Prediction method for fracture length of'cantilever beam 'of top plate of steeply inclined super-thick coal seam

Abstract

The invention discloses a method for predicting the fracture length of a cantilever beam of a top plate of a steeply-inclined super-thick coal seam, and aims to solve the problems that in the mining process of the steeply-inclined super-thick coal seam, a large amount of coal is recycled, the filling rate of a goaf is small, a fractured top plate rock stratum has a large free space, and a hinged beam type dynamic stable structure is difficult to form. An overlying hard top plate forms a cantilever beam type stress structure with an edge crack, and an impact load caused by instability of the cantilever beam type stress structure is a structural dynamic factor for inducing rock burst. The condition of crack instability expansion is the condition of rock beam instability caving, on this basis, the fracture evolution process and characteristics of a roof cantilever beam are discussed with the roof cantilever beam as a research object, the stress and fracture conditions of the roof cantilever beam are analyzed, mechanical modeling is carried out, and in combination with a fracture mechanical analysis method, it is proposed that a working face roof rock stratum is simplified into a cantilever beam with a crack, and the fracture evolution process and the fracture evolution characteristics are discussed. A fracture mechanical model of which the stability of the cantilever beam is controlled by a structural plane is constructed, and a fracture instability criterion of a rock beam under the action of a load and a calculation formula of the ultimate overhanging length of the cantilever beam are deduced.

Description

Technical Field

[0001] This invention relates to a method for predicting the fracture length of a "cantilever beam" in the roof of a steeply inclined, extra-thick coal seam, belonging to the field of coal mining. Background Technology

[0002] Steeply dipping coal seams account for 15% to 20% of my country's proven coal reserves. With the shift of national coal mining focus to western regions, steeply dipping coal seams have become a significant target for mining. In recent years, with the continuous increase in mining depth and intensity, several rockburst disasters have occurred in some mining areas involving steeply dipping, extra-thick coal seams. These disasters involve large overburden fracturing steps, strong instantaneous energy release from roof fracturing and instability impacts, and disturbance of the high-stress zone in the bottom coal, inducing rockburst manifestations and seriously threatening safe coal mine production.

[0003] Because there are few steeply dipping, extra-thick coal seams in foreign countries, research on this type of impact mechanism has been mainly carried out by domestic scholars, who have achieved a great deal of results. Among them, Cui Feng et al. analyzed the bending deformation effect of rock pillars and roof in Wudong Coal Mine and assessed the risk of mining different coal seams; Lai Xingping et al. pointed out that the rock pillars held together in Wudong Coal Mine are the main cause of the disaster; Lan Hang derived the "lever effect" of the goaf rock pillars on the coal body on both sides of the near-vertical extra-thick coal seam and obtained an expression; Du Taotao et al. concluded that stress anomalies and "inducing key layers" are the main causes of rockburst in near-vertical extra-thick coal seams; Gao Mingshi et al. established a mechanical model of rock plate fracture between coal seams and obtained the energy calculation formula when the rock plate fractures; Wu Zhenhua, Li Donghui, He Xueqiu, He Quansheng et al. all concluded through analysis that the main cause of rockburst in Wudong Coal Mine is the "pressure-lever" effect of roof compression and rock pillar prying; Li Anning et al. concluded that the holding effect of the roof and floor of the near-vertical coal seam is the main effect of rockburst; Zhang Hongwei et al., based on the geological dynamic zoning method, determined that rockburst in Wudong Coal Mine mostly occurs in high stress and stress gradient areas.

