CN116973549A - Rock burst prediction method and system - Google Patents

Rock burst prediction method and system Download PDF

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Publication number
CN116973549A
CN116973549A CN202311213674.5A CN202311213674A CN116973549A CN 116973549 A CN116973549 A CN 116973549A CN 202311213674 A CN202311213674 A CN 202311213674A CN 116973549 A CN116973549 A CN 116973549A
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tunnel
shell
equivalent
stress
wave number
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CN116973549B (en
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章新生
钱文欣
梁超
穆朝民
彭波
李辉
曾霖
靳毅
周云飞
寇学超
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Anhui University of Science and Technology
China Tiesiju Civil Engineering Group Co Ltd CTCE Group
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Anhui University of Science and Technology
China Tiesiju Civil Engineering Group Co Ltd CTCE Group
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/24—Earth materials
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V9/00—Prospecting or detecting by methods not provided for in groups G01V1/00 - G01V8/00
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention provides a rock burst prediction method and a rock burst prediction system, which relate to the technical field of geotechnical engineering and are used for obtaining physical characteristics of a tunnel and analyzing an equivalent shell type of the tunnel; determining a value range of wave numbers in the tunnel ring direction according to the type of the equivalent shell, the circumferential length, the thickness and the radius of the equivalent shell; determining a minimum destabilization wave number of the tunnel according to the elastic modulus, the poisson ratio, the thickness and the radius of the equivalent shell and a destabilization stress model; determining the minimum critical yield stress of the tunnel according to the value range of the wave number and the minimum instability wave number; and when the hoop stress of the tunnel is equal to or larger than the minimum critical yield stress, judging that the tunnel is about to be unstable. Therefore, whether surrounding rocks around the tunnel are likely to be subjected to rock burst or not can be known in advance, pressure relief or protection can be performed timely, personnel and equipment in the tunnel can be evacuated timely, and secondary damage is avoided.

Description

Rock burst prediction method and system
Technical Field
The invention relates to the technical field of geotechnical engineering, in particular to a method and a system for predicting rock burst.
Background
Before tunnel excavation, the rock is in an equilibrium state under the action of three-dimensional stress; after the tunnel is excavated, rock and soil at the position of the tunnel are transferred, and an excavation interface is in a single face to be empty, so that the stress state of surrounding rock is redistributed, and strain energy needs to be released. When the stress is too large, the rock structure is unstable, or the strain energy release rate is too large, so that the surrounding rock still has larger kinetic energy after being broken, and rock fragments or fragments are ejected out at a larger speed, namely rock burst occurs.
The rock burst is a sudden damage with larger strength, and is very easy to occur under the geological condition of high ground stress hard rock. The occurrence of rock burst not only seriously damages the working table surface, but also has great threat to the life safety of personnel and working equipment. However, due to the nonlinearity and complexity of the rock burst itself, the research on the rock burst inoculation mechanism is insufficient, and the occurrence of rock burst cannot be well predicted, so that preventive measures are not timely implemented.
Disclosure of Invention
The problem to be solved by the invention is that the rock burst is difficult to predict due to the nonlinearity and complexity characteristics of the rock burst, so that preventive measures are not timely implemented.
In order to solve the above problems, in one aspect, the present invention provides a rock burst prediction method, including:
obtaining physical characteristics of a tunnel, and analyzing an equivalent shell type of the tunnel, wherein the physical characteristics of the tunnel comprise thickness, radius and circumferential length of an equivalent shell of the tunnel, and elasticity modulus and poisson ratio of a rock body of the tunnel;
determining a value range of wave numbers in the tunnel ring direction according to the type of the equivalent shell, the circumferential length, the thickness and the radius of the equivalent shell;
determining a minimum destabilization wave number of the tunnel according to the elastic modulus, the poisson ratio, the thickness and the radius of the equivalent shell and a destabilization stress model;
determining the minimum critical yield stress of the tunnel according to the value range of the wave number and the minimum instability wave number;
and when the hoop stress of the tunnel is equal to or larger than the minimum critical yield stress, judging that the tunnel is about to be unstable.
Optionally, the obtaining physical characteristics of the tunnel, and analyzing the equivalent shell type of the tunnel includes:
when the circumferential length of the tunnel is larger than a preset size, judging that the equivalent shell type is a long shell;
when the circumferential length of the tunnel is smaller than or equal to the preset size, analyzing whether constraint exists at two ends of the tunnel;
when two ends of the tunnel are unconstrained, judging that the equivalent shell type is a simply supported short shell;
when the two ends of the tunnel are restrained, the equivalent shell type is judged to be a solid support short shell.
Optionally, the determining the range of values of the wave numbers in the tunnel ring direction according to the equivalent shell type, the ring length, the thickness of the equivalent shell and the radius includes:
determining a deformation period of the equivalent shell according to the type of the equivalent shell and the circumferential length;
and determining the value range of the wave number in the tunnel ring according to the deformation period.
