CN110096809B - Modeling method for material unstable roadway rock burst based on double-yield contour model - Google Patents
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Abstract
The invention provides a modeling method of material unstable roadway rock burst based on a double-yield isoline model, which comprises the following steps: s1: dividing the stress working condition of the roadway coal body into two working conditions according to the stress condition of the roadway coal body in the vertical direction; s2: establishing a yield function model of unbalanced force applied to the roadway coal body to obtain a relation model of roadway rock burst, roadway cohesive force and an internal friction angle under different working conditions; the method can represent the critical state of the unstable rock burst of the roadway material by calculating the maximum elastic swelling amount, and can accurately and quickly trigger the roadway rock burst to perform early warning by taking the calculated maximum elastic swelling amount as the threshold value of the early warning judgment of the roadway rock burst, thereby being widely applied to field engineering guidance, avoiding or reducing the occurrence of impact accidents and ensuring the safe production of mines.
Description
Technical Field
The invention relates to the technical field of coal mine underground safety prediction, in particular to a modeling method of material unstable roadway rock burst based on a double-yield contour model.
Background
The problem of rock burst is a prominent problem which puzzles the mining and rock engineering world, and the coal mine rock burst is increasingly severe and complex in China with the increase of mining depth and the continuous increase of mining strength, so that the generation mechanism of the rock burst is researched, and the generation process is revealed to have great significance for the safe and efficient production of coal mines in China. The rock burst is a complex mine dynamic phenomenon, various national scholars successively put forward a series of rock burst triggering theories, mainly comprising an intensity theory, a rigidity theory, an energy theory, a rock burst tendency theory, a three-criterion theory, a three-factor theory, a destabilization theory, a dynamic and static load superposition theory and the like, systematically describe and demonstrate the rock burst generating conditions and process from different angles, and obtain a plurality of precious achievements.
Three mechanical models of coal mine rock burst are proposed by ginger dazzler et al: material instability type rock burst, slippage dislocation type rock burst and structure instability type rock burst. The unstable material type rock burst refers to a burst protrusion which is generated by continuous expansion, penetration and convergence of internal cracks of a coal rock material after stress concentration in the coal rock body reaches a certain degree in a roadway or a rock body around a working face in an excavation process, and causes ejection and explosive type damage to the coal rock body within a certain range, and is common in mine operation.
However, due to the complex mechanism and numerous influencing factors of rock burst, the understanding of the generation and prevention mechanism of material-destabilizing rock burst is not specific enough so far, and the guidance on field engineering is limited, so that the frequent occurrence of rock burst still exists at present, and the safety production of mines is seriously threatened.
Therefore, it is necessary to provide a modeling method of rock burst danger of the roadway.
Disclosure of Invention
In view of the above, the invention aims to provide a method for modeling material destabilization type roadway rock burst based on a double-yield-contour model, which analyzes the elastoplasticity conversion characteristics of surrounding rocks by simplifying a method of solving a mine pressure stress field by a mechanical model, carrying out an indoor coal body compression failure experiment and finite element simulation to obtain a critical state judgment model for the roadway rock burst based on the double-yield-contour model, can accurately and quickly perform early warning on the triggering of the roadway rock burst, can be widely applied to field engineering guidance, avoids or reduces the occurrence of impact accidents, and ensures the safe production of mines.
The invention provides a modeling method of material unstable roadway rock burst based on a double-yield isoline model, which comprises the following steps:
s1: according to the stress condition of the vertical direction that the tunnel coal body received, fall into two kinds of operating modes with tunnel coal body atress operating mode: the working condition I is as follows: the stress in the vertical direction on the roadway coal body is uniform load; working conditions are as follows: the stress in the vertical direction on the roadway coal body is increased along with the increase of the height;
s2: and establishing a yield function model of unbalanced force borne by the roadway coal body to obtain a relation model of roadway rock burst, roadway cohesive force and internal friction angle under different working conditions.
Further, the method also comprises the step S3: and drawing yield function contour lines under different working conditions according to a yield function model of unbalanced force borne by the roadway coal body.
Further, the yield function model of the unbalanced force suffered by the roadway coal body is as follows:
wherein C and
respectively is cohesive force and an internal friction angle, L is a roadway height, x is an x-direction coordinate of an Airy stress distribution coordinate, y is a y-direction coordinate of the Airy stress distribution coordinate, and the Airy stress distribution coordinate specifically comprises the following steps: introducing an Airy stress field distribution theory, establishing an Airy stress distribution coordinate of the wall surface of the roadway coal body by taking any point on an intersection line of any roadway coal body wall surface and a roadway ground plane as a circle center, taking a vertical stress direction borne by the wall surface of the roadway coal body as a y direction and taking a horizontal stress direction borne by the wall surface of the roadway coal body as an x direction according to the definition of the Airy stress field distribution theory on a stress equivalence zone; q is a pressure coefficient, B is a dimensionless coefficient, K is a discrimination factor,
in the first working condition, C is a constant; in condition two, C varies with x.
Further, in the second working condition, the calculation formula of C is:
wherein a represents a threshold value of the ratio of the maximum horizontal stress to the vertical stress of the roadway working face; and b represents the vertical stress concentration coefficient of the roadway working face.
Further, in the second working condition, the correction is needed to be performed on the correction value calculated by the formula (2), and the correction formula of the C is as follows:
C'＝d·C (3)
c' is the corrected C, d represents a correction coefficient, and a represents a threshold value of the ratio of the maximum horizontal stress to the vertical stress of the roadway working surface; and b represents the vertical stress concentration coefficient of the roadway working face.
Further, the derivation process of the formula (1) is as follows:
given that coal bodies are subject to the Moore-Coulomb yield criterion, the yield function of the imbalance force F can be expressed as:
wherein σ 1 And σ 3 Are all ultimate principal stresses, σ 1 Is the median principal stress, σ 3 To confining pressure, C and
respectively is cohesive force and an internal friction angle, and K is a discrimination factor; (3) The formula shows that when the unbalanced force F is larger than or equal to the discrimination factor K, the coal body generates yield failure;
will sigma x ，σ y And τ xy The belt of formula (11) can be:
wherein σ x Representing the vertical component of the stress to which the coal body is subjected, σ y Representing the horizontal component of the stress, tau, to which the coal is subjected xy Representing the tangential stress to which the coal body is subjected;
reduction of τ in formula (4) xy And the sigma under the Airy stress distribution coordinate is used x ，σ y And τ xy Substituting the expression of (2) into the expression of (4) to obtain the expression of (1).
Further, σ in the Airy stress distribution coordinate x ，σ y And τ xy The expression of (a) is:
further, σ in the Airy stress distribution coordinate x ，σ y And τ xy The derivation of the expression of (a) is as follows:
introducing an Airy stress distribution theory, and establishing an Airy stress distribution coordinate of the wall surface of the roadway coal body by taking any one point on an intersection line of any one wall surface of the roadway coal body and the ground plane of the roadway as a circle center, taking the vertical stress direction borne by the wall surface of the roadway coal body as the y direction and the horizontal stress direction borne by the wall surface of the roadway coal body as the x direction;
the Airy stress function phi stressed at any point of the wall surface of the roadway coal body can be written as follows:
wherein, P represents the concentrated force that the tunnel lateral wall received, l represents the board thickness, theta represents the arbitrary one point of tunnel coal wall and the contained angle of load action point line and load direction, r represents arbitrary one point of tunnel coal wall and load action point line distance, and each stress component of arbitrary one point of tunnel coal wall can be write:
wherein σ r Representing the radial stress, sigma, on any point of the wall surface of the coal body of the roadway θ Representing the circumferential stress on any point of the wall surface of the roadway coal body;
using the moire circle to convert the polar coordinates to rectangular coordinates, the stress in the x, y directions can be expressed as:
wherein σ x Representing the component force, sigma, of the stress on any point of the wall surface of the roadway coal body in the vertical direction y Shows the component force, tau, of the stress on any point of the wall surface of the roadway coal body in the horizontal direction xy Representing the tangential stress applied to any point of the wall surface of the roadway coal body;
if the distance between the two loads is L and the two concentrated loads are the same, the two concentrated stresses can adopt the principle of elastomechanics superposition to convert the formula (8), and the stress at any point of the wall surface of the roadway coal body can be expressed as follows:
wherein r is 1 Represents the connecting line distance r between any point of the wall surface of the roadway coal body and one load action point 2 Represents the connecting line distance theta between any point of the wall surface of the roadway coal body and another load acting point 1 Represents the included angle theta between the connecting line of any point of the wall surface of the roadway coal body and one load acting point and the load direction 2 And the included angle between the connecting line of any point of the wall surface of the roadway coal body and the other load acting point and the load direction is shown.
