Ground surface crack deformation quantitative identification method based on strain tensor inversion

Abstract

The invention discloses a surface crack deformation quantitative identification method based on strain tensor inversion. The method comprises the following specific steps: arranging a plurality of triangular observation units in a crack influence area and arranging observation equipment; constructing a strain observation model based on side length change and a shear strain observation model based on included angle change; periodically collecting the lengths of the three sides of each triangular observation unit and the included angles of the three interior angles of each triangular observation unit; obtaining a strain tensor component according to the collected data in combination with the constructed model; obtaining a final strain tensor component from the strain tensor component through a linear least square method; calculating a surface swelling amount, a maximum shear strain value, a first main strain, a second main strain and a strain main direction according to the final strain tensor component; and dividing risk levels. The method is high in mining area earth surface crack deformation recognition capability.

Description

Technical Field

[0001] The present invention belongs to the technical field of surface crack identification methods, and in particular relates to a surface crack deformation quantitative identification method based on strain tensor inversion. Background Art

[0002] With the continued development of underground resources, especially during deep mining activities such as coal and metal mines, the surface stress structure is constantly changing, which can easily induce large-scale surface subsidence and fracture. Surface fracture is not only an important indicator of mining subsidence, but also a key factor in geological disaster early warning and engineering safety management. Therefore, establishing high-precision and timely fracture deformation monitoring and identification technology is one of the core technical requirements for smart mine construction and geological disaster prevention and control.

[0003] Currently, monitoring of surface cracks relies primarily on the following methods: manual inspections and crack measurement, GNSS or total station displacement monitoring, and remote sensing technologies such as InSAR. However, these three monitoring methods generally focus on describing displacement when observing "cracks," and their ability to extract information about local relative deformations, such as shear, tension, dislocation, and rotation, is insufficient. Strain analysis, a core tool in continuum mechanics, can reveal the relative deformation relationship between adjacent points and has inherent advantages for identifying early-stage microcracks and quantitatively assessing deformation trends. However, traditional strain calculations often rely on continuous field models (such as finite element methods), which are difficult to adapt to the complex characteristics of mining areas, such as discrete on-site measurement points, irregular structures, and strong discontinuity of cracks. This results in a weak ability to identify surface cracks in mining areas. Summary of the Invention

[0004] The purpose of the present invention is to provide a quantitative identification method for surface crack deformation based on strain tensor inversion, so as to solve the problem that the existing strain analysis method has weak ability to identify surface crack deformation in mining areas.

[0005] The technical solution adopted by the present invention is a quantitative identification method of surface crack deformation based on strain tensor inversion, and the specific steps are as follows: Step 1: deploy several triangular observation units and observation equipment in the crack impact area; Step 2: construct a strain observation model based on side length change and a shear strain observation model based on angle change; Step 3: Periodically collect the lengths of the three sides and the included angles of the three internal angles of each triangular observation unit; Step 4, obtaining strain tensor components based on the data collected in step 3 and combined with the model constructed in step 2; Step 5, the strain tensor components obtained in step 4 are used to obtain the final strain tensor components by linear least square method; Step 6: Calculate the surface expansion, maximum shear strain value, first principal strain, second principal strain, and strain principal direction based on the final strain tensor components; Step 7: Classify the hazard level and identify the deformation in the crack area.

[0006] The present invention is also characterized in that: The specific process of step 1 is: The crack impact zone is determined based on the existing mining boundaries, subsidence evolution trends, and actual crack development in the field. Several triangular observation units are deployed within the crack impact zone. A laser rangefinder is set at any vertex of each triangular observation unit, and reflective targets or prisms are set at the other two vertices of each triangular observation unit to observe the internal angle and side length of the triangular observation unit. The three vertices of each triangular observation unit are set on both sides of the crack, that is, one vertex is located on one side of the crack, and the other two vertices are located on the other side of the crack.

