A method and system for determining the minimum safety distance of a tunnel excavation face crossing a goaf

Abstract

The application discloses a kind of minimum safety distance determination method and system of tunnel excavation face crossing gob area, method includes the following steps: set the failure mode of tunnel excavation face instability under the condition that coal mine gob area is contained in stratum, and establish theoretical model based on failure mode;Minimum safety distance condition is judged based on theoretical model;The shape of the failure region is optimized, and the optimal solution of minimum safety distance is obtained based on minimum safety distance condition.The application proposes a failure mode suitable for the instability of tunnel excavation face crossing coal mine gob area, and the analytical solution of minimum safety distance is derived using the upper bound method of limit analysis.Compared with numerical simulation and analytical solution, the model proposed by the application has high precision and can reflect the mechanism of tunnel excavation face instability and failure.

Description

Technical Field

[0001] This invention belongs to the field of tunnel engineering technology, specifically relating to a method and system for determining the minimum safe distance of the excavation face of a tunnel traversing a mining subsidence area. Background Technology

[0002] Controlling the stability of the excavation face is a core challenge for safe tunnel construction, especially in complex urban environments. Excavation face instability leading to ground subsidence often results in serious consequences such as damage to nearby buildings and pipeline ruptures, causing enormous economic losses and threatening personnel safety. Among various adverse geological conditions, goaf areas, due to their underground cavities and unstable geological structures, are highly susceptible to disasters such as water and mud inrushes and rock collapses, significantly increasing the risks and difficulties of tunnel construction.

[0003] Extensive and in-depth research has been conducted by scholars both at home and abroad on the stability of tunnel excavation faces. Currently, scholars both at home and abroad have conducted very thorough research on tunnel stability. In terms of theoretical analysis, the limit analysis method was introduced into geotechnical engineering analysis by Chen (CHEN W F. Limit analysis and soil plasticity[M]. Amersterdam: Elsevier, 1975.), and later Leca and Dormiex (LECA E, DORMIEUX L. Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material[J]. Géotechnique, 1990, 40(4): 581–606.) first proposed using a combination of cones to construct the collapse mode of the excavation face. To improve computational accuracy, the instability mechanism of the excavation face was further optimized into a combination of truncated cones ([HAN K, ZHANG C, ZHANG D. Upper-bound solutions for the face stability of a shield tunnel in multilayered cohesive–frictional soils[J]. Computers and Geotechnics, 2016, 79: 1-9.), a combination of truncated cones and logarithmic spirals (SOUBRA AH, DIAS D, EMERIAULT F et al. Three-Dimensional Face Stability Analysis of Circular Tunnels by a Kinematical Approach[J]. GeoCongress 2008, 2008.), and a spatially discretized logarithmic spiral failure mode (MOLLON G, DIAS D, SOUBRA A H. Face stability analysis of circular tunnels driven by a pressurized shield[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2010, 136(1): 215–229.) More precise instability mechanisms. In terms of numerical simulation, many scholars have used various numerical analysis methods such as the finite element method, discrete element method, and material point method to conduct relevant analyses on the stability of the excavation face.Qin Jianshe (Qin Jianshe, Yu Xingfu, Zhong Xiaochun, et al. Numerical simulation study on deformation and failure of shield tunnel excavation face in clay[J]. Rock and Soil Mechanics, 2007(S1): 511-515.) used the finite difference software FLAC3D to simulate the active failure of the tunnel excavation face in clay strata and analyzed the influence of the ultimate support force of the excavation face on the soil arching effect in clay strata. Chen et al. (CHEN RP, TANG LJ, LING DS, et al. Face stability analysis of shallow shield tunnels in dry sandy ground using the discrete element method[J]. Computers and Geotechnics, 2011, 38: 187–195.) used the DEM method to simulate the active failure of the excavation face and summarized the failure process of the excavation face into two stages. Scholars have also conducted relevant research on the stability of the surrounding rock of tunnels crossing goaf areas. Li Tianfu et al. (Li Tianfu, Jiang Dewu, Li Ke. Numerical simulation and treatment strategy study on tunnel crossing coal seam goaf [J]. Highway Transportation Technology, 2017, 33(1): 78-81, 87.) conducted numerical simulation studies on two cases of Huayan Tunnel crossing coal seam without goaf and crossing coal seam with goaf, determined the range of influence of goaf on tunnel stability, and provided information for formulating reinforcement schemes for tunnel crossing goaf. Huang et al. ([HUANG F, SHI X, WU C, et al. Stability analysis of tunnel under coal seam goaf: Numerical and physical modeling[J]. Underground Space, 2023, 11: 246-261.) conducted a numerical simulation study on the stability of the goaf under the tunnel. They used FLAC3D to simulate the surrounding rock of the bending zone and fracture zone undergoing continuous elastoplastic deformation in the "three zones" of the goaf, and used PFC3D to simulate the large porosity and discrete gravel in the caving zone. They obtained the influence of key factors such as coal seam dip angle, thickness, and distance from the tunnel on the tunnel stability, and verified the accuracy of the numerical simulation through model tests.

