Design method of compensation support force of short arm beam roof anchor cable in self-forming roadway without coal pillar

Abstract

The present invention discloses a method for designing the anchor cable compensation support force for the roof of a short-arm beam in a self-contained, pillar-free tunnel. The method relates to the field of mining technology and includes the following steps: S1. Determining the primary action phase of the anchor cable compensation support force and establishing the failure mechanism of the surrounding rock of the short-arm beam roof under the action of the anchor cable support; S2. Proposing a method for designing the anchor cable compensation support force based on the upper limit analysis theory of plastic mechanics and the failure mechanism of the surrounding rock of the short-arm beam roof. The present invention solves the problems existing in the prior art and can provide a theoretical basis for the design of the anchor cable compensation support force for the short-arm beam roof.

Description

Technical Field

[0001] The invention relates to the technical field of mining, in particular to a design method for compensating supporting force of a short-arm beam roof anchor cable of a self-forming laneway without coal pillars. Background Art

[0002] Pillarless, self-forming tunneling technology is a novel longwall mining method. First introduced in Shropshire, England in the early 18th century, this technology revolutionized the traditional longwall mining face and tunnel layout. Leveraging the N00 technology, processes, and equipment system, it eliminates the need for pre-drilling tunnels and the need for sectioned coal pillars, effectively reducing tunnel surrounding rock stress and facilitating safe and efficient mining. The core of the N00 method lies in the use of roof-cutting and pressure-relieving technology to create a directional slit in the tunnel roof. This slit creates a "short-arm beam" structure, and maintaining the stability of this structure is crucial for tunneling in the N00 method.

[0003] Research has shown that anchor cables play a crucial role in controlling the stability of tunnel roofs. During the initial stages of tunnel excavation, when the triaxial stress state of the surrounding rock changes, timely compensatory support using high-prestressed anchor cables can maximize the restoration of surrounding rock strength. To ensure the stability of the short-arm beam roof and provide a reliable support method that adapts to the large deformation characteristics of the rock mass, He Manchao and his colleagues developed a new constant-resistance, large-deformation anchor cable with an NPR structure. This cable consists of a constant-resistance device, a rod, a tray, and a nut. It features a simple structure, easy construction, and excellent performance in impact resistance, shear resistance, and energy absorption.

[0004] However, in the on-site anchor cable support design of the short arm beam top plate, there is still no design method that considers the influence of comprehensive factors such as rock mass surrounding rock stress, cutting parameters, tunnel width, asymmetry coefficient, etc. for the anchor cable compensation support force.

[0005] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute prior art known to ordinary technicians in the field. Summary of the Invention

[0006] The purpose of the present invention is to provide a design method for the anchor cable compensation support force of the short arm beam roof of a self-forming lane without coal pillars, so as to solve the above-mentioned problems existing in the prior art and provide a theoretical basis for the design of the anchor cable compensation support force of the short arm beam roof.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] The present invention provides a design method for compensating support force of short-arm beam roof anchor cables in a self-forming roadway without coal pillars, comprising the following steps:

[0009] S1. Determine the main action stage of the anchor cable compensation support force and establish the anchor cable compensation support force action mechanism based on the deformation characteristics of the surrounding rock of the short arm beam top plate;

[0010] S2. Based on the upper limit analysis theory of plastic mechanics and combined with the deformation characteristics of the surrounding rock of the short arm beam top plate, the anchor cable compensation support force is determined.

[0011] Preferably, in step S1, based on experiments and / or on-site monitoring, combined with the structural characteristics and change process of the short arm beam top plate, it is determined that the state of the short arm beam top plate has three stages: friction collapse stage, dynamic pressure influence stage, and lane formation stability stage; and it is determined that the main action stages of the anchor cable compensation support force include the friction collapse stage and the lane formation stability stage.

[0012] Preferably, in step S1, establishing an anchor cable compensation support force action mechanism based on the deformation characteristics of the surrounding rock of the short arm beam top plate includes:

[0013] When the short arm beam top plate is in the friction collapse stage, the main function of the anchor cable compensation support force is to prevent the short arm beam from being greatly deformed under the action of the friction force of the gangue collapse in the goaf. At this time, the stress state of the short arm beam top plate is tensile. The design of the anchor cable compensation support force should take into account the horizontal stress effect and determine the collapse friction force.