If the roadway height is L, in the cartesian coordinate system, equation (9) can be expressed as:
order to
And a coefficient Q × B representing a compression force in the vertical direction is introduced, and B is a dimensionless coefficient, the expression (10) can be changed to the expression (5).
The invention has the beneficial effects that: according to the invention, the elastic-plastic conversion characteristics of the surrounding rock are analyzed by simplifying a mechanical model to solve a mine compressive stress field and developing an indoor coal body compression failure experiment and finite element simulation, so that a critical state judgment model of the roadway rock burst generation based on the double-yield contour model is obtained, the roadway rock burst triggering can be accurately and quickly pre-warned, the method can be widely applied to field engineering guidance, the occurrence of impact accidents is avoided or reduced, and the safety production of a mine is ensured.
Drawings
The invention is further described below with reference to the following figures and examples:
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 shows the internal friction angle in a Cartesian coordinate system
Yield function F contour;
FIG. 3 shows the internal friction angle in a two-Cartesian coordinate system under operating conditions
Yield function F contour;
FIG. 4 shows the internal friction angle in the two Cartesian coordinate system under operating conditions
Yield function F contour;
FIG. 5 shows the internal friction angle in the two Cartesian coordinate system under operating conditions
Yield function F contour;
FIG. 6 shows the internal friction angle in a two-Cartesian coordinate system under operating conditions
Yield function F contour;
FIG. 7 is a schematic view of a semi-infinite plate force;
FIG. 8 is a schematic view of a standard cylindrical coal sample;
FIG. 9 is a schematic representation of a coal sample when the stress reaches about 60% of its compressive strength;
FIG. 10 is a schematic representation of a coal sample when the stress reaches about 78% of its compressive strength;
FIG. 11 is a schematic view of a coal sample at peak stress intensity;
FIG. 12 is a schematic diagram of the calculation result of plastic strain of a planar square model using a coal body as a material model;
FIG. 13 is a schematic diagram of a tunnel excavation plane model, which simulates plastic deformation of a tunnel under an overlying 20MPa pressure;
FIG. 14 is a diagram I of a site where one side of a coal wall shows a concave surface shape and a triangular shape rushing out of a rock mass after coal mine impact ground pressure occurs;
FIG. 15 is a field diagram II of a coal wall side showing a concave surface shape and a triangular shape punched out of a rock mass after coal mine ground pressure occurs.
Detailed Description
As shown in fig. 1, the method for modeling material unstable roadway rock burst based on the double-yield contour model provided by the invention comprises the following steps:
s1: according to the stress condition of the vertical direction that the tunnel coal body received, fall into two kinds of operating modes with the tunnel coal body atress condition: the working condition I is as follows: the stress in the vertical direction on the roadway coal body is uniform load; working conditions are as follows: the stress in the vertical direction on the roadway coal body is increased along with the increase of the height; the roadway rock burst referred to in the application refers to a material instability type rock burst, and the roadway referred to in the application is a rectangular roadway and is not described in detail hereinafter.
S2: establishing a yield function model of unbalanced force borne by the roadway coal body to obtain a relation model of roadway rock burst, roadway cohesive force and internal friction angle under different working conditions;
further, the method also comprises the step S3: and (4) drawing yield function contour lines under different working conditions according to the yield function model of the unbalanced force applied to the roadway coal body, and inputting the yield function model of the unbalanced force applied to the roadway coal body into the MATLAB to calculate the contour line of the yield function F. The law of roadway rock burst can be observed according to yield function contour lines under different working conditions, and the method has great significance for researching roadway surrounding rock changes and ensuring roadway working safety. By the method, the method that the mechanical model resolves the mine compressive stress field, the indoor coal compression failure experiment is carried out, and the finite element simulation method analyzes the elastoplasticity conversion characteristics of the surrounding rock, the critical state judgment model of the roadway rock burst generation based on the double-yield contour line model is obtained, the roadway rock burst triggering can be accurately and quickly pre-warned, the method can be widely applied to field engineering guidance, the occurrence of rock burst accidents is avoided or reduced, and the safety production of mines is ensured.