Optionally, the determining the deformation period of the equivalent shell according to the equivalent shell type and the circumferential length includes:
when the equivalent shell type is the long shell, the deformation period is (0, 2)πr]Wherein, the method comprises the steps of, wherein,r-said radius for said equivalent shell;
when the equivalent shell type is the short simple support shell, the deformation period is (0, 2)rφ]Wherein 2 isφA central angle corresponding to the equivalent shell;
when the equivalent shell type is the solid support short shell, the deformation cycle is (0,rφ]。
optionally, the determining the value range of the wave number in the tunnel ring according to the deformation period includes:
substituting the deformation period into a relation between the deformation period and the wave number to obtain the wave number, and carrying out dimensionless treatment on the wave number;
wherein when the equivalent shell type is the long shell, the value range of the wave number is [1 ]rInfinity), wherein,r-said radius for said equivalent shell;
when the equivalent shell type is the simple short shell, the value range of the wave number is [ [π/rφInfinity), wherein,rφhalf the circumferential length of the equivalent housing;
when the equivalent shell type is the fixed support short shell, the value range of the wave number is [2 ]π/rφ，∞)。
Optionally, before determining the minimum destabilizing wave number of the tunnel according to the elastic modulus, the poisson ratio, the thickness and the radius of the equivalent shell and the destabilizing stress model, the method further comprises:
obtaining the relation between the strain and the stress of the tunnel in each direction according to the assumption that the tunnel is equivalent to a shell;
obtaining the mechanical energy of the equivalent shell according to the relation between the strain and the stress in each direction;
and according to a variation principle, the variation of the mechanical energy is zero, and a balance equation and boundary conditions of the equivalent shell are obtained.
Optionally, after the mechanical energy is divided into zero according to the principle of variation and the equilibrium equation and the boundary condition of the equivalent shell are obtained, the method further includes:
according to the form of the equivalent shell after destabilization, obtaining displacement of the equivalent shell in a plurality of directions, wherein the directions comprise an axial direction, a circumferential direction and a radial direction of the equivalent shell;
substituting the displacement into the balance equation to obtain the hoop stress and the unsteady stress model of the tunnel.
Optionally, the unsteady stress model isThe method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is critical yield stress, +.>，/>，/>，EIs the modulus of elasticity of the material,μpoisson's ratio->Is the wave number after dimensionless treatment, +.>In the form of a non-dimensionalized radius,kfor the wave number of the wave number,tfor the thickness of the equivalent shell,ris the radius of the equivalent shell.
Optionally, the determining the minimum number of destabilization of the tunnel according to the modulus of elasticity, the poisson ratio, the thickness and the radius of the equivalent shell and the model of destabilizing stress includes:
deriving the unsteady stress model to obtain a first derivative of the unsteady stress model;
substituting the elastic modulus, the poisson ratio, the thickness and the radius of the equivalent shell into the first derivative, and enabling the first derivative to be equal to zero to obtain the minimum destabilization wave number of the tunnel.
Optionally, the determining the minimum critical yield stress of the tunnel according to the value range of the wave number and the minimum destabilizing wave number includes:
when the equivalent shell type is the long shell, the wave number corresponding to the minimum critical yield stress is the minimum destabilizing wave number, and the minimum destabilizing wave number is substituted into the destabilizing stress model to obtain the minimum critical yield stress;
when the equivalent shell type is the simple short shell or the solid short shell, the wave number corresponding to the minimum critical yield stress is the minimum end value of the value range, and the minimum end value is substituted into the unstability stress model to obtain the minimum critical yield stress.
In another aspect, the present invention further provides a rock burst prediction system, including:
the shell type analysis module is used for obtaining physical characteristics of the tunnel and analyzing the equivalent shell type of the tunnel, wherein the physical characteristics of the tunnel comprise the thickness, the radius and the circumferential length of the equivalent shell of the tunnel, and the elastic modulus and the poisson ratio of the rock mass of the tunnel;
the wave number range analysis module is used for determining a value range of wave numbers in the tunnel ring direction according to the equivalent shell type, the ring length, the thickness and the radius of the equivalent shell;
the critical stress analysis module is used for determining the minimum instability wave number of the tunnel according to the elastic modulus, the Poisson ratio, the thickness and the radius of the equivalent shell and the instability stress model; the method is also used for determining the minimum critical yield stress of the tunnel according to the value range of the wave number and the minimum destabilization wave number;
and the instability judging module is used for judging that the tunnel is about to be unstable when the hoop stress of the tunnel is equal to or larger than the minimum critical yield stress.
Compared with the prior art, the invention has the following beneficial effects:
according to the rock burst prediction method and system provided by the invention, the tunnel is equivalent to the shell according to the physical characteristics of the tunnel; determining a value range of wave numbers in the tunnel ring direction according to the type of the equivalent shell, the circumferential length, the thickness and the radius of the equivalent shell; determining a minimum destabilization wave number of the tunnel according to the elastic modulus, the poisson ratio, the thickness and the radius of the equivalent shell and a destabilization stress model; determining the minimum critical yield stress of the tunnel according to the value range of the wave number and the minimum destabilization wave number, so as to obtain the critical destabilization condition of the tunnel, and utilizing the destabilization condition; and when the hoop stress of the tunnel is equal to or larger than the minimum critical yield stress, judging that the tunnel is about to be unstable. Therefore, before tunnel excavation, whether surrounding rocks around the tunnel are likely to be subjected to rock burst or not can be known in advance after the tunnel excavation is completed, and pressure relief or protection can be timely carried out, so that secondary damage is avoided. After the tunnel is completed, the tunnel can be continuously monitored, and early warning signals are sent out in advance, so that personnel and equipment in the tunnel can be evacuated in time, or the protective measures of the tunnel can be enhanced.
Drawings
FIG. 1 shows a flow diagram of a rock burst prediction method in an embodiment of the invention;
FIG. 2 shows a schematic structural view of an equivalent cylindrical housing in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a long-shell destabilization mode according to an embodiment of the invention;
FIG. 4 shows a schematic diagram of a short shell destabilizing mode in an embodiment of the invention;
fig. 5 shows a schematic diagram of a short-leg-housing destabilization mode in an embodiment of the invention.
