Rectangular roadway surrounding rock plastic zone prediction system under three-dimensional far-field principal stress rotation

Abstract

The invention relates to the field of mine engineering and geotechnical mechanics, in particular to a rectangular roadway surrounding rock plastic zone prediction system under three-dimensional far-field principal stress rotation. According to the method, the magnitude and direction of the far-field principal stress of the rectangular roadway are obtained through field actual measurement, six stress components of the far-field principal stress of the roadway in a space rectangular coordinate system are obtained through matrix transformation of three-dimensional stress rotation, and a stress component function and a principal stress function of any unit around the roadway are obtained through a complex variable function analytical solution. A proper strength criterion is selected to obtain a roadway surrounding rock plastic zone boundary implicit equation, and the calculation process is coded into an executable automatic system through modular programming. Spatial feature points are extracted through a geometric reconstruction algorithm, and a scientific calculation visualization tool is called to automatically generate a two-dimensional section roadway surrounding rock plastic zone distribution diagram.

Description

Technical Field

[0001] The present invention relates to the fields of mine engineering and rock and soil mechanics, and specifically to a prediction system for the plastic zone of the surrounding rock of a rectangular roadway under the rotation of three-dimensional far-field principal stresses. Background Technique

[0002] In mining activities, the excavation of roadways and the mining of working faces disrupt the original in-situ stress balance, resulting in a redistribution of stress, which causes stress concentration phenomena within a certain range. The magnitude and direction of the stress will change accordingly. The magnitude of the stress will increase or decrease to varying degrees, and the direction of the stress will rotate in different directions.

[0003] The plastic zone of the roadway surrounding rock is affected by the superposition of the magnitude and direction of the principal stress, and its morphological distribution will be significantly asymmetric. Assuming that the direction of the principal stress remains unchanged may cause distortion in the calculation of the plastic zone morphology. At the same time, the change in the magnitude and direction of the shear stress will also be caused during the deflection of the principal stress. There will also be certain errors in the calculation of the plastic zone when the change in the shear stress is ignored. In addition, most of the existing calculations of the plastic zone of the roadway surrounding rock are based on the equivalent circle method, and the stress rotation problem is only the rotation of plane stress. Although it can simplify the calculation process, it ignores the true geometric characteristics and stress distribution characteristics of the roadway and fails to consider the stress concentration effect at the corners of the rectangular cross-section roadway. Summary of the Invention

[0004] In view of the above problems, the present invention provides a prediction system for the plastic zone of the surrounding rock of a rectangular roadway under the rotation of three-dimensional far-field principal stresses: obtaining the magnitude and direction of the far-field principal stress of the rectangular roadway through on-site measurement, obtaining the six stress components of the far-field principal stress of the roadway in the spatial rectangular coordinate system through matrix transformation of three-dimensional stress rotation, using the analytical solution of complex variable functions to obtain the stress component function and principal stress function of any unit around the roadway, and then selecting an appropriate strength criterion to obtain the implicit equation of the plastic zone boundary of the roadway surrounding rock, and encoding this calculation process into an executable automated system through modular programming.

[0005] To achieve the above purpose, the present invention is carried out according to the following steps.

[0006] (1) Determine the roadway cross-section parameters and the far-field principal stress parameters of the roadway through on-site measurement.

[0007] (2) Determine the cohesion, internal friction angle, and Poisson's ratio parameters of the roadway surrounding rock through rock mechanics tests.

[0008] (3) Obtain the expressions of the six stress components of the far-field principal stress of the roadway in the spatial rectangular coordinate system based on coordinate matrix transformation.

[0009] (4) Based on the roadway parameters measured on-site in step (1), the far-field principal stresses, the surrounding rock mechanical parameters obtained in step (2), and the expressions of the six stress components of the far-field principal stresses in the space rectangular coordinate system obtained in step (3), the stress component function expressions of any unit around the roadway are obtained based on the analytic solution theory of complex variable functions.

[0010] (5) Based on the stress component function expressions of any unit around the roadway obtained in step (4), the principal stress function expressions of any unit around the roadway are solved based on the characteristic equation of the principal stress.