The yield function model of the unbalanced force suffered by the roadway coal body is as follows:
wherein C and
respectively is cohesive force and an internal friction angle, L is a roadway height, x is an x-direction coordinate of an Airy stress distribution coordinate, y is a y-direction coordinate of the Airy stress distribution coordinate, and the Airy stress distribution coordinate specifically comprises the following steps: introducing an Airy stress field distribution theory, establishing an Airy stress distribution coordinate of the wall surface of the roadway coal body by taking any point on an intersecting line of the wall surface of any roadway coal body and the roadway ground plane as a circle center, taking a vertical stress direction borne by the wall surface of the roadway coal body as a y direction and taking a horizontal stress direction borne by the wall surface of the roadway coal body as an x direction according to the definition of the Airy stress field distribution theory on a stress equivalent zone; q is a pressure coefficient, B is a dimensionless coefficient, K is a discrimination factor,
in the first working condition, C is a constant; in condition two, C varies with x. For example: under the condition of the working condition one, the vertical stress is uniform load (namely C = 3.2), and the internal friction angle is taken
The values of equation 8 and C are taken into equation (13), and the contour of the yield function F is calculated using MATLAB. The yield function contour line is shown in figure 2 in a Cartesian coordinate system and is in a hyperbolic-like form, and the maximum yield contour line appears at a part close to the outer edge of the roadway, which shows that the coal body is gradually damaged layer by layer from outside to inside in the stress process of the coal body. (1) The formula is a relation model of the roadway rock burst, the roadway cohesive force and the internal friction angle under different working conditions.
Further, in the second operating condition, the calculation formula of C is:
wherein a represents a threshold value of the ratio of the maximum horizontal stress to the vertical stress of the roadway working face, and is determined by a measured value of the ground stress of the rock burst coal mine, and in general, a is more than or equal to 1.2 and less than or equal to 2; b represents the vertical stress concentration coefficient of the roadway working surface and is determined by the actually measured roadway or working surface concentrated stress, and b is more than or equal to 2 and less than or equal to 4.
Further, in the second working condition, the correction is needed to be performed on the correction value calculated by the formula (2), and the correction formula of the C is as follows:
C'＝d·C (3)
wherein C' is C after correction, d represents a correction coefficient, in this embodiment, d =0.6, a represents a threshold value of a ratio of the maximum horizontal stress to the vertical stress of the roadway working face; and b represents the vertical stress concentration coefficient of the roadway working face.
In the actual measurement of the ground stress of a rock burst coal mine, the maximum horizontal main stress is 1.2-2 times of the vertical stress (1.5 is taken as an example in the embodiment), and the horizontal stress value in the formula (2) is (0, 2Q). Taking 2-4 (taking 3 as an example in the embodiment) in a roadway or a working face according to an actually measured vertical stress concentration coefficient, assuming that the vertical stress in a stress rising area gradually rises linearly, then:
the calculation model adopts an L multiplied by L range at one side of the roadway, and the correction coefficient is set to be 0.6, so that the C value can be corrected as follows:
C'＝0.6·C＝2.4x (3-1)
and (3) bringing the C' back to the formula (1), obtaining a relation model of the roadway impact ground pressure, the roadway cohesive force and the internal friction angle under the working condition two, and further calculating the contour line of the yield function F by using MATLAB. Internal friction angle
Taking 37 degrees, and the yield function contour line is in a Cartesian coordinate system and is shown in figure 3, the maximum yield contour line appears in the deep part of the roadway, which shows that the coal rock is damaged from deep to shallow parts, the shallow parts are complete, and finally a complete block body on the outer edge is suddenly stripped.
The internal friction angles are adjusted to be 40 degrees, 45 degrees and 50 degrees respectively. The value of C is determined by the formula (3-1),the contour plots are shown in fig. 4, 5 and 6: following the internal friction angle
The yield contour line gradually moves to the deep part, the numerical value F of the maximum yield contour line is increased, and the fact that the rock burst or the hard coal roadway basically occurs is verified. From equation (1), the lithological conditions of rock burst and zonal rupture are as follows: of surrounding rock
The larger the yield contour, the more favorable the yield contour will be to form the case of large deep part and small shallow part, i.e. of the surrounding rock
The larger the impact, the deeper the impact occurs, the stronger the energy release, and the more severe the damage caused; meanwhile, the larger the C value of the surrounding rock, the closer the fracture surface is to the deep part. In fig. 2 to 6, the abscissa represents a Distance in the horizontal direction (Distance in horizontal direction), and the ordinate represents a Height in the vertical direction (Height of roadway), which is the y direction in the Airy stress distribution coordinates of the wall surface of the roadway coal body, generally, the y direction is the direction perpendicular to the ground plane.