[0004] Shi Pingwu et al. proposed a cross-layer arch structure model to explain the fracture, migration, and structural instability of the roof under horizontal segmented top coal caving conditions in steeply inclined extra-thick coal seams; Lai Xingping et al., through mechanical analysis combined with field measurements, believed that the concentrated stress caused by mining easily induces dynamic disasters; Wang Jiachen et al. believed that the support load of horizontal segmented mining in steeply inclined thick coal seams mainly comes from the collapse and uneven accumulation of the upper layer strata; Wu Yongping et al., through ground radar and theoretical analysis, believed that repeated mining and improper support parameters can lead to asymmetric damage in the roadway; Ju Wenjun et al., through mechanical analysis of the overlying surrounding rock structure, determined that the impact load caused by the instability of the overlying rock layer "cantilever beam" structure is the structural dynamic factor inducing rockburst; Zhang Jiwei et al. studied the energy distribution of the overlying suspended roof of steeply inclined extra-thick coal seams and identified the dangerous area with highly concentrated energy; Chen Zemin et al. found that the stress level of the surrounding rock above and below the roadway in diagonally inclined segmented mining is lower, which is more conducive to the prevention and control of rockburst; Wang Zhengyi studied the dynamic and static combined loading similarity simulation test. Dynamic response of coal and rock and its impact failure characteristics in the mining of steeply inclined extra-thick coal seams; Chen Jianqiang et al. analyzed the impact hazard factors of near-vertical coal seams and proposed a static-dynamic coupled evaluation method for rockburst hazard that is more in line with actual field conditions; Wu Zhenhua et al., based on field surveys and theoretical analysis, proposed comprehensive pressure relief measures including pre-splitting blasting of the roof and rock pillars and surface blasting of the rock pillars; Wang Hongwei et al., through analysis of the deformation and failure law of the surrounding rock in multi-segment mining, determined the reasonable stage height for short-wall fully mechanized longwall mining of steeply inclined coal seams; Sun Chuang et al. studied... The study investigated the laws governing the collapse of the hard roof in steeply inclined coal seams and the characteristics and extent of abrupt roof collapse. Liu Yong et al. pointed out that local stress concentration in the "segmented-layered" composite mining of steeply inclined extra-thick coal seams is the main cause of coal pillar instability. Cao Jinrong et al. theoretically analyzed the asymmetric distribution characteristics of bottom coal stress in steeply inclined extra-thick coal seams and revealed the regional differences in the loading characteristics of the coal body along the dip. He Jiang, Dou Linming et al. summarized the fracture of steeply inclined roofs into three types of instability impact processes: fracture rotation, block fall, and structural compression subduction.

[0005] In summary, the above research findings provide a relatively comprehensive understanding of the roof fracture patterns and characteristics of hazards in steeply inclined coal seams. However, there is limited research on the mechanism and control technology of rockbursts induced by roof fractures in horizontally layered longwall top-coal caving mining roadways of steeply inclined extra-thick coal seams. Furthermore, mining practice shows that existing theories still cannot fully guide the handling of rockburst problems in the mining process of steeply inclined extra-thick coal seams, and accidents continue to occur frequently, failing to fully meet the production needs of enterprises. The main problems are as follows:

[0006] (1) Existing research results on rockbursts in steeply inclined and extra-thick coal seams mainly focus on the fracture and rotation characteristics of the roof and the resulting rockburst disasters. There are few separate analyses of the fracture instability of the "cantilever beam". However, the structure after the fracture of the hard overlying roof cannot meet the requirement of the "masonry beam" theory that the thickness of the fractured rock block is much greater than the height of the free space. The basic roof often appears in the form of a "cantilever beam". Therefore, the rotational instability of the "cantilever beam" is a major cause of rockburst disasters in steeply inclined and extra-thick coal seams and needs to be taken seriously.

[0007] (2) Existing theories have conducted extensive research on the fracture rotation of the "cantilever beam" and its interaction with the support during the rotation process, but have rarely calculated the ultimate overhang length of the "cantilever beam". This is because the longer the overhang of the "cantilever beam", the greater the impact on the working surface when it breaks. Therefore, its analysis needs to be given sufficient attention.

[0008] (3) Current "cantilever beam" structural models generally assume that the rock strata are a homogeneous and continuous medium, and are based on the basic theories and methods of theoretical mechanics and elasticity to analyze the stability and fracture of the rock strata. However, during long-term geological tectonic movements, the rock mass inevitably contains joints and fissures of varying sizes, which play a controlling role in the fracture of the "cantilever beam" rock strata. The theoretical methods of analyzing crack propagation and penetration in fracture mechanics are more suitable for the fracture and instability of the "cantilever beam," and can make the theoretical analysis results more accurate. Therefore, multiple models are needed for correction.

