CN113533042B - A comprehensive index calculation method and application for characterizing rock stress and fracture - Google Patents

Abstract

The invention provides a comprehensive index calculation method and application for characterizing rock stress and fracture, and belongs to the technical field of rock stress and fracture evaluation. When calculating this index, first determine the tensile and shear force vector T, then decompose the tensile and shear force vector, and then determine the components of each tensile and shear force in the three-dimensional space, and finally obtain the tensile and shear force index through coordinate transformation. Combined with the currently commonly used geotechnical analysis software, this index uses the built-in programming language FISH to compile the calculation process of the tensile and shear force index into a software-callable solution program, and uses the ZoneExtra function to realize the visualization of the index. The invention can comprehensively reflect the stress magnitude, direction, fracture position and damage degree of the rock, and is more in line with the actual engineering. By being used in combination with the currently commonly used FLAC and 3DEC numerical simulation software, the visualization of the tensile and shear force indicators can be realized and intuitive. It comprehensively reflects the stable state of surrounding rock.

Description

A comprehensive index calculation method and application for characterizing rock stress and fracture

technical field

The invention relates to the technical field of rock stress and fracture evaluation, in particular to a comprehensive index calculation method and application for characterizing rock stress and fracture.

Background technique

Rock engineering is any engineering in which construction is carried out in or on the surface of a rock mass. The main engineering activities of human beings, such as tunnel engineering, mining engineering, subway engineering, water conservancy engineering, etc., all belong to rock engineering. Since the object of engineering activities is rock mass, the stability of surrounding rock directly determines the safety of the project. The accurate evaluation of the stable state of the surrounding rock is an important basis for the support of the surrounding rock and the reinforcement of the engineering structure.

At present, the evaluation methods of surrounding rock stability mainly include on-site monitoring, surrounding rock quality classification, fuzzy comprehensive evaluation and numerical simulation. Among them, numerical simulation has the advantages of flexibility, high repeatability and accuracy. With the improvement of computer capabilities, it has gradually become one of the main methods of rock engineering stability evaluation. When numerical simulation is used to analyze the stability of surrounding rock, indicators such as stress, displacement and plastic zone are usually used, but the above indicators are independent of each other. Therefore, a new index is urgently needed, which can comprehensively reflect the stress, damage and fracture state of rock, and improve the efficiency and accuracy of stability analysis.

Among the existing methods, a dynamic evaluation method of surrounding rock stability based on BQ and numerical simulation proposes a dynamic evaluation method for stability that integrates BQ and numerical simulation, but this method needs to combine multiple indicators and is complicated to apply. A numerical simulation method of multi-block surrounding rock deformation of underground powerhouse A numerical simulation method of multi-block surrounding rock deformation of underground powerhouse is proposed, which effectively combines the advantages of discontinuous deformation and finite element method. The evaluation index of the surrounding rock can still only reflect one state of the surrounding rock. Numerical simulation evaluation method of surrounding rock failure risk based on Mohr-Coulomb criterion A numerical simulation evaluation method of surrounding rock failure risk based on Mohr-Coulomb criterion is proposed. Stress and failure state of rock.

It can be seen that the current numerical simulation surrounding rock index can only reflect the single state of the surrounding rock, and cannot visually display the stable state of the surrounding rock; the plastic zone index cannot accurately and effectively reflect the damage degree of the surrounding rock in actual engineering.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a comprehensive index calculation method and application for characterizing rock stress and fracture.

The surrounding rock is a typical hard and brittle material, and its tensile strength and shear strength are far less than the compressive strength. A large number of laboratory tests and engineering cases show that the plastic zone formed by mining or excavation is mostly located in the tensile stress zone, showing tensile or Pull shear yield. The damage of surrounding rock is often caused by the expansion of internal pores and gaps, and is usually caused by tensile shear stress. Based on this, the present invention proposes a tensile shear force index to characterize the stress and fracture distribution inside the rock.