Detailed Description
In order that the above objects, features and advantages of the invention will be readily understood, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings.
It is noted that the terms "first," "second," and the like in the description and claims of the invention and in the foregoing figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the invention described herein may be implemented in sequences other than those illustrated or otherwise described herein.
In the description of the present specification, the descriptions of the terms "embodiment," "one embodiment," and the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or embodiment is included in at least one embodiment or implementation of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same examples or implementations. Furthermore, the particular features, structures, materials, or characteristics may be combined in any suitable manner in any one or more embodiments or implementations.
In general, structural instability, which is associated with abrupt changes in structure and which has many similarities to fracturing of rock burst, mostly occurs on at least one small-sized structure such as a plate, shell, rod, etc., that is subjected to longitudinal pressure. Therefore, the occurrence of fracturing and pulling type rock burst can be simulated as the structural instability of a slab bridge structure formed by surrounding rocks under the combined action of longitudinal pressure and transverse pressure.
Fig. 1 shows a flow diagram of a rock burst prediction method in an embodiment of the present invention, where the rock burst prediction method includes:
s1: obtaining physical characteristics of a tunnel, and analyzing an equivalent shell type of the tunnel, wherein the physical characteristics of the tunnel comprise thickness, radius and circumferential length of an equivalent shell of the tunnel, and elasticity modulus and poisson ratio of a rock body of the tunnel;
specifically, as shown in fig. 2, based on the above analysis, the tunnel is equivalent to a cylindrical shell, and a coordinate system of three directions is established on the tunnel, wherein the three directions are respectively the axial direction, the circumferential direction and the radial direction of the cylindrical shell, and the corresponding coordinates are respectivelyx、θAndzassume that the housing has axial and circumferential dimensions of 2, respectivelylAnd 2rφ，φHalf of the radian corresponding to the circumferential arc length, and the thickness istRadius ofrThe coordinate value range of the corresponding direction is-l≤x≤l、-φ≤θ≤φA kind of-t/2≤z≤t/2. Due to the different cross-sectional shapes of the tunnels, such as the various tunnel cross-sectional schematic diagrams shown in fig. 3-5, the equivalent shells of the tunnels can be classified according to the size of the circumferential dimension of the tunnels.
S2: determining a value range of wave numbers in the tunnel ring direction according to the type of the equivalent shell, the circumferential length, the thickness and the radius of the equivalent shell;
specifically, when the tunnel is unstable, the tunnel is pressed by the ground stress in surrounding rocks and is deformed inwards, so that rock burst is generated. Different types of tunnels produce different deformations, for example, when the circumferential dimension of the tunnel is large, as in fig. 3, rock burst may occur at any point around the tunnel, the deformation may occur at any point around the tunnel, and the deformation period (i.e., deformation range) may occurλIs 2πrThe method comprises the steps of carrying out a first treatment on the surface of the However, when the circumferential dimension of the tunnel is small, the deformation of the tunnel is affected by the constraint of the two ends of the tunnel, and when the two ends of the tunnel are unconstrained or weakly constrained, as shown in fig. 4, the deformation of the tunnel may occur in the whole circumferential direction, and the deformation period is 2rφWhen there is strong constraint at both ends of the tunnel, as shown in fig. 5, deformation of the tunnel mainly occurs at a position far from the constraint, i.e., in the middle of the circumferential direction of the tunnelAt the position, its deformation period isrφ. Therefore, when the tunnel is unstable or deformed, the fluctuation generated by the instability of the tunnel can be distinguished according to the equivalent shell types. The relation between wavenumber and deformation period is thatk=2π/λ，kFor the wavenumber of the equivalent shell in the circumferential direction,λfor the deformation period, a range of values of the wave number can be obtained. In order to reduce the number units introduced during the calculation, the wave numbers may be dimensionless,，/>in order to obtain the wave number after dimensionless treatment,kfor the wave number of the wave number,tis the thickness of the equivalent housing.
S3: determining a minimum destabilization wave number of the tunnel according to the elastic modulus, the poisson ratio, the thickness and the radius of the equivalent shell and a destabilization stress model; specifically, analyzing equivalent shells of various tunnels, and obtaining an unsteady stress model according to a variation principle and boundary constraint conditions, wherein the unsteady stress model isThe method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is critical yield stress, +.>，，/>，EIs the modulus of elasticity of the material,μpoisson's ratio->Is the wave number after dimensionless treatment, +.>In the form of a non-dimensionalized radius,kfor the wave number of the wave number,tfor the thickness of the equivalent shell,ris the radius of the equivalent shell. Substituting parameters of physical characteristics of the tunnel related to the unstable stress model into the unstable stress model, and analyzing the minimum value of the unstable stress model so as to find out the minimum unstable wave number corresponding to the minimum value.
S4: determining the minimum critical yield stress of the tunnel according to the value range of the wave number and the minimum instability wave number; specifically, although the minimum destabilizing wave number is found, different shell types have different wave number value ranges, sometimes the minimum destabilizing wave number is not necessarily in the wave number value range, at this time, further analysis of the minimum critical yield stress which can be achieved in the wave number value range is needed, and the minimum critical yield stress analyzed is the stress in the circumferential direction. The stress on the ring is mainly analyzed, because of the cylindrical modeling of the tunnel, when the ground stress extrudes the tunnel or gathers in the tunnel, the ground stress can deviate or shift along the cambered surface of the tunnel, so that the trend of the ground stress is distributed along the cambered surface, and due to the reason, under the action of the ground stress, the top area of the tunnel is prone to rock burst.