The derivation process of the formula (1) is as follows:
for rock, the yield criterion is usually expressed as a yield surface or yield position, which is an assumption about the elastic limit under any combination of stresses. Given that coal bodies are subject to the Moore-Coulomb yield criterion, the yield function of the imbalance force F can be expressed as:
wherein σ 1 And σ 3 Are all ultimate principal stresses, σ 1 Is the median principal stress, σ 3 To confining pressure, C and
are respectively provided withThe cohesive force and the internal friction angle are shown, and K is a discrimination factor; (3) The formula shows that when the unbalanced force F is larger than or equal to the discrimination factor K, the coal body generates yield failure;
will sigma x ，σ y And τ xy The belt of formula (11) can be:
wherein σ x Representing the vertical component of the stress to which the coal body is subjected, σ y Representing the horizontal component of the stress, tau, to which the coal body is subjected xy Representing the tangential stress to which the coal body is subjected;
reduction of τ in formula (4) xy And the sigma under the Airy stress distribution coordinate is used x ，σ y And τ xy Substituting the expression of (b) into the expression (4) to obtain the expression (1).
Further, σ in the Airy stress distribution coordinate x ，σ y And τ xy The expression of (c) is:
in practice, the vertical stress σ y The formation has a complexity that is not only dependent on the concentrated load, but is also influenced by the overburden load and the stress concentration factor (ratio of maximum vertical stress to in-situ vertical stress). Therefore, the derivation process of the formula (3) and the formula (4) is applied to σ x And σ y The relative relationship of the measured data between the two is further analyzed.
Further, σ in the Airy stress distribution coordinate x ，σ y And τ xy The derivation of the expression of (a) is as follows:
introducing an Airy stress distribution theory, and establishing an Airy stress distribution coordinate of the wall surface of the roadway coal body by taking any one point on an intersection line of any one wall surface of the roadway coal body and the ground plane of the roadway as a circle center, taking the vertical stress direction borne by the wall surface of the roadway coal body as the y direction and the horizontal stress direction borne by the wall surface of the roadway coal body as the x direction;
in the traditional roadway stress field solution, round hole excavation or rectangular excavation in an infinite plate is usually adopted, so that the solution of the stress field can be well obtained, but the characteristic of layered sedimentary rock of coal mine overburden rock is neglected. And selecting the side wall of the rectangular roadway as a research object (which can be conditionally popularized to any side of the roadway). The tunnel lateral wall receives vertical direction's ground stress, simultaneously because the friction constraint effect of top bottom plate, the tunnel lateral wall can simplify to the compression body that the tip is retrained. As shown in fig. 7, firstly considering the end constraint effect, the end constraint can consider that a concentrated force P acts on the upper end and the lower end of a roadway, selecting a rectangular roadway side wall as a research object, establishing a compression body model with a constrained end, introducing an Airy stress field distribution theory, defining a stress isosphere according to the Airy stress field distribution theory, and establishing an Airy stress distribution coordinate of the roadway coal body wall surface by taking any one point on an intersection line of any roadway coal body wall surface and a roadway ground plane as a circle center, taking a vertical stress direction borne by the roadway coal body wall surface as a y direction, and taking a horizontal stress direction borne by the roadway coal body wall surface as an x direction.
The infinite plate is acted by a concentrated force, wherein an Airy stress function phi which represents the stress of the point A, namely the Airy stress function phi which represents the stress of any point of the wall surface of the roadway coal body can be written as follows:
wherein, P represents the concentrated force applied to the side wall of the roadway, l represents the plate thickness, θ represents the included angle between the connecting line of any point of the wall surface of the roadway coal body and the load acting point and the load direction, and r represents the connecting line distance between any point of the wall surface of the roadway coal body and the load acting point, that is, the connecting line distance between the point a and the load acting point in fig. 7.