[0004] Studies on excavation face stability by relevant scholars have mostly focused on intact strata or homogeneous soft-hard composite strata, with a lack of systematic research on the special and complex condition of strata containing goafs. Research on the collapse patterns and instability mechanisms of excavation faces when goafs exist in front of the tunnel is insufficient, and relevant theoretical analysis is lacking. Summary of the Invention

[0005] This invention aims to address the shortcomings of existing technologies and provides the following solutions: A method for determining the minimum safe distance of a tunnel excavation face traversing a goaf includes the following steps: A failure mode for tunnel excavation face instability is defined under the condition that the strata contain coal mine goaf, and a theoretical model is established based on the failure mode; Determine the minimum safe distance condition based on the aforementioned theoretical model; The shape of the damaged area is optimized, and the optimal solution for the minimum safe distance is obtained based on the minimum safe distance condition.

[0006] Preferably, the failure mode consists of three parts: a truncated cone of the original surrounding rock in the three zones of the goaf ahead of the tunnel excavation face, a truncated cone in the caving zone, and a truncated cone in the fracture zone.

[0007] Preferably, the method for obtaining the minimum safe distance calculation formula includes: Let truncated cone ABDC, truncated cone CDFR, and truncated cone EFG be block I, block II, and block III, respectively; Based on the velocity of block I, calculate the velocity of block II, the relative velocity between block I and block II, the velocity of block III, and the relative velocity between block II and block III; Calculate the block areas of block I, block II, and block III to obtain the areas of block I, block II, and block III; Based on the velocity of block I, the velocity of block II, the velocity of block III, the area of ​​block I, the area of ​​block II, and the area of ​​block III, calculate the work done by the soil gravity of block I, block II, and block III respectively, and calculate the virtual power of the soil gravity in the failure zone; The power exerted by external forces on the damaged block is calculated based on the virtual power of the soil weight in the damaged area and the virtual power of the excavation face. The internal power dissipation is calculated based on the velocities of block I, block II, and block III. According to the upper bound theorem of limit analysis, the condition for the tunnel excavation face to remain stable is that the internal dissipated power is not less than the power exerted by the external force on the damaged block. Based on the internal dissipated power and the power applied to the damaged block by the external force, the safety factor is calculated. When the safety factor is less than 1, the whole is in an unstable state; when the safety factor is greater than 1, the whole is in a safe state; when the safety factor is equal to 1, the whole is in a critical state, at which point the distance between the tunnel excavation face and the goaf is the minimum safe distance.

[0008] Preferably, the method for calculating the velocity of block II, the relative velocity between block I and block II, the velocity of block III, and the relative velocity between block II and block III includes: in, Indicates the velocity of block I. Indicates the velocity of block II. This represents the angle between the velocity field direction of block I and the horizontal plane. Indicates the drop angle. This represents the internal friction angle of the stratum where block I is located. This represents the angle between the velocity field direction of block II and the horizontal plane. This represents the relative velocity between block I and block II. Indicates the velocity of block III. This indicates the internal friction angle of the stratum in which block II is located. This indicates the internal friction angle of the stratum in which block III is located. This indicates the relative velocity between block II and block III.