[0014] When the short arm beam top plate is in the stage of dynamic pressure influence, the main function of the anchor cable compensation support force is to maintain the stability of the short arm beam together with the temporary support beside the roadway. At this time, the stress state of the short arm beam top plate is compressive. The design of the anchor cable compensation support force should take into account the role of the roadway support force and the influence of mining, and determine the roadway support resistance range and mining influence coefficient.

[0015] When the top plate of the short arm beam is in the stable stage of tunnel formation, the temporary support beside the tunnel is withdrawn. The main function of the anchor cable compensation support force is to maintain the stability of the short arm beam together with the supporting force of the collapsed gangue in the goaf. At this time, the stress state of the top plate of the short arm beam is tensile. The design of the anchor cable compensation support force should consider the supporting effect of the gangue in the goaf on the top plate of the short arm beam and determine the supporting force of the crushed and expanded gangue.

[0016] Preferably, in step S2, based on the upper limit analysis theory of plastic mechanics and combined with the deformation characteristics of the surrounding rock of the short-arm beam top plate, the internal energy dissipation rate of the surrounding rock is solved, the work power of the external force is determined, the compensation support force of a single anchor cable at each stage of the short-arm beam top plate is calculated and compared, and the compensation support force of the anchor cable is determined.

[0017] Preferably, solving the internal energy dissipation rate of the surrounding rock includes:

[0018] According to the plastic potential theory, the plastic strain increment at the fracture surface of the surrounding rock mass is obtained;

[0019] The energy dissipation rate inside the rock mass at the fracture surface is obtained according to the plastic strain increment.

[0020] Preferably, determining the external force work power includes:

[0021] Obtain the work power of surrounding rock stress;

[0022] Obtain the work power done by the surrounding rock's own weight;

[0023] Obtain the working power of the anchor cable compensation support force;

[0024] Obtain the work power of the collapse friction force during the roof friction collapse stage;

[0025] Obtain the working power of the crushed and expanded gangue supporting force during the stable stage of the roof roadway;

[0026] Obtain the working power of the tunnel side support force;

[0027] Obtain the supporting power of the solid coal seam.

[0028] Preferably, the compensation support force required for a single anchor cable in each stage of the short arm beam top plate movement is determined according to the anchor cable compensation support parameters;

[0029] Among them, the anchor compensation support parameters include surrounding rock stress, cutting angle, cutting height, tunnel width, lateral pressure coefficient, crushed and expanded gangue support coefficient, mining influence coefficient, tunnel side support force, spacing between anchor cables, rock cohesion, asymmetry coefficient, rock mass weight, and rock mass internal friction angle.

[0030] Preferably, when the short arm beam top plate is in the friction collapse stage, the critical value of the compensation support force of a single anchor cable is:

[0031]

[0032] Among them, Pa1 is the compensatory support force required by a single anchor cable when the short arm beam top plate is in the friction collapse stage, l is the tunnel width, c is the rock mass cohesion, h is the cutting height, γ is the rock mass weight, is the internal friction angle of the rock mass, θ is the cutting angle, q is the surrounding rock stress, n is the number of anchor cables, k is the asymmetry coefficient, λ1 is the mining influence coefficient, λ0 is the lateral pressure coefficient, and μ is the friction coefficient between rock blocks;

[0033] When the short arm beam top plate is in the stage of dynamic pressure influence, the critical value of the compensation support force of a single anchor cable is:

[0034]

[0035] Where Pa2 is the compensatory support force required by a single anchor cable when the short arm beam top plate is in the dynamic pressure influence stage, l is the tunnel width, c is the rock mass cohesion, h is the cutting height, γ is the rock mass weight, is the internal friction angle of the rock mass, θ is the cutting angle, q is the surrounding rock stress, F is the roadside support force, n is the number of anchor cables, k is the asymmetry coefficient, λ1 is the mining influence coefficient, and λ2 is the support coefficient of crushed and expanded waste rock;

[0036] When the short arm beam top plate is in the stable stage of tunnel formation, the critical value of the compensation support force of a single anchor cable is:

[0037]

[0038] Among them, Pa3 is the compensation support force required by a single anchor cable in the stable stage of the roadway, l is the roadway width, c is the rock mass cohesion, h is the cutting height, γ is the rock mass weight, is the internal friction angle of the rock mass, θ is the cutting angle, q is the surrounding rock stress, n is the number of anchor cables, k is the asymmetry coefficient, λ1 is the mining influence coefficient, and λ2 is the support coefficient of crushed and expanded gangue.