[0011] (6) Using the theory of elastic-plastic mechanics, the roadway cross-section parameters and far-field principal stresses measured in step (1), the surrounding rock mechanical parameters measured in step (2), and the principal stress function expressions of any unit around the roadway solved in step (6), the implicit equation of the plastic zone boundary of the rectangular roadway surrounding rock under the rotation of the three-dimensional far-field principal stresses is derived.

[0012] (7) The calculation processes in (3)-(6) are encoded into an executable automated system through modular programming.

[0013] Further, in step (1), the roadway cross-section parameters include the length W and width H of the roadway, and the included roadway cross-sections can be common rectangular, arched, trapezoidal, and circular cross-sections; the roadway far-field principal stress parameters include the numerical values of σ1, σ2, and σ3; the dip angle α1 and azimuth angle β1 of the maximum principal stress; the dip angle α2 and azimuth angle β2 of the intermediate principal stress; the dip angle α3 and azimuth angle β3 of the minimum principal stress.

[0014] Further, in step (3), the expressions of the six stress components of the roadway far-field principal stresses in the space rectangular coordinate system are obtained based on the coordinate matrix transformation.

[0015] The stress tensor expression in the roadway far-field principal stress coordinate system is:

[0016]

[0017] In the formula, σ1 is the maximum far-field principal stress of the roadway, MPa; σ2 is the intermediate far-field principal stress of the roadway, MPa; σ3 is the minimum far-field principal stress of the roadway, MPa.

[0018] In the rectangular coordinate system, the stress tensor can be expressed as:

[0019]

[0020] In the formula, σ x is the normal stress in the horizontal direction of the roadway, MPa; σ y is the normal stress in the axial direction of the roadway, MPa; σ z is the normal stress in the plumb direction of the roadway, MPa; τxy is the shear stress in the xy plane of the roadway, MPa; τ yz is the shear stress in the yz plane of the roadway, MPa; τ xz is the shear stress in the xz plane of the roadway, MPa; According to the shear stress reciprocity theorem, τ xy =τ yx , τ yz =τ zy , τ xz =τ zx .

[0021] The transformation formula of the stress tensor is:

[0022] σ ij =R T σR

[0023] In the formula, the rotation matrix R determined based on the direction vector is:

[0024]

[0025] From this, the expressions of the six stress components of the far-field principal stress of the roadway in the space rectangular coordinate system are as follows:

[0026] σ x =cos 2 α1·sin 2 β1·σ1+cos 2 a2·sin 2 β2·σ2+cos 2 a3·sin 2 β3·σ3

[0027] σ y =cos 2 α1·cos 2 β1·σ1+cos 2 α2·cos 2 β2·σ2+cos 2 a3·cos 2 β3·σ3

[0028] σ z =sin 2 α1·σ1+sin 2 α2·σ2+sin 2 α3·σ3

[0029] τ xy =cos 2 α1·sinβ1·cosβ1·σ1+cos 2 α2·sinβ2·cosβ2·σ2+cos 2 α3·sinβ3·c osβ3·σ3

[0030] τ yz = cosα1·sinβ1·sinα1·σ1 + cosα2·sinβ2·sinα2·σ2 + cosa3·sinβ3·sina3·σ3

[0031] τ zx = cosα1·cosβ1·sinα1·σ1 + cosα2·cosβ2·sinα2·σ2 + cosα3·cosβ3·sina3·σ3

[0032] Further, in step (4), based on the roadway section parameters measured on-site in step (1), the far-field principal stress of the roadway, the surrounding rock mechanical parameters obtained in step (2), and the six stress component expressions of the far-field principal stress of the roadway obtained in step (3) in the spatial rectangular coordinate system, and based on the analytical solution theory of complex variable functions, the stress component function expression of any unit on the roadway perimeter is obtained.

[0033] Based on the plane strain problem of the whole plane, the roadway mechanical model can be divided into a plane strain model, an out-of-plane shear model, and a uniaxial compression model.