S5: and when the hoop stress of the tunnel is equal to or larger than the minimum critical yield stress, judging that the tunnel is about to be unstable. Specifically, before tunnel excavation, the ground stress around the tunnel can be obtained first, stress analysis is carried out according to the ground stress to obtain the hoop stress, then the hoop stress and the minimum critical yield stress are compared, whether rock burst is likely to occur in surrounding rocks around the tunnel after the tunnel excavation is completed in the tunnel excavation area is known in advance, if the tunnel is predicted to be unstable after the tunnel excavation, the possibility of rock burst is high, and therefore pressure relief or protection can be timely carried out after the tunnel excavation, and secondary damage is avoided. Besides, after the tunnel is completed, the ground stress in surrounding rock of the tunnel can be monitored in real time, the tunnel can be continuously monitored, when the hoop stress of the tunnel is close to the minimum critical yield stress, an early warning signal can be sent out in advance, personnel and equipment in the tunnel can be evacuated in time, or the protective measures of the tunnel can be enhanced.
In the present embodiment, by making the tunnel equivalent to a housing according to the physical characteristics of the tunnel; determining a value range of wave numbers in the tunnel ring direction according to the type of the equivalent shell, the circumferential length, the thickness and the radius of the equivalent shell; determining a minimum destabilization wave number of the tunnel according to the elastic modulus, the poisson ratio, the thickness and the radius of the equivalent shell and a destabilization stress model; determining the minimum critical yield stress of the tunnel according to the value range of the wave number and the minimum destabilization wave number, so as to obtain the critical destabilization condition of the tunnel, and utilizing the destabilization condition; and when the hoop stress of the tunnel is equal to or larger than the minimum critical yield stress, judging that the tunnel is about to be unstable. Therefore, before tunnel excavation, whether surrounding rocks around the tunnel are likely to be subjected to rock burst or not can be known in advance after the tunnel excavation is completed, and pressure relief or protection can be timely carried out, so that secondary damage is avoided. And after the tunnel is completed, the tunnel can be continuously monitored, and early warning signals are sent out in advance, so that personnel and equipment in the tunnel can be evacuated in time, or the protective measures of the tunnel can be enhanced. The rock burst prediction method provided by the embodiment of the invention can predict rock burst, is beneficial to timely starting preventive measures according to the prediction result, and avoids damage and threat of the rock burst to the working table surface, the life safety of personnel and working equipment.
In one embodiment of the present invention, the obtaining physical characteristics of the tunnel, analyzing the equivalent shell type of the tunnel includes:
when the circumferential length of the tunnel is larger than a preset size, judging that the equivalent shell type is a long shell; for example, in fig. 3, the tunnel has a larger circumferential dimension, dividing its equivalent shell type into long shells, while for the tunnels of fig. 4 and 5, its circumferential dimension is smaller, dividing its equivalent shell type into short shells.
When the circumferential length of the tunnel is smaller than or equal to the preset size, analyzing whether constraint exists at two ends of the tunnel; for the short shells, the constraint intensity at two ends of the short shells has a certain influence on subsequent analysis, so the short shells are further classified according to the constraint form at two ends of the short shells.
When two ends of the tunnel are unconstrained, judging that the equivalent shell type is a simply supported short shell;
when the two ends of the tunnel are restrained, the equivalent shell type is judged to be a solid support short shell.
Specifically, when the tunnel is deformed, the strength of the constraint at two ends influences the deformation range and the deformation trend, under the action of the ground stress, the tunnel with stronger constraint at two ends is difficult to deform due to the constraint limit, and when the constraint at two ends is not strong or free, the deformation of the tunnel can not only occur at the middle position of the tunnel, but also occur at two ends of the tunnel. According to the analysis, the two deformation forms of the tunnel can be equivalently simulated into a solid support short shell and a simple support short shell.
In one embodiment of the present invention, the determining the range of values of the wave numbers in the tunnel ring direction according to the equivalent shell type, the ring length, the thickness of the equivalent shell, and the radius includes:
determining a deformation period of the equivalent shell according to the type of the equivalent shell and the circumferential length;
and determining the value range of the wave number in the tunnel ring according to the deformation period.
In this embodiment, the determining the deformation period of the equivalent shell according to the equivalent shell type and the circumferential length includes:
when the equivalent shell type is the long shell, the deformation period is (0, 2)πr]Wherein, the method comprises the steps of, wherein,r-said radius for said equivalent shell; as shown in fig. 3, the deformation range of the long housing can extend over the entire circumferential arc.
When the equivalent shell type is the short simple support shell, the deformation period is (0, 2)rφ]Wherein 2φA central angle corresponding to the equivalent shell; as shown in FIG. 4, a short simple support shellThe deformation range of the body can be spread on the annular cambered surface of the whole shell.
When the equivalent shell type is the solid support short shell, the deformation cycle is (0,rφ]. As shown in fig. 5, since both ends of the short-leg case are fixed and are hard to move, the regions at both ends and the vicinity of both ends are hard to move or deform, and deformation occurs only in the middle region of the case, so that the deformation range can be regarded as ideal as occurring on the annular cambered surface of the middle stage.
