A method and system for determining the spacing of pressure relief boreholes in a three-dimensional stress field

Abstract

The present application discloses a method and system for determining the spacing of pressure relief boreholes in a three-dimensional stress field, which relates to the field of borehole spacing arrangement and includes: obtaining the peak range of roadway abutment pressure; obtaining the corresponding magnitudes of in-situ stress, the azimuth angle and dip angle of in-situ stress; determining the cohesion C, internal friction angle φ and Poisson's ratio v of roadway surrounding rock and the radius of the pressure relief borehole; converting the stress into the stress load in the borehole coordinate system through the coordinate transformation method; based on the Kirsch solution method and using the determined borehole radius and the stress load obtained in the borehole coordinate system, obtaining the normal stresses σr, σt, σv and shear stresses τrt, τrv, τtv at any point within the preset range of the hole in the borehole coordinate system; based on the M-C strength criterion in the three-dimensional state and using the rock mechanics parameters, solving to obtain the radius r of the permeability enhancement circle of the pressure relief borehole; determining the layout mode of the pressure relief boreholes according to r. Aiming at the unreasonable layout of pressure relief boreholes and unclear pressure relief parameters in the prior art, the present application improves the standardization of borehole pressure relief in roadway surrounding rock.

Description

Technical Field

[0001] This application relates to the field of borehole spacing arrangement, and particularly to a method and system for determining the relief borehole spacing in a three-dimensional stress field. Background Art

[0002] Coal is a key industrial raw material in China. Its huge demand has led to the annual extension of mine exploitation towards deeper depths. Under the conditions of deep exploitation, the control of the surrounding rock stability of chambers, roadways, and boreholes is the focus and difficulty of research. The excavation of roadways will break the original stress balance state, resulting in stress redistribution and stress concentration. Under the influence of high-stress environments and superimposed mining disturbances, the surrounding rock of roadways will undergo large swelling deformations. The single bolt-cable support has a poor control effect on the stability of the surrounding rock of roadways. Therefore, using the method of borehole pressure relief to transfer the high stress concentrated around the roadway to the deep stable rock mass and reduce the deformation and damage degree of the surrounding rock of the roadway is an effective auxiliary support means.

[0003] However, currently, when designing the borehole pressure relief scheme, most use the empirical analogy method or numerical simulation method to determine the layout parameters of relief boreholes, lacking theoretical basis and quantitative analysis means. Although a few studies have carried out theoretical calculations, most simplify the calculation model into a plane strain problem, ignoring the real three-dimensional stress environment of underground rock masses and failing to accurately reflect the interaction mechanism between relief boreholes and complex in-situ stress fields, resulting in deviations between the obtained borehole layout parameters and actual engineering conditions. Due to the unreasonable determination of borehole spacing, problems such as insufficient pressure relief in some areas, unsatisfactory pressure relief effects, and difficulty in transferring high stress to the deep often occur, ultimately leading to poor control effects on the stability of the surrounding rock of roadways. In severe cases, it may even trigger dynamic disasters such as roof falls and rib spalls, and large-area bolt / cable failures, posing potential hazards to coal mine safety production. Summary of the Invention

[0004] Aiming at the problem of stress concentration in the surrounding rock of roadways caused by unreasonable layout of relief boreholes in the prior art, this application provides a method and system for determining the relief borehole spacing in a three-dimensional stress field. By obtaining the magnitude and direction of in-situ stress corresponding to the peak value of abutment pressure, establishing the in-situ stress coordinate system, the geodetic rectangular coordinate system, and the borehole coordinate system and performing coordinate transformation, an implicit equation for the boundary of the plastic zone around the borehole is established based on the Kirsch solution method and the Mohr-Coulomb yield criterion, and the reasonable radius of the permeability enhancement circle of the relief borehole and the borehole row spacing are solved, improving the stability of the surrounding rock of the roadway.

[0005] The objectives of this application are achieved through the following technical solutions.

[0006] One aspect of the present application provides a method for determining the spacing of pressure relief boreholes in a three-dimensional stress field, including: S1, obtaining the peak range of roadway abutment pressure through borehole stress gauges; S2, obtaining the magnitude of in-situ stress, the azimuth angle and dip angle of in-situ stress corresponding to the peak range of abutment pressure through in-situ stress measurement; S3, determining the parameters of the roadway surrounding rock through rock mechanics tests, where the parameters include cohesion C, internal friction angle φ, and Poisson's ratio v; S4, determining the radius of the pressure relief borehole according to the engineering geological parameters and construction conditions of the construction mine; S5, establishing an in-situ stress coordinate system, a geodetic rectangular coordinate system, and a borehole coordinate system, and converting the magnitude, azimuth angle, and dip angle of the in-situ stress in the in-situ stress coordinate system obtained in S2 into stress loads in the borehole coordinate system through coordinate transformation methods; S6, in the borehole coordinate system, based on the Kirsch solution method and using the borehole radius determined in S4 and the stress loads in the borehole coordinate system obtained in S5, obtaining the normal stresses σr, σt, σv and shear stresses τrt, τrv, τtv at any point within the preset range of the hole in the borehole coordinate system; S7, based on the M-C strength criterion in three-dimensional state, using the rock mechanics parameters obtained in S3, establishing an implicit equation for the boundary of the plastic zone around the borehole, substituting the stress components at any point within the preset range of the hole in the borehole coordinate system obtained in S6 into the implicit equation, and solving to obtain the radius r of the permeability enhancement circle of the pressure relief borehole; S8, determining the row spacing PR of two adjacent pressure relief boreholes and the layout method of the pressure relief boreholes according to the radius r of the permeability enhancement circle of the pressure relief borehole.