The calculation method of this indicator is as follows:

(1) Determine the tensile shear force vector T:

Under the action of three-dimensional stress, the actual force of the internal rock mass micro-unit is decomposed into 6 independent stress components, namely σ _xx , σ _yy , σ _zz , τ _xy , τ _xz and τ _yz , and the calculation formula of the tensile-shear force vector T is as follows :

T=F/A

Among them, F is the tensile shear force vector on the fracture surface, T is the tensile shear force vector on the unit area, and A is the fracture surface area;

(2) Decomposition of tensile shear force vector:

Decomposing T into two components in the vertical and parallel directions of the fracture surface, namely the normal vector n and the tangential vector s, the normal stress σ and tangential stress τ of the fracture surface are respectively:

σ=T·n, τ=T·s

The normal stress σ and the tangential stress τ in the above formula are both scalars on the fracture surface. The relationship between the tensile shear force vector and the total stress tensor is:

T=δ·n

where δ is the total stress tensor in three-dimensional space;

Substituting the above formula into the scalar calculation formula of the normal stress and tangential stress of the fracture surface, we can get:

σ=n·δ·n, τ=s·δ·n

Using tensor representation, we can get:

σ=σ _ij n _i n _j , τ=σ _ij s _i n _j ,

Among them, the subscripts i and j represent the coordinate system x, y, z;

(3) Determine the components of each tensile and shear force in three-dimensional space:

where σ _xx is the normal stress in the x direction, τ _xy is the xoy plane shear stress, τ _xz is the xoz plane shear stress, τ _yx is the yox plane shear stress, which is opposite to τ _xy , σ _yy is the y direction normal stress, and τ _yz is the yoz plane shear stress, τ _zx is the zox plane shear stress, opposite to τ _xz , τ _zy is the zoy plane shear stress, opposite to τ _yz , σ _zz is the z-direction normal stress, n _x is the x-direction vector, n _y is the y Direction vector, n _z is the z-direction vector, T _x is the x-direction pull-shear vector, _Ty is the y-direction pull-shear vector, and T _z is the z-direction pull-shear vector.

(4) Coordinate transformation to obtain the tensile shear force index:

F=∫TdA=∫δ·n dA

The magnitude of the tensile shear force F represents the resultant force of the stress on the fissure surface of the surrounding rock. The greater the resultant force, the more likely the fissure surface will expand, resulting in the destruction of the surrounding rock. Therefore, the tensile shear force can also reflect the stability of the surrounding rock.

Among them, in step (3), the fracture surface is firstly placed in the entire rock unit, and the result is obtained

Among them, cosθ and sinθ are the unit components perpendicular to the crack surface, that is, n=(cosθ, sinθ), that is, n _x = cosθ, n _y = sinθ, and θ is the angle between the crack surface and the x-axis, then the above formula is:

Then expand the above two-dimensional plane form into three-dimensional space, that is:

The specific application of this index is as follows: Combined with the currently commonly used geotechnical analysis software, the calculation process of the tensile and shear force index is compiled into a software-callable solution program by using the software's built-in programming language FISH, and the Zone Extra function is used to realize this index. The visualization of indicators, specifically:

①Read and save the stress values of each unit inside the surrounding rock before mining, including σ _xx , σ _yy , σ _zz , τ _xy , τ _xz and τ _yz ;

②Call the solution program to calculate the tension and shear force index;

③ Call the Zone Extra program to output the tension and shear force distribution diagram.

The beneficial effects of the above-mentioned technical solutions of the present invention are as follows:

In the above scheme, the stress magnitude, direction, fracture position and damage degree of the rock can be comprehensively reflected, and it is more in line with the actual engineering. By combining with the commonly used FLAC and 3DEC numerical simulation software, the visualization of tensile and shear force indicators can be realized. , which can intuitively and comprehensively reflect the stable state of the surrounding rock.

Description of drawings

FIG. 1 is a schematic diagram of the stress of a rock mass unit involved in the comprehensive index calculation method for characterizing rock stress and fracture of the present invention;

Fig. 2 is the schematic diagram of the force on the fracture surface of the rock mass in the comprehensive index calculation method for characterizing rock stress and fracture of the present invention;

3 is a schematic diagram of the microscopic stress on the fracture surface of the rock mass in the comprehensive index calculation method for characterizing rock stress and fracture of the present invention;

4 is a schematic diagram of the macroscopic stress on the fracture surface of the rock mass in the comprehensive index calculation method for characterizing rock stress and fracture of the present invention;

FIG. 5 is a schematic diagram showing the display effect of the tensile shear force index when the comprehensive index characterizing rock stress and fracture of the present invention is applied;

Fig. 6 is the numerical calculation model without adding joints in the embodiment of the present invention;

Fig. 7 is the numerical calculation model of adding joints in the embodiment of the present invention;

Fig. 8 is the superposition diagram of the tensile shear force index and the plastic zone when no joints are added in the embodiment of the present invention;

Fig. 9 is the superposition diagram of the tensile shear force index and the plastic zone after adding joints in the embodiment of the present invention;

FIG. 10 is a comparison diagram of the tensile shear force index and the plastic zone in the embodiment of the present invention.

