Prediction system for plastic zone of surrounding rock of rectangular roadway under rotation of three-dimensional far-field principal stress

Abstract

The present application relates to the field of mine engineering and geotechnical mechanics, in particular to a system for predicting the plastic zone of the surrounding rock of a rectangular roadway under three-dimensional far-field principal stress rotation. The present application obtains the magnitude and direction of the far-field principal stress of the rectangular roadway through field measurement, obtains the six stress components of the far-field principal stress of the roadway in the space rectangular coordinate system through matrix transformation of three-dimensional stress rotation, obtains the stress component function and the principal stress function of any unit around the roadway by using the analytic solution of complex function, further selects a suitable strength criterion to obtain the implicit equation of the plastic zone boundary of the surrounding rock of the roadway, and codes the calculation process into an executable automatic system through modular programming. The present application extracts the spatial feature points through a geometric reconstruction algorithm, and automatically generates a two-dimensional cross-sectional plastic zone distribution map of the surrounding rock of the roadway by calling a scientific calculation visualization tool.

Description

Technical Field

[0001] The present invention relates to the fields of mining engineering and rock and soil mechanics, and in particular to a system for predicting the plastic zone of surrounding rock of a rectangular tunnel under three-dimensional far-field principal stress rotation. Background Art

[0002] During mining activities, tunnel excavation and working face mining destroy the original ground stress balance, and the stress is redistributed, resulting in stress concentration within a certain range. The magnitude and direction of the stress will change accordingly, the stress magnitude will increase or decrease to varying degrees, and the stress direction will rotate in different directions.

[0003] The plastic zone of the roadway surrounding rock is affected by the superimposed changes in the magnitude and direction of the principal stresses, resulting in a distinctly asymmetric distribution of its morphology. The assumption that the principal stress directions remain unchanged can lead to distorted calculations of the plastic zone morphology. Furthermore, the deflection of the principal stresses also causes changes in the magnitude and direction of the shear stresses. Ignoring shear stress changes can also lead to errors in the plastic zone calculation. Furthermore, existing calculations of the plastic zone of roadway surrounding rock are mostly based on the equivalent circle method, and the stress rotation problem is simply the rotation of plane stresses. While this simplifies the calculation process, it ignores the actual geometric characteristics and stress distribution characteristics of the roadway and fails to consider the stress concentration effects at the corners of rectangular roadways. Summary of the Invention

[0004] In response to the above-mentioned problems, the present invention provides a prediction system for the plastic zone of the surrounding rock of a rectangular tunnel under three-dimensional far-field principal stress rotation: the magnitude and direction of the far-field principal stress of the rectangular tunnel are obtained by on-site measurement, and the six stress components of the far-field principal stress of the tunnel in the spatial rectangular coordinate system are obtained through matrix transformation of the three-dimensional stress rotation. The stress component function and principal stress function of any unit around the tunnel are obtained by analytical solution of complex variable functions, and then the implicit equation of the boundary of the plastic zone of the surrounding rock of the tunnel is obtained by selecting a suitable strength criterion, and the calculation process is encoded into an executable automation system through modular programming.

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

[0006] (1) Determine the tunnel cross-sectional parameters and tunnel far-field principal stress parameters through on-site measurements.

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

[0008] (3) Based on the coordinate matrix transformation, the six stress component expressions of the far-field principal stress of the tunnel in the spatial rectangular coordinate system are obtained.

[0009] (4) Based on the tunnel cross-sectional parameters and tunnel far-field principal stress parameters determined by on-site measurement in step (1), the surrounding rock mechanical parameters obtained in step (2), and the six stress component expressions of the far-field principal stress in the spatial rectangular coordinate system obtained in step (3), the stress component function expression of any unit around the tunnel is obtained based on the theory of analytical solution of complex functions.

[0010] (5) According to the stress component function expression of any unit around the roadway obtained in step (4), the principal stress function expression of any unit around the roadway is solved based on the characteristic equation of the principal stress.

[0011] (6) Using the theory of elastic-plastic mechanics, the tunnel 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 expression of any unit around the tunnel solved in step (6), the implicit equation of the plastic zone boundary of the rectangular tunnel surrounding rock under three-dimensional far-field principal stress rotation is derived.

[0012] (7) Encode the computational processes (3)-(6) into an executable automation system through modular programming.

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

[0014] Furthermore, in the step (3), six stress component expressions of the far-field principal stress of the tunnel in the spatial rectangular coordinate system are obtained based on the coordinate matrix transformation.