[0007] Specifically, the peak abutment pressure: After the roadway surrounding rock is excavated, the maximum abutment pressure value formed at the advanced position of the roadway due to stress redistribution. The peak abutment pressure reflects the stress state of the rock around the roadway and is an important basis for determining the location of in-situ stress measurement. Borehole stress gauge: An instrument used to measure the stress state of rock mass in a borehole. By installing strain gauges or other sensors in the borehole, strain data on the borehole wall can be obtained, and then the magnitude and direction of the stress of the rock mass can be calculated. In-situ stress azimuth and dip angle: Two angular parameters reflecting the spatial direction of in-situ stress. The azimuth represents the angle between the in-situ stress and the due north direction in the horizontal plane, with a value range of 0° to 360°; the dip angle represents the angle between the in-situ stress and the horizontal plane, with a value range of 0° to 90°. In-situ stress coordinate system: An orthogonal coordinate system established with the main directions of in-situ stress as the coordinate axes. Usually, the maximum principal stress σ1, the intermediate principal stress σ2, and the minimum principal stress σ3 are used as the coordinate axes respectively to represent the spatial distribution state of in-situ stress. Borehole coordinate system: An orthogonal coordinate system established with the borehole axis as the coordinate axis. Usually, the borehole axis direction is taken as the z-axis, the borehole radius direction is taken as the x-axis, and the direction perpendicular to the x-axis and z-axis is taken as the y-axis. The borehole coordinate system is used to analyze the stress distribution around the borehole. Kirsch solution method: An analytical method used to solve the stress distribution around a circular hole. Based on the Kirsch solution under the plane strain state, the normal stress and shear stress states at any point around the hole can be obtained. Mohr-Coulomb strength criterion (M-C strength criterion): An empirical criterion describing the shear strength characteristics of geotechnical materials. Pressure-relief borehole permeability enhancement zone: A stress reduction area formed around the borehole due to the pressure-relief effect of the pressure-relief borehole with the pressure-relief borehole as the center. The radius of the pressure-relief borehole permeability enhancement zone reflects the pressure-relief range of a single borehole and is a key parameter for determining the borehole spacing.

[0008] More specifically, when determining the radius of the pressure relief borehole, it is necessary to comprehensively consider factors such as the engineering geological parameters and construction conditions of the construction mine. According to the geological data of the mine, geological parameters such as the lithology of the rock around the roadway, the stratigraphic structure, and the integrity of the rock mass are obtained. Lithology: Determine the main rock types of the roadway surrounding rock, such as sandstone, mudstone, limestone, etc. The mechanical properties and pressure relief effects of different lithologies are different. Stratigraphic structure: Analyze the dip angle, thickness, bedding characteristics, etc. of the strata where the roadway is located, and evaluate the influence of the stratigraphic structure on borehole construction and pressure relief effect. Rock mass integrity: Evaluate the degree of development of joints and fissures in the roadway surrounding rock. The higher the rock mass integrity, the greater the difficulty of borehole construction, but the better the pressure relief effect. Combining the construction conditions of the mine, determine the process parameters of borehole construction. Borehole diameter: Select a suitable bit diameter according to the specifications and construction capabilities of the existing drilling rig equipment, usually 50 - 100 mm. Borehole depth: Determine the borehole depth according to the stress distribution characteristics of the roadway surrounding rock and the pressure relief requirements, generally 2 - 5 m. Borehole dip angle: Determine the borehole dip angle according to the pressure relief design requirements and on-site conditions, usually perpendicular to the roadway wall surface or inclined at a small angle. In this application, the value range of the borehole radius is 0.1 m to 0.5 m.

[0009] Further, in S2, the magnitudes of the in-situ stresses, the azimuth angles of the in-situ stresses, and the dip angles corresponding to the peak ranges of the abutment pressures are obtained through in-situ stress measurement, including: within the peak ranges of the abutment pressures determined in step S1, the maximum principal stress σ1, the intermediate principal stress σ2, and the minimum principal stress σ3 within the corresponding ranges are obtained through in-situ stress measurement; the stress dip angles α1, α2, and α3, and the stress azimuth angles β1, β2, and β3 corresponding to the maximum principal stress σ1, the intermediate principal stress σ2, and the minimum principal stress σ3 are obtained through in-situ stress measurement.