[0009] Preferably, the power of the work done by the soil's gravity is: in, Represents a block i The density of the strata in which it is located Represents the area of ​​the block. This represents the angle between the velocity field direction of the block and the horizontal plane. i =1,2,3; The virtual power of the soil's gravity is: in, This represents the virtual power of the soil's weight. The power exerted by the external force on the destroyed block is: in, Wv Indicates the energy dissipation rate within the damaged area. WT This represents the virtual power of the excavation face.

[0010] Preferably, the method for calculating the internal power dissipation includes: in, We Represents the virtual power of external force. c 1 represents the cohesion of the stratum containing block I. LAC express A Click C The length of the line segment at the point. LBD express B Click D The length of the line segment at the point. LCD express C Click D The length of the line segment at the point. c 2 represents the cohesion of the stratum in which block II is located. LDF express D Click F The length of the line segment at the point. LEF express E Click F The length of the line segment at the point. c 3 represents the cohesion of the stratum in which block III is located. LEG express E Click G The length of the line segment at the point. LFG express F Click G The length of the line segment at a point.

[0011] Preferably, the safety factor is: Where F represents the safety factor.

[0012] Preferably, the shape of the damaged area is optimized using MATLAB software, and the optimal solution for the minimum safe distance is obtained based on the minimum safe distance condition.

[0013] The present invention also provides a system for determining the minimum safe distance of the tunnel excavation face through a goaf area. The system applies the above-mentioned method and includes: a model building module, a condition determination module, and a solution module. The model building module is used to define the failure mode of tunnel excavation face instability under the condition that the stratum contains coal mine goaf, and to build a theoretical model based on the failure mode. The condition determination module determines the minimum safe distance condition based on the theoretical model; The solution module optimizes the shape of the damaged area and obtains the optimal solution for the minimum safe distance based on the minimum safe distance condition.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention proposes a method and system for determining the minimum safe distance of the tunnel excavation face through the goaf area. The analytical solution of the minimum safe distance is derived by using the upper limit method of limit analysis. By comparing with numerical simulation and analytical solution, it is found that the model proposed in this invention has high accuracy and can reflect the mechanism of instability and failure of the tunnel excavation face. (2) This invention finds that the farther the excavation face is from the goaf, the smaller the damage range, the smaller the displacement of the excavation face, and the more stable the surrounding rock. When the excavation face is more than a certain distance from the goaf, the stability of the excavation face is only related to the original surrounding rock of the tunnel; (3) Theoretical research shows that within a certain range, the damage range of the excavation face increases with the increase of the width of the caving zone in the goaf. When the caving zone is wide enough to form an arch effect within the zone, the damage range no longer increases. (4) Theoretical studies show that when the width of the caving zone is small, the minimum safe distance first decreases and then slightly increases with the increase of the dip angle. As the width of the caving zone increases, the minimum safe distance increases with the increase of the dip angle. The width of the caving zone significantly affects the sensitivity of the excavation face stability to changes in dip angle. Attached Figure Description

[0015] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the instability model of the tunnel excavation face crossing the goaf in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the relative velocity relationship between different sliding blocks in an embodiment of the present invention; Figure 4 This is a schematic diagram of the numerical model of an embodiment of the present invention; Figure 5 This is a comparative diagram of the analytical solution and numerical solution of the excavation face failure range in an embodiment of the present invention, wherein (a) is a comparison diagram when the dip angle is 45° and (b) is a comparison diagram when the dip angle is 60°. Figure 6 This is a schematic diagram comparing the analytical solutions of the failure mechanism under different goaf dip angles in an embodiment of the present invention; Figure 7 This is a schematic diagram comparing the analytical solutions for the minimum safe distance under different collapse zone widths and inclination angles according to an embodiment of the present invention; Figure 8This is a comparative diagram of the analytical solutions for the minimum safe distance under different caving zone cohesion and internal friction angles in an embodiment of the present invention. (a) is a comparison diagram of internal friction angles, and (b) is a comparison diagram of cohesion. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Example 1 In this embodiment, as Figure 1 As shown, a method for determining the minimum safe distance of a tunnel excavation face traversing a goaf includes the following steps: S1. Determine the failure mode of tunnel excavation face instability under the condition that the stratum contains coal mine goaf, and establish a theoretical model based on the failure mode.