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

[0016]

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

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

[0019]

[0020] 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 plumb bob 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 tunnel, MPa; the shear stress reciprocity theorem shows that 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 six stress components of the far-field principal stress of the roadway in the spatial rectangular coordinate system can be expressed as follows:

[0026] σ x =cos 2 α1·sin 2 β1·σ1+cos 2 α2·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 α3·cos 2 β3·σ3

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

[0029]

[0030] T yz =cosα1·sinβ1·sinα1·σ1+cosα2·sinβ2·sinα2·σ2+cosα3·sinβ3·sinα3·σ3

[0031] T zx =cosα1·cosβ1·sinα1·σ1+cosα2·cosβ2·sinα2·σ2+cosα3·cosβ3·sinα3·σ3

[0032] Furthermore, in step (4), based on the tunnel cross-sectional parameters and tunnel far-field principal stress measured on-site in step (1), the surrounding rock mechanical parameters obtained in step (2), and the six stress component expressions of the tunnel far-field principal stress in the spatial rectangular coordinate system obtained in step (3), the stress component function expression of any unit around the tunnel is obtained based on the theory of analytical solutions of complex functions.

[0033] Based on the full plane strain problem, the tunnel mechanics model can be divided into plane strain model, out-of-plane shear model and uniaxial compression model.

[0034] In the plane strain model, the complex variable theory solves the plane strain problem when σ′ x ,σ′ z and τ′ zx The expressions are (23) and (24):

[0035]

[0036] Where σ′ x is the horizontal normal stress 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′ xz is the shear stress in the xz plane of any unit around the roadway, 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′, C′ are the stress components σ of the far-field principal stress of the roadway in the spatial rectangular coordinate system. x , σ z and τ zxRelated functions; R, C1, C3 and C5 are parameters related to the length and width of the tunnel section;

[0043] ψ(ε) is the complex potential analytical function, expressed as:

[0044]

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

[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 shear stress τ′ of any element around the roadway is xy and τ′ yz The stress function is:

[0052]

[0053] Where 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; C1, C3 and C5 are parameters related to the length and width of the roadway section;

[0054] In the uniaxial compression model, σ′ can be obtained from the physical equation y and σ′ x ,σ′ z The relational expression is:

[0055] σ′ y =Eε y +v(σ x ′+σ z ′)

[0056] Where: σ′ x is the horizontal normal stress 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 tunnel, MPa; E is the elastic modulus, v is the Poisson's ratio, ε y is the axial strain.

[0057] After the tunnel is excavated, the stress distribution around the tunnel changes dynamically. As the tunnel extends deeper, the tunnel σ′ y and σ′ x ,σ′ z The stress value is close to the stress component of the far-field principal stress of the roadway in the spatial rectangular coordinate system, that is, σ′ x =σ x ,σ′ y =σ y ,σ′ z =σ z , change σ x , σ y and σ z Substitute into the formula σ′ y and σ′ x ,σ′ z The relational expression of Eε is obtained y The expression 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 step (5), the principal stress function expression of any unit around the tunnel is obtained based on the analytical solution of the complex function.

[0061] The stress component of any unit around the roadway is expressed as:

[0062]

[0063] Where: σ x is the horizontal normal stress 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 of any unit in the xy plane around the roadway, MPa; τ yz is the shear stress of any unit in the yz plane around the roadway, MPa; τ xz is the shear stress of any unit xz plane around the roadway, MPa; the shear stress reciprocity theorem shows that τ xy =τ yx , τ yz =τ zy , τxz =τ zx .

[0064] It satisfies:

[0065]

[0066] Where: σ is the principal stress of any unit around the roadway.

[0067] Expanding the determinant yields:

[0068] σ 3 -I1σ 2 -I2σ-I3=0

[0069] Where:

[0070]

[0071] The stress component function σ′ of any unit around the roadway x ,σ′ y ,σ′ z ,τ′ xy , τ′ yz and τ′ zx Substituting the principal stress characteristic equation into the equation, the principal stress function σ of any unit around the roadway can be obtained: (1) , σ (2) , σ (3) Function expressions.

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

[0073] The three-dimensional MC strength criterion expression is as follows:

[0074]

[0075] Where:

[0076]

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

[0078]

[0079] Where 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 roadway surrounding rock, MPa; σ2 is the intermediate principal stress of the roadway surrounding rock, MPa; σ3 is the minimum principal stress of the roadway surrounding rock, MPa; α i (i=1, 2, 3) is the inclination angle of the three-dimensional principal stress of the tunnel surrounding rock, °; β i (i=1, 2, 3) is the azimuth of the three-dimensional principal stress of the tunnel surrounding rock, °; c is the cohesion of the tunnel surrounding rock, MPa; is the internal friction angle of the tunnel surrounding rock, °; v is the Poisson's ratio of the tunnel surrounding rock.