[0010] Further, in S5, establish the in-situ stress coordinate system, the geodetic rectangular coordinate system, and the borehole coordinate system, and convert the in-situ stress magnitude, azimuth, and dip angle in the in-situ stress coordinate system obtained in S2 into the stress load in the borehole coordinate system through coordinate transformation methods, including: taking the directions of the maximum principal stress σ1, the intermediate principal stress σ2, and the minimum principal stress σ3 obtained in step S2 as the coordinate axes to establish an orthogonal coordinate system O-XYZ. The X-axis coincides with the direction of the maximum principal stress σ1, the Y-axis coincides with the direction of the intermediate principal stress σ2, and the Z-axis coincides with the direction of the minimum principal stress σ3. Taking the borehole construction position as the origin, establish the geodetic rectangular coordinate system O-X'Y'Z'. The X'-axis points due east, the Y'-axis points due north, and the Z'-axis points vertically upward. According to the borehole dip angle δ and the borehole azimuth w of the borehole spatial layout position relative to the geodetic coordinate system, establish the borehole coordinate system O-X''Y''Z''. The borehole dip angle δ is the angle between the borehole axis and the vertical direction (Z'-axis), and its value range is 0° to 90°. The borehole azimuth w is the angle between the projection of the borehole axis on the horizontal plane (X'O'Y' plane) and the due north direction (Y'-axis), and its value range is 0° to 360°. The Z''-axis coincides with the borehole axis, and the X''-axis and the Y''-axis are orthogonal to the Z''-axis on the borehole cross-section. According to the coordinate transformation formula, convert the stress state in the in-situ stress coordinate system O-XYZ into the stress load in the borehole coordinate system O-X''Y''Z''. The stress state in the in-situ stress coordinate system is represented by the maximum principal stress σ1, the intermediate principal stress σ2, and the minimum principal stress σ3, as well as the corresponding stress dip angles α1, α2, and α3, and the stress azimuth angles β1, β2, and β3. Through the rotation transformation matrix, convert the stress tensor in the in-situ stress coordinate system into the stress tensor in the geodetic rectangular coordinate system. Then, through the rotation transformation matrix, convert the stress tensor in the geodetic rectangular coordinate system into the stress tensor in the borehole coordinate system. Obtain the stress components σ'x, σ'y, σ'z, τ'xy, τ'yz, and τ'zx in the borehole coordinate system O-X''Y''Z'', which are the stress loads in the borehole coordinate system.

[0011] Further, the coordinate transformation formula:

[0012]

[0013] Where: l1, m1, and n1 represent the cosine values of the angles between X and the X, Y, and Z of the borehole coordinate system; l2, m2, and n2 represent the cosine values of the angles between Y and the X, Y, and Z of the borehole coordinate system; l3, m3, and n3 represent the cosine values of the angles between Z and the X, Y, and Z of the borehole coordinate system. d1, e1, and f1 represent the cosine values of the angles between X and the X, Y, and Z of the geodetic coordinate system; d2, e2, and f2 represent the cosine values of the angles between Y and the X, Y, and Z of the geodetic coordinate system; d3, e3, and f3 represent the cosine values of the angles between Z and the X, Y, and Z of the geodetic coordinate system.

[0014] dᵢ = cosαᵢ + i sinβᵢ (i = 1, 2, 3), eᵢ = cosαᵢ·cosβᵢ (i = 1, 2, 3), fᵢ = sinαᵢ (i = 1, 2, 3), l₁ = cosδ·cosω, m₁ = cosδ·sinω, n₁ = -sinδ, l₂ = -sinω, m₂ = cosω, n₂ = 0, l₃ = sinδ·cosω, m₃ = sinδ·sinω, n₃ = cosδ.

[0015] Further, in step S6, in the drilling coordinate system, based on the Kirsch solution method and using the drilling radius determined in S4 and the stress load in the drilling coordinate system obtained in S5, the normal stresses σᵣ, σₜ, σᵥ and shear stresses τᵣₜ, τᵣᵥ, τₜᵥ at any point within the preset range of the hole in the drilling coordinate system are obtained, including: the stress load σ'ₓ, σ'ᵧ, σ'ₛ, τ'ₓᵧ, τ'ᵧₛ and τ'ₛₓ in the drilling coordinate system O-X''Y''Z'' obtained according to step S5, and the normal stresses σᵣ, σₜ, σᵥ and shear stresses τᵣₜ, τᵣᵥ, τₜᵥ at any point around the hole in the polar coordinate system in three-dimensional space obtained by the Kirsch solution method:

[0016]

[0017] where θ and r are the polar coordinates of any point, ν is the Poisson's ratio, and a is the equivalent radius of the drill hole.