[0009] (4) The treatment of "cantilever beams" in steeply inclined extra-thick coal seams is generally carried out by blasting based on engineering experience. However, due to the geological structure, the ultimate extension length of the "cantilever beam" is difficult to predict. Often, it will induce impact instability before blasting, causing rockburst disaster. Therefore, it is urgent to conduct theoretical analysis and judgment on the ultimate extension length of the "cantilever beam".

[0010] In summary, existing technologies have the problem that methods for predicting the fracture length of the "cantilever beam" roof of steeply inclined, extra-thick coal seams cannot fully guide mining practices. Therefore, this invention is proposed. Summary of the Invention

[0011] This invention provides a method for predicting the fracture length of the "cantilever beam" in the roof of a steeply inclined, extra-thick coal seam. The aim is to construct a more reasonable, accurate, and efficient method for predicting the fracture length of the "cantilever beam" in the roof of a steeply inclined, extra-thick coal seam, providing a theoretical basis for the prevention of rockburst disasters during the mining of steeply inclined, extra-thick coal seams, and thereby determining the influencing factors of the stability of the "cantilever beam" under dynamic load.

[0012] The technical solution adopted in this invention is a method for predicting the fracture length of a "cantilever beam" in the roof of a steeply inclined, extra-thick coal seam, comprising the following steps:

[0013] 1) Construct a structural mechanics model of a "cantilever beam" and perform stress analysis on the cantilever beam structure. Under complex external loads, the roof strata are simplified into a cracked cantilever beam structure. When the cantilever length of the overlying basic roof exceeds the limit, the crack will propagate and fracture, moving towards the goaf. The dynamic process of the overlying roof will release a large amount of elastic energy, which will have a catastrophic impact on the lower mining roadways and is prone to rockburst accidents. Simplify the stress model of the cantilever beam, analyze the stress characteristics of the cantilever beam, and simplify the load state of the cantilever beam: the cantilever beam is subjected to its own weight (W), W = γlh is the weight of the "cantilever beam", γ is the unit weight of the rock strata; the length of the structural surface (crack) is a, the rock beam inclination angle is α (0 < α < 90°); l is the length of the cantilever beam; h is the thickness of the basic roof strata; β is the inclination angle of the basic roof strata; for ease of calculation, the load of the overlying rock strata on the basic roof is simplified to a uniformly distributed load q.

[0014] 2) Perform stress analysis on the cantilever beam structure with edge cracks, decomposing it into several crack propagation models under basic loads for calculation.

[0015] (1) The strength factor caused by the normal stress acting on the crack is ( Figure 3 a)

[0016] (1)

[0017]

[0018] (2) The strength factor caused by the shear stress acting on the crack is ( Figure 3 b).

[0019] (2)

[0020] in, Q is the resultant force of the shear force.

[0021] (3) The strength factor caused by the bending moment acting on the crack is ( Figure 3 c).

[0022] (3)

[0023] in, M is the bending moment.

[0024] From equations (1-3), it can be seen that the thickness of the rock strata and the length of the cracks are directly related to the stress intensity factor at the crack tip. For ease of calculation, the load ql from the overlying rock strata and the self-weight W of the rock block are decomposed along the directions perpendicular to and parallel to the structural plane, as follows:

[0025] (4)

[0026] (5)

[0027] In the formula, N and P are the forces exerted by the rock block's own weight along the directions perpendicular to and parallel to the structural plane, respectively.

[0028] Figure 3 In the cantilever beam fracture model of a, the horizontal compressive force N causes the propagation of type I cracks. Substituting equation (4) into equation (1) yields:

[0029] (6)

[0030] Figure 3 In the fracture model of the cantilever beam b, the resultant shear force is:

[0031] (7)

[0032] Q is the stress intensity factor that causes type II cracks, therefore equation (2) should be:

[0033] (8)

[0034] Figure 3 The bending moment in the fracture model of the cantilever beam c is:

[0035] (9)

[0036] Substituting the expression for the stress intensity factor of type I crack induced by bending moment (2), we get:

[0037] (11)

[0038] The stress intensity factor at the tip of a rock fracture under the basic load is equal to the sum of the individual stress intensity factors, i.e.