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

[0081] The system is divided into three modules: data input module, core algorithm implementation module and visual drawing module.

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

[0083] Core calculation module: used to realize efficient numerical analysis of the plastic zone of the surrounding rock of rectangular tunnels under three-dimensional far-field principal stress rotation. Specifically, it includes: the analytical model of the stress tensor components corresponding to the principal stress of the surrounding rock in the three-dimensional rectangular coordinate system, the stress component distribution function of any unit at the tunnel boundary, the eigenvalue function of any single principal stress at the tunnel 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 plastic zone boundaries output by the numerical solver, spatial feature points are extracted through the geometric reconstruction algorithm, and the scientific computing visualization tool is called to automatically generate a two-dimensional cross-sectional plastic zone distribution map of the tunnel surrounding rock. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0087] Reference numerals:

[0088] Figure 2 Middle: 1. Boundary of roadway; 2. Boundary of plastic zone of roadway surrounding rock; DETAILED DESCRIPTION

[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 used to illustrate and explain the present invention and are not used to limit the present invention.

[0090] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[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 by on-site measurement, and the six stress components of the far-field principal stress of the roadway in a spatial rectangular coordinate system are obtained through matrix transformation of the three-dimensional stress rotation. The stress component function and the principal stress function of any unit around the roadway are obtained by analytical solution of complex variable functions, and then the implicit equation of the boundary of the plastic zone of the surrounding rock of the roadway is obtained by selecting a suitable strength criterion. The calculation process is encoded into an executable automation system through modular programming.

[0092] (1) The tunnel cross-sectional parameters were determined through field measurements: length 5.3 m, width 3.2 m. The tunnel far-field principal stress parameters were: maximum principal stress σ1 was 21.2 MPa, intermediate principal stress σ2 was 15.2 MPa, and minimum principal stress σ3 was 11.7 MPa.

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

[0094] (2) Through rock mechanics tests, the cohesion c of the tunnel surrounding rock is determined to be 3.2 MPa and the internal friction angle is The angle is 34° and the Poisson's ratio is 0.3.

[0095] (3) Based on the coordinate matrix transformation, the six stress component expressions of the far-field principal stress of the tunnel in the spatial rectangular coordinate system are obtained.

[0096] Furthermore, in step (3), six stress component expressions in a spatial 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] 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; 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 reciprocal 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] In the formula, the rotation matrix R determined based on the direction vector is:

[0105]

[0106] σ x = cos 2 α1· sin 2 β11· 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 a3· cos 2 β3· σ3= 13.2 MPa

[0108] σ z = sin 2 a1· σ1+ sin 2 α2· σ2+ sin 2a3- σ3= 16.1 MPa

[0109]

[0110] T yz = cos α1- sin β1- sin α1- σ1+ cos α2- sin β2- sin α2- σ2+ cos α3- sin β3- sin α3- σ3= -0.3 MPa

[0111] T zx = cos α1- cos β1- sin α1- σ1+ cos α2- cos β2- sin α2- σ2+ cos α3- cos β3- sin α3- σ3= -2.3 MPa

[0112] From the six stress component expressions in the spatial rectangular coordinate system, it is calculated that 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, and τ zx is -2.3 MPa.

[0113] (4) Based on the six stress component expressions in the spatial rectangular coordinate system of the roadway section parameters, the roadway far-field principal stress parameters determined according to the field measurement of step (1), the surrounding rock mechanical parameters obtained in step (2) and the far-field principal stress obtained in step (3), the stress component function expression of any unit around the roadway is obtained based on the complex variable function analytical solution theory.

[0114] Further, in step (4), based on the six stress component expressions in the spatial rectangular coordinate system of the roadway parameters and the far-field principal stress determined according to the field measurement of step (1), the surrounding rock mechanical parameters obtained in step (2) and the far-field principal stress obtained in step (3), the stress component function expression of any unit around the roadway is obtained based on the complex variable function analytical solution theory.