[0018] Further, in step S7, based on the M-C strength criterion in three-dimensional state and using the rock mechanics parameters obtained in S3, an implicit equation for the boundary of the plastic zone around the drill hole is established. Substituting the stress components at any point within the preset range of the hole in the drilling coordinate system obtained in S6 into the implicit equation, the radius r of the pressure-relief and permeability-increasing zone of the relief drill hole is solved, including: using the stress invariant I₁ and the Lode angle θₛ, the Mohr-Coulomb yield surface is expressed as:

[0019]

[0020] where I₁ represents the principal stress invariant, reflecting the average level of the stress state; θₛ represents the Lode angle, indicating the angle of the stress state on the π plane and reflecting the relative magnitude relationship of the stress state; φ represents the internal friction angle of the rock mass; C represents the cohesion of the rock mass; J₂ represents the second invariant deviatoric stress;

[0021]

[0022]

[0023]

[0024]

[0025] Among them, J3 represents the third invariant deviatoric stress; σ(1) represents the maximum principal stress of the element; σ(2) represents the intermediate principal stress of the element; σ(3) represents the minimum principal stress of the element; based on the normal stresses σr, σt, σv and shear stresses τrt, τrv, τtv at any point (r, θ) within the preset range of the hole in the borehole coordinate system obtained according to step S6, an implicit expression for the approximate solution of the failure size of the borehole at any rotation angle in the three-dimensional stress field is established: , where α1, α2, α3, β1, β2 and β3 represent the azimuth angles and dip angles corresponding to the principal stresses; δ, ω represent the dip angle and azimuth angle of the roadway relative to the geodetic coordinate system; R represents the equivalent radius of the borehole; C represents the cohesion of the rock mass; φ represents the internal friction angle of the rock mass; v represents the Poisson's ratio of the rock mass; by using numerical solution methods such as the Newton iteration method, the arc length method, etc., to solve the implicit expression, the coordinates (r, θ) of the boundary points of the plastic zone around the borehole that satisfy the yield condition are obtained, where r is the radius of the pressure relief borehole permeability enhancement circle.

[0026] Among them, the rock mass strength criterion is not limited to the M-C strength criterion, but also includes classical strength criteria such as the Matsuoka-Nakai criterion, the Mogi-Coulomb criterion, the Drucker-Prager criterion, and the Lade-Duncan criterion.

[0027] Furthermore:

[0028]

[0029] In the formula:

[0030]

[0031] Among them, p is the mean stress, reflecting the influence of hydrostatic pressure on material yield; q is the generalized shear stress, reflecting the influence of shear stress on material yield.

[0032] Furthermore:

[0033]

[0034]

[0035]

[0036] Among them: σr, σθ, σv represent normal stresses; τrθ, τrv, τθv represent shear stresses;

[0037] Further, in S8, according to the radius r of the pressure-relief borehole permeability enhancement circle, determine the row spacing PR between two adjacent pressure-relief boreholes and the layout method of the pressure-relief boreholes, including: adopting a single-row parallel layout method, that is, arranging a row of pressure-relief boreholes on each side of the roadway. This layout method is simple and easy to implement, can form a relatively uniform pressure-relief effect on both sides of the roadway, and is conducive to maintaining the stability of the surrounding rock mass of the roadway. Layout position of the first borehole: The first borehole is arranged at a position r away from the working face, that is, starting to arrange the borehole at a position of one permeability enhancement circle radius r in front of the working face. This can ensure that during the advancement of the working face, there is always a complete pressure-relief permeability enhancement circle in front of the working face, releasing the stress in the rock mass near the working face in advance and reducing the stress concentration degree of the working face. Layout method of subsequent boreholes: Along the advancement direction of the working face, the second to the nth boreholes are arranged in parallel. Parallel arrangement can ensure that the pressure-relief effect of each borehole is relatively independent, and the mutual interference between adjacent boreholes is small, which is conducive to forming a continuous and uniform pressure-relief area. Row spacing PR between two adjacent pressure-relief boreholes: According to the radius r of the pressure-relief borehole permeability enhancement circle, determine that the row spacing PR between two adjacent pressure-relief boreholes is PR = 2r. The selection of this row spacing is based on the following considerations: When the row spacing PR = 2r, the permeability enhancement circles of two adjacent boreholes are exactly tangent, and a continuous pressure-relief area can be formed, avoiding the existence of pressure-relief blind areas. If the row spacing PR > 2r, there will be pressure-relief blind areas between adjacent boreholes, and the rock mass stress cannot be effectively released, which may lead to local stress concentration and surrounding rock failure. If the row spacing PR < 2r, the permeability enhancement circles of adjacent boreholes will overlap. Although the pressure-relief effect is more significant, it will increase the number of boreholes and construction costs, and excessive pressure relief may cause excessive damage and deformation of the surrounding rock. Therefore, the row spacing PR = 2r is an optimal choice that balances the pressure-relief effect and construction costs, which can not only form a continuous and effective pressure-relief area but also control the number of boreholes and engineering investment.