In this embodiment, the determining, according to the deformation period, the value range of the wave number in the tunnel ring includes:
substituting the deformation period intok=2π/λObtaining the wave number, and carrying out dimensionless treatment on the wave number, wherein,kfor the wave number of the wave number,λis the deformation period;
specifically, it is known from the above formula and the value range of the deformation period that when the equivalent shell type is the long shell, the value range of the wave number is [1 ]rInfinity), wherein,r-said radius for said equivalent shell; when the equivalent shell type is the simple short shell, the value range of the wave number is [ [π/rφInfinity), wherein 2rφThe circumferential length of the equivalent housing; when the equivalent shell type is the fixed support short shell, the value range of the wave number is [2 ]π/rφ，∞)。
In one embodiment of the present invention, before determining the minimum number of destabilization waves of the tunnel according to the elastic modulus, the poisson ratio, the thickness and the radius of the equivalent shell, and the model of destabilizing stress, the method further comprises:
obtaining the relation between the strain and the stress of the tunnel in each direction according to the assumption that the tunnel is equivalent to a shell;
specifically, based on the plane section assumption, a geometric equation is established:
wherein, the liquid crystal display device comprises a liquid crystal display device,u、v、waxial, circumferential and radial displacements, respectively;、/>and->Respectively axial, circumferential line strain +.>In-plane shear strain; />And->The intrinsic strains, axial and circumferential, respectively, correspond to the initial strain resulting from the stress reconstruction caused by the ground stress and the excavation; />、/>、/>Respectively representing the axial and circumferential positive strain and the tangential strain of the middle plane caused by the in-plane deformation, and calculating by using corresponding formulas;zradial coordinate->、、/>Respectively representing the change of the curvature of the axial and annular middle surfaces and the change of the torsion rate caused by bending deformation, and calculating by using a corresponding formula;ris the radius of the equivalent shell. In the above formula, comma plus subscript indicates derivation of specific coordinates, e.g. +.>Representing in axial displacementxDerivation and->Representing in a pair of circumferential displacementsxDerivation and->Representing the radial displacementθAnd (5) deriving. Here, to facilitate analysis of the destabilization condition, the quadratic term of the deflection displacement derivative is retained in the geometric equation. Meanwhile, in the process of rewriting the geometric equation of a general shell into the geometric equation of a cylindrical shell, the shell is thinnerz/rThe related terms are retained to second order.
The stress component is，/>，/>Wherein->。EIs the modulus of elasticity of the material,μpoisson's ratio for the housing, here +.>(subscript)i，jMay bexOr (b)θ) The first subscript indicates the normal direction of the face on which the stress component is located, and the second subscript indicates the direction of the stress component.
Obtaining the mechanical energy of the equivalent shell according to the relation between the strain and the stress in each direction;
specifically, in conjunction with the physical equation, the mechanical energy expression of the surrounding rock shell system is given:
wherein, the liquid crystal display device comprises a liquid crystal display device,Uas the mechanical energy of the surrounding rock casing,Ais the area of the middle surface of the shell,tis cylindrical shell thickness. The surrounding rock shell is constrained by the external rock mass when deformed, the external rock can be equivalent to a spring,、/>、/>representing the restraining forces of the outer rock in the axial, circumferential and radial directions, respectively.
And according to a variation principle, the variation of the mechanical energy is zero, and a balance equation and boundary conditions of the equivalent shell are obtained.
Specifically, according to the principle of variation, letThe system balance equation and boundary conditions are found =0.
Before deformation, the round shell is only subjected tozThe compressive stress in the direction is recorded asAfter deformation, the external rock has weaker constraint on circumferential and axial displacement of the surrounding rock, and under a small deformation frame, the influence on stability is negligible, and only the consideration is given tozConstraint of direction, i.e.)>. For the convenience of calculation, on the premise of ensuring rationality, the constraint of the internal rock mass on the surrounding rock shell can be equivalent to the constraint of springs uniformly distributed on the periphery of the surrounding rock shell, namely +.>. Here->Representing the initial external pressure of the fluid,Kthe first sign here indicates, for equivalent spring stiffness, that the surrounding rock is subjected to before deformationzThe negative axial pressure, the second negative sign indicates that the surrounding rock is subjected to positive displacement along the coordinate axiszAnd (5) restraining counterforce in the axial negative direction. The equilibrium equation is thus obtained as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,(subscript)i，jMay bexOr (b)θ) For the film force component, the first subscript indicates the stress component +.>The second subscript indicates the stress component in the normal direction of the plane>Is directed at (I)>Corresponding stress component per unit width sectionResultant forces of (e.g.)>The first subscript of (a) indicates that the normal direction of the plane of the stress component isxThe second subscript indicates the direction of the stress component asxAxial direction (s)/(s)>Is a unit width section->Resultant force of stress components>(subscript)i，jMay bexOr (b)θ) The first subscript indicates the stress component +.>The second subscript indicates the stress component in the normal direction of the plane>Is directed at (I)>Corresponding stress component per unit width section>The resultant moment of the centroid of the section; in the above formula, comma plus subscript indicates derivation of specific coordinates, e.g. +.>Representing the radial displacementxDerivation and->Representing the radial displacementθAnd (5) deriving.
The boundary conditions are as follows:
(1) At the position ofxBoundary of facex=±l) Upper part
(2) At the position ofθBoundary of faceθ=±φ) Upper part
The internal stress component is here defined by the following integral:
wherein the method comprises the steps of，/>The axial and circumferential positive stresses in the housing before destabilization, respectively, can be considered as constants independent of coordinates.