[0115] Based on the full plane strain problem, 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 expressions of σ' x , σ' z and τ' zx obtained by the complex variable theory for the plane strain problem are formula (23) and (24):

[0117]

[0118] In the formula, σ' xis the horizontal normal stress 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′ xz is the shear stress in the xz plane of any unit around the roadway, MPa;

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

[0120] Z=w(ε)=R(ε+C1ε -1 +C3ε -3 +C5ε -5 )

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

[0122] is the complex potential analytical function, and its expression is:

[0123]

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

[0125] ψ(ε) is the complex potential analytical function, expressed as:

[0126]

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

[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 is xy and τ′ yz The stress function is:

[0134]

[0135] Where τ′ xyis 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; C1, C3 and C5 are parameters related to the length and width of the roadway section;

[0136] In the uniaxial compression model, σ′ can be obtained from the physical equation y and σ′ x ,σ′ z The relational expression is:

[0137] σ′ y =Eε y +v(σ x ′+σ z ′)

[0138] Where: σ′ x is the horizontal normal stress 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 tunnel, MPa; E is the elastic modulus, v is the Poisson's ratio, ε y is the axial strain.

[0139] After the tunnel is excavated, the stress distribution around the tunnel changes dynamically. As the tunnel extends deeper, the tunnel σ′ y and σ′ x ,σ′ z The stress value is close to the stress component of the far-field principal stress of the roadway in the spatial rectangular coordinate system, that is, σ′ x =σ x ,σ′ y =σ y ,σ′ z =σ z , change σ x , σ y and σ z Substitute into the formula σ′ y and σ′ x ,σ′ z The relational expression of Eε is obtained y The expression is:

[0140] Eε y =σ y -v(σ x +σ z )

[0141] σ′ y =×σ y -v(σ x +σ z )+v(σ′ x +σ′ z)

[0142] (5) According to the stress component function expression of any unit around the roadway obtained in step (5), the principal stress function expression of any unit around the roadway is solved based on the characteristic equation of the principal stress.

[0143] The stress component of any unit around the roadway is expressed as:

[0144]

[0145] Where: σ x is the horizontal normal stress 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 of any unit in the xy plane around the roadway, MPa; τ yz is the shear stress of any unit in the yz plane around the roadway, MPa; τ xz is the shear stress of any unit xz plane around the roadway, MPa; the shear stress reciprocity theorem shows that τ xy =τ yx , τ yz =τ zy , τ xz =τ zx .

[0146] It satisfies:

[0147]

[0148] Where: σ is the principal stress of any unit around the roadway.

[0149] Expanding the determinant yields:

[0150] σ 3 -I1σ 2 -I2σ-I3=0

[0151] Where:

[0152]

[0153] The stress component function σ′ of any unit around the roadway x ,σ′ y ,σ′ z ,τ′ xy , τ′ yz and τ′ zx Substituting the principal stress characteristic equation into the equation, the principal stress function σ of any unit around the roadway can be obtained: (1) , σ (2) , σ (3)Function expressions.

[0154] Furthermore, in step (6), the boundary equation of the plastic zone of the surrounding rock of the rectangular tunnel under three-dimensional far-field principal stress rotation is derived.

[0155] The three-dimensional MC strength criterion expression is as follows:

[0156]

[0157] Where:

[0158]

[0159] By substituting the tunnel section parameters and principal stresses measured in step (1), the rock mechanics parameters measured in step (2), and the principal stress function expression of any unit around the tunnel solved in step (6) into the strength criterion, the boundary equation of the plastic zone of the rectangular tunnel surrounding rock under three-dimensional far-field principal stress rotation can be obtained:

[0160]

[0161] Where 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 roadway surrounding rock, MPa; σ2 is the intermediate principal stress of the roadway surrounding rock, MPa; σ3 is the minimum principal stress of the roadway surrounding rock, MPa; α i (i=1, 2, 3) is the inclination angle of the three-dimensional principal stress of the tunnel surrounding rock, °; β i (i=1, 2, 3) is the azimuth of the three-dimensional principal stress of the tunnel surrounding rock, °; c is the cohesion of the tunnel surrounding rock, MPa; is the internal friction angle of the tunnel surrounding rock, °; v is the Poisson's ratio of the tunnel surrounding rock.

[0162] (7) Encode the computational processes (3)-(6) into an executable automation system through modular programming.

[0163] Furthermore, in step (7), the calculation process of (3)-(6) is encoded into an executable automation system through modular programming.

[0164] The system is divided into three modules: data input module, core algorithm implementation module and visual drawing module.

[0165] Data input module: used to input various parameters measured on site and in the laboratory, including roadway section parameters, principal stress magnitude and direction of roadway surrounding rock, cohesion of roadway surrounding rock, Poisson's ratio of roadway surrounding rock, and internal friction angle of roadway surrounding rock.

[0166] Core calculation module: used to realize efficient numerical analysis of the plastic zone of the surrounding rock of rectangular tunnels under three-dimensional far-field principal stress rotation. Specifically, it includes: the analytical model of the stress tensor components corresponding to the principal stress of the surrounding rock in the three-dimensional rectangular coordinate system, the stress component distribution function of any unit at the tunnel boundary, the eigenvalue function of any single principal stress at the tunnel boundary, and the implicit equation of the plastic zone boundary of the surrounding rock based on the theory of elastic-plastic mechanics.