[0038] Preferably, the reduction rate of surrounding rock stress is selected as the evaluation index for the pressure relief and permeability enhancement effect, and the objective function is established. The reduction rate of surrounding rock stress reflects the effectiveness of the pressure relief borehole layout scheme in reducing the degree of surrounding rock stress concentration. The optimal borehole layout scheme X_opt and the optimal borehole row spacing PR_opt are solved by the particle swarm algorithm. Specifically, the objective function is established, and the expression is: f(X) = E(X), where X represents the borehole layout scheme, and E(X) represents the reduction rate of surrounding rock stress. The reduction rate of surrounding rock stress E(X): According to the geological conditions and initial stress state of the rock mass around the roadway, a surrounding rock stress distribution model is established when the pressure relief boreholes are not constructed, and the initial maximum principal stress σ_max_0 is obtained; for the given borehole layout scheme X, a surrounding rock stress distribution model after the construction of the pressure relief boreholes is established, and the maximum principal stress σ_max_X after pressure relief is obtained; calculate the reduction rate of surrounding rock stress E(X): E(X) = (σ_max_0 - σ_max_X) / σ_max_0 × 100%. The adjacent borehole row spacing range, the borehole layout range, and the upper limit of the number of boreholes are converted into mathematical constraint conditions: Adjacent borehole row spacing constraint: PRmin ≤ PR ≤ PRmax; Borehole layout range constraint: The boreholes are arranged within a certain range from the working face, such as [d_min, d_max]; Borehole number constraint: The number of boreholes n ≤ Nmax. Construct a complete optimization model: Objective function: maxf(X) = E(X); Decision variables: X = {(x1, y1), (x2, y2),..., (xn, yn), PR}; Constraint conditions: PRmin ≤ PR ≤ PRmax; d_min ≤ xi ≤ d_max, i = 1, 2,..., n; n ≤ Nmax, where (xi, yi) represents the position coordinates of the i-th borehole, and PR represents the row spacing between adjacent boreholes.

[0039] The particle swarm algorithm is used to solve the optimization model: Initialize the particle swarm, and each particle represents a borehole layout scheme, including the borehole position coordinates and the row spacing; for each particle, calculate the reduction rate of surrounding rock stress E(X) as the fitness value of the particle; update the individual optimal position and the global optimal position of the particle; update the velocity and position of the particle according to the individual optimal position and the global optimal position of the particle.

[0040] Another aspect of the present application also provides a system for determining the spacing of pressure relief boreholes in a three-dimensional stress field, which is used to execute a method for determining the spacing of pressure relief boreholes in a three-dimensional stress field of the present application.

[0041] Compared with the prior art, the advantages of the present application are as follows:

[0042] The in-situ stress component corresponding to the peak of roadway abutment pressure is obtained by combining borehole stress gauges and in-situ stress measurements, considering the actual stress state of the roadway, which provides a reliable stress boundary condition for determining the subsequent borehole layout parameters.

[0043] Three coordinate systems, namely the in-situ stress coordinate system, the geodetic rectangular coordinate system, and the borehole coordinate system, are introduced. Through coordinate transformation, the in-situ stress components are converted into stress loads around the borehole, realizing the coupled analysis of the spatial distribution characteristics of in-situ stress and borehole layout parameters, and improving the accuracy of determining borehole layout parameters.

[0044] Based on the Kirsch solution method, an analytical expression for the stress components around the borehole is established. Combining with the Mohr-Coulomb yield criterion, an implicit equation for the boundary of the plastic zone around the borehole is established. By solving this equation, the radius of the permeability enhancement zone of the pressure-relief borehole is obtained, realizing the quantitative analysis and evaluation of the pressure-relief and permeability enhancement effect of the borehole.

[0045] On the basis of determining the radius of the permeability enhancement zone of the pressure-relief borehole, by reasonably setting the row and column spacing between adjacent boreholes, the optimal matching of the borehole layout form and the pressure-relief and permeability enhancement effect is realized, avoiding problems such as incomplete pressure relief caused by too dense or too sparse boreholes, and realizing the optimization of the pressure-relief and permeability enhancement effect.

[0046] A single row of parallel arrangement is adopted to arrange a row of pressure-relief boreholes on both sides of the roadway. The first borehole is arranged at a distance equal to the radius of the permeability enhancement zone of the pressure-relief borehole from the working face, and subsequent boreholes are arranged parallel to the advancing direction of the working face. The arrangement method is simple and feasible, facilitating engineering implementation.