[0007] In step 2, the specific process of constructing the strain observation model based on edge length change is as follows: Assume that the coordinates of any point P in three-dimensional space before deformation are , the coordinates of any point P in three-dimensional space after deformation are , Indicates that point P is in the process of deformation x The displacement in the axial direction, Indicates that point P is in the process of deformation y The displacement in the axial direction, Indicates that point P is in the process of deformation z The displacement in the axial direction, the displacement vector of point P during the deformation process is for: (1) Suppose another point Q is any point in the neighborhood of point P, and the coordinates of point Q are , Indicates that point Q and point P are x The coordinate difference of the axis, Indicates that point Q and point P are x The coordinate difference of the axis, Indicates that point Q and point P are x The coordinate difference of the axis, the displacement component of point Q is expanded by the first order Taylor, and we have: (2) In formula (2), represents the displacement gradient tensor, It represents the small position increment of point Q relative to point P; in, (3) In the theory of elasticity, the strain tensor is expressed as the symmetric part of the displacement gradient tensor, that is: (4) In formula (4), is the strain tensor, represents the transpose of the displacement increment vector; strain tensor It has 6 independent components, which can be expressed as: (6) Due to symmetry e ij = e ji ,but , , , , , ; If the unit vector If represents a certain direction, the linear elongation e in that direction can be expressed as: (7) Then, for any direction , linear elongation for: (8) Formula (8) is used as the strain observation model based on the change of edge length.

[0008] In step 2, the specific process of constructing the shear strain observation model based on angle change is as follows: Assume that the vectors of the three sides ABC of the triangular observation unit before deformation are: (9) Then the corresponding angle θ satisfies the cosine formula: (10) Then the vectors of the three sides ABC of the deformed triangle observation unit are: , (11) In formula (11), Represents the edge vector The increment after deformation is equal to the displacement difference of point B relative to point A. Represents the edge vector The increment after deformation is equal to the displacement difference of point C relative to point A; Direction cosine variation for: (12) In formula (12), is the angle after deformation; According to the relationship between strain tensor and vector change in the small deformation theory of classical elastic mechanics, the direction cosine change By strain tensor Expressed as: (13) In formula (13), 、 is the unit direction vector, ; For a unit direction vector 、 , then formula (13) can be expanded as: (14) Formula (14) is used as the shear strain observation model based on the angle change.

[0009] The specific process of step 3 is: use a total station or GNSS and a reflective target or prism to measure the lengths of the three sides and the angles of the three internal angles of each triangular observation unit according to a set period, and obtain the initial lengths of the three sides and the initial angles of the three internal angles of each triangular observation unit, the measured lengths of the three sides, and the measured angles of the three internal angles.

[0010] The specific process of step 4 is as follows: according to the initial length, measured length, initial angle and measured angle obtained in step 3, the linear extension of each side (change in side length) and the direction cosine change of each internal angle (reflecting shear or rotational deformation) are calculated by formulas (1) to (7) and (9) to (12). The obtained linear extension of each side and the direction cosine change of each internal angle are substituted into formulas (8) and (14) respectively to obtain the strain tensor components.

[0011] In step 6, the surface expansion is equal to the sum of the main diagonal elements of the strain tensor; Maximum shear strain value The expression is: (15) The expressions for the first and second principal strains are: (16) (17) represents the first principal strain, represents the second principal strain; principal direction of strain The expression is: (17).

[0012] The specific process of step 7 is as follows: the surface expansion, maximum shear strain value, first principal strain, second principal strain, and strain main direction obtained in step 6 are compared with the surface expansion threshold, maximum shear strain threshold, first principal strain threshold, second principal strain threshold, and strain main direction threshold, respectively, to divide the hazard level. The hazard level is divided into four levels: Level I is the safe zone, Level II is the mild warning zone, Level III is the obvious warning zone, and Level IV is the high-risk fracture zone; the method for determining the threshold for each level is one of the following: statistical method (background mean + multiple standard deviation), empirical calibration of the test area, or dynamic adjustment of the partition.

[0013] The beneficial effects of the present invention are: (1) The present invention proposes a quantitative identification method for surface crack deformation based on strain tensor inversion. By constructing a triangular observation unit across the crack, periodically collecting changes in side length and angle, and inverting the local three-dimensional strain tensor based on linear least squares theory, the method achieves quantitative, interpretable, and traceable analysis of crack deformation behavior. (2) The quantitative identification method of surface crack deformation based on strain tensor inversion is applicable to high-gradient discontinuous deformation bodies of crack-like structures. Conventional methods based on displacement differences are difficult to accurately capture complex crack deformation characteristics such as local opening, shearing, or dislocation. The present invention can identify microscopic geometric changes such as relative tension, shearing, and rotation in the crack area on a spatial scale through strain tensor inversion. It is particularly suitable for monitoring high-gradient crack zones induced by mining subsidence and has a strong ability to identify surface crack deformation. (3) The quantitative identification method of surface crack deformation based on strain tensor inversion of the present invention can comprehensively characterize the tensile, shear and rotational deformation characteristics of the crack area by integrating the strain observation model based on side length change and the shear strain observation model based on angle change, thus avoiding the error of subjective judgment of crack activity level and providing a basis for building a standardized and engineered surface crack identification system. (4) The quantