress distribution in the main roof
During mining in the coal seam, when the roof's maximum tensile stress exceeds its tensile strength Meanwhile, in Fig.2 Hence, x  the main factor controlling the fracturing instability of the overburden rock, while the dip angle of the coal seam only changes the rock's tensile stress (i.e., the ultimate span of workface). When the maximum tensile stress reaches the tensile strength limit at a certain point in the thin rock plate, the tensile fracture occurs, and gradually thin rock plate evolves into spatial surrounding rock structure. Current studies show that when the tensile stress exceeds the shear stress, while the latter exceeds the compressive stress (σtensile < σshear < σcompressive), the tensile or shear failure is likely to take place in stratum, and the failure pattern is determined by its tension and shear strengths as well as the stress within the stratum (Yang et al. 2015). Therefore, the analysis of distributions of principal stress and shear stress on the main roof is of great significance. Relations between the roof stress components and principal stress, as well as shear stress, are described by the following equations. x y x y xy Equations (13) and (14)  The maximum shear stress distribution in the main roof with the same parameters is depicted in Fig. 4. The maximum shear stress max  occurs periodically in the upper-middle zone of the main roof in the SDCS longwall workface as mining is advancing, and it is large in the middle but small on both sides. Since rock has a very low tensile strength, failure is likely to occur in the bottom roof's upper-middle zone. Both sides of the long boundaries of the top roof, as well as the upper zone of the short boundary, and the failure in the middle zone of the bottom roof will develop toward the long boundaries. in the range 50°~60°, meaning that the dip angle has a weak effect on the roof stress in this range. The maximum shear stress max  exhibits the same evolution trend as the dip angle increases. The principal stress variation rate is defined by η, which turns out to be constant, meaning that max  and min  have the same variation rates for the same dip angle increments.

Slip instability of the main roof
Asymmetrical mechanical characteristics of the SDCS workface, as well as dip strata movements, are resulte d from the heterogeneous features of dip angle and g angue, and the lager the dip angle is, the more distin ct the asymmetrical features strata movement has (Hu et al. 2018).Strata movement undergoes "failure-fall ing-fracturing-settling-rotating" when exposed to c omplex stress state conditions.
As workface advances, the vertical and separation fractures occur in a certain range of overburden rock. The extrusion between rock blocks induces an asymmetrical hinged rock structure. It gradually develops into a macroscopic "shell" structure (Xie et al. 2009;Zhang et al. 2015;Xie et al. 2019). A typical rock block is subjected to the stress state shown in Fig. 6. The hinged structure is framed into the Cartesian coordinate system and satisfies the following mechanical equilibrium equations: Solving these equations, one can derive shear stresses R1 and R2 and the extrusion stress T   where  is the friction angle of the fractured rock block, which is usually taken as  =38~45°, tan =0.8~1 .
Lengths of hinged rock blocks are assumed to be the same, that is, 1 When the ratio of the hinged rock block's length to the thickness of the main roof is constant, the slip coefficient changes with the dip angle ranging from 20º to 70º, and the relationship is depicted in Fig. 7.   Fig. 7. Relationship between slip coefficient λ and dip angle α Figure 7 shows that the fractured rock block's slip coefficient linearly decreases as the dip angle increases, indicating the larger dip angle provides a higher anti-sliding capacity of the rock block with a hinge structure, making sliding unlikely to occur. Taking the friction angle of the fractured rock block at 38°, we get tan =0.78 as the critical sliding coefficient,< Thus, the green area in Fig. 7  At constant dip angle α values, the slip coefficient's evolution trend for the main roof thickness h and length l ranges of 5m < h < 15m and 10m < l < 30m is shown in Fig. 8. instability. The greater the thickness of the main roof and the fractured rock block's length, the larger load support will have to bear when the roof is unstable, inducing high mining pressures.