[0034] In the plane strain model, for the plane strain problem obtained by the complex variable theory, the expressions of σ′ x σ′ z and τ′ zx are given by equations (23) and (24):

[0035]

[0036] where σ′ x is the normal stress in the horizontal direction of any unit on the roadway perimeter, in MPa; σ′ z is the normal stress in the vertical direction of any unit on the roadway perimeter, in MPa; τ′ xz is the shear stress in the xz plane of any unit on the roadway perimeter, in MPa;

[0037] ω(ε) is the mapping function, and its expression is:

[0038] w(ε) = R(ε + C1ε -1 + C3ε -3 + C5ε -5 )

[0039] R, C1, C3, and C5 are parameters related to the length and width of the roadway section;

[0040] is the complex potential analytical function, and its expression is:

[0041]

[0042] B, B′, and C′ are functions related to the stress components σ x , σ z , and τ zx associated with the far - field principal stress of the roadway in a spatial rectangular coordinate system; R, C1, C3, and C5 are parameters related to the length and width of the roadway cross - section;

[0043] ψ(ε) is an analytic function of the complex potential, and its expression is:

[0044]

[0045] S1 and S3 are coefficients, and their expressions are respectively:

[0046]

[0047] L1, L2, and L3 are constants related to C1, C3, and C5, and their relationship is:

[0048]

[0049] The expressions of a1, a2, and a3 are:

[0050]

[0051] In the out - of - plane shear model, the stress functions of the shear stresses τ′ xy and τ′ yz of any element on the roadway perimeter are:

[0052]

[0053] In the formula, τ′ xy is the shear stress in the xy plane of any element on the roadway perimeter, in MPa; τ′ yz is the shear stress in the yz plane of any element on the roadway perimeter, in MPa; C1, C3, and C5 are parameters related to the length and width of the roadway cross - section;

[0054] In the uniaxial compression model, from the physical equations, the relationship expressions of σ′ y and σ′ x , σ′ z are:

[0055] σ′ y = Eε y + v(σ x ′ + σ z ′)

[0056] In the formula: σ′ x is the normal stress in the horizontal direction of any element on the roadway perimeter, in MPa; σ′ y is the normal stress in the axial direction of any element on the roadway perimeter, in MPa; σ′ zis the normal stress in the plumb direction of any unit around the roadway, MPa; E is the elastic modulus, v is the Poisson's ratio, and ε y is the axial strain.

[0057] After the roadway is excavated, the stress distribution around the roadway shows dynamic changes. As it extends deeper into the roadway, the σ′ y and σ′ x , σ′ z The stress values are close to the stress components of the far-field principal stress of the roadway in the space rectangular coordinate system, that is, σ′ x =σ x , σ′ y =σ y , σ′ z =σ z , substituting σ x , σ y and σ z into the relational expressions of σ′ y and σ′ x , σ′ z , the expression of Eε y is:

[0058] Eε y =σ y -v(σ x +σ z )

[0059] σ′ y =σ y -v(σ x +σ z )+v(σ′ x +σ′ z )

[0060] Furthermore, in the step (5), the principal stress function expression of any unit around the roadway is obtained based on the analytical solution of the complex variable function.

[0061] The stress components of any unit around the roadway are expressed as:

[0062]

[0063] Where: σ x is the normal stress in the horizontal direction of any unit around the roadway, MPa; σ y is the normal stress in the axial direction of any unit around the roadway, MPa; σ z is the normal stress in the plumb direction of any unit around the roadway, MPa; τ xy is the shear stress in the xy plane of any unit around the roadway, MPa; τ yz is the shear stress in the yz plane of any unit around the roadway, MPa; τ xzis the shear stress on the xz plane of any unit on the roadway perimeter, MPa; according to the theorem of reciprocal shear stresses, τ xy = τ yx , τ yz = τ zy , τ xz = τ zx .

[0064] It satisfies:

[0065]

[0066] In the formula: σ is the principal stress of any unit on the roadway perimeter.

[0067] Expanding the determinant gives:

[0068] σ 3 - I1σ 2 - I2σ - I3 = 0

[0069] In the formula:

[0070]

[0071] Substituting the stress component functions σ′ x , σ′ y , σ′ z , τ′ xy , τ yz and τ′ zx of any unit on the roadway perimeter into the principal stress characteristic equation, the principal stress functions σ (1) , σ (1) , σ (3) function expressions can be obtained.

[0072] Furthermore, in step (6), the boundary equation of the plastic zone of the surrounding rock of a rectangular roadway under three-dimensional far-field principal stress rotation is derived.

