CN113533042A - Comprehensive index calculation method for representing rock stress and fracture and application - Google Patents
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Abstract
The invention provides a comprehensive index calculation method for representing rock stress and fracture and application thereof, belonging to the technical field of rock stress and fracture evaluation. When the index is calculated, firstly, a pull-shear force vector T is determined, then, pull-shear force vector decomposition is carried out, then, each component of each pull-shear force in a three-dimensional space is determined, and finally, the pull-shear force index is obtained through coordinate conversion. The index combines with the current commonly used rock-soil analysis software, adopts a programming language FISH built in the software to compile the calculation process of the tension and shear index into a resolving program which can be called by the software, and realizes the visualization of the index by utilizing the ZoneExtra function. The method can comprehensively reflect the stress magnitude, the direction, the fracture position and the damage degree of the rock, is more consistent with the actual engineering, and can realize the visualization of the tension and shear index and intuitively and comprehensively reflect the stable state of the surrounding rock by combining with the currently common FLAC and 3DEC numerical simulation software.
Description
Technical Field
The invention relates to the technical field of rock stress and fracture evaluation, in particular to a comprehensive index calculation method for representing rock stress and fracture and application thereof.
Background
Rock engineering is any work that is performed inside or on the surface of a rock mass. The main engineering activities of human beings, such as tunnel engineering, mining engineering, subway engineering, hydraulic engineering and the like, all belong to rock engineering. Because the object of engineering activity is the rock mass, the stability of the surrounding rock directly determines the safety of the engineering. The method can be used for accurately evaluating the stable state of the surrounding rock, and is an important basis for supporting the surrounding rock and reinforcing an engineering structure.
The existing method for evaluating the stability of the surrounding rock mainly comprises field monitoring, surrounding rock quality grading, fuzzy comprehensive evaluation, numerical simulation and the like. The numerical simulation has the advantages of flexibility, high repeatability, accuracy and the like, and gradually becomes one of the main means for evaluating the stability of the current rock engineering along with the improvement of the computer capability. When adopting numerical simulation to carry out surrounding rock stability analysis, adopt indexes such as stress, displacement and plastic zone usually, but above-mentioned index is mutually independent, need synthesize the contrast with above-mentioned index usually, just can carry out more accurate judgement to surrounding rock stability, improved the analysis degree of difficulty, consequently need a new index urgently, can synthesize the stress, damage and the state of rupture of reaction rock, improve stability analysis work's efficiency and precision.
In the existing method, a dynamic evaluation method for stability of surrounding rock based on BQ and numerical simulation provides a dynamic evaluation method for stability integrating BQ and numerical simulation, but the method needs to combine a plurality of indexes and is complex to apply. A numerical simulation method for deformation of multi-block surrounding rock of an underground factory building is provided, and advantages of discontinuous deformation and a finite element method are effectively combined, but evaluation indexes of the surrounding rock can only reflect one state of the surrounding rock. A surrounding rock damage risk numerical simulation evaluation method based on the Mohr-Coulomb criterion provides a surrounding rock damage risk numerical simulation evaluation method based on the Mohr-Coulomb criterion, and has the advantage of strong operability, but the stress and damage state of the surrounding rock cannot be intuitively displayed.
Therefore, the current numerical simulation surrounding rock index can only reflect the single state of the surrounding rock and can not 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 the actual engineering.
Disclosure of Invention
The invention aims to provide a comprehensive index calculation method for representing rock stress and fracture and application thereof.
The surrounding rock is a typical hard and brittle material, the tensile strength and the shear strength are far less than the compressive strength, and a large number of indoor tests and engineering cases show that a plastic zone formed by mining or excavation is mostly positioned in a tensile stress zone and is in tensile or tensile-shear yield. Based on the fact that the destruction of surrounding rocks is usually caused by internal pores and gaps and is usually caused by tensile and shear stress, the invention provides a tensile and shear force index for representing the stress and fracture distribution in the rocks.