Rotatory instability model of the main roof
Under the overburden stress, the hinge area of the rock block is bearing compressive force and is likely to experience plastic failure, thus accelerating the rotatory instability of the hinged structure Sun et al. 2019). The rotatory instability model of fractured rock block is shown in Fig. 9.   Fig. 9. Rotatory instability mechanical model of fractured rock block When the hinged rock block is in the limit equilibrium, the sum of all moments is zero, i.e., M  =0. Then: where a is the width of the hinged area of the rock block in the main roof, θ is the angle of rotation of the fractured rock block, and x is the rock block length.
When a is relatively small, we get: Combining Eq (19) and (20)  The angle of rotation and settlement changed with dip angle, which is in the range [20,70], and the relationship is displayed in Fig. 10. The angle of rotation is positively correlated with the dip angle, indicating that it increases with the dip angle. Equation (25) yields the hinged rock block  's settlement. When the settlement of the hinged area of the fractured rock block exceeds  , rotatory instability takes place in the roof, and the larger is the dip angle, the more likely is this failure. When the dip angle is constant, the relationships between the angle of rotation and thickness of the main roof, as well as the length of the rock block take the form, as shown in Fig. 11, where 2m<h<5m and 10m< x <30m. It can be seen from Fig. 11 that the angle of rotation  grows with an increase of h and x by 1.4~4.3°/m and 0.25~0.69°/m, respectively. It shows that a change in thickness has a larger impact on the hinged structure. When the rotation angle reaches its minimum value depending on the allowable deformation, the deformation instability occurs (He et al. 2020;Ju et al. 2018). The rotation angle's magnitude reflects the differences of overburden rock structure and its stability, thus exerting a significant effect on the support (Xie et al. 2020).

Analysis of the support stability
Hydraulic supports are critical in protecting the roof and the dynamic mechanical environment where surrounding rocks impact and constrain each other Luo et al. 2019). The load magnitude, direction, and point of application to the support vary with the roof kinematic state changes. Therefore, determining the critical work resistance of support can ensure the particular mining requirements (Yang et al. 2018).
The mechanical model of a single inclined support is shown in Fig. 13, where the x-axis is upward positive and coincides with the workface dip, the y-axis is upward positive and normal to the x-axis, b and h are the support width and height, respectively, h1 is the height of the support center of gravity, 1 x is the point of application of the normal load to the roof, 2 x is the point of application of the normal load resultant to the floor, G is the support weight, P is the normal load of the roof acting on the support (support work resistance), 1 f is the tangential load of the roof acting on the support (friction between roof and support), N F is the floor tangential load on the support, 2 f is the tangential load of the floor on the support (friction between support and floor), i1 P  and i1 P  are forces acting between two adjacent supports. During mining in SDCS, forces between adjacent supports are much smaller than friction between support and roof or floor, so forces between adjacent supports are assumed to be the same. The mechanical response of the support in the critical instability state was analyzed in detail.
To avoid rotatory instability, the anti-rotating moment should exceed the turning moment, which means that During mining in the workface, the loading characteristics of the support, roof, and floor change with time due to the roof and floor movements. When the support work resistance P is applied to A ( 1 x =0), the resultant force of normal loads on the floor N F has a point of application C ( 2 x =0), the support experiences the worst condition before non-rotatory instability. In this case, Eq. (30) can be reduced to the following form As a case study for the proposed method, the 12124 workface in the Pansidong coal was selected to investigate the impact of the dip angle of coal seam on the critical work resistance of support analyzed via Eqs. (29) and (32).
The 12124 workface in the Pansidong mine is fully-mechanized, with the average dip angle of the coal seam  =40°. A ZZ7200/22/45 covering hydraulic support was adopted in the workface, the support width was 1.5 m, the height of the center of gravity of support h1 = 2.25 m, the gravity of support was 176.4 kN, the coefficients of friction between support and roof/floor were equal ( 1  = 2  =0.25). The relationship between the critical work resistance of support and the dip angle is shown in Fig. 13, where the dip angle ranges from 20º to 70º. It can be seen from Fig. 13 that before slip and rotation of the support, the critical work resistance of support was positively correlated with the dip angle of coal seam and, under the same dip angle, the critical slip work resistance of support exceeded its critical rotation work resistance.

Conclusions
A mechanical model of the main roof under linear load in the SDCS longwall workface was proposed in this study, which made it possible to derive the main roof stresses. The results obtained show that the bottom floor had features of compression at three sides and tension on the middle part, whereas the top floor had tensile stresses at three sides and compressive stress in the middle area.
The maximum shear stress max  slightly exceeded the middle of workface and occurred periodically during the workface advance.
The main principal stresses max angle, making the slip instability unlikely to occur. The critical dip angle of the fractured rock block was 57° when instability occurred. The possibility of slip instability of a fractured rock block workface increased as the thickness of the main roof and length of the rock block increased.
The critical work resistance of a support under non-sliding and non-rotating conditions was positively correlated with the coal seam's dip angle. The critical work resistance under sliding condition exceeded that under rotating condition at the same dip angles of the coal seam.