[0039] (12)

[0040] Based on on-site engineering and extensive laboratory research, the criterion for rock compressive-shear fracture under complex stress states is as follows:

[0041] (13)

[0042] Where λ is the compression-shear ratio coefficient; K Ic Let be the fracture toughness of the rock. Substituting equation (12) into the above equation, and substituting W = γlh, we get:

[0043] (14)

[0044] Substituting into equation (14) and further deriving, we can obtain the limiting length of the cantilever rock beam:

[0045] (15)

[0046] This application's technical solution, combining the roof fracture and structural evolution laws of rockburst disasters in horizontally segmented fully mechanized longwall mining faces of steeply inclined extra-thick coal seams, determines that the impact load caused by the structural instability of the overlying strata's "cantilever beam" structure is the structural dynamic factor inducing rockbursts. Based on this, it proposes simplifying the working face roof strata into a fractured cantilever beam, constructing a fracture mechanics model where the stability of the "cantilever beam" is controlled by a structural plane, and deriving the equivalent stress intensity factor of the structural plane and the calculation formula for the ultimate cantilever length of the cantilever beam. This has certain theoretical significance and practical value for achieving safe mining of steeply inclined extra-thick coal seams, providing theoretical guidance and technical support for the prevention of rockbursts in steeply inclined extra-thick coal seams. Attached Figure Description

[0047] Figure 1 The overlying basic roof is a "cantilever beam" structure: ① cantilever beam structure breakage and rotation, ② bottom plate, ③ transport tunnel;

[0048] Figure 2 Schematic diagram of the stress on the cantilever beam structure of the overlying basic roof: ① Schematic diagram of the stress on the cantilever beam structure;

[0049] Figure 3 Static equivalent diagram of cantilever beam fracture: (a) tensile stress, (b) shear stress, (c) bending moment;

[0050] Figure 4 The scaffolding at the accident site broke;

[0051] Figure 5 The tunnel at the accident site was damaged;

[0052] Figure 6 Changes in support resistance during periodic pressure on the working face: ① Periodic pressure warning, ② Periodic pressure warning, ③ Periodic pressure warning; a. Middle part, b. Lower part, c. Upper part. Detailed Implementation

[0053] The present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0054] As shown in the figure, this invention provides a method for predicting the fracture length of a "cantilever beam" in the roof of a steeply inclined, extra-thick coal seam, comprising the following steps:

[0055] 1) Considering the rockburst disaster caused by the failure and instability of the "cantilever beam" structure of the basic roof of a steeply inclined and extra-thick coal seam, a fracture mechanics model is constructed to control the stability of the "cantilever beam" by a structural plane. The stress analysis of the "cantilever beam" structure is carried out, considering factors such as the weight of the cantilever beam itself, the length of the structural plane (crack), the dip angle of the rock beam, the length of the cantilever beam, the thickness of the basic roof rock layer, the dip angle of the basic roof rock layer, and the uniformly distributed load of the overlying rock layer, to construct a fracture mechanics model to control the stability of the "cantilever beam" by a structural plane.

[0056] 2) Based on step 1), simplify the "cantilever beam" into a finite plate beam model with edge cracks; decompose the load it is subjected to into a crack propagation model under the three basic loads of normal stress, shear stress and bending moment, and calculate the stress intensity factor.

[0057] 3) Decompose the load ql of the overlying rock strata and the self-weight W of the cantilever beam along the directions perpendicular to and parallel to the structural plane, and obtain the force N of the self-weight of the cantilever beam along the direction perpendicular to the structural plane and the force P of the self-weight of the cantilever beam along the direction parallel to the structural plane.

[0058] 4) Based on the expression for the horizontal compressive force N determined in step 3), and combined with the method for calculating the strength factor caused by the normal stress on the crack in step 2), the expression for the stress intensity factor caused by the normal stress can be obtained.

[0059] 5) The resultant force of shear force in the fracture model of cantilever beam is obtained according to the mechanical model. According to the strength factor calculation method caused by shear stress on crack in step 2), the expression of stress intensity factor caused by shear stress can be obtained.

[0060] 6) Obtain the bending moment in the cantilever beam fracture model based on the mechanical model. Based on the strength factor calculation method caused by the bending moment on the crack in step 2), the expression for the stress intensity factor caused by the bending moment force can be obtained.