The stress components of the point A, namely the stress components of any point of the wall surface of the roadway coal body can be written as follows:
wherein σ r Representing the radial stress, sigma, on any point of the wall surface of the coal body of the roadway θ Representing the circumferential stress on any point of the wall surface of the roadway coal body;
using the moire circle to convert the polar coordinates to rectangular coordinates, the stress in the x, y directions can be expressed as:
wherein σ x Representing the component force, sigma, of the stress on any point of the wall surface of the roadway coal body in the vertical direction y Shows the horizontal component force, tau, of the stress applied to any point of the wall surface of the roadway coal body xy Representing the tangential stress on any point of the wall surface of the roadway coal body;
if the distance between the two loads is L and the two concentrated loads are the same, the two concentrated stresses can adopt the principle of elastomechanics superposition to convert the formula (8), and the stress at any point of the wall surface of the roadway coal body can be expressed as:
wherein r is 1 Represents the connecting line distance r of any point (point A) of the wall surface of the roadway coal body and one load action point (load action point 1) 2 Represents the connecting line distance theta between any point (point A) of the wall surface of the roadway coal body and another load acting point (load acting point 2) 1 Represents the included angle theta between the connecting line of any point (point A) of the wall surface of the roadway coal body and one load acting point (load acting point 1) and the load direction 2 And an included angle between a connecting line of any point (point A) of the wall surface of the roadway coal body and another load acting point (load acting point 2) and the load direction is shown.
If the roadway height is L, in the cartesian coordinate system, equation (9) can be expressed as:
order to
And the coefficient Q × B represents the compression force in the vertical direction, and B is a dimensionless coefficient, then expression (10) can be changed to expression (5).
In summary, the method herein is mainly obtained according to the following steps: 1. selecting the side wall of a rectangular roadway as a research object, and establishing a compression body model with a constrained end part; 2. solving a stress expression of any point in the compression body model by adopting an Ariy stress function; 3. dividing the roadway coal body into two working conditions according to the stress condition of the roadway coal body, and respectively solving the stress state and the yield contour line of the mechanical model; 4. and establishing a yield function model of unbalanced force of the roadway coal body and a rock burst judgment criterion according to the coal body material yield failure criterion.
In order to verify the significance of the modeling method and the yield contour, the formation of the plastic zone was observed by respectively using the distribution of the numerical simulation plastic zone and an indoor test.
1.1 end constraint compression test
A rock mechanics rigidity testing machine (MTS 815.03 electro-hydraulic servo rock experiment system) for coal mine disaster dynamics and national key experiments is selected for the experiment, and a coal sample is taken from a certain coal mine (an impact mine). The sample is processed into a standard cylindrical sample with the diameter of 50mm (as shown in figure 8), the flatness of the end face of the sample is controlled to be +/-0.02 mm, the constant loading rate is set to be 0.2mm/min, and the test is carried out according to a conventional single-shaft loading procedure. The unstable rock burst of the material is mainly reflected in that after the middle coal body is damaged, the coal body is thrown out by redundant elastic energy to cause a damage effect, and the coal body with the upper part and the lower part in contact with the top bottom plate keeps relatively intact due to certain displacement constraint on the end coal body under the action of the top bottom plate, so that the clamp is adopted at the end part to fix the displacement in the test process so as to simulate the displacement constraint. The coal sample destruction during the loading process of the test presents stage characteristics:
(1) the stress of the coal sample slowly and linearly increases in the elastic stage. When the stress reaches about 60% of its compressive strength, the coal body undergoes a first impact, a small amount of coal is ejected, and a "snap" sound is accompanied (see fig. 9). (2) Then the coal body continues to deform, and the phenomenon of flushing out is relatively mild. When the stress reaches about 78%, the coal body is flushed out again, the coal amount is large, and the obvious sound is also accompanied (as shown in figure 10). (3) The coal then bulges out layer by layer from the inside to the outside, but the impact phenomenon is not obvious. When the peak intensity is reached, the coal body has a central portion with oblique shear cracking and coal sample instability (as shown in FIG. 11). The fracture surface is not significantly different from the conventional uniaxial test. The fracture surface of the coal sample basically presents a similar hyperbolic shape, and the development process of the fracture surface is very similar to that of the analysis of the previous isoline (figure 2).
1.2 numerical analysis of coal destruction tendency
Because the asymmetric distribution of the vertical stress is difficult to realize in the experiment, a numerical simulation COMSOL Multiphysics 4.4 computing platform is adopted to verify the condition of numerical unbalanced stress. The molar coulomb yield criterion and the Prandtl-reus incremental equation are selected in the calculation process. The parameters of the materials are shown in table 1.