[0020] like Figure 2 As shown, the failure mode consists of three parts: the truncated cone of the original surrounding rock in the three zones of the goaf ahead of the tunnel excavation face, the truncated cone in the caving zone, and the truncated cone in the fracture zone.

[0021] S2. Determine the minimum safe distance condition based on the theoretical model.

[0022] In this embodiment, the tunnel is... H Assuming the tunnel is deeply buried and the support force is The support force at the excavation face is AB; the boundaries of the failure zone in the original surrounding rock are AC and BD; the boundaries of the failure zone in the caving zone are CE and DF; and the boundaries of the failure zone in the fracture zone are GE and GF. The horizontal distance between the tunnel top and the caving zone is s, and the width of the caving zone is d.

[0023] Methods for obtaining the formula for calculating the minimum safe distance include: With B as the origin of the coordinate system, let the truncated cones ABDC, CDFR, and EFG be block I, block II, and block III, respectively.

[0024] Before the upper limit analysis, a reasonable system velocity field needs to be assumed to provide a premise for the upper limit solution model to solve for the external load power and internal energy dissipation power.

[0025] According to the plasticity-related flow law, the angle between the boundary of the failure region and the velocity of the failure cone, and the angle between the relative velocity of the two failure cones and their interface, are both internal friction angles of the formation. .

[0026] like Figure 3 The diagram illustrates the relative velocity relationships between three rigid sliding blocks. Based on the velocity of block I, the velocity of block II, the relative velocity between block I and block II, the velocity of block III, and the relative velocity between block II and block III are calculated. The methods for calculating the velocity of block II, the relative velocity between block I and block II, the velocity of block III, and the relative velocity between block II and block III include: in, Indicates the velocity of block I. Indicates the velocity of block II. This represents the angle between the velocity field direction of block I and the horizontal plane. Indicates the drop angle. This represents the internal friction angle of the stratum where block I is located. This represents the angle between the velocity field direction of block II and the horizontal plane. This represents the relative velocity between block I and block II. Indicates the velocity of block III. This indicates the internal friction angle of the stratum in which block II is located. This indicates the internal friction angle of the stratum in which block III is located. This indicates the relative velocity between block II and block III. , , Forming a closed velocity triangle; , , They form a closed velocity triangle.

[0027] There are four possible combinations of relative velocities. In the optimization calculation, each of the four combinations must be calculated individually, and the one with the smallest required safe distance is recorded as the minimum safe distance.

[0028] According to the upper bound theorem of limit analysis, the condition for the tunnel excavation face to remain stable is that the power exerted by external forces on the damaged block does not exceed the energy dissipation rate within the damaged zone: in, We Indicates internal power dissipation. WvThis represents the power exerted by an external force on the fragmented block. Wv Including the virtual power of the excavation face WT The virtual power of the weight of the soil in the damaged area Wγ ,Right now: .

[0029] The patent proposes a three-part truncated cone failure zone in front of the excavation face, forming the ABDC zone, CDFE zone, and EFG zone. The rectangle to the left of AB is the excavated tunnel, and A and B are the upper and lower points of the tunnel excavation face. This patent proposes an excavation face failure model in which the front of the excavation face is in the form of three truncated cones when it fails.

[0030] Based on the velocities of block I, block II, and block III, and the areas of block I, block II, and block III, calculate the work done by the soil gravity of block I, block II, and block III respectively, and calculate the virtual power of the soil gravity in the failure zone. Specifically, the areas of blocks I, II, and III are calculated to obtain the areas of block I, II, and III. Let the slope of the caving zone boundary be... kzone The intercepts of the upper and lower boundaries are bup , blow : in, H Indicates the diameter of the tunnel.

[0031] For block I, we have: Then we can find C , D Coordinates of two points: .

[0032] For block II, which is truncated by the boundary of the caving zone at CD and EF respectively, then: The coordinates of points E and F can be obtained: .

[0033] For block III, then: Then the coordinates of point G can be obtained: .

[0034] According to the formulas, we can obtain the following: , , The size is: .

[0035] The power of the work done by the soil's gravity is: in, Represents a block i The density of the strata in which it is located Represents the area of ​​the block. This represents the angle between the velocity field direction of the block and the horizontal plane. i =1,2,3; The virtual power of soil gravity is: in, This represents the virtual power of the soil's weight.