[0061] 7) By superimposing the stress intensity factor expressions caused by each force in steps 4), 5), and 6), we can obtain the Type I and Type II stress intensity factor expressions at the crack tip of the "cantilever beam".

[0062] 8) Based on the superimposed stress intensity factor obtained in step 7), substitute it into the rock compression-shear fracture criterion under complex stress state, and substitute it into the expression of the gravity W of the "cantilever beam". Further derivation can yield the formula for calculating the ultimate cantilever length of the "cantilever beam".

[0063] During the mining of steeply inclined, extra-thick coal seams, the fractured roof strata have considerable free space, and the overlying hard roof is in a suspended state, forming a "cantilever beam" type stress structure with edge cracks, such as... Figure 1As shown. Under certain load and cantilever length conditions, the crack propagation and fracture of the cantilever beam release a large amount of energy, causing intense mine pressure manifestation. To address the instability problem of the "cantilever beam," a mechanical model is constructed, such as... Figure 2 As shown.

[0064] like Figure 1 and Figure 2 The diagram shows the structure and stress of the cantilever beam of the basic roof. A stress analysis of the cantilever beam structure is performed. Under complex external loads, the roof strata are simplified into a cracked cantilever beam structure. When the cantilever length of the overlying basic roof exceeds its limit, the crack will propagate and fracture, moving towards the goaf. The dynamic process of the overlying roof releases a large amount of elastic energy, which can have a catastrophic impact on the lower mining roadways, easily leading to rockburst accidents. A simplified stress model of the cantilever beam is used to analyze its stress characteristics. The load state of the cantilever beam is simplified as follows: the cantilever beam is subjected to its own weight (W), where W = γlh is the weight of the cantilever beam, and γ is the unit weight of the rock strata; the length of the structural surface (crack) is a, and the rock beam inclination angle is α (0 < α < 90°); l is the length of the cantilever beam; h is the thickness of the basic roof strata; β is the inclination angle of the basic roof strata; for ease of calculation, the load from the overlying rock strata on the basic roof is simplified to a uniformly distributed load q.

[0065] During long-term geological tectonic movements, rock masses inevitably contain joints and fissures of varying sizes, which control the fracture of the "cantilever beam" rock strata. The conditions for fissure instability and propagation are the conditions for the collapse of the rock beam. Therefore, the "cantilever beam" rock strata are treated as a finite plate beam model with cracks, and a fracture mechanics model is constructed. The stress analysis of the rock strata is as follows: Figure 3 As shown.

[0066] The specific theoretical derivation process is as follows:

[0067] (1) The strength factor caused by the normal stress acting on the crack is ( Figure 3 a).

[0068] (1)

[0069]

[0070] (2) The strength factor caused by the shear stress acting on the crack is ( Figure 3 b).

[0071] (2)

[0072] in, Q is the resultant force of the shear force.

[0073] (3) The strength factor caused by the bending moment acting on the crack is ( Figure 3 c).

[0074] (3)

[0075] in, M is the bending moment.

[0076] From equations (1-3), it can be seen that the thickness of the rock strata and the length of the cracks are directly related to the stress intensity factor at the crack tip. For ease of calculation, the load ql from the overlying rock strata and the self-weight W of the rock block are decomposed along the directions perpendicular to and parallel to the structural plane, as follows:

[0077] (4)

[0078] (5)

[0079] In the formula, N and P are the forces exerted by the rock block's own weight along the directions perpendicular to and parallel to the structural plane, respectively.

[0080] Figure 3 In the cantilever beam fracture model of a, the horizontal compressive force N causes the propagation of type I cracks. Substituting equation (4) into equation (1) yields:

[0081] (6)

[0082] Figure 3 In the fracture model of the cantilever beam b, the resultant shear force is:

[0083] (7)

[0084] Q is the stress intensity factor that causes type II cracks, therefore equation (2) should be:

[0085] (8)

[0086] Figure 3 The bending moment in the fracture model of the cantilever beam c is:

[0087] (9)

[0088] Substituting into the expression for the stress intensity factor of type I crack induced by bending moment (2), we get:

[0089] (11)

[0090] The stress intensity factor at the tip of a rock fracture under the basic load is equal to the sum of the individual stress intensity factors, i.e.