The plastic strain calculation results of a plane square model (the end is restrained, the vertical stress center is large, and the periphery is slightly smaller) taking the coal body as a material model are shown in fig. 12, and the plastic region distribution of a very obvious hyperbolic form can be found, the tip part has larger plastic deformation accumulation, and the coal body is cut off in a triangular block body integrally step by step. Fig. 13 is a roadway excavation plane model, the plastic deformation condition of the roadway under the overlying 20MPa pressure is simulated, similar hyperbolic plastic deformation distribution is found on two sides of the roadway, and the calculation result is very consistent with the yield function contour line (fig. 3) obtained by stress analysis. Simulation can also find that in a roof-coal wall-floor structure system of a mine roadway, the rigidity of a material applying fixed constraint is closer to the rigidity of a constrained material, and high-degree stress concentration can be counteracted to a great extent. Meanwhile, some collected photographs of the field show that the coal wall side shows a concave surface shape and a triangular shape (shown in detail in fig. 14 and 15) which is punched out of the rock mass after the occurrence of the rock burst.
TABLE 1 surrounding rock Material parameters
| Surrounding rock | Density (Kg/m) 3 ) | Modulus of elasticity (GPa) | Poisson ratio |
| Top board | 2550 | 5.55 | 0.16 |
| Coal seam | 1600 | 0.80 | 0.37 |
| Base plate | 2550 | 5.55 | 0.16 |
In conclusion, the indoor end part constraint uniaxial compression test shows that the coal body destruction has stage characteristics and premonitory characteristics, the coal body destruction is in layer-by-layer destruction from the outside and the inside, and the final fracture surface is also very close to hyperbolic characteristics; the numerical simulation results show that when the vertical stress is gradually increased from outside to inside, an obvious plastic deformation zone is easily formed inside the rock mass, so that the cutting-off and impact of the surrounding rock mass are induced. The overall experimental result is similar to the theoretical analysis result, so the modeling method is feasible. The modeling method simplifies the method of solving a mine pressure stress field by a mechanical model, carrying out an indoor coal body compression failure experiment and finite element simulation to analyze the elastoplasticity conversion characteristics of surrounding rocks, obtains a critical state judgment model of the occurrence of the roadway rock burst based on the double-yield isoline model, can accurately and quickly trigger the roadway rock burst to carry out early warning, can be widely applied to field engineering guidance, avoids or reduces the occurrence of the rock burst and ensures the safe production of mines.
Finally, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that various changes and modifications may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (7)
1. A modeling method of material unstable roadway rock burst based on a double-yield contour model is characterized by comprising the following steps: the method comprises the following steps:
s1: according to the stress condition of the vertical direction that the tunnel coal body received, fall into two kinds of operating modes with tunnel coal body atress operating mode: the working condition I is as follows: the stress in the vertical direction on the roadway coal body is uniform load; and a second working condition: the stress in the vertical direction on the roadway coal body is increased along with the increase of the height;
s2: establishing a yield function model of unbalanced force borne by the roadway coal body to obtain a relation model of roadway rock burst, roadway cohesive force and internal friction angle under different working conditions;
the yield function model of the unbalanced force applied to the roadway coal body is as follows:
wherein C and
respectively the cohesive force and the internal friction angle, L is the roadwayThe height, x is the x-direction coordinate of the Airy stress distribution coordinate, y is the y-direction coordinate of the Airy stress distribution coordinate, and the Airy stress distribution coordinate is specifically as follows: introducing an Airy stress field distribution theory, establishing an Airy stress distribution coordinate of the wall surface of the roadway coal body by taking any point on an intersection line of any roadway coal body wall surface and a roadway ground plane as a circle center, taking a vertical stress direction borne by the wall surface of the roadway coal body as a y direction and taking a horizontal stress direction borne by the wall surface of the roadway coal body as an x direction according to the definition of the Airy stress field distribution theory on a stress equivalence zone; q is a pressure coefficient, B is a dimensionless coefficient, K is a discrimination factor,
in the first working condition, C is a constant; in the second working condition, C is changed along with the change of x; f represents an unbalanced force; sigma x Representing the vertical component of the stress to which the coal is subjected, σ y Which represents the horizontal component of the stress to which the coal is subjected.
2. The modeling method of the material destabilization type roadway rock burst based on the double-yield contour model according to claim 1, characterized by comprising the following steps: further comprising step S3: and drawing yield function contour lines under different working conditions according to a yield function model of unbalanced force borne by the roadway coal body.
3. The modeling method of the material destabilization type roadway rock burst based on the double-yield contour model according to claim 1, characterized by comprising the following steps: in the second working condition, the calculation formula of C is as follows:
wherein a represents a threshold value of the ratio of the maximum horizontal stress to the vertical stress of the roadway working face; and b represents the vertical stress concentration coefficient of the roadway working face.