The method comprises the steps of according to a variation principle, enabling the variation of the mechanical energy to be zero, and after obtaining a balance equation and boundary conditions of the equivalent shell, further comprising:
according to the form of the equivalent shell after destabilization, obtaining displacement of the equivalent shell in a plurality of directions, wherein the directions comprise an axial direction, a circumferential direction and a radial direction of the equivalent shell;
in particular, the method comprises the steps of,；
wherein, the liquid crystal display device comprises a liquid crystal display device,、/>、/>for the displacement amplitude in the corresponding direction,kis thatθWave number of direction, and corresponding deformation periodλThe space satisfiesk=2π/λ. Under the critical destabilization condition, even if destabilization occurs, the displacement is very small, so that the three deformation amplitudes are very small, the high-order quantity of the displacement in the geometric equation can be ignored, and only the first-order item is reserved.
Substituting the displacement into the balance equation, and combining the boundary conditions to obtain the hoop stress and the unsteady stress model of the tunnel.
Specifically, substituting the displacements in the above-described multiple directions into the equilibrium equation yields:
wherein, the liquid crystal display device comprises a liquid crystal display device,(ithe number of times of,j=2 or 3) is about +.>And->The specific expressions of the coefficients of the two amplitudes are as follows:
the first equation in the resulting equilibrium equation represents the conditions required to maintain equilibrium with the initial in-shell pressure.Is a hoop stress component in the shell when the shell is not deformed in a unsteady state. In general, the stress difference in all directions before excavation is not large, so the hoop stress and the radial stress are relatively close. After excavation, the surrounding rock shell is subjected to stress reconstruction for maintaining balance until the first formula is met. Since the shell radius is much larger than the thickness, the hoop stress will increase and the radial stress will decrease after stress reconstruction, i.e. a side pressure coefficient greater than 1 is generated. This is also true in practical engineering.
If the system is unstable, it means that the balance equation has a non-zero solution, requiring the coefficient determinant of the last two equations in the balance equation to be equal to zero. Since the thin shell thickness is small, the following assumptions can be made:t/rand 1 < 1. For the deformation of the shell on the elastomer, the equivalent rigidity can be usedAnd (5) estimating. The critical stress of instability, namely an instability stress model, can be obtained by the method:
；
wherein, the liquid crystal display device comprises a liquid crystal display device,is critical yield stress, +.>，/>And->The wavenumber and the radius are respectively dimensionless,Eis the modulus of elasticity of the material,μpoisson's ratio->Is the wave number after dimensionless treatment, +.>In the form of a non-dimensionalized radius,kfor the wave number of the wave number,tfor the thickness of the equivalent shell,ris the radius of the equivalent shell.
Said determining a minimum number of destabilization of said tunnel based on said modulus of elasticity, said poisson ratio, said thickness and said radius of said equivalent shell and a model of destabilizing stress comprising:
deriving the unsteady stress model to obtain a first derivative of the unsteady stress model; different destabilizing modes have different critical conditions. The mode of the system which is most prone to destabilization corresponds to the situation of minimum critical stress when。
Substituting the elastic modulus, the poisson ratio, the thickness and the radius of the equivalent shell into the first derivative, enabling the first derivative to be equal to zero, and obtaining the minimum destabilization wave number of the tunnel, namely solving the inflection point of the destabilization stress model, so that the minimum destabilization wave number corresponding to the minimum value position of the destabilization stress model is obtained.
In one embodiment of the present invention, the determining the minimum critical yield stress of the tunnel according to the value range of the wave number and the minimum destabilizing wave number includes:
when the equivalent shell type is the long shell, the wave number corresponding to the minimum critical yield stress is the minimum destabilizing wave number, and the minimum destabilizing wave number is substituted into the destabilizing stress model to obtain the minimum critical yield stress;
when the equivalent shell type is the simple short shell or the solid short shell, the wave number corresponding to the minimum critical yield stress is the minimum end value of the value range, and the minimum end value is substituted into the unstability stress model to obtain the minimum critical yield stress.
In particular, for shells of sufficiently large circumferential dimensions, i.e. when the equivalent shell type is the long shell, the minimum critical yield stress and the minimum number of destabilization wavesCorrespondingly, the minimum critical yield stress:when->At the moment, the tunnel is unstable, wherein, according to the first formula in the equilibrium equationIf the initial external pressure is measured in advance +.>And the size of the tunnel to be excavated can be obtained, namely the hoop stress can be obtained, and then the excavation is judgedThe possibility of a post-rock burst. However, for harder surrounding rock, regular periodic folds are difficult to generate, but sudden instability deformation is directly generated at the position with more defects, so that rock burst is caused. Due to the larger radius, the minimum critical yield stress is reduced to +.>Thus, the greater the elastic modulus of the rock, the more difficult the casing is to destabilize. The greater the initial hoop stress for a particular shell, the more it exceeds the critical yield stress, and the higher the burst strength and rating upon occurrence of a burst.
For the shell with smaller circumferential dimension, due to the limitation of the dimension, the shell can leadIs constant and cannot generate +.>The specific possible modes are determined by the shell circumferential dimensions and boundary conditions.