Detailed ways

In order to make the technical problems, technical solutions and advantages to be solved by the present invention more clear, the following will be described in detail with reference to the accompanying drawings and specific embodiments.

The invention provides a comprehensive index calculation method and application for characterizing rock stress and fracture.

The calculation process of this indicator is as follows:

(1) Determine the tensile shear force vector T:

Under the action of three-dimensional stress, the actual force of the internal rock mass micro-unit is decomposed into 6 independent stress components, namely σ _xx , σ _yy , σ _zz , τ _xy , τ _xz and τ _yz , and the calculation formula of the tensile-shear force vector T is as follows :

T=F/A

Among them, F is the tensile shear force vector on the fracture surface, T is the tensile shear force vector on the unit area, and A is the fracture surface area;

(2) Decomposition of tensile shear force vector:

Decomposing T into two components in the vertical and parallel directions of the fracture surface, namely the normal vector n and the tangential vector s, the normal stress σ and tangential stress τ of the fracture surface are respectively:

σ=T·n, τ=T·s

The normal stress σ and the tangential stress τ in the above formula are both scalars on the fracture surface. The relationship between the tensile shear force vector and the total stress tensor is:

T=δ·n

where δ is the total stress tensor in three-dimensional space;

Substituting the above formula into the scalar calculation formula of the normal stress and tangential stress of the fracture surface, we can get:

σ=n·δ·n, τ=s·δ·n

Using tensor representation, we can get:

σ=σ _ij n _i n _j , τ=σ _ij s _i n _j

(3) Determine the components of each tensile and shear force in three-dimensional space:

where σ _xx is the normal stress in the x direction, τ _xy is the xoy plane shear stress, τ _xz is the xoz plane shear stress, τ _yx is the yox plane shear stress, which is opposite to τ _xy , σ _yy is the y direction normal stress, and τ _yz is the yoz plane shear stress, τ _zx is the zox plane shear stress, opposite to τ _xz , τ _zy is the zoy plane shear stress, opposite to τ _yz , σ _zz is the z-direction normal stress, n _x is the x-direction vector, n _y is the y Direction vector, n _z is the z-direction vector, T _x is the x-direction pull-shear vector, _Ty is the y-direction pull-shear vector, and T _z is the z-direction pull-shear vector.

(4) Coordinate transformation to obtain the tensile shear force index:

F=∫TdA=∫δ·n dA

The magnitude of the tensile shear force F represents the resultant force of the stress on the fissure surface of the surrounding rock. The greater the resultant force, the more likely the fissure surface will expand, resulting in the destruction of the surrounding rock. Therefore, the tensile shear force can also reflect the stability of the surrounding rock.

The specific principle process is as follows:

Generally, under the action of three-dimensional stress, the internal micro-units are stressed as shown in Figure 1. It can be seen from Fig. 1 that under the action of three-dimensional stress, the actual force of the internal rock mass micro-unit can be decomposed into 9 stress components, but in fact there are only 6 independent components, namely σ _xx , σ _yy , σ _zz , τ _xy , τ _xz and τ _yz . The micro-fractures inside the rock are much larger than the size of the whole rock, so the fracture of the internal micro-fractures is actually a plane problem. Under the action of the above stress, the tensile shear stress is generated on the micro-crack surface inside the rock mass, which can actually be equivalent to a tensile-shear force on the micro-crack surface. The schematic diagram of the force is shown in Figure 2.

In Figure 2, T is the traction vector, which can be simply expressed as the ratio of the force on the contact surface to the area of the contact surface, namely:

T=F/A Formula (1)

In the formula, F is the tensile shear force vector on the fracture surface, T is the tensile shear force vector per unit area, and A is the fracture surface area.

It can be seen that the tensile shear force vector T is the same as the stress unit, but is actually a simple vector, not a stress tensor.

Further, decompose T into two components in the vertical and parallel directions of the fracture surface, namely the normal vector n and the tangential vector s, as shown in Fig. 3.

In Fig. 3, σ is the normal stress of the fracture surface, and τ is the tangential stress, which can be expressed by Equation 2:

σ=T·n, τ=T·s Equation (2)

It should be noted that due to the calculation method of the vector dot product, σ and τ here are not all tensor values, but two independent components of the full stress tensor, and they are scalars, not tensors. In addition, in three-dimensional space, there are actually infinitely many s-vectors parallel to the fracture surface, and each vector has different components inside or outside the fracture section, so during analysis, one should be specified to be parallel to the fracture section, and the other One is perpendicular to the fracture section.