The index calculation method is as follows:
(1) determining a tensile shear vector T:
under the action of three-dimensional stress, the actual stress of the internal rock mass microcell is decomposed into 6 independent stress components which are respectively sigmaxx、σyy、σzz、τxy、τxzAnd τyzThe pull and shear vector T is calculated as follows:
T＝F/A
wherein F is a tensile and shearing force vector on a crack surface, T is a tensile and shearing force vector on a unit area, and A is the area of the crack surface;
(2) and (3) decomposing a tensile and shearing force vector:
and decomposing T into components in two directions of a vertical crack surface and a parallel crack surface, namely a normal vector n and a tangential vector s, wherein the normal stress sigma and the tangential stress tau of the crack surface are respectively as follows:
σ＝T·n，τ＝T·s
the normal stress sigma and the tangential stress tau in the above formula are scalar quantities on the fracture surface. For the relationship between the tensile and shear force vectors and the full stress tensor, the following is given:
T＝σ·n
wherein σ is a full stress tensor in the three-dimensional space;
substituting the above formula into a crack surface normal stress and tangential stress scalar calculation formula to obtain:
σ＝n·σ·n，τ＝s·σ·n
using the tensor representation, we can obtain:
σ＝σijninj，τ＝σijsinj，
wherein the indices i and j represent coordinate systems x, y, z;
(3) determining each component of the three-dimensional space in the pulling and shearing force:
wherein σxxIs normal stress in the x direction, τxyFor xoy plane shear stress, τxzIs xoz plane shear stress, tauyxIs yox plane shear stress, andxyin contrast, σyyIs normal stress in the y direction, τyzShear stress in the yoz plane, τzxIs zox plane shear stress, andxzin contrast, τzyIs zoy plane shear stress, andyzin contrast, σzzIs normal stress in the z direction, nxIs a vector in the x direction, nyIs a y-direction vector, nzIs a vector in the z direction, TxIs a tensile shear vector in the x direction, TyIs a y-direction pull shear vector, TzIs the z-direction pull shear vector.
(4) And (3) coordinate conversion to obtain a tensile and shearing force index:
F＝∫TdA＝∫σ·n dA
the magnitude of the tensile and shearing force F represents the resultant force of the stress borne on the surrounding rock fracture surface, and the larger the resultant force is, the more easily the fracture surface expands to cause the surrounding rock to be damaged, so that the tensile and shearing force can also reflect the stability degree of the surrounding rock.
Wherein, in the step (3), the crack surface is firstly put in the whole rock unit to obtain
Where cos θ and sin θ are unit components perpendicular to the fracture plane, i.e., n is (cos θ, sin θ), i.e., nx＝cosθ，nySin θ, θ is the angle between the fracture plane and the x-axis, and the above formula is:
and expanding the two-dimensional plane form into a three-dimensional space to obtain the following three-dimensional space:
when the index is specifically applied, the method comprises the following steps: combining with the currently common geotechnical analysis software, programming a computing process of the pull-shear index into a resolving program which can be called by the software by using a programming language FISH (software in-software), and realizing the visualization of the index by using a Zone Extra function, which specifically comprises the following steps:
reading and storing stress values of all units in surrounding rock before mining, including sigmaxx、σyy、σzz、τxy、τxzAnd τyz；
Calling a resolving program to resolve the tensile and shearing force indexes;
and thirdly, calling a Zone Extra program to output a pulling and shearing force distribution diagram.
The technical scheme of the invention has the following beneficial effects:
in the scheme, the stress size, the direction, the fracture position and the damage degree of the rock can be comprehensively reflected, the stress is more consistent with the actual engineering, the pulling and shearing force index can be visualized by combining with the currently common FLAC and 3DEC numerical simulation software, and the stable state of the surrounding rock can be intuitively and comprehensively reflected.
Drawings
FIG. 1 is a schematic diagram of stress of a rock mass unit involved in the comprehensive index calculation method for representing rock stress and fracture;
FIG. 2 is a schematic diagram of stress of a rock mass fracture surface in the comprehensive index calculation method for representing rock stress and fracture;
FIG. 3 is a schematic view of the rock mass crack surface micro stress in the comprehensive index calculation method for characterizing rock stress and cracking of the present invention;
FIG. 4 is a schematic diagram of macroscopic stress of a rock mass crack surface in the comprehensive index calculation method for representing rock stress and cracking;
FIG. 5 is a schematic diagram showing the effect of the comprehensive indicator for characterizing rock stress and fracture in applying the time-shear indicator;
FIG. 6 is a numerical model with no joints added according to an embodiment of the present invention;
FIG. 7 is a numerical model with joints added according to an embodiment of the present invention;
FIG. 8 is a graph showing the overlay of the tensile and shear strength index and the plastic region without joints added in the embodiment of the present invention;
FIG. 9 is a graph showing the tensile and shear strength index and the plastic area after the joint is added in the embodiment of the present invention;
FIG. 10 is a graph comparing the tensile and shear strength index to the plastic region in an example of the invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
The invention provides a comprehensive index calculation method for representing rock stress and fracture and application thereof.