[0036] The energy dissipation rate within the damaged area is calculated based on the virtual power of the soil weight in the damaged area and the virtual power of the excavation face. Analysis shows that internal power dissipation mainly occurs between the sliding block and the non-sliding area, and at the discontinuities between blocks. Assuming the relative velocity relationship is: The internal power dissipation is calculated based on the velocities of block I, block II, and block III. Methods for calculating internal power dissipation include: in, c 1 represents the cohesion of the stratum containing block I. LAC express A Click C The length of the line segment at the point. LBD express B Click D The length of the line segment at the point. LCD express C Click DThe length of the line segment at the point. c 2 represents the cohesion of the stratum in which block II is located. LDF express D Click F The length of the line segment at the point. LEF express E Click F The length of the line segment at the point. c 3 represents the cohesion of the stratum in which block III is located. LEG express E Click G The length of the line segment at the point. LFG express F Click G The length of the line segment at a point.

[0037] The lengths of each line segment can be expressed as: In conventional mountain tunnel construction, mining methods and New Austrian Tunneling Method (NATM) typically employ unsupported excavation, which makes it difficult to apply methods for evaluating the ultimate support capacity of the excavation face.

[0038] For this type of unpressurized open tunnel cross-section, using the excavation face safety factor as a stability evaluation index is more convenient and effective. In engineering practice, the energy ratio method is often used to calculate the safety factor, which is based on the internal dissipated power and the power exerted by external forces on the failing block. in, F This represents the safety factor. When the safety factor is less than 1, the whole system is in an unstable state; when the safety factor is greater than 1, the whole system is in a safe state; when the safety factor is equal to 1, the whole system is in a critical state, at which point the distance between the tunnel excavation face and the goaf is the minimum safe distance.

[0039] S3. Optimize the shape of the damaged area and obtain the optimal solution for the minimum safe distance based on the minimum safe distance condition.

[0040] The shape of the damaged area was optimized using MATLAB software, and the optimal solution for the minimum safe distance was obtained based on the minimum safe distance condition.

[0041] like Figure 4As shown, to verify the applicability and accuracy of the theoretical model, the calculation results of the theoretical model proposed in this invention are compared with the numerical simulation results. Soil parameters are shown in Table 1. The "shell" element is applied around the excavated tunnel to simulate the lining.

[0042] Table 1 like Figure 5 The results show a comparison between numerical simulation and ultimate analysis of the failure mechanism under different dip angles. The comparative analysis reveals that the expansion of the plastic zone within this area is significantly inhibited by the fractured rock mass, resulting in a smaller failure range; the failure characteristics are mainly concentrated within the caving zone.

[0043] At this point, the slip surface of block I, assumed in the theoretical analysis to be located in front of the excavation face, closely matches the range of plastic shear strain in the numerical simulation. Simultaneously, the main failure area reflected in the numerical simulation within the caving zone is basically close to the range of block II in the theoretical model.

[0044] Furthermore, theoretical calculations show that block III is relatively small, which is consistent with the relatively slight deformation of the fracture zone in the simulation. Under both dip angles, the numerically affected area is slightly larger than the theoretically affected area. When the goaf dip angle is 45°, the numerically affected area is 0.39 cm wider than the theoretically affected area along the tunnel excavation direction. H 0.24 meters wide along the direction of gravity. H When the dip angle of the goaf is 60°, the numerical failure zone along the tunnel excavation direction is 0.16 wider than the theoretical failure zone. H 0.28 meters wide along the direction of gravity. H When the inclination angle is smaller, the damage range along the direction of gravity is relatively smaller, while the damage range along the tunnel excavation direction is larger.

[0045] In summary, the numerical simulation results are in good agreement with the theoretically derived failure mechanism, thus validating the limit analysis model presented in this paper.

[0046] like Figure 6 The figure shows the spatial distribution characteristics and evolution of the failure mechanism in the limit analysis model when the dip angle of the goaf varies from 20° to 70°. The study found that as the dip angle of the goaf increases, the movement direction of each sliding block gradually concentrates towards the horizontal direction of the tunnel excavation face. When the goaf dip angle is 20°, the upper boundary of block I approaches parallel to the tunnel axis, and the downward inclination of this boundary increases with the goaf dip angle. Simultaneously, the increased inclination leads to a further expansion of the failure range, and this pattern shows a high degree of consistency under different goaf width conditions.