[0047] By optimizing the pressure-relief borehole layout parameters, the stress state of the roadway surrounding rock is effectively improved, the stress concentration degree of the surrounding rock is reduced, and the stability of the roadway surrounding rock is enhanced, providing a reliable measure for effectively preventing dynamic disasters such as roof fall, rib spalling, and bolt failure. Description of the Drawings

[0048] This application will be further described by way of exemplary embodiments, which will be described in detail through the drawings. These embodiments are not restrictive. In these embodiments, the same numbers represent the same structures, where:

[0049] Figure 1 is a schematic diagram of the roadway borehole pressure-relief scheme in the three-dimensional stress field provided by this application;

[0050] Figure 2 is a top view schematic diagram of the roadway borehole pressure-relief scheme in the three-dimensional stress field provided by this application;

[0051] Figure 3 is an exemplary flowchart of a method for determining the spacing of pressure-relief boreholes in a three-dimensional stress field.

[0052] Description of reference numerals in the figure:

[0053] 1. Coal mining face in this section; 2. Goaf in the upper section; 3. Return airway in this section. Specific implementation manner

[0054] The methods and systems provided in the embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0055] The construction mine of the present application is as Figure 1 shown, including the coal mining face 1 in this section and the goaf 2 in the upper section. The advancing direction of the working face is as indicated by the arrow in the figure. Drilling pressure relief treatment is carried out on the return airway 3 in this section shown in the figure. Figure 3 is an exemplary flowchart of a method for determining the spacing of pressure relief boreholes in a three-dimensional stress field. A method for determining the spacing of pressure relief boreholes in a three-dimensional stress field includes: obtaining the peak range of roadway abutment pressure through a borehole stress gauge; obtaining the magnitude of in-situ stress, the azimuth angle and dip angle of in-situ stress corresponding to the peak range of abutment pressure through in-situ stress measurement; determining the parameters of the roadway surrounding rock through rock mechanics tests, and the parameters include cohesion C, internal friction angle φ and Poisson's ratio v; determining the radius of the pressure relief borehole according to the engineering geological parameters and construction conditions of the construction mine; establishing an in-situ stress coordinate system, a geodetic rectangular coordinate system and a borehole coordinate system, and converting the magnitude, azimuth angle and dip angle of in-situ stress in the in-situ stress coordinate system into stress loads in the borehole coordinate system through coordinate transformation methods; in the borehole coordinate system, based on the Kirsch solution method and using the determined radius of the pressure relief borehole and the stress loads obtained in the borehole coordinate system, obtaining the normal stresses σr, σt, σv and shear stresses τrt, τrv, τtv at any point within the preset range of the hole in the borehole coordinate system; based on the M-C strength criterion in three-dimensional state, using the obtained rock mechanics parameters, establishing an implicit equation for the boundary of the plastic zone around the borehole, substituting the stress components at any point within the preset range of the hole obtained in the borehole coordinate system into the implicit equation, and solving to obtain the radius r of the permeability enhancement zone of the pressure relief borehole; determining the row spacing PR of adjacent two pressure relief boreholes and the layout method of the pressure relief boreholes according to the radius r of the permeability enhancement zone of the pressure relief borehole.

[0056] Through on-site measurement with a borehole stress gauge, the position of the peak abutment pressure is obtained to be 5 m away from the working face, and this data is used as the basis for determining the position of the pressure relief borehole layout area. The magnitude of in-situ stress, the azimuth angle and dip angle of in-situ stress at the peak range of abutment pressure measured based on the in-situ stress measurement method are shown in Table 1:

[0057] Through rock mechanics tests, it is determined that the cohesion C of the coal seam in the roadway where the pressure relief boreholes are arranged is 0.8 MPa, the internal friction angle φ is 25°, and the Poisson's ratio v is 0.25. Through on-site measurement, the roadway cross-sectional size is determined to be 5400×3600 mm. According to the engineering geological parameters and construction conditions of the construction mine, the radius a of the pressure relief borehole is determined to be 0.2 m.

[0058] Establish the in-situ stress coordinate system O-XYZ, and coincide the maximum principal stress σ1, the intermediate principal stress σ2, and the minimum principal stress σ3 with the coordinate axes X, Y, and Z respectively. According to the in-situ stress measurement results, σ1 = 10.82 MPa, σ2 = 5.75 MPa, and σ3 = 4.79 MPa. Establish the geodetic rectangular coordinate system O-X'Y'Z', with the roadway axis as the Z' axis, the horizontal right direction of the roadway section as the X' axis, and the vertical upward direction of the roadway section as the Y' axis. According to the in-situ stress azimuth and dip data, α1 = 39.37°, α2 = 50.59°, α3 = -1.47°, β1 = 119.35°, β2 = -63.65°, β3 = 208.14°, and transform the stress components in the in-situ stress coordinate system to the geodetic rectangular coordinate system through the coordinate transformation matrix.

[0059] Establish the borehole coordinate system O-X''Y''Z'', with the borehole axis as the Z'' axis, the borehole radial direction as the X'' axis, and the borehole tangential direction as the Y'' axis. According to the borehole dip and borehole azimuth of the borehole spatial layout position relative to the geodetic coordinate system are both 90°, and transform the stress components in the geodetic rectangular coordinate system to the borehole coordinate system through the coordinate transformation matrix:

[0060]

[0061] Take the stress components in the borehole coordinate system O-X''Y''Z'' as the stress loads around the borehole, denoted as σx, σy, σz, τxy, τyz, τzx, for subsequent calculation of the radius of the borehole plastic zone and the borehole spacing.