[0073] The expression of the three-dimensional M-C strength criterion is as follows:

[0074]

[0075] In the formula:

[0076]

[0077] Substituting the roadway section parameters and principal stresses measured in step (1), the rock mechanics parameters measured in step (2), and the principal stress function expressions of any unit on the roadway perimeter solved in step (6) into the strength criterion, the boundary equation of the plastic zone of the surrounding rock of a rectangular roadway under three-dimensional far-field principal stress rotation can be obtained:

[0078]

[0079] In the formula, W is the length of the roadway cross-section, in m; H is the width of the roadway cross-section, in m; σ1 is the maximum principal stress of the roadway surrounding rock, in MPa; σ2 is the intermediate principal stress of the roadway surrounding rock, in MPa; σ3 is the minimum principal stress of the roadway surrounding rock, in MPa; α i (i = 1, 2, 3) is the dip angle of the three-dimensional principal stress of the roadway surrounding rock, in °; β i (i = 1, 2, 3) is the azimuth angle of the three-dimensional principal stress of the roadway surrounding rock, in °; c is the cohesive force of the roadway surrounding rock, in MPa; is the internal friction angle of the roadway surrounding rock, in °; v is the Poisson's ratio of the roadway surrounding rock.

[0080] Furthermore, in step (7), the calculation processes of (3)-(6) are encoded into an executable automated system through modular programming.

[0081] This system is divided into three modules, namely the data input module, the core algorithm implementation module, and the visualization drawing module.

[0082] Data input module: Used to input various parameters measured on-site and in the laboratory, including roadway cross-section parameters, the magnitude and direction of the far-field principal stress of the roadway surrounding rock, the cohesive force of the roadway surrounding rock, the Poisson's ratio of the roadway surrounding rock, and the internal friction angle of the roadway surrounding rock.

[0083] Core calculation module: Used to achieve efficient numerical analysis of the plastic zone of rectangular roadway surrounding rock under the rotation of three-dimensional far-field principal stress, specifically including: the stress tensor component analysis model corresponding to the principal stress of the surrounding rock in a three-dimensional space rectangular coordinate system, the stress component distribution function of any unit on the roadway boundary, the principal stress eigenvalue function of any single unit on the roadway boundary, and the implicit equation of the plastic zone boundary of the surrounding rock based on the theory of elastic-plastic mechanics.

[0084] Visualization drawing module: Based on the discrete data set of the plastic zone boundary output by the numerical solver, extract spatial feature points through the geometric reconstruction algorithm, and automatically generate a two-dimensional cross-section distribution map of the plastic zone of the roadway surrounding rock by calling the scientific computing visualization tool. Description of the Drawings

[0085] Figure 1 is the flow chart of the prediction system for the plastic zone of rectangular roadway surrounding rock under the rotation of three-dimensional far-field principal stress provided by the present invention;

[0086] Figure 2 is the schematic diagram of the shape of the plastic zone of rectangular roadway surrounding rock under the rotation of three-dimensional far-field principal stress drawn based on the automated system provided by the present invention;

[0087] Reference Signs:

[0088] Figure 2 In which: 1. Roadway boundary; 2. Plastic zone boundary of roadway surrounding rock; Detailed implementation manners

[0089] The present invention will be further described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only for illustrating and explaining the present invention, and are not used to limit the present invention.

[0090] The specific implementation manners of the present invention will be described below to facilitate those skilled in the art to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation manners. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions created using the concept of the present invention are within the scope of protection.

[0091] The present invention provides a prediction system for the plastic zone of the surrounding rock of a rectangular roadway under three-dimensional far-field principal stress rotation: the magnitude and direction of the far-field principal stress of the rectangular roadway are obtained through on-site measurement, six stress components of the far-field principal stress of the roadway in the space rectangular coordinate system are obtained through matrix transformation of three-dimensional stress rotation, the stress component function and principal stress function of any unit around the roadway are obtained by using the analytical solution of complex variable functions, and then an implicit equation of the plastic zone boundary of the roadway surrounding rock is obtained by selecting an appropriate strength criterion, and the calculation process is encoded into an executable automated system through modular programming.

[0092] (1) Determine the roadway section parameters through on-site measurement: the length is 5.3 m and the width is 3.2 m. Roadway far-field principal stress parameters: the maximum principal stress σ1 is 21.2 MPa, the intermediate principal stress σ2 is 15.2 MPa, and the minimum principal stress σ3 is 11.7 MPa.