(1) When the equivalent shell type is the simply supported short shell, the two sides of the equivalent shell are weak in constraint (such as no support), the two sides of the shell can rotate, both sides can be regarded as hinge supports, and the number of destabilization waves corresponding to the minimum critical yield stress is=πt/(rφ) At this time, the->The minimum critical yield stress:。/>
(2) When the equivalent shell is of the fixed support short shell type, the two sides of the equivalent shell are restricted strongly (certain support or stepwise excavation is provided), the rotation of the two sides of the shell is limited, both sides can be regarded as fixed ends, and the number of destabilization corresponding to the minimum critical yield stress is=2πt/(rφ) The minimum critical yield stress:。
generally, the radius of the surrounding rock shell is determined in advance, and the excavation mode is easy to change, so that the central angle of the shell corresponding to each excavation step is changedφ. For the case of two shells with smaller circumferential dimensions, the expression of the critical yield stress under the above two constraints can be obtained whenThe critical yield stress is asφIs increased by decreasing. Therefore, the excavation is carried out step by step during the excavation, the central angle corresponding to the new surrounding rock shell generated by each step of excavation is reduced, and the possibility of instability of the surrounding rock can be effectively reduced.
According to the analysis, the critical condition of destabilization of the surrounding rock shell under the combined action of the annular pressure and the radial pressure can be deduced, so that the occurrence of rock burst is predicted. By combining the actual stress level, rock parameters, tunnel size and excavation mode, the possibility and strength of rock burst occurrence can be preliminarily judged: the initial hoop stress exceeds the critical stress, and the system is unstable; the greater the initial hoop stress exceeds the critical stress, the greater the burst strength at destabilization. According to the minimum critical yield stress obtained by the instability stress model, the factors influencing the occurrence of rock burst can be analyzed, the mode for reducing the occurrence possibility of rock burst is explored, for example, the effective length of a shell is reduced by optimizing an excavation mode or a supporting mode, the boundary condition is changed, and the critical instability stress is increased; the local ground stress is reduced by blasting in advance, and the initial hoop stress is finally reduced.
The surrounding rock shell instability theoretical analysis is adopted, and the principle is as follows: for many rock bursts, particularly fracture-fracturing rock bursts, the occurrence of rock bursts is often accompanied by ejection of flaky rock. And the fracturing and buckling processes of the plate shell are quite similar. For the surrounding rock casing, the presence of ground stress is such that it is subject to an initial tangential stress. When the initial stress is smaller, the surrounding rock shell cannot be unstable, and at the moment, the surrounding rock shell is slightly deformed under the action of the radial stress, and the internal stress of the surrounding rock is reconstructed; when the initial stress exceeds a certain value, the rock casing will have a second stable form in addition to the initial form, and the presence of radial stress may cause the casing to jump from the initial form to the second stable form. For softer rocks, the kick can be realized under the condition that the rock is not broken, and larger instability deformation is generated; for harder surrounding rock shells, this jumping action causes the shell to fracture, creating rock fragments and ejecting. The above phenomenon can be observed under different geological conditions, verifying the feasibility of the above method.
The surrounding rock shell instability theoretical analysis is adopted, and the method has the advantages that: the rock burst inoculation and generation mechanism is understood from a new angle, the rock burst generation condition is given by using a relatively simple and visual theoretical result, the rock burst generation can be well predicted by combining with the actual working condition, and the basic thought for reducing the rock burst generation probability is further deduced.
In another embodiment of the present invention, there is also provided a rock burst prediction system including:
the shell type analysis module is used for obtaining physical characteristics of the tunnel and analyzing the equivalent shell type of the tunnel, wherein the physical characteristics of the tunnel comprise the thickness, the radius and the circumferential length of the equivalent shell of the tunnel, and the elastic modulus and the poisson ratio of the rock mass of the tunnel;
the wave number range analysis module is used for determining a value range of wave numbers in the tunnel ring direction according to the equivalent shell type, the ring length, the thickness and the radius of the equivalent shell;
the critical stress analysis module is used for determining the minimum instability wave number of the tunnel according to the elastic modulus, the Poisson ratio, the thickness and the radius of the equivalent shell and the instability stress model; the method is also used for determining the minimum critical yield stress of the tunnel according to the value range of the wave number and the minimum destabilization wave number;
and the instability judging module is used for judging that the tunnel is about to be unstable when the hoop stress of the tunnel is equal to or larger than the minimum critical yield stress.
The rock burst prediction system provided by the invention has similar technical effects to the rock burst prediction method, and is not described in detail herein.
Although the present invention is disclosed above, the present invention is not limited thereto. Various changes and modifications may be made by one skilled in the art without departing from the spirit and scope of the invention, and the scope of the invention should be assessed accordingly to that of the appended claims.

Claims (11)

1. The rock burst prediction method is characterized by comprising the following steps of:
obtaining physical characteristics of a tunnel, and analyzing an equivalent shell type of the tunnel, wherein the physical characteristics of the tunnel comprise thickness, radius and circumferential length of an equivalent shell of the tunnel, and elasticity modulus and poisson ratio of a rock body of the tunnel;
determining a value range of wave numbers in the tunnel ring direction according to the type of the equivalent shell, the circumferential length, the thickness and the radius of the equivalent shell;
determining a minimum destabilization wave number of the tunnel according to the elastic modulus, the poisson ratio, the thickness and the radius of the equivalent shell and a destabilization stress model;
determining the minimum critical yield stress of the tunnel according to the value range of the wave number and the minimum instability wave number;
and when the hoop stress of the tunnel is equal to or larger than the minimum critical yield stress, judging that the tunnel is about to be unstable.