[0039] Preferably, according to the upper limit analysis theory of plastic mechanics, the judgment criterion is determined as when the tunnel width l is equal to the falling body width b, the critical value of the compensating support force required by a single anchor cable is obtained.

[0040] Preferably, the limit state λ2=0 is taken to calculate the compensatory support force required for a single anchor cable in each stage of the short arm beam top plate;

[0041] Anchor cable pre-tightening force is applied asymmetrically and linearly to the top plate of the short arm beam.

[0042] Compared with the prior art, the present invention has achieved the following technical effects:

[0043] The present invention constructs the rock failure mechanism of the short-arm beam top plate under the action of anchor cable support. According to the upper limit analysis theory of plastic mechanics and combined with the above-mentioned rock failure mechanism of the short-arm beam top plate, the sensitivity analysis method can be used to analyze the influencing factors of the anchor cable compensation support force, and corresponding engineering suggestions are put forward, providing a theoretical basis for the design of the anchor cable compensation support force of the short-arm beam top plate. DETAILED DESCRIPTION

[0044] The following is a clear and complete description of the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0045] The purpose of the present invention is to provide a design method for the anchor cable compensation support force of the short arm beam roof of a self-forming lane without coal pillars, so as to solve the above-mentioned problems existing in the prior art and provide a theoretical basis for the design of the anchor cable compensation support force of the short arm beam roof.

[0046] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below in conjunction with specific embodiments.

[0047] This embodiment provides a method for designing the compensatory support force of the short-arm beam roof anchor cable of a self-forming roadway without coal pillars, including the following steps:

[0048] S1. Determine the main action stage of the anchor cable compensation support force and establish the anchor cable compensation support force action mechanism based on the deformation characteristics of the surrounding rock of the short arm beam top plate;

[0049] S2. According to the upper limit analysis theory of plastic mechanics (in plastic mechanics, it is assumed that the displacement state of the plastic deformation zone is a dynamically admissible velocity field. Since the velocity field is set as long as it meets the dynamically admissible conditions and the stress conditions should not be considered, the velocity field is not necessarily a real velocity field. The obtained load is always greater than the real load, so it is called the upper limit method. This is a basic mechanics theory known in this field), combined with the deformation characteristics of the surrounding rock of the short arm beam top plate, a design method for the anchor compensation support force is proposed (i.e., determining the anchor compensation support force).

[0050] In this embodiment, in step S1, based on the test (physical model test of the N00 method mining process) and on-site monitoring, combined with the structural characteristics and change process of the short arm beam top plate, it is determined that the state of the short arm beam top plate has three stages: friction collapse stage, dynamic pressure influence stage, and lane formation stability stage; and the anchor cable compensation support force focuses on the friction collapse and lane formation stability stages, and it is determined that the main action stages of the anchor cable compensation support force include the friction collapse stage and the lane formation stability stage.

[0051] During the frictional collapse phase, in the initial stage of retaining tunnels using the N00 construction method, after the cracks are cut, the goaf roof collapses layer by layer from bottom to top. Due to the cracks, the collapsing rock blocks will not significantly impact the short-arm beam structure. However, due to the influence of horizontal stress, friction exists at this stage, necessitating the timely application of anchor cables and other components to ensure the stability of the short-arm beam. Anchor cables: ① Apply high preload to provide timely compensatory support, improve the stress state of the rock mass after excavation, and restore the strength of the surrounding rock; ② Act as a suspension, anchoring the anchor end to a stable rock stratum to control the stability of the short-arm beam roof.

[0052] During the dynamic pressure impact phase, as the working face advances, the basic roof rock reaches its ultimate stress and begins to break, further bending and sagging. The broken waste rock in the goaf is continuously compacted, but some uncompacted space remains. At this point, temporary support measures such as hydraulic supports or single pillars are used to strengthen the support and ensure the stability of the short-arm beam roof. Compared to the friction collapse phase, the roof deformation during this phase is greater.