4. The modeling method of the material destabilization type roadway rock burst based on the double-yield contour model according to claim 3, characterized by comprising the following steps: and in the working condition II, the correction is needed to be carried out on the correction obtained by the calculation of the formula (2), wherein the correction formula of C is as follows:
C'＝d·C(3)
c' is the corrected C, d represents a correction coefficient, and a represents a threshold value of the ratio of the maximum horizontal stress to the vertical stress of the roadway working surface; and b represents the vertical stress concentration coefficient of the roadway working face.
5. The modeling method of the material destabilization type roadway rock burst based on the double-yield contour model according to claim 4, characterized by comprising the following steps: the derivation process of the formula (1) is as follows:
given that a coal body obeys the Moore-Coulomb yield criterion, the yield function of the imbalance force F can be expressed as:
wherein σ 1 And σ 3 Are all ultimate principal stresses, σ 1 Is the median principal stress, σ 3 To confining pressure, C and
respectively is cohesive force and an internal friction angle, and K is a discrimination factor; (3) The formula shows that when the unbalanced force F is larger than or equal to the discrimination factor K, the coal body generates yield failure;
will sigma x ，σ y And τ xy By carrying out formula (11), there can be obtained:
wherein σ x Representing the vertical component of the stress to which the coal body is subjected, σ y Representing the horizontal component of the stress, tau, to which the coal is subjected xy Representing the tangential stress to which the coal body is subjected;
simplified formula (4)τ in (1) xy And the sigma under the Airy stress distribution coordinate is used x ，σ y And τ xy Substituting the expression of (b) into the expression (4) to obtain the expression (1).
6. The modeling method of the material destabilization type roadway rock burst based on the double-yield contour model according to claim 5, characterized by comprising the following steps: σ in the Airy stress distribution coordinate x ，σ y And τ xy The expression of (a) is:
7. the modeling method of the material destabilization type roadway rock burst based on the double-yield contour model according to claim 6, characterized by comprising the following steps: σ in the Airy stress distribution coordinate x ，σ y And τ xy The derivation of the expression of (a) is as follows:
introducing an Airy stress distribution theory, and establishing an Airy stress distribution coordinate of the wall surface of the tunnel coal body by taking any point on an intersection line of any tunnel coal body wall surface and a tunnel ground plane as a circle center, taking a vertical stress direction borne by the tunnel coal body wall surface as a y direction and taking a horizontal stress direction borne by the tunnel coal body wall surface as an x direction;
the Airy stress function phi stressed at any point of the wall surface of the roadway coal body can be written as follows:
wherein, P represents the concentrated force that the tunnel lateral wall received, l represents the board thickness, theta represents the arbitrary one point of tunnel coal wall and the contained angle of load action point line and load direction, r represents arbitrary one point of tunnel coal wall and load action point line distance, and each stress component of arbitrary one point of tunnel coal wall can be write:
wherein σ r Represents the radial stress, sigma, suffered by any point of the wall surface of the roadway coal body θ The circumferential stress on any point of the wall surface of the roadway coal body is represented;
using the moire circle to convert the polar coordinates to rectangular coordinates, the stress in the x, y directions can be expressed as:
wherein σ x Representing the component force, sigma, of the stress on any point of the wall surface of the roadway coal body in the vertical direction y Shows the horizontal component force, tau, of the stress applied to any point of the wall surface of the roadway coal body xy Representing the tangential stress applied to any point of the wall surface of the roadway coal body;
if the distance between the two loads is L and the two concentrated loads are the same, the two concentrated stresses can adopt the principle of elastomechanics superposition to convert the formula (8), and the stress at any point of the wall surface of the roadway coal body can be expressed as:
wherein r is 1 Represents the connecting line distance r between any point of the wall surface of the roadway coal body and one load action point 2 Represents the connecting line distance theta between any point of the wall surface of the roadway coal body and another load acting point 1 Represents the included angle theta between the connecting line of any point of the wall surface of the roadway coal body and one load acting point and the load direction 2 The included angle between the connecting line of any point of the wall surface of the roadway coal body and the other load acting point and the load direction is shown;
if the roadway height is L, in the cartesian coordinate system, equation (9) can be expressed as:
order to
And the coefficient Q × B represents the compression force in the vertical direction, and B is a dimensionless coefficient, then expression (10) can be changed to expression (5).
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