[0091] (12)

[0092] Based on on-site engineering and extensive laboratory research, the criterion for rock compressive-shear fracture under complex stress states is as follows:

[0093] (13)

[0094] Where λ is the compression-shear ratio coefficient; K Ic Let be the fracture toughness of the rock. Substituting equation (12) into the above equation and into W = γlh, we get:

[0095] (14)

[0096] Substituting into equation (14) and further deriving, we can obtain the limiting length of the cantilever rock beam:

[0097] (15)

[0098] Example

[0099] Taking the rockburst-prone 412 longwall face of a coal mine in Lanzhou, Gansu Province as the research background, the minefield has a strike length of 1.7 km, a dip length of 0.34 km, and an area of ​​0.48 km². 2 The No. 6 coal seam being mined has an average dip angle of 47°, a strike of N13.1°~12.3°W, an average thickness of 52.24m, and a mining depth of 490~610m. It is a steeply dipping, extra-thick coal seam, susceptible to various natural disasters including rockburst, CO2 outburst, water, fire, and gas. It is classified as a rockburst and coal (rock) and CO2 outburst mine, with a rated production capacity of 1.7 million tons per year. The physical and mechanical characteristics of the roof and floor of the No. 6 coal seam are listed in Table 1. During the advance of the working face along the strike, periodic pressure is not significant, but the periodic pressure along the dip of the roof strata is strong. Generally, a major collapse of the basic roof occurs every 2-5 sections of mining, resulting in strong mine pressure manifestation and severe deformation and damage to the roadways. The roof roadways suffer particularly severe damage, precisely due to the formation and fracture of the basic roof's "cantilever beam" structure. The on-site damage situation is as follows: Figure 4 and Figure 5 As shown. The vibration originated from the roof direction, with an accident magnitude of 2.4, and the ground was strongly tremored. The accident resulted in the collapse of a total of 38 supports on the roof side of the working face to varying degrees; among them, the end bottom bulge on the roof side of the working face was 1.3~1.8m, and the bottom coal in the middle of the working face cracked by 100~150mm.

[0100] Mine pressure monitoring stations were set up at 13.5, 40.5, 54, and 81 m along the dip of the working face from bottom to top to continuously monitor the changes in support resistance at four locations: lower, lower-middle, upper-middle, and upper part of the working face. The monitoring results are as follows: Figure 6As shown, when the working face advances 11m, the resistance of the lower and middle supports suddenly increases, reaching a maximum of over 23MPa, with a large dynamic load coefficient and severe periodic pressure. The resistance of the upper supports then increases after another 6m of advance, causing spalling in the middle of the working face. The upper supports arrive at pressure later, lagging behind the middle supports by about 7m. However, for most of the remaining time, the working face is under low load or even no load.

[0101] Table 1 Physical and mechanical characteristics of the roof and floor of the coal seam

[0102]

[0103] To analyze the influence of various parameters on the ultimate length of the cantilever beam, the physical and mechanical parameters of the rock strata are taken as an example for analysis and calculation, as follows: The rock strata are siltstones with a dip angle α = 47°, a thickness h = 5.3m, a structural plane length a = 1.4m, an average breaking depth l = 22.7m, and a rock unit weight γ = 25.7kN / m³. 3 The internal friction angle of the rock beam is φ = 62°, the cohesion is c = 51 kPa, the crack compressive-shear ratio coefficient is λ = 1, and the fracture toughness of the rock is K. IC =0.62MPa·m 1 / 2 Substituting the above data into the equation yields the stress intensity factor coefficient F. σ =1.841, F M =1.403, F τ =1.231.

[0104] Based on on-site investigation, the "cantilever beam" is controlled by an outward-sloping structural plane, forming an unstable rock block. If it breaks, it will not only threaten the lives of workers below, but also affect normal production and cause huge economic losses. Therefore, it is of great significance to conduct stability analysis on the "cantilever beam" and propose guiding measures. Relevant measurement data and mechanical parameters were obtained from the survey report and substituted into the calculation method (15) established in this paper to analyze the ultimate length of the "cantilever beam". The relevant parameters and calculation results are listed in Table 2.