[0053] During the lane stabilization phase, as the working face continues to be mined and the remaining lane length reaches a certain distance, the collapsed waste rock in the goaf is compacted and stabilized. Leveraging the stabilizing force of the crushed waste rock and the support of the NPR anchor cables, the short-arm beam roof reaches a stable equilibrium. At this point, the temporary support in the stable area is gradually removed.

[0054] In this embodiment, in step S1, establishing the anchor cable compensation support force action mechanism based on the deformation characteristics of the surrounding rock of the short arm beam top plate includes:

[0055] When the short arm beam top plate is in the friction collapse stage, the main function of the anchor cable compensation support force is to prevent the short arm beam from being greatly deformed under the action of the friction force of the gangue collapse in the goaf. At this time, the stress state of the short arm beam top plate is tensile. The design of the anchor cable compensation support force should take into account the horizontal stress effect and determine the collapse friction force.

[0056] When the short arm beam top plate is in the stage of dynamic pressure influence, the main function of the anchor cable compensation support force is to maintain the stability of the short arm beam together with the temporary support beside the roadway. At this time, the stress state of the short arm beam top plate is compressive. The design of the anchor cable compensation support force should take into account the role of the roadway support force and the influence of mining, and determine the roadway support resistance range and mining influence coefficient.

[0057] When the top plate of the short arm beam is in the stable stage of tunnel formation, the temporary support beside the tunnel is withdrawn. The main function of the anchor cable compensation support force is to maintain the stability of the short arm beam together with the supporting force of the collapsed gangue in the goaf. At this time, the stress state of the top plate of the short arm beam is tensile. The design of the anchor cable compensation support force should consider the supporting effect of the gangue in the goaf on the top plate of the short arm beam and determine the supporting force of the crushed and expanded gangue.

[0058] Furthermore, based on the deformation characteristics of the surrounding rock of the short arm beam roof, the anchor cable compensation support force action mechanism is established, including:

[0059] The stress of the surrounding rock of the tunnel roof is considered to be a distributed load acting around the falling body, its direction is perpendicular to the broken roof, and it is evenly distributed along the breaking curve of the falling rock mass.

[0060] Furthermore, the anchor cable compensation support force action mechanism is established based on the deformation characteristics of the surrounding rock of the short arm beam top plate, which also includes:

[0061] Obtain the first supporting load generated by the crushed and expanded gangue in the goaf on the top plate of the short arm beam; wherein, considering the first supporting load generated by the crushed and expanded gangue in the goaf on the top plate of the short arm beam in the stable stage of the roadway, the first supporting load is linearly distributed;

[0062] Obtain the second support load generated by the anchor cable on the top plate of the short arm beam;

[0063] Obtain the third support load generated by the coal body on the top plate of the short arm beam;

[0064] Consider that when the power of the external force is greater than the energy dissipation rate of the rock mass, the top plate of the short arm beam will fracture and fail;

[0065] The model establishes the motion-allowed velocity field;

[0066] Consider the falling rock around the short arm beam roof and the surrounding rock of the fracture range as rigid bodies;

[0067] Considering that the deformation and failure of the surrounding rock of the short-arm beam top plate conform to the nonlinear Hoek-Brown strength criterion of the rock mass (according to the nature of nonlinear failure of rock mass, Hoek proposed the internationally famous Hoek-Brown criterion, which is a well-known basic theory in this field), and that the yield function surface in the principal stress space coincides with the plastic potential function surface.

[0068] Furthermore, the anchor cable compensation support force action mechanism is established based on the deformation characteristics of the surrounding rock of the short arm beam top plate, including:

[0069] Based on the mechanical mechanism of surrounding rock failure, the collapse friction force is obtained according to the static equilibrium condition;

[0070] Among them, it is assumed that the collapse friction force is the first supporting load generated by the collapsed gangue on the short arm beam top plate during the friction collapse stage of the short arm beam top plate. When calculating the anchor cable compensation support force at this stage, the supporting load generated by the crushed and expanded gangue in the goaf on the short arm beam top plate is ignored, and the side support force is not considered.