[0062] Where:

[0063] The normal stresses σ r 、 σ t 、 σ v and the shear stresses τ rt 、 τ rv 、 τ tv at any point in the polar coordinate system in the three-dimensional space obtained based on the Kirsch solution method are calculated by the following formulas:

[0064]

[0065] In the formula, θ and r are the polar coordinates of any point, ν is the Poisson's ratio, and a is the equivalent radius of the borehole.

[0066] The normal stresses σr, σt, σv and shear stresses τrt, τrv, τtv at any point around the borehole can be expressed by the following cubic equations in one variable:

[0067]

[0068] Where: I1, I2 and I3 are stress state invariants, and their expressions are respectively:

[0069]

[0070]

[0071]

[0072] The calculation formula for the principal stresses at any point around the borehole is:

[0073]

[0074] Where:

[0075]

[0076] Using stress invariants and the Lode angle, the Mohr - Coulomb yield surface can be expressed as:

[0077]

[0078] The expressions of each physical quantity in the formula are as follows:

[0079]

[0080]

[0081]

[0082]

[0083] The implicit expression of the approximate solution of the failure size of the borehole at any rotation angle in the three - dimensional stress field is as follows:

[0084]

[0085] Substitute the borehole dip angle δ = 90° and the azimuth angle ω = 90° into the implicit expression of the approximate solution of the borehole failure size, and solve to obtain the radius r of the pressure-relief borehole permeability enhancement zone as r = 0.648 m. According to the calculated radius r of the borehole plastic zone, determine the row spacing PR between two adjacent pressure-relief boreholes. Since it is necessary to ensure that the edges of the plastic zones of adjacent boreholes are tangent to achieve the best pressure-relief effect, the borehole row spacing PR should satisfy: PR = 2r = 2 × 0.648 = 1.296 m. Determine the borehole layout method as single-row parallel layout, and arrange a row of pressure-relief boreholes on each side of the roadway. The first borehole is arranged at a position 0.648 m (i.e., r) away from the working face; along the advancing direction of the working face, with a spacing of 1.296 m (i.e., R), the second, third... the nth boreholes are arranged in parallel in sequence; the borehole sequence on the side close to the coal wall is represented as d11, d12... d1n; the borehole sequence on the side close to the coal pillar is represented as d21, d22... d2n. So far, according to the measured in-situ stress results and the calculated radius of the borehole pressure-relief permeability enhancement zone, the row spacing of the pressure-relief boreholes is determined to be 1.296 m, the layout method is single-row parallel layout, and the actual number of boreholes arranged is determined according to the roadway section size, providing guidance for borehole construction.

Claims

1. A method for determining the spacing of pressure relief boreholes in a three-dimensional stress field, comprising: S1, obtain the peak range of tunnel support pressure through the borehole stress gauge; S2, obtain the ground stress magnitude, ground stress azimuth and inclination angle corresponding to the peak value of the support pressure through ground stress measurement; S3, determine the parameters of the tunnel surrounding rock through rock mechanics tests, including cohesion C, internal friction angle φ and Poisson's ratio v; S4, determine the radius of the pressure relief drilling hole according to the engineering geological parameters and construction conditions of the construction mine; S5, establishing a geostress coordinate system, a geodetic rectangular coordinate system and a borehole coordinate system, and converting the geostress magnitude, azimuth and inclination angle in the geostress coordinate system obtained in S2 into a stress load in the borehole coordinate system through a coordinate conversion method; S6, based on the Kirsch solution and using the drilling radius determined by S4 and the stress load in the drilling coordinate system obtained by S5, obtain the normal stress at any point within the preset range of the hole in the drilling coordinate system and shear stress ; S7, based on the MC strength criterion of the three-dimensional state, using the rock mechanics parameters obtained in S3, establish the implicit equation of the boundary of the plastic zone around the borehole, and bring the stress component of any point within the preset range of the hole in the borehole coordinate system obtained in S6 into the implicit equation to solve and obtain the radius r of the pressure relief borehole anti-reflection circle; S8, determining the row spacing PR of two adjacent pressure relief boreholes and the arrangement of the pressure relief boreholes according to the radius r of the pressure relief borehole anti-reflection ring.

2. The method for determining the spacing between pressure relief boreholes in a three-dimensional stress field according to claim 1, characterized in that: S2, obtain the ground stress magnitude, ground stress azimuth and inclination corresponding to the peak value of the abutment pressure through ground stress measurement, including: Within the support pressure peak range determined in step S1, the maximum principal stress within the corresponding range is obtained by measuring the ground stress. , intermediate principal stress and minimum principal stress ; Obtaining the maximum principal stress through ground stress measurement , intermediate principal stress and minimum principal stress The corresponding stress inclination , and , and the stress azimuth , and .