The index calculation process is as follows:
(1) determining a tensile shear vector T:
under the action of three-dimensional stress, the actual stress of the internal rock mass microcell is decomposed into 6 independent stress components which are respectively sigmaxx、σyy、σzz、τxy、τxzAnd τyzThe pull and shear vector T is calculated as follows:
T＝F/A
wherein F is a tensile and shearing force vector on a crack surface, T is a tensile and shearing force vector on a unit area, and A is the area of the crack surface;
(2) and (3) decomposing a tensile and shearing force vector:
and decomposing T into components in two directions of a vertical crack surface and a parallel crack surface, namely a normal vector n and a tangential vector s, wherein the normal stress sigma and the tangential stress tau of the crack surface are respectively as follows:
σ＝T·n，τ＝T·s
the normal stress sigma and the tangential stress tau in the above formula are scalar quantities on the fracture surface. For the relationship between the tensile and shear force vectors and the full stress tensor, the following is given:
T＝σ·n
wherein σ is a full stress tensor in the three-dimensional space;
substituting the above formula into a crack surface normal stress and tangential stress scalar calculation formula to obtain:
σ＝n·σ·n，τ＝s·σ·n
using the tensor representation, we can obtain:
σ＝σijninj，τ＝σijsinj
(3) determining each component of the three-dimensional space in the pulling and shearing force:
wherein σxxIs normal stress in the x direction, τxyFor xoy plane shear stress, τxzIs xoz plane shear stress, tauyxIs yox plane shear stress, andxyin contrast, σyyIs normal stress in the y direction, τyzShear stress in the yoz plane, τzxIs zox plane shear stress, andxzin contrast, τzyIs zoy plane shear stress, andyzin contrast, σzzIs normal stress in the z direction, nxIs a vector in the x direction, nyIs a y-direction vector, nzIs a vector in the z direction, TxIs a tensile shear vector in the x direction, TyIs a y-direction pull shear vector, TzIs the z-direction pull shear vector.
(4) And (3) coordinate conversion to obtain a tensile and shearing force index:
F＝∫TdA＝∫σ·n dA
the magnitude of the tensile and shearing force F represents the resultant force of the stress borne on the surrounding rock fracture surface, and the larger the resultant force is, the more easily the fracture surface expands to cause the surrounding rock to be damaged, so that the tensile and shearing force can also reflect the stability degree of the surrounding rock.
The specific principle and process are as follows:
in general, when the rock body is under three-dimensional stress, the force applied to the inner micro-unit is shown in figure 1. As can be seen from fig. 1, the actual stress of the internal rock mass microcells under the three-dimensional stress can be decomposed into 9 stress components, but actually, there are only 6 independent components, which are σxx、σyy、σzz、τxy、τxzAnd τyz. The micro-fractures within the rock are much larger than the overall rock size, so the fracture of the internal micro-fractures is actually a planar problem. Under the action of the stress, tensile-shear stress is generated on the microcrack surface in the rock body, and the tensile-shear stress can be actually equivalent to the tensile-shear stress on the microcrack surface, and the stress schematic diagram is shown in fig. 2.
In fig. 2, T is a tensile shear vector (traction vector), which can be simply expressed as a ratio of force on the contact surface to the contact surface area, that is:
t ═ F/A formula (1)
Where F is a tensile-shear vector at the fracture surface, T is a tensile-shear vector per unit area, and A is the fracture surface area.
From this, it can be seen that the tensile-shear vector T is the same as the unit of stress, but is actually a simple vector, not a stress tensor.
Further, T is decomposed into components in both the vertical and parallel fracture planes, i.e., normal vector n and tangential vector s, as shown in fig. 3.
In fig. 3, σ is the normal stress of the fracture surface, τ is the tangential stress, and can be expressed by equation 2:
σ ═ T · n, τ ═ T · s formula (2)
It should be noted that because of the vector dot product calculation method, σ and τ are not all tensor values, but two independent components of the full stress tensor, and a scalar is not a tensor. In addition, in three-dimensional space, there are virtually an infinite number of s-vectors parallel to the fracture surface, each with a different component in or out of the fracture cross-section, so that during analysis, one should be assigned to be parallel to the fracture cross-section and the other perpendicular to the fracture cross-section.