[0071] In this embodiment, step S2 specifically includes: according to the upper limit analysis theory of plastic mechanics, combined with the deformation characteristics of the surrounding rock of the short arm beam top plate, solving the internal energy dissipation rate of the surrounding rock, determining the work power of the external force, calculating and comparing the compensation support force value of a single anchor cable at each stage of the short arm beam top plate, and determining the anchor cable compensation support force.

[0072] In this embodiment, solving the internal energy dissipation rate of the surrounding rock includes:

[0073] According to the traditional plastic potential theory (in 1928, Mises extended the concept of elastic potential to plasticity theory, assuming that for the plastic flow state, there is also a plastic potential function similar to the elastic potential function, and its plastic flow direction is consistent with the gradient or external normal direction of the plastic potential function. This is the traditional plastic potential theory), the plastic strain increment at the fracture surface of the surrounding rock mass is obtained;

[0074] The energy dissipation rate inside the rock mass at the fracture surface is obtained according to the plastic strain increment.

[0075] In this embodiment, determining the work power of the external force includes:

[0076] Obtain the work power of surrounding rock stress;

[0077] Obtain the work power done by the surrounding rock's own weight;

[0078] Obtain the working power of the anchor cable compensation support force;

[0079] Obtain the work power of the collapse friction force during the roof friction collapse stage;

[0080] Obtain the working power of the crushed and expanded gangue supporting force during the stable stage of the roof roadway;

[0081] Obtain the working power of the tunnel side support force;

[0082] Obtain the supporting power of the solid coal seam.

[0083] In this embodiment, the compensatory support force required for a single anchor cable in each stage of the short arm beam top plate movement is determined based on the anchor cable compensation support parameters; wherein the anchor cable compensation support parameters include surrounding rock stress, cutting angle, cutting height, tunnel width, lateral pressure coefficient, crushed and expanded gangue support coefficient, mining influence coefficient, tunnel side support force, spacing between anchor cables, rock cohesion, asymmetry coefficient, rock mass weight, rock mass internal friction angle and other parameters.

[0084] In this embodiment, determining the compensating support force required by a single anchor cable in each stage of the short arm beam top plate movement includes:

[0085] According to the principle of virtual work, the work power of the internal and external forces of the surrounding rock is equal, the Euler equation and the corresponding boundary conditions, and using the required surrounding rock stress, slit angle, roadway width, lateral pressure coefficient, slit height, anchor cable spacing, rock mass cohesion, asymmetry coefficient, rock mass weight and other parameters, the critical value of the compensatory support force of a single anchor cable is determined when the short arm beam top plate is in the friction collapse stage:

[0086]

[0087] Among them, Pa1 is the compensatory support force required by a single anchor cable when the short arm beam top plate is in the friction collapse stage, l is the tunnel width, c is the rock mass cohesion, h is the cutting height, γ is the rock mass weight, is the internal friction angle of the rock mass, θ is the cutting angle, q is the surrounding rock stress, n is the number of anchor cables, k is the asymmetry coefficient, λ1 is the mining influence coefficient, λ0 is the lateral pressure coefficient, and μ is the friction coefficient between rock blocks;

[0088] According to the principle of virtual work, the work power of the internal and external forces of the surrounding rock is equal, the Euler equation and the corresponding boundary conditions, and using the required surrounding rock stress, slit angle, roadway width, lateral pressure coefficient, slit height, anchor cable spacing, rock mass cohesion, asymmetry coefficient, rock mass weight and other parameters, the critical value of the compensation support force of a single anchor cable is determined when the short arm beam top plate is in the stable stage of roadway formation:

[0089]

[0090] Among them, Pa3 is the compensation support force required by a single anchor cable in the stable stage of the roadway, l is the roadway width, c is the rock mass cohesion, h is the cutting height, γ is the rock mass weight, is the internal friction angle of the rock mass, θ is the cutting angle, q is the surrounding rock stress, n is the number of anchor cables, k is the asymmetry coefficient, λ1 is the mining influence coefficient, and λ2 is the support coefficient of crushed and expanded waste rock;

[0091] Similarly, using the determined parameters such as the tunnel side support force and mining influence coefficient, the critical value of the compensation support force of a single anchor cable when the short arm beam top plate is in the dynamic pressure influence stage is determined as follows:

[0092]

[0093] Where Pa2 is the compensatory support force required by a single anchor cable when the short arm beam top plate is in the dynamic pressure influence stage, l is the tunnel width, c is the rock mass cohesion, h is the cutting height, γ is the rock mass weight, is the internal friction angle of the rock mass, θ is the cutting angle, q is the surrounding rock stress, F is the roadside support force, n is the number of anchor cables, k is the asymmetry coefficient, λ1 is the mining influence coefficient, and λ2 is the crushed and expanded waste rock support coefficient.