[0105] Table 2 Calculation parameters and results for the ultimate length of cantilever beams

[0106]

[0107] Analysis of the calculation results reveals that, under the current mining progress and rock beam overhang length conditions, the ultimate rock stratum length of the "cantilever beam" is 14.9m, which is less than the measured cantilever beam length of 15.2m. Therefore, the instability of the basic roof cantilever beam structure causes impact loads, releases a large amount of energy, and causes rockburst in the mining roadway. This is consistent with the actual engineering situation and reflects the scientific validity and rationality of the theory.

[0108] It is evident that the method for predicting the fracture length of the "cantilever beam" in the roof of a steeply inclined, extra-thick coal seam provided by this invention is feasible. Theoretical calculations can be used to predict whether the working face is safe during the mining of steeply inclined, extra-thick coal seams, whether the support parameters of the supports need adjustment, and whether the "cantilever beam" should be reduced by blasting to break the roof, thereby homogenizing concentrated stress and preventing excessive energy accumulation. Due to the irrationality of previous research methods, the "cantilever beam" cantilever length was excessive, and failure to take timely measures led to frequent rockburst disasters at the working face. This analytical method provides a new means of analyzing "cantilever beam" instability. As long as the reasonable "cantilever beam" cantilever length is less than the theoretically calculated value, the occurrence of rockburst disasters can be effectively prevented.

[0109] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for predicting the fracture length of a "cantilever beam" in the roof of a steeply inclined, extra-thick coal seam, characterized in that, Includes the following steps: 1) Perform stress analysis on the "cantilever beam" structure, simplify it into a cantilever beam structure with cracks, simplify the stress model of the cantilever beam, and consider factors such as the weight of the cantilever beam itself, the length of the structural surface (crack), the inclination angle of the rock beam, the length of the cantilever beam, the thickness of the basic top rock layer, the inclination angle of the basic top rock layer, and the uniformly distributed load of the overlying rock layer, and construct a fracture mechanics model in which the stability of the "cantilever beam" is controlled by a structural surface; 2) Based on the analysis method of the main control crack propagation in fracture mechanics, and combined with the characteristics of joints and fissures in the "cantilever beam" of the basic top layer, the "cantilever beam" rock stratum is simplified into a finite plate beam model with edge cracks; the load it receives is decomposed into a crack propagation model under three basic loads for calculation, namely the strength factor caused by normal stress, shear stress, and bending moment, where the strength factor caused by the normal stress acting on the crack is: ,in, The strength factor caused by the shear stress acting on the crack is: ,in, Q is the resultant shear force; the strength factor caused by the bending moment acting on the crack is ,in, M is the bending moment; 3) Decompose the load ql from the overlying rock strata and the self-weight W of the cantilever beam along the directions perpendicular to and parallel to the structural plane, and obtain the following results: , In the formula, N and P are the forces of the self-weight of the "cantilever beam" along the directions perpendicular to and parallel to the structural surface, respectively; 4) Based on the expression for the horizontal compressive force N determined in step 3), since the horizontal compressive force N causes the propagation of the type I crack, the strength factor expression caused by the normal stress on the crack in step 2) is used. The expression for the stress intensity factor can be obtained as follows: ; 5) The resultant shear force in the cantilever beam fracture model is obtained from the mechanical model as follows: Q is the stress intensity factor that causes type II cracks, based on the expression for the intensity factor caused by shear stress on the crack in step 2). The expression for the stress intensity factor can be obtained as follows: ; 6) The bending moment in the cantilever beam fracture model is According to the expression for the stress intensity factor of type I crack caused by bending moment in step 2), The expression for the stress intensity factor caused by bending moment can be obtained: ; 7) Based on the expressions for the strength factors caused by the normal stress, shear stress, and bending moment acting on the crack in steps 4), 5), and 6), the stress intensity factor at the crack tip of the rock stratum under the basic load is equal to the superposition of their individual stress intensity factors, that is: ； 8) Based on the superimposed stress intensity factor obtained in step 7), substitute it into the rock compression-shear fracture criterion under complex stress conditions. Where λ is the compression-shear ratio coefficient, and K Ic The fracture toughness of the rock; substituting W = γlh, we can obtain Further derivation yields the formula for calculating the ultimate cantilever length of a cantilever beam: 。 2. The method for predicting the fracture length of the "cantilever beam" of the roof of a steeply inclined, extra-thick coal seam according to claim 1 is characterized in that: In step 1), starting from the structural and fracture characteristics of the overlying strata, the basic top strata are approximated as a "cantilever beam" with edge cracks. The stress analysis of the basic top "cantilever beam" structure is carried out, and the stress model of the cantilever beam is simplified. Considering factors such as the weight of the cantilever beam itself, the length of the structural surface (crack), the dip angle of the rock beam, the length of the cantilever beam, the thickness of the basic top strata, the dip angle of the basic top strata, and the uniformly distributed load of the overlying strata, a fracture mechanics model in which the stability of the "cantilever beam" is controlled by a structural surface is constructed.