3. The method for determining the spacing between pressure relief boreholes in a three-dimensional stress field according to claim 2, characterized in that: S5, establish the geostress coordinate system, the earth rectangular coordinate system and the borehole coordinate system, and transform the geostress magnitude, azimuth and inclination obtained in S2 in the geostress coordinate system into the stress load in the borehole coordinate system through the coordinate transformation method, including: Establishing a geostress coordinate system O-XYZ, wherein the three coordinate axes of the geostress coordinate system O-XYZ coincide with the directions of the maximum principal stress σ1, the intermediate principal stress σ2, and the minimum principal stress σ3 obtained in step S2 respectively; Establish a geodetic rectangular coordinate system O-X'Y'Z', and establish a drilling coordinate system O-X''Y''Z'' according to the drilling inclination angle δ and the drilling azimuth angle w of the drilling spatial arrangement position relative to the geodetic coordinate system; According to the coordinate conversion formula, the maximum principal stress in the geostress coordinate system obtained in step S2 is , intermediate principal stress and minimum principal stress And the corresponding stress inclination , and , and the stress azimuth , and , converted into stress components in the drilling coordinate system O-X''Y''Z'' , , , , and , and obtain the stress load in the drilling coordinate system.

4. The method for determining the spacing between pressure relief boreholes in a three-dimensional stress field according to claim 3, characterized in that: Coordinate transformation formula: in: , and express With drilling coordinate system , and The cosine of the angle; , and express With drilling coordinate system , and The cosine of the angle; , and express Drilling coordinate system , and The cosine of the angle; , and Represents X and the geodetic coordinate system , and The cosine of the angle; , and Indicates Y and geodetic coordinate system , and The cosine of the angle; , and Represents Z and the geodetic coordinate system , and The cosine of the angle.

5. The method for determining the spacing between pressure relief boreholes in a three-dimensional stress field according to claim 4, characterized in that: S6, obtain the normal stress at any point within the preset range of the hole in the drilling coordinate system and shear stress ,include: According to the stress load under the drilling coordinate system O-X''Y''Z'' obtained in step S5 , , , , and , the normal stress at any point around the borehole in the polar coordinate system in three-dimensional space obtained by the Kirsch solution method and shear stress : Among them, θ and r are the polar coordinates of any point, ν is the Poisson's ratio, and R is the equivalent radius of the drill hole.

6. The method for determining the spacing between pressure relief boreholes in a three-dimensional stress field according to claim 5, characterized in that: S7, solving to obtain the radius r of the pressure relief drilling anti-reflection circle, including: Using stress invariants and Lode Point , the Mohr-Coulomb yield surface is expressed as: in, represents the principal stress invariants; represents the Lode angle; φ represents the friction angle in the rock mass; C represents the cohesion in the rock mass; represents the second invariant deviatoric stress; in, represents the third invariant deviatoric stress; represents the maximum principal stress of the unit cell; represents the intermediate principal stress of the unit cell; Represents the minimum principal stress of the unit cell; According to any point within the preset range of the hole in the drilling coordinate system obtained in step S6 Normal stress at and shear stress , an implicit expression for the approximate solution of the failure size of the drill hole at any rotation angle in space in a three-dimensional stress field is established: in, , , , , and represents the azimuth and inclination corresponding to the principal stress; δ and ω represent the inclination and azimuth of the tunnel relative to the geodetic coordinate system; R represents the equivalent radius of the borehole; C represents the cohesion of the rock mass; φ represents the friction angle in the rock mass; v represents the Poisson's ratio of the rock mass; By solving the implicit expression, the radius r of the pressure relief borehole anti-reflection circle is obtained.

7. The method for determining the spacing between pressure relief boreholes in a three-dimensional stress field according to claim 6, characterized in that: Where: Where p represents the average stress; q represents the generalized shear stress; is the stress state invariant.

8. The method for determining the spacing between pressure relief boreholes in a three-dimensional stress field according to claim 7, characterized in that: in, represents normal stress; shear stress represents shear stress; Represents shear stress.

9. The method for determining the spacing between pressure relief boreholes in a three-dimensional stress field according to claim 8, characterized in that: S8, determining the row spacing PR of two adjacent pressure relief boreholes and the arrangement of the pressure relief boreholes according to the radius r of the pressure relief borehole anti-reflection ring, including: The drilling arrangement adopts a single-row parallel arrangement, with a row of pressure relief drilling holes arranged on both sides of the tunnel; The first drill hole is arranged at a distance r from the working surface, and the second to nth drill holes are arranged parallel to the advancing direction of the working surface; The row spacing between two adjacent pressure relief boreholes is PR=2r.

10. A system for determining the spacing of pressure relief boreholes in a three-dimensional stress field, characterized in that: Used to execute instructions to implement the method for determining the spacing between pressure relief drilling holes in a three-dimensional stress field as described in any one of claims 1 to 9.

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