[0093] Among them, the dip angle α1 of the maximum principal stress σ1 is 24.1°, and the azimuth angle β1 is 248.1°; the dip angle α2 of the intermediate principal stress σ2 is 63.7°, and the azimuth angle β2 is 43.8°; the dip angle α3 of the minimum principal stress σ3 is 9.6°, and the azimuth angle β3 is 153.8°.

[0094] (2) Determine the cohesion c of the roadway surrounding rock, the internal friction angle is 34°, and the Poisson's ratio is 0.3 through rock mechanics tests.

[0095] (3) Obtain the expressions of six stress components of the far-field principal stress of the roadway in the space rectangular coordinate system based on coordinate matrix transformation.

[0096] Further, in step (3), the expressions of six stress components in the space rectangular coordinate system are obtained based on coordinate matrix transformation.

[0097] The stress tensor expression in the principal stress coordinate system is:

[0098]

[0099] In the rectangular coordinate system, the stress tensor can be expressed as:

[0100]

[0101] where, σ x is the normal stress in the horizontal direction of the roadway, MPa; σ y is the normal stress in the axial direction of the roadway, MPa; σ z is the normal stress in the vertical direction of the roadway, MPa; τ xy is the shear stress in the xy plane of the roadway, MPa; τ yz is the shear stress in the yz plane of the roadway, MPa; τ xz is the shear stress in the xz plane of the roadway, MPa; According to the shear stress reciprocity theorem, τ xy =τ yx , τ yz =τ zy , τ xz =τ zx .

[0102] The transformation formula of the stress tensor is:

[0103] σ ij =R T σR

[0104] where, the rotation matrix R determined based on the direction vector is:

[0105]

[0106] σ x =cos 2 α1·sin 2 β1·σ1+cos 2 α2·sin 2 β2·σ2+cos 2 α3·sin 2 β3·σ3 = 18.9 MPa

[0107] σ y =cos 2 α1·cos 2 β1·σ1+cos 2 α2·cos 2 β2·σ2+cos 2 α3·cos 2 β3·σ3 = 13.2 MPa

[0108] σ z =sin 2 α1·σ1+sin 2 α2·σ2+sin2 α3·σ3 = 16.1 MPa

[0109] τ xy = cos 2 α1·sinβ1·cosβ1·σ1 + cos 2 α2·sinβ2·cosβ2·σ2 + cos 2 α3·sinβ3·cosβ3·σ3 = 3.1 MPa

[0110] τ yz = cosα1·sinβ1·sinα1·σ1 + cosα2·sinβ2·sina2·σ2 + cosα3·sinβ3·sinα3·σ3 = -0.3 MPa

[0111] τ zx = cosα1·cosβ1·sinα1·σ1 + cosα2·cosβ2·sinα2·σ2 + cosα3·cosβ3·sinα3·σ3 = -2.3 MPa

[0112] Calculated from the six stress component expressions in the space rectangular coordinate system: σ x is 18.9 MPa, σ y is 13.2 MPa, σ z is 16.1 MPa, τ xy is 3.1 MPa, τ yz is -0.3 MPa, τ zx is -2.3 MPa.

[0113] (4) Based on the six stress component expressions of the roadway parameters measured on-site in step (1), the far-field principal stresses, the mechanical parameters of the surrounding rock obtained in step (2), and the far-field principal stresses obtained in step (3) in the space rectangular coordinate system, and based on the analytical solution theory of complex variable functions, the stress component function expressions of any unit on the roadway perimeter are obtained.

[0114] Furthermore, in step (4), based on the six stress component expressions of the roadway parameters measured on-site in step (1), the far-field principal stresses, the mechanical parameters of the surrounding rock obtained in step (2), and the far-field principal stresses obtained in step (3) in the space rectangular coordinate system, and based on the analytical solution theory of complex variable functions, the stress component function expressions of any unit on the roadway perimeter are obtained.

[0115] Based on the plane strain problem of the whole plane, the roadway mechanical model can be divided into a plane strain model, an out-of-plane shear model, and a uniaxial compression model.