[0094] In this embodiment, the critical values of the compensation support force of the short arm beam top plate anchor cable in the friction collapse stage, dynamic pressure influence stage, and lane stability stage are compared and selected, and the larger value is selected for the compensation support force design.

[0095] In this embodiment, according to the upper limit analysis theory of plastic mechanics, the judgment criterion is determined as when the tunnel width l is equal to the falling body width b, the critical value of the compensatory support force required by a single anchor cable is obtained.

[0096] In this embodiment, considering that the specific value of the support coefficient of the crushed and expanded waste rock at each stage is difficult to determine, from the perspective of engineering design safety, the limit state λ2=0 is taken to calculate the compensatory support force required for a single anchor cable at each stage of the short arm beam top plate;

[0097] When the top plate is affected by asymmetric loads, an asymmetric linear anchor preload is applied to the top plate of the short arm beam, and the asymmetric coefficient of the anchor preload is k.

[0098] The design method of the short arm beam top plate compensating support force provided by the present invention actually takes into account the design parameters of the compensating support force, which are the result of the comprehensive effect of multiple parameters such as surrounding rock stress, cutting angle, tunnel width, lateral pressure coefficient, mining influence coefficient, cutting height, anchor cable spacing, rock cohesion, asymmetry coefficient, and rock mass weight.

[0099] This specification uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A design method for compensating support force of short-arm beam roof anchor cables in a self-contained laneway without coal pillars, characterized in that: The following steps are involved: S1. Determine the main action stage of the anchor cable compensation support force and establish the anchor cable compensation support force action mechanism based on the deformation characteristics of the surrounding rock of the short arm beam top plate; In step S1, based on tests and / or on-site monitoring, combined with the structural characteristics and change process of the short arm beam top plate, it is determined that the state of the short arm beam top plate has three stages: friction collapse stage, dynamic pressure influence stage, and lane formation stability stage; and it is determined that the main action stages of the anchor cable compensation support force include the friction collapse stage and the lane formation stability stage; S2. Determine the anchor cable compensation support force based on the upper limit analysis theory of plastic mechanics and the deformation characteristics of the surrounding rock of the short arm beam top plate; In step S2, based on the upper limit analysis theory of plastic mechanics and the deformation characteristics of the surrounding rock of the short arm beam top plate, the internal energy dissipation rate of the surrounding rock is solved, the work power of the external force is determined, and the compensation support force of a single anchor cable at each stage of the short arm beam top plate is calculated and compared to determine the compensation support force of the anchor cable; According to the anchor cable compensation support parameters, the compensation support force required by a single anchor cable in each stage of the short arm beam top plate movement is determined; The anchor cable compensation support parameters include surrounding rock stress, cutting angle, cutting height, roadway width, lateral pressure coefficient, crushed and expanded waste rock support coefficient, mining influence coefficient, roadside support force, spacing between anchor cables, rock mass cohesion, asymmetry coefficient, rock mass weight, and rock mass internal friction angle. When the short arm beam top plate is in the friction collapse stage, the critical value of the compensation support force of a single anchor cable is: Among them, Pa1 is the compensatory support force required by a single anchor cable when the short arm beam top plate is in the friction collapse stage, l is the tunnel width, c is the rock mass cohesion, h is the cutting height, γ is the rock mass weight, is the internal friction angle of the rock mass, θ is the cutting angle, q is the surrounding rock stress, n is the number of anchor cables, k is the asymmetry coefficient, λ1 is the mining influence coefficient, λ0 is the lateral pressure coefficient, and μ is the friction coefficient between rock blocks; When the short arm beam top plate is in the stage of dynamic pressure influence, the critical value of the compensation support force of a single anchor cable is: Where Pa2 is the compensatory support force required by a single anchor cable when the short arm beam top plate is in the dynamic pressure influence stage, l is the tunnel width, c is the rock mass cohesion, h is the cutting height, γ is the rock mass weight, is the internal friction angle of the rock mass, θ is the cutting angle, q is the surrounding rock stress, F is the roadside support force, n is the number of anchor cables, k is the asymmetry coefficient, λ1 is the mining influence coefficient, and λ2 is the support coefficient of crushed and expanded waste rock; When the short arm beam top plate is in the stable stage of tunnel formation, the critical value of the compensation support force of a single anchor cable is: Among them, Pa3 is the compensation support force required by a single anchor cable in the stable stage of tunnel formation, l is the tunnel width, c is the rock mass cohesion, h is the cutting height, γ is the rock mass weight, is the internal friction angle of the rock mass, θ is the cutting angle, q is the surrounding rock stress, n is the number of anchor cables, k is the asymmetry coefficient, λ1 is the mining influence coefficient, and λ2 is the support coefficient of crushed and expanded gangue.