3. The method for predicting the fracture length of the "cantilever beam" of the roof of a steeply inclined, extra-thick coal seam according to claim 1, characterized in that: In step 2), based on the analysis method of the main control crack propagation in fracture mechanics, and combined with the characteristics of the joints and fissures in the basic top "cantilever beam", the "cantilever beam" rock stratum is simplified into a finite plate beam model with edge cracks. The load it receives is decomposed into crack propagation models under three basic loads for calculation, namely the strength factors caused by normal stress, shear stress, and bending moment. Among them, the strength factor caused by the normal stress acting on the crack is: ,in, The strength factor caused by the shear stress acting on the crack is: ,in, Q is the resultant shear force; the strength factor caused by the bending moment acting on the crack is ,in, M is the bending moment.

4. The method for predicting the fracture length of the "cantilever beam" of the roof of a steeply inclined, extra-thick coal seam according to claim 1, characterized in that: In step 3), the load ql from the overlying rock strata and the self-weight W of the rock block are decomposed along the directions perpendicular to and parallel to the structural plane, respectively, to obtain... , In the formula, N and P are the forces exerted by the rock block's own weight along the directions perpendicular to and parallel to the structural plane, respectively.

5. The method for predicting the fracture length of the "cantilever beam" of the roof of a steeply inclined, extra-thick coal seam according to claim 1, characterized in that: In step 4), based on the expression for the horizontal compressive force N determined in step 3), since the horizontal compressive force N causes the propagation of the type I crack, the strength factor expression caused by the normal stress on the crack in step 2) is used. Finally, the expression for the stress intensity factor is obtained: .

6. The method for predicting the fracture length of the "cantilever beam" of the roof of a steeply inclined, extra-thick coal seam according to claim 1, characterized in that: In step 5), the resultant shear force in the cantilever beam fracture model is obtained from the mechanical model as follows: Since Q causes a type II crack, the intensity factor is determined according to the expression for the intensity factor caused by the shear stress on the crack in step 2). The expression for the stress intensity factor can be obtained as follows: .

7. The method for predicting the fracture length of the "cantilever beam" of the roof of a steeply inclined, extra-thick coal seam according to claim 1, characterized in that: In step 6), the bending moment in the cantilever beam fracture model is According to the expression for the stress intensity factor of type I crack caused by bending moment in step 2), The expression for the stress intensity factor can be obtained as follows: .

8. The method for predicting the fracture length of the "cantilever beam" of the roof of a steeply inclined, extra-thick coal seam according to claim 1, characterized in that: In step 7), based on the strength factor expressions caused by the normal stress, shear stress, and bending moment acting on the crack in step 2), the stress intensity factor at the crack tip of the rock stratum under the basic load is equal to the superposition of their individual stress intensity factors, that is: .

9. The method for predicting the fracture length of the "cantilever beam" of the roof of a steeply inclined, extra-thick coal seam according to claim 1, characterized in that: In step 8), the superimposed stress intensity factor obtained in step 7) is substituted into the rock compression-shear fracture criterion under complex stress state. Where λ is the compression-shear ratio coefficient, and K Ic The fracture toughness of the rock; substituting W = γlh, we can obtain Further derivation yields the formula for calculating the ultimate cantilever length of a cantilever beam: By using the expression for l and combining it with the parameters obtained from the test under actual engineering conditions, the ultimate length of the "cantilever beam" can be predicted, so that timely engineering measures can be taken to avoid safety accidents.

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