[0116] In the plane strain model, the complex variable theory gives the plane strain problem as σ′ x 、σ′ z and τ′zx The expressions are equations (23) and (24):

[0117]

[0118] In the formula, σ′ x is the normal stress in the horizontal direction of any element around the roadway, in MPa; σ′ z is the normal stress in the vertical direction of any element around the roadway, in MPa; τ′ xz is the shear stress in the xz plane of any element around the roadway, in MPa;

[0119] ω(ε) is a mapping function, and its expression is:

[0120] Z = w(ε) = R(εC1ε -1 +C3ε -3 +C5ε -5 )

[0121] R, C1, C3, and C5 are parameters related to the length and width of the roadway cross-section;

[0122] is an analytic function of the complex potential, and its expression is:

[0123]

[0124] B, B′, and C′ are functions related to the stress components σ x , σ z and τ zx of the far-field principal stresses of the roadway in the space rectangular coordinate system; R, C1, C3, and C5 are parameters related to the length and width of the roadway cross-section;

[0125] ψ(ε) is an analytic function of the complex potential, and its expression is:

[0126]

[0127] S1 and S3 are coefficients, and their expressions are respectively:

[0128]

[0129] L1, L2, and L3 are constants related to C1, C3, and C5, and their relationship is:

[0130]

[0131] The expressions of a1, a2, and a3 are:

[0132]

[0133] In the out-of-plane shear model, the shear stress τ′ of any element around the roadway xyand τ′ yz The stress function is as follows:

[0134]

[0135]

[0136] where τ′ xy is the shear stress of any element on the xy plane around the roadway, in MPa; τ′ yz is the shear stress of any element on the yz plane around the roadway, in MPa; C1, C3, and C5 are parameters related to the length and width of the roadway cross-section;

[0137] In the uniaxial compression model, from the physical equations, the relational expressions of σ′ y and σ′ x , σ′ z are as follows:

[0138] σ′ y = Eε y + v(σ′ x + σ z ′)

[0139] where: σ′ x is the normal stress in the horizontal direction of any element around the roadway, in MPa; σ′ y is the normal stress in the axial direction of any element around the roadway, in MPa; σ′ z is the normal stress in the vertical direction of any element around the roadway, in MPa; E is the elastic modulus, v is the Poisson's ratio, and ε y is the axial strain.

[0140] After the roadway is excavated, the stress distribution around the roadway shows dynamic changes. As it extends deeper into the roadway, the stress values of σ′ y and σ′ x , σ′ z approach the stress components of the far-field principal stress of the roadway in the space rectangular coordinate system, that is, σ′ x = σ x , σ′ y = σ y , σ′ z = σ z . Substituting σ x , σ y and σ z into the relational expressions of σ′ y and σ′ x , σ′ z , the expression of Eε y is as follows:

[0141] Eε y = σ y - v(σx +σ z )

[0142] σ′ y = σ y -v(σ x +σ z ) + v(σ′ x +σ′ z )

[0143] (5) Based on the stress component function expression of any element around the roadway obtained in step (5), and based on the characteristic equation of the principal stress, the principal stress function expression of any element around the roadway is solved.

[0144] The stress components of any element around the roadway are expressed as:

[0145]

[0146] Where: σ x is the normal stress in the horizontal direction of any element around the roadway, MPa; σ y is the normal stress in the axial direction of any element around the roadway, MPa; σ z is the normal stress in the vertical direction of any element around the roadway, MPa; τ xy is the shear stress in the xy plane of any element around the roadway, MPa; τ yz is the shear stress in the yz plane of any element around the roadway, MPa; τ xz is the shear stress in the xz plane of any element around the roadway, MPa; According to the shear stress reciprocity theorem, τ xy = τ yx , τ yz = τ zy , τ xz = τ zx .

[0147] It satisfies:

[0148]

[0149] Where: σ is the principal stress of any element around the roadway.

[0150] Expanding the determinant gives:

[0151] σ 3 - I1σ 2 - I2σ - I3 = 0

[0152] Where:

[0153]

[0154] Substitute the stress component function σ′ of any element around the roadway x, σ′ y , σ′ z , τ′ xy , τ yz and τ′ zx Substituting into the principal stress characteristic equation, the principal stress functions σ (1) , σ (1) , σ (3) function expressions of any element around the roadway can be obtained.