On the basis of the above analysis, when the fracture surface is placed in the entire rock unit, the schematic diagram of the force is shown in Figure 4. According to the stress balance, we can get:

In the formula, cosθ and sinθ are the unit components perpendicular to the crack surface, that is, n=(cosθ, sinθ), that is, n _x = cosθ, _ny = sinθ, and θ is the angle between the crack surface and the x-axis, after substituting into the above formula ,Available:

The above expression can be expressed in vector form as:

T=δ·n or T _i =σ _ij n _j Formula (5)

The above formula is that in a two-dimensional plane and a three-dimensional space, the components of each tensile and shear force are:

Substituting Equation (5) into Equation (2), the normal stress and tangential stress of the fracture surface can be obtained as:

σ=n·δ·n, τ=s·δ·n Equation (7)

Expressed as a tensor:

σ=σ _ij n _i n _j , τ=σ _ij s _i n _j Equation (8)

In summary, the tensile and shear force vectors on the fracture surface are:

F=∫TdA=∫δ·n dA

Through the above calculation, the tensile shear force index of the fracture surface is obtained.

According to the above analysis, the tensile shear force is actually the most direct factor causing the failure of the rock unit, and its magnitude also directly determines the stability of the surrounding rock.

The application of this indicator in numerical simulation is as follows:

Combined with the currently commonly used geotechnical analysis software, such as FLAC, 3DEC, etc., the above calculation process is compiled into a software-callable solution program by using the software's built-in programming language FISH, and the Zone Extra function is used to realize the visualization of this indicator.

①Read and save the stress values of each unit inside the surrounding rock before mining, including σ _xx , σ _yy , σ _zz , τ _xy , τ _xz and τ _yz ;

②Call the solution program to calculate the tension and shear force index;

③ Call the Zone Extra program to output the cloud map of the tensile and shear force distribution.

The display effect of this indicator in the software is shown in Figure 5.

The diameter of the circle in the figure represents the size of the tensile shear force index, the arrow represents the direction of the tensile shear force index, and the starting point of the arrow is the center of the rock fracture surface.

The following description will be given in conjunction with specific embodiments.

In a gold mine, the thickness of the ore body is 1.2m and the inclination angle is 75°. There are joints and fissures in the mining area. The medium-deep hole and subsequent waste rock filling method is used to carry out retreat mining along the trend of the ore body, forming a goaf with a length of about 60m. The element method software is used to analyze the stability of the goaf. The established numerical calculation model is shown in the figure, and the physical and mechanical parameters of the model rock are shown in Table 1.

Table 1 Physical and mechanical parameters

The numerical calculation results of unjoined and added joints are shown in Fig. 6 and Fig. 7, respectively. Figure 8 shows the superposition of the tensile shear force index and the plastic zone when no joints are added. In Figure 8, the irregular color blocks are the plastic zone, and the circles are the tensile shear force indicators.

It can be seen from Fig. 8 that the tensile-shear force index proposed by the present invention has a large overlap with the plastic zone index that comes with the software. The more the surrounding rock plastic zone is, the denser the circles representing the tensile-shear force index are, indicating that the index can be used. It can effectively characterize the rupture of the surrounding rock in the goaf. In addition, the size of the circle can be used to obtain the size of the stress in the area. The maximum tensile stress at the top plate is about 1.2MPa, and the maximum shear stress at the bottom plate is about 1.5MPa. According to the direction of the inner arrow of the circle, the maximum tensile shear force index of the top plate is inclined upward, and the maximum tensile shear force index of the bottom plate is inclined downward.

As shown in Figure 9, it is the distribution of the tensile and shear force indexes and the superposition of the plastic zone after adding the joints. It can be seen from Figure 9 that after adding the joints, the density of the tensile and shear force indicators has increased significantly, which is consistent with the actual results. There is no obvious change in the area, therefore, the tensile and shear force index proposed by the present invention is more in line with engineering practice. According to the circle size of the tensile shear force index, the maximum tensile stress at the top plate reaches 2.1MPa, which is a relatively large increase compared to when no joints are added, while the shear stress at the bottom plate decreases slightly to 1.47MPa. At the same time, according to the distribution of the tensile shear force index, it can be seen that there is a large tensile shear force at the intersection of the joints about 10m inside the upper plate, which should be paid attention to.