[0047] Furthermore, a wider caving zone means a larger range of block II within the caving zone and a smaller range of block III within the fracture zone. It can be observed that when the caving zone width is 6m, the apex of block III is very close to the top of the caving zone, at which point the range of plastic failure of the caving zone becomes the main factor controlling the stability of the excavation face.

[0048] like Figure 7 The evolution of the dip angle (15°~70°) of the caving zone in the goaf and the minimum safe distance were revealed. The study shows that the relationship between the minimum safe distance and the dip angle of the caving zone is not a simple linear one, but exhibits significant nonlinear characteristics, and is strongly influenced by the width d of the caving zone. (1) Narrow width condition (d=4m): When the width of the caving zone is narrow, the minimum safe distance first decreases and then slightly increases with the increase of the dip angle. When the dip angle is 55°, the safe distance reaches a minimum value (1.87m), indicating that under this specific geometric condition, the self-stabilizing ability of the excavation face is relatively strong; once the dip angle exceeds 55°, the safe distance increases slightly with the increase of the dip angle.

[0049] (2) Width-dependent working conditions (d≥4m): As the width of the caving zone increases, the curve characteristics change significantly. When d>5m, the minimum safe distance increases with the increase of the dip angle. This means that the larger the dip angle, the higher the risk of instability of the excavation face. When the dip angle reaches 70° and the width is 6m, the minimum safe distance reaches a peak of 2.52m, which is the most dangerous state under all working conditions.

[0050] The width of the caving zone significantly affects the sensitivity of the excavation face stability to changes in dip angle. The wider the caving zone, the wider the distribution of fractured rock mass in front of the tunnel. Under conditions where the caving zone in the goaf has a large dip angle, the fractured rock mass has a stronger tendency to slide towards the excavation face under the action of gravity. This effect directly exacerbates the risk of collapse of the surrounding rock, thus leading to a corresponding increase in the required safety distance.

[0051] like Figure 8 The diagram illustrates the influence of the cohesion and internal friction angle of the caving zone on the minimum safe distance. Analysis shows that the minimum safe distance decreases approximately linearly with the cohesion of the caving zone, but decreases non-linearly with the internal friction angle. When the cohesion of the caving zone is less than 12.5 kPa, the minimum safe distance is significantly affected by the cohesion; when the cohesion is greater than 12.5 kPa, the influence of the cohesion on the minimum safe distance weakens.

[0052] Example 2 In this embodiment, a system for determining the minimum safe distance of a tunnel excavation face traversing a goaf includes: a model building module, a condition determination module, and a solution module.

[0053] The model building module is used to define the failure mode of tunnel excavation face instability under the condition that there is a coal mine goaf in the stratum, and to build a theoretical model based on the failure mode; the condition determination module determines the minimum safe distance condition based on the theoretical model; the solution module optimizes the shape of the failure area and obtains the optimal solution of the minimum safe distance based on the minimum safe distance condition.

[0054] 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 to the technical solutions of the present invention by those skilled in the art 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 determining the minimum safety distance of a tunnel excavation face crossing a goaf, characterized in that, Includes the following steps: A failure mode for tunnel excavation face instability is defined under the condition that the strata contain coal mine goaf, and a theoretical model is established based on the failure mode; Determine the minimum safe distance condition based on the theoretical model; The shape of the damaged area is optimized, and the optimal solution for the minimum safe distance is obtained based on the minimum safe distance condition.

2. The method for determining the minimum safe distance of a tunnel excavation face traversing a goaf area according to claim 1, characterized in that, The failure mode consists of three parts: a truncated cone of the original surrounding rock in the three zones of the goaf ahead of the tunnel excavation face, a truncated cone in the caving zone, and a truncated cone in the fracture zone.