[0155] Furthermore, in step (6), the boundary equation of the plastic zone of the surrounding rock of a rectangular roadway under the rotation of the three-dimensional far-field principal stress is derived.

[0156] The expression of the three-dimensional M-C strength criterion is as follows:

[0157]

[0158] In the formula:

[0159]

[0160] Substituting the roadway section parameters and principal stresses measured in step (1), the rock mechanics parameters measured in step (2), and the principal stress function expressions of any element around the roadway solved in step (6) into the strength criterion, the boundary equation of the plastic zone of the surrounding rock of a rectangular roadway under the rotation of the three-dimensional far-field principal stress can be obtained:

[0161]

[0162] In the formula, W is the length of the roadway section, m; H is the width of the roadway section, m; σ1 is the maximum principal stress of the surrounding rock of the roadway, MPa; σ2 is the intermediate principal stress of the surrounding rock of the roadway, MPa; σ3 is the minimum principal stress of the surrounding rock of the roadway, MPa; α i (i = 1, 2, 3) is the dip angle of the three-dimensional principal stresses of the surrounding rock of the roadway, °; β i (i = 1, 2, 3) is the azimuth angle of the three-dimensional principal stresses of the surrounding rock of the roadway, °; c is the cohesion of the surrounding rock of the roadway, MPa; is the internal friction angle of the surrounding rock of the roadway, °; v is the Poisson's ratio of the surrounding rock of the roadway.

[0163] (7) Encoding the calculation processes in (3)-(6) into an executable automated system through modular programming.

[0164] Furthermore, in step (7), the calculation processes in (3)-(6) are encoded into an executable automated system through modular programming.

[0165] This system is divided into three modules, namely the data input module, the core algorithm implementation module, and the visualization drawing module.

[0166] Data input module: It is used to input various parameters measured on-site and in the laboratory, including roadway cross-section parameters, magnitudes and directions of principal stresses in roadway surrounding rock, cohesion of roadway surrounding rock, Poisson's ratio of roadway surrounding rock, and internal friction angle of roadway surrounding rock.

[0167] Core calculation module: It is used to achieve efficient numerical analysis of the plastic zone of rectangular roadway surrounding rock under the rotation of three-dimensional far-field principal stresses. Specifically, it includes: an analytical model of stress tensor components corresponding to principal stresses in surrounding rock in a three-dimensional space rectangular coordinate system, a stress component distribution function of any unit on the roadway boundary, a principal stress eigenvalue function of any unit on the roadway boundary, and an implicit equation of the plastic zone boundary of surrounding rock based on elastoplastic mechanics theory.

[0168] Visualization and plotting module: Based on the discrete data set of the plastic zone boundary output by the numerical solver, spatial feature points are extracted through a geometric reconstruction algorithm, and a two-dimensional cross-section distribution map of the plastic zone of roadway surrounding rock is automatically generated by calling a scientific computing visualization tool.

Claims

1. A prediction system for the plastic zone of the surrounding rock of a rectangular roadway under the rotation of three-dimensional far-field principal stresses, characterized in that, Including: (1) Determine the roadway section parameters and the far-field principal stress parameters of the roadway through on-site measurement; (2) Determine the cohesion, internal friction angle, and Poisson's ratio parameters of the roadway surrounding rock through rock mechanics tests; (3) Obtain the expressions of the six stress components of the far-field principal stress of the roadway in the space rectangular coordinate system based on coordinate matrix transformation; (4) According to the roadway parameters and far-field principal stress measured on-site in step (1), the surrounding rock mechanical parameters obtained in step (2), and the expressions of the six stress components of the far-field principal stress in the space rectangular coordinate system obtained in step (3), based on the analytical solution theory of complex variable functions, obtain the stress component function expressions of any unit on the roadway perimeter; (5) According to the stress component function expressions of any unit on the roadway perimeter obtained in step (4), based on the principal stress characteristic equation, solve the principal stress function expressions of any unit on the roadway perimeter; (6) Use the theory of elastoplastic mechanics, the roadway section parameters and far-field principal stress measured in step (1), the surrounding rock mechanical parameters measured in step (2), and the principal stress function expressions of any unit on the roadway perimeter solved in step (6) to derive the implicit equation of the plastic zone boundary of the rectangular roadway surrounding rock under the rotation of the three-dimensional far-field principal stress; (7) Encode the calculation processes in (3)-(6) into an executable automated system through modular programming.