Based on the above analysis, the stress diagram when the fracture surface is placed in the whole rock unit is shown in fig. 4. From the stress balance we can get:
where cos θ and sin θ are unit components perpendicular to the fracture plane, that is, n is (cos θ, sin θ), that is, n isx＝cosθ，nySin θ, θ is the angle between the fracture plane and the x-axis, and can be obtained by substituting the formula:
the above equation can be expressed in vector form as:
t ═ σ · n or Ti＝σijnjFormula (5)
The above formula is in a two-dimensional plane, and in a three-dimensional space, each component of each pulling and shearing force is as follows:
by substituting formula (5) for formula (2), the normal stress and the tangential stress of the crack surface can be respectively:
σ n, τ s σ n, τ n formula (7)
Expressing in tensor form:
σ＝σijninj，τ＝σijsinjformula (8)
To sum up, the tensile and shear force vectors on the fracture surface are:
F＝∫TdA＝∫σ·n dA
through the above calculation, the tensile and shearing force index of the fracture surface is obtained.
From the above analysis, it can be seen that the tensile shear force is actually the most direct factor causing the rock unit to be damaged, and the size of the tensile shear force directly determines the stability of the surrounding rock.
The application of the index in numerical simulation is as follows:
by combining with the current common geotechnical analysis software such as FLAC, 3DEC and the like, the computing process is compiled into a resolving program which can be called by the software by adopting a programming language FISH arranged in the software, and the visualization of the index is realized by utilizing the Zone Extra function.
Reading and storing stress values of all units in surrounding rock before mining, including sigmaxx、σyy、σzz、τxy、τxzAnd τyz；
Calling a resolving program to resolve the tensile and shearing force indexes;
and thirdly, calling a Zone Extra program to output a pull-shear distribution cloud picture.
The display effect of the index in the software is shown in fig. 5.
The diameter of the circle in the figure represents the size of the tensile and shearing force index, the arrow represents the direction of the tensile and shearing force index, and the starting point of the arrow is the central position of the rock fracture surface.
The following description is given with reference to specific examples.
The thickness of a gold ore body is 1.2m, the inclination angle is 75 degrees, joint cracks are distributed in the ore area, backward stoping is carried out along the trend of the ore body by adopting a medium-length hole subsequent barren rock filling method, a goaf with the length of about 60m is formed, and the stability analysis of the goaf is carried out by adopting 3DEC discrete unit method software. The established numerical calculation model is shown in the figure, and the physical and mechanical parameters of the model ore rock are shown in the table 1.
TABLE 1 parameters of physical mechanics
The numerical calculation results of the non-added joints and the added joints are shown in fig. 6 and 7, respectively. The overlay of the tensile and shear strength index and the plastic region without joints is shown in fig. 8, irregular color blocks are plastic regions, and circles are the tensile and shear strength indexes.
As can be seen from fig. 8, the tensile and shearing force index provided by the invention is greatly overlapped with the plastic zone index of the software, the more the area of the plastic zone of the surrounding rock is, the denser the circle representing the tensile and shearing force index is, which means that the index can effectively represent the fracture condition of the surrounding rock of the goaf, and in addition, the magnitude of the stress of the area can be obtained according to the magnitude of the circle, the maximum tensile stress at the top plate is about 1.2MPa, and the maximum shearing stress at the bottom plate is about 1.5 MPa. The direction of the inner arrow of the circle shows that the maximum pulling shear index of the top plate is obliquely upward, and the maximum pulling shear index of the bottom plate is obliquely downward.
As shown in fig. 9, which is a drawing and shearing index distribution and a plasticity zone overlay chart after the joint is added, as can be seen from fig. 9, after the joint is added, the density of the drawing and shearing index is obviously increased, which is consistent with the actual result, and the plasticity zone area has no obvious change, so that the drawing and shearing index provided by the invention is more consistent with the engineering practice. According to the size of the circle of the tensile and shearing force index, the maximum tensile stress at the top plate reaches 2.1MPa, and is greatly increased compared with the maximum tensile stress without adding joints, the shear stress at the bottom plate is slightly reduced to 1.47MPa, and meanwhile, according to the distribution of the tensile and shearing force index, the large tensile and shearing force is generated at the joint of about 10m in the upper disc, and attention is paid.