The comparison curve between the tensile shear force index of the upper and lower disks and the size of the plastic zone is shown in Figure 10. It can be seen from the figure that the stability of the upper wall is better than that of the lower wall if only based on the volume comparison of the plastic zone, but in actual engineering, the damage degree of the surrounding rock of the upper wall is often greater than that of the lower wall, and the tensile shear force index reflects To understand this phenomenon, it can be seen from the figure that the tensile shear of the surrounding rock on the hanging wall is generally greater than that in the lower wall, indicating that the surrounding rock of the hanging wall has a deeper plasticity, which also causes the stability of the surrounding rock on the hanging wall to be worse, which is also in line with the actual engineering situation. .

The above are the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the principles of the present invention, several improvements and modifications can be made. These improvements and modifications It should also be regarded as the protection scope of the present invention.

Claims (4)

1. a comprehensive index calculation method characterizing rock stress and fracture, is characterized in that: comprise steps as follows: (1) Determine the tensile shear force vector T: Under the action of three-dimensional stress, the actual force of the internal rock mass micro-unit is decomposed into 6 independent stress components, namely σ _xx , σ _yy , σ _zz , τ _xy , τ _xz and τ _yz , and the calculation formula of the tensile-shear force vector T is as follows : T=F/A Among them, F is the tensile shear force vector on the fracture surface, T is the tensile shear force vector on the unit area, and A is the fracture surface area; (2) Decomposition of tensile shear force vector: Decomposing T into two components in the vertical and parallel directions of the fracture surface, namely the normal vector n and the tangential vector s, the normal stress σ and tangential stress τ of the fracture surface are respectively: σ=T·n, τ=T·s The normal stress σ and the tangential stress τ in the above formula are both scalars on the fracture surface, and the relationship between the tensile shear force vector and the total stress tensor is: T=δ·n where δ is the total stress tensor in three-dimensional space; Substituting the above formula into the scalar calculation formula of the normal stress and tangential stress of the fracture surface, we can get: σ=n·δ·n, τ=s·δ·n Using tensor representation, we can get: σ=σ _ij n _i n _j , τ=σ _ij s _i n _j , Among them, the subscripts i and j represent the coordinate system x, y, z; (3) Determine the components of each tensile and shear force in three-dimensional space:

where σ _xx is the normal stress in the x direction, τ _xy is the xoy plane shear stress, τ _xz is the xoz plane shear stress, τ _yx is the yox plane shear stress, which is opposite to τ _xy , σ _yy is the y direction normal stress, and τ _yz is the yoz plane shear stress, τ _zx is the zox plane shear stress, opposite to τ _xz , τ _zy is the zoy plane shear stress, opposite to τ _yz , σ _zz is the z-direction normal stress, n _x is the x-direction vector, n _y is the y Direction vector, n _z is the z-direction vector, T _x is the x-direction pull-shear vector, T _y is the y-direction pull-shear vector, T _z is the z-direction pull-shear vector; (4) Coordinate transformation to obtain the tensile shear force index: F=∫TdA=∫δ·n dA The magnitude of the tensile shear force F represents the resultant force of the stress on the fracture surface of the surrounding rock. The larger the resultant force is, the easier the fracture surface is to expand, resulting in the destruction of the surrounding rock. Therefore, the tensile shear force reflects the stability of the surrounding rock. 2. The comprehensive index calculation method for characterizing rock stress and fracture according to claim 1, characterized in that: in the step (3), firstly, the fracture surface is placed in the entire rock unit to obtain

Among them, cosθ and sinθ are the unit components perpendicular to the crack surface, that is, n=(cosθ, sinθ), that is, n _x = cosθ, n _y = sinθ, and θ is the angle between the crack surface and the x-axis, then the above formula is:

Then expand the above two-dimensional plane form into three-dimensional space, that is:

3. The application of the comprehensive index characterizing rock stress and fracture according to claim 1, characterized in that: in combination with the currently commonly used geotechnical analysis software, the calculation process of the tensile and shear force index is compiled by using the software built-in programming language FISH It is a software-callable solver, and uses the Zone Extra function to visualize the indicator. 4. the application of the comprehensive index of characterizing rock stress and fracture according to claim 3, is characterized in that: specifically comprises the steps as follows: ①Read and save the stress values of each unit inside the surrounding rock before mining, including σ _xx , σ _yy , σ _zz , τ _xy , τ _xz and τ _yz ; ②Call the solution program to calculate the tension and shear force index; ③ Call the Zone Extra program to output the tension and shear force distribution diagram.

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