3. The method for determining the minimum safe distance of a tunnel excavation face traversing a goaf area according to claim 1, characterized in that, The method for obtaining the minimum safe distance calculation formula includes: Let truncated cone ABDC, truncated cone CDFR, and truncated cone EFG be block I, block II, and block III, respectively; Based on the velocity of block I, calculate the velocity of block II, the relative velocity between block I and block II, the velocity of block III, and the relative velocity between block II and block III; Calculate the block areas of block I, block II, and block III to obtain the areas of block I, block II, and block III; Based on the velocity of block I, the velocity of block II, the velocity of block III, the area of ​​block I, the area of ​​block II, and the area of ​​block III, calculate the work done by the soil gravity of block I, block II, and block III respectively, and calculate the virtual power of the soil gravity in the failure zone; The power exerted by external forces on the damaged block is calculated based on the virtual power of the soil weight in the damaged area and the virtual power of the excavation face. The internal power dissipation is calculated based on the velocities of block I, block II, and block III. According to the upper bound theorem of limit analysis, the condition for the tunnel excavation face to remain stable is that the internal dissipated power is not less than the power exerted by the external force on the damaged block. Based on the internal dissipated power and the power applied to the damaged block by the external force, the safety factor is calculated. When the safety factor is less than 1, the whole is in an unstable state; when the safety factor is greater than 1, the whole is in a safe state; when the safety factor is equal to 1, the whole is in a critical state, at which point the distance between the tunnel excavation face and the goaf is the minimum safe distance.

4. The method for determining the minimum safe distance of a tunnel excavation face traversing a goaf area according to claim 3, characterized in that, The method for calculating the velocity of block II, the relative velocity between block I and block II, the velocity of block III, and the relative velocity between block II and block III includes: in, Indicates the velocity of block I. Indicates the velocity of block II. This represents the angle between the velocity field direction of block I and the horizontal plane. Indicates the drop angle. This represents the internal friction angle of the stratum where block I is located. This represents the angle between the velocity field direction of block II and the horizontal plane. This represents the relative velocity between block I and block II. Indicates the velocity of block III. This indicates the internal friction angle of the stratum in which block II is located. This indicates the internal friction angle of the stratum in which block III is located. This indicates the relative velocity between block II and block III.

5. The method for determining the minimum safe distance of a tunnel excavation face traversing a goaf area according to claim 3, characterized in that, The power of the work done by the soil's gravity is: in, Represents a block i The density of the strata in which it is located Represents the area of ​​the block. This represents the angle between the velocity field direction of the block and the horizontal plane. i =1,2,3; The virtual power of the soil's gravity is: in, This represents the virtual power of the soil's weight. The power exerted by the external force on the destroyed block is: in, Wv Indicates the energy dissipation rate within the damaged area. WT This represents the virtual power of the excavation face.

6. The method for determining the minimum safe distance of a tunnel excavation face traversing a goaf area according to claim 5, characterized in that, The method for calculating the internal power dissipation includes: in, c 1 represents the cohesion of the stratum containing block I. LAC express A Click C The length of the line segment at the point. LBD express B Click D The length of the line segment at the point. LCD express C Click D The length of the line segment at the point. c 2 represents the cohesion of the stratum in which block II is located. LDF express D Click F The length of the line segment at the point. LEF express E Click F The length of the line segment at the point. c 3 represents the cohesion of the stratum in which block III is located. LEG express E Click G The length of the line segment at the point. LFG express F Click G The length of the line segment at a point.

7. The method for determining the minimum safe distance of a tunnel excavation face traversing a goaf area according to claim 6, characterized in that, The safety factor is: Where F represents the safety factor.

8. The method for determining the minimum safe distance of a tunnel excavation face traversing a goaf area according to claim 1, characterized in that, The shape of the damaged area was optimized using MATLAB software, and the optimal solution for the minimum safe distance was obtained based on the minimum safe distance condition.

9. A system for determining the minimum safe distance of a tunnel excavation face traversing a goaf, the system employing the method described in any one of claims 1-8, characterized in that, include: Model building module, condition determination module, and solution module; The model building module is used to define the failure mode of tunnel excavation face instability under the condition that the stratum contains coal mine goaf, and to build a theoretical model based on the failure mode. The condition determination module determines the minimum safe distance condition based on the theoretical model; The solution module optimizes the shape of the damaged area and obtains the optimal solution for the minimum safe distance based on the minimum safe distance condition.

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