The comparison curve of the upper and lower disc pull shear indexes and the plastic zone size is shown in FIG. 10. It can be seen from the figure that if the stability of the upper wall is better than that of the lower wall only according to the volume comparison of the plastic zone, in the actual engineering, the damage degree of the surrounding rock of the upper wall is often greater than that of the lower wall, and the pulling and shearing indexes reflect the phenomenon.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (4)
1. A comprehensive index calculation method for representing rock stress and fracture is characterized by comprising the following steps: the method comprises the following steps:
(1) determining a tensile shear vector T:
under the action of three-dimensional stress, the actual stress of the internal rock mass microcell is decomposed into 6 independent stress components which are respectively sigmaxx、σyy、σzz、τxy、τxzAnd τyzThe pull and shear vector T is calculated as follows:
T＝F/A
wherein F is a tensile and shearing force vector on a crack surface, T is a tensile and shearing force vector on a unit area, and A is the area of the crack surface;
(2) and (3) decomposing a tensile and shearing force vector:
and decomposing T into components in two directions of a vertical crack surface and a parallel crack surface, namely a normal vector n and a tangential vector s, wherein the normal stress sigma and the tangential stress tau of the crack surface are respectively as follows:
σ＝T·n，τ＝T·s
the normal stress σ and the tangential stress τ in the above formula are scalar quantities on the fracture surface, and the relation between the tensile and shearing force vector and the full stress tensor is:
T＝σ·n
wherein σ is a full stress tensor in the three-dimensional space;
substituting the above formula into a crack surface normal stress and tangential stress scalar calculation formula to obtain:
σ＝n·σ·n，τ＝s·σ·n
using the tensor representation, we can obtain:
σ＝σijninj，τ＝σijsinj，
wherein the indices i and j represent coordinate systems x, y, z;
(3) determining each component of the three-dimensional space in the pulling and shearing force:
wherein σxxIs normal stress in the x direction, τxyFor xoy plane shear stress, τxzIs xoz plane shear stress, tauyxIs yox plane shear stress, andxyin contrast, σyyIs normal stress in the y direction, τyzShear stress in the yoz plane, τzxIs zox plane shear stress, andxzin contrast, τzyIs zoy plane shear stress, andyzin contrast, σzzIs normal stress in the z direction, nxIs a vector in the x direction, nyIs a y-direction vector, nzIs a vector in the z direction, TxIs a tensile shear vector in the x direction, TyIs a y-direction pull shear vector, TzA z-direction pull shear vector;
(4) and (3) coordinate conversion to obtain a tensile and shearing force index:
F＝∫TdA＝∫σ·n dA
the magnitude of the tensile and shearing force F represents the resultant force of stress borne on the surrounding rock fracture surface, and the larger the resultant force is, the more easily the fracture surface expands to cause the surrounding rock to be damaged, so that the tensile and shearing force reflects the stability degree of the surrounding rock.
2. The method for calculating a comprehensive index for characterizing rock stress and fracture as claimed in claim 1, wherein: in the step (3), firstly, the crack surface is placed in the whole rock unit to obtain
Where cos θ and sin θ are unit components perpendicular to the fracture plane, i.e., n is (cos θ, sin θ), i.e., nx＝cosθ，nySin θ, θ is the angle between the fracture plane and the x-axis, and the above formula is:
and expanding the two-dimensional plane form into a three-dimensional space to obtain the following three-dimensional space:
3. use of a composite indicator for characterising rock stress and cracking according to claim 1, characterized in that: combining with the current common geotechnical analysis software, programming language FISH built in the software is adopted to compile the calculation process of the tension and shear index into a resolving program which can be called by the software, and the visualization of the index is realized by utilizing the Zone Extra function.
4. Use of a composite indicator for characterising rock stress and cracking according to claim 3, characterized in that: the method specifically comprises the following steps:
reading and storing stress values of all units in surrounding rock before mining, including sigmaxx、σyy、σzz、τxy、τxzAnd τyz；
Calling a resolving program to resolve the tensile and shearing force indexes;
and thirdly, calling a Zone Extra program to output a pulling and shearing force distribution diagram.
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