[0167] Visualization drawing module: Based on the discrete data set of plastic zone boundaries output by the numerical solver, spatial feature points are extracted through the geometric reconstruction algorithm, and the scientific computing visualization tool is called to automatically generate a two-dimensional cross-sectional plastic zone distribution map of the tunnel surrounding rock.

Claims

1. The plastic zone prediction system for rectangular roadway surrounding rock under three-dimensional far-field principal stress rotation is characterized by: include: (1) Determine the tunnel cross-sectional parameters and tunnel far-field principal stress parameters through on-site measurements; (2) Determine the cohesion, internal friction angle, and Poisson's ratio parameters of the tunnel surrounding rock through rock mechanics tests; (3) Based on the coordinate matrix transformation, the six stress component expressions of the far-field principal stress of the roadway in the spatial rectangular coordinate system are obtained; (4) Based on the tunnel cross-sectional parameters and the tunnel far-field principal stress parameters determined by on-site measurement in step (1), the surrounding rock mechanical parameters obtained in step (2), and the six stress component expressions of the far-field principal stress in the spatial rectangular coordinate system obtained in step (3), the stress component function expression of any unit around the tunnel is obtained based on the theory of analytical solution of complex variable functions; (5) According to the stress component function expression of any unit around the roadway obtained in step (4), based on the principal stress characteristic equation, the principal stress function expression of any unit around the roadway is solved; (6) Using the theory of elastic-plastic mechanics, the tunnel 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 expression of any unit around the tunnel solved in step (6), the implicit equation of the plastic zone boundary of the rectangular tunnel surrounding rock under three-dimensional far-field principal stress rotation is derived; (7) Encode the computational processes (3)-(6) into an executable automation system through modular programming.

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

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

4. The system for predicting the plastic zone of surrounding rock of rectangular roadway under three-dimensional far-field principal stress rotation according to claim 1 is characterized in that: The stress component function expression of any unit around the roadway is obtained based on the analytical solution theory of complex variable functions, including: Based on the full plane strain problem, the tunnel mechanics model is divided into plane strain model, out-of-plane shear model and uniaxial compression model. Based on the complex variable theory, the normal stress σ′ in the horizontal direction of any unit around the tunnel under the plane strain problem is obtained x , normal stress σ′ in the plumb direction z , shear stress τ′ on the xz plane zx Function expression of ; Determine the shear stress τ′ of any unit xy plane around the tunnel when the out-of-plane shear is applied xy , shear stress τ′ of any unit yz surface around the tunnel yz Function expression of ; The normal stress σ′ in the axial direction of any unit around the tunnel is obtained by the uniaxial compression model y Function expressions.

5. The system for predicting the plastic zone of surrounding rock of rectangular roadway under three-dimensional far-field principal stress rotation according to claim 1 is characterized in that: The characteristic equation based on the principal stress is solved to obtain the principal stress function expression of any unit around the roadway, including: Determine the stress component expression of any element around the roadway; Write the characteristic equations for the principal stresses; The stress component σ′ of any unit around the roadway x ,σ′ y ,σ′ z , τ′ xy , τ′ yz and τ′ zx Substitute the function expression into the principal stress characteristic equation to obtain the principal stress function σ of any unit around the tunnel (1) , σ (2) , σ (3) expression.

6. The system for predicting the plastic zone of surrounding rock of rectangular tunnel under three-dimensional far-field principal stress rotation according to claim 1 is characterized in that: The derivation of the boundary equation of the plastic zone of the surrounding rock of a rectangular roadway under three-dimensional far-field principal stress rotation includes: By the mean stress σ m , the second deviatoric stress invariant J2, the third deviatoric stress invariant J3 and the stress Lode angle θ σ Express the MC criterion under three-dimensional stress state; By substituting the tunnel section parameters, far-field principal stress parameters, rock mechanics parameters and the principal stress function expression of any unit around the tunnel into the strength criterion, the implicit equation of the plastic zone boundary of the rectangular tunnel surrounding rock under three-dimensional far-field principal stress rotation is obtained.

7. The system for predicting the plastic zone of surrounding rock of rectangular roadway under three-dimensional far-field principal stress rotation according to claim 1 is characterized in that: The computational processes (3)-(6) are encoded into an executable automated system through modular programming, including: a data input module, a core algorithm implementation module, and a visual drawing module.

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