2. The three-dimensional far-field principal stress rotation rectangular roadway surrounding rock plastic zone prediction system according to claim 1, characterized in that The determination of the roadway section parameters and the far-field principal stress parameters of the roadway through on-site measurement includes: Roadway section parameters: the length and width of the roadway; Far-field principal stress parameters of the roadway: the values of the maximum principal stress σ1, the intermediate principal stress σ2, and the minimum principal stress σ3; The dip angle α1 and azimuth angle β1 of the maximum principal stress σ1, the dip angle α2 and azimuth angle β2 of the intermediate principal stress σ2, and the dip angle α3 and azimuth angle β3 of the minimum principal stress σ3.

3. The three-dimensional far-field principal stress rotation rectangular roadway surrounding rock plastic zone prediction system according to claim 1, characterized in that, The obtaining of the expressions of the six stress components of the far-field principal stress of the roadway in the space rectangular coordinate system based on coordinate matrix transformation includes: Determine the rotation matrix R based on the direction vector; Using the transformation formula of the stress tensor, the stress tensor in the far-field principal stress coordinate system of the roadway is converted into the stress tensor in the spatial rectangular coordinate system, and the expressions of the six stress components in the spatial rectangular coordinate system, σ x , σ y , σ z , τ zx , τ yz , τ xy are obtained.

4. The three-dimensional far-field principal stress rotation-based rectangular roadway surrounding rock plastic zone prediction system according to claim 1, characterized in that The obtaining of the stress component function expressions of any unit on the roadway perimeter based on the analytical solution theory of complex variable functions includes: Based on the full plane strain problem, the roadway mechanical model is divided into a plane strain model, an out-of-plane shear model (τ′ yz and a uniaxial compression model; The function expressions of the normal stress σ′ in the horizontal direction of any unit on the roadway periphery, the normal stress σ′ in the plumb direction, and the shear stress τ′ on the xz plane under the plane strain problem based on the complex variable theory x , the normal stress σ′ in the plumb direction z , and the shear stress τ′ on the xz plane zx ; Determine the function expressions of the shear stress τ′ on the xy plane and the shear stress τ′ on the yz plane of any element around the roadway under out-of-plane shear action xy and the shear stress τ′ on the yz plane of any element around the roadway yz ; The normal stress σ′ in the axial direction of any element around the roadway is obtained through the uniaxial compression model y Function expression.

5. The three-dimensional far-field principal stress rotation rectangular roadway surrounding rock plastic zone prediction system according to claim 1, characterized in that, The solving of the principal stress function expressions of any unit on the roadway perimeter based on the principal stress characteristic equation includes: Determine the stress component expressions of any unit on the roadway perimeter; Write out the principal stress characteristic equation; Substitute the stress component functions σ′ x 、σ′ y 、σ′ z 、τ′ xy 、τ yz and τ′ zx into the principal stress characteristic equation to obtain the principal stress functions σ (1) 、σ (1) 、σ (3) expressions for any element around the roadway.

6. The three-dimensional far-field principal stress rotation-based rectangular roadway surrounding rock plastic zone prediction system according to claim 1, characterized in that, The derivation of the plastic zone boundary equation of the rectangular roadway surrounding rock under the rotation of the three-dimensional far-field principal stress includes: Through the mean stress σ m , the second invariant J2 of the deviatoric stress, the third invariant J3 of the deviatoric stress, and the stress Lode angle θ σ represent the M-C criterion under the three-dimensional stress state; Substitute the roadway section parameters, far-field principal stress parameters, rock mechanics parameters, and the principal stress function expressions of any unit on the roadway perimeter into the strength criterion to obtain the implicit equation of the plastic zone boundary of the rectangular roadway surrounding rock under the rotation of the three-dimensional far-field principal stress.

7. The three-dimensional far-field principal stress rotation-based rectangular roadway surrounding rock plastic zone prediction system according to claim 1, wherein The encoding of the calculation processes in (3)-(6) into an executable automated system through modular programming includes: a data input module, a core algorithm implementation module, and a visualization drawing module.

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