2. The method of claim 1, wherein the obtaining physical characteristics of the tunnel and analyzing an equivalent shell type of the tunnel comprise:
when the circumferential length of the tunnel is larger than a preset size, judging that the equivalent shell type is a long shell;
when the circumferential length of the tunnel is smaller than or equal to the preset size, analyzing whether constraint exists at two ends of the tunnel;
when two ends of the tunnel are unconstrained, judging that the equivalent shell type is a simply supported short shell;
when the two ends of the tunnel are restrained, the equivalent shell type is judged to be a solid support short shell.
3. The method according to claim 2, wherein determining the range of values of the wave numbers in the tunnel ring direction according to the equivalent shell type, the circumferential length, the thickness of the equivalent shell, and the radius comprises:
determining a deformation period of the equivalent shell according to the type of the equivalent shell and the circumferential length;
and determining the value range of the wave number in the tunnel ring according to the deformation period.
4. A rock burst prediction method according to claim 3, wherein the determining the deformation period of the equivalent shell according to the equivalent shell type and the circumferential length comprises:
when the equivalent shell type is the long shell, the deformation period is (0, 2)πr]Wherein, the method comprises the steps of, wherein,r-said radius for said equivalent shell;
when the equivalent shell type is the short simple support shell, the deformation period is (0, 2)rφ]Wherein 2 isφA central angle corresponding to the equivalent shell;
when the equivalent shell type is the solid support short shell, the deformation cycle is (0,rφ]。
5. the method of claim 4, wherein determining the range of values of the wave numbers in the tunnel ring according to the deformation period comprises:
substituting the deformation period into a relation between the deformation period and the wave number to obtain the wave number, and carrying out dimensionless treatment on the wave number;
wherein when the equivalent shell type is the long shell, the value range of the wave number is [1 ]rInfinity), wherein,r-said radius for said equivalent shell;
when the equivalent shell type is the simple short shell, the value range of the wave number is [ [π/rφInfinity), wherein,rφhalf the circumferential length of the equivalent housing;
when the equivalent shell type is the fixed support short shell, the value range of the wave number is [2 ]π/rφ，∞)。
6. The method of claim 1, wherein before determining the minimum number of destabilization waves of the tunnel based on the modulus of elasticity, the poisson ratio, the thickness and the radius of the equivalent shell and the model of destabilizing stress, further comprising:
obtaining the relation between the strain and the stress of the tunnel in each direction according to the assumption that the tunnel is equivalent to a shell;
obtaining the mechanical energy of the equivalent shell according to the relation between the strain and the stress in each direction;
and according to a variation principle, the variation of the mechanical energy is zero, and a balance equation and boundary conditions of the equivalent shell are obtained.
7. The method of claim 6, wherein the dividing the mechanical energy into zero according to the dividing principle, after obtaining the equilibrium equation and the boundary condition of the equivalent shell, further comprises:
according to the form of the equivalent shell after destabilization, obtaining displacement of the equivalent shell in a plurality of directions, wherein the directions comprise an axial direction, a circumferential direction and a radial direction of the equivalent shell;
substituting the displacement into the balance equation to obtain the hoop stress and the unsteady stress model of the tunnel.
8. The rock burst prediction method according to claim 1, wherein the unsteady stress model isThe method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is critical yield stress, +.>，，/>，EIs the modulus of elasticity of the material,μpoisson's ratio->Is the wave number after dimensionless treatment, +.>In the form of a non-dimensionalized radius,kfor the wave number of the wave number,tfor the thickness of the equivalent shell,ris the radius of the equivalent shell.
9. The method of claim 1, wherein said determining a minimum number of destabilizes of said tunnel based on said modulus of elasticity, said poisson ratio, said thickness and said radius of said equivalent shell and a model of destabilizing stress comprises:
deriving the unsteady stress model to obtain a first derivative of the unsteady stress model;
substituting the elastic modulus, the poisson ratio, the thickness and the radius of the equivalent shell into the first derivative, and enabling the first derivative to be equal to zero to obtain the minimum destabilization wave number of the tunnel.
10. The method of claim 2, wherein determining the minimum critical yield stress of the tunnel based on the range of values of the wavenumbers and the minimum destabilizing wavenumber comprises:
when the equivalent shell type is the long shell, the wave number corresponding to the minimum critical yield stress is the minimum destabilizing wave number, and the minimum destabilizing wave number is substituted into the destabilizing stress model to obtain the minimum critical yield stress;
when the equivalent shell type is the simple short shell or the solid short shell, the wave number corresponding to the minimum critical yield stress is the minimum end value of the value range, and the minimum end value is substituted into the unstability stress model to obtain the minimum critical yield stress.
11. A rock burst prediction system, comprising:
the shell type analysis module is used for obtaining physical characteristics of the tunnel and analyzing the equivalent shell type of the tunnel, wherein the physical characteristics of the tunnel comprise the thickness, the radius and the circumferential length of the equivalent shell of the tunnel, and the elastic modulus and the poisson ratio of the rock mass of the tunnel;
the wave number range analysis module is used for determining a value range of wave numbers in the tunnel ring direction according to the equivalent shell type, the ring length, the thickness and the radius of the equivalent shell;
the critical stress analysis module is used for determining the minimum instability wave number of the tunnel according to the elastic modulus, the Poisson ratio, the thickness and the radius of the equivalent shell and the instability stress model; the method is also used for determining the minimum critical yield stress of the tunnel according to the value range of the wave number and the minimum destabilization wave number;
and the instability judging module is used for judging that the tunnel is about to be unstable when the hoop stress of the tunnel is equal to or larger than the minimum critical yield stress.
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