2. The design method for the compensation support force of the short-arm beam roof anchor cable of the non-pillar self-forming roadway according to claim 1 is characterized in that: In step S1, establishing the anchor cable compensation support force action mechanism based on the deformation characteristics of the surrounding rock of the short arm beam top plate includes: When the short arm beam top plate is in the friction collapse stage, the anchor cable compensation support force is used to prevent the short arm beam from deforming under the action of the friction force of the goaf rock collapse. At this time, the stress state of the short arm beam top plate is tensile. The design of the anchor cable compensation support force takes into account the horizontal stress effect and determines the collapse friction force. When the short arm beam top plate is in the stage of dynamic pressure influence, the anchor cable compensation support force is used to maintain the stability of the short arm beam together with the temporary support beside the roadway. At this time, the stress state of the short arm beam top plate is under compression. The design of the anchor cable compensation support force takes into account the effect of the roadside support force and the influence of mining, and determines the roadside support resistance range and the mining influence coefficient. When the top plate of the short arm beam is in the stable stage of tunnel formation, the temporary support beside the tunnel is withdrawn, and the anchor cable compensation support force is used to maintain the stability of the short arm beam together with the support force of the collapsed gangue in the goaf. At this time, the stress state of the top plate of the short arm beam is tensile. The design of the anchor cable compensation support force takes into account the supporting effect of the gangue in the goaf on the top plate of the short arm beam to determine the supporting force of the crushed and expanded gangue.

3. The design method for the compensation support force of the short-arm beam roof anchor cable of the non-pillar self-forming roadway according to claim 1 is characterized in that: Solving the internal energy dissipation rate of the surrounding rock includes: According to the plastic potential theory, the plastic strain increment at the fracture surface of the surrounding rock mass is obtained; The energy dissipation rate inside the rock mass at the fracture surface is obtained according to the plastic strain increment.

4. The design method for the compensation support force of the short-arm beam roof anchor cable of the non-pillar self-forming roadway according to claim 1 is characterized in that: Determining the work done by an external force includes: Obtain the work power of surrounding rock stress; Obtain the work power done by the surrounding rock's own weight; Obtain the working power of the anchor cable compensation support force; Obtain the work power of the collapse friction force during the roof friction collapse stage; Obtain the working power of the crushed and expanded gangue supporting force during the stable stage of the roof roadway; Obtain the working power of the tunnel side support force; Obtain the supporting power of the solid coal seam.

5. The design method for the compensation support force of the short-arm beam roof anchor cable of the non-pillar self-forming roadway according to claim 1 is characterized in that: According to the upper limit analysis theory of plastic mechanics, the judgment criterion is determined as the critical value of the compensatory support force required by a single anchor cable when the tunnel width l is equal to the width b of the falling body.

6. The design method for the compensation support force of the short-arm beam roof anchor cable of the non-pillar self-forming roadway according to claim 1 is characterized in that: Taking the ultimate limit state λ2=0, calculate the required compensatory support force of a single anchor cable in each stage of the short arm beam top plate; Anchor cable pre-tightening force is applied asymmetrically and linearly to the top plate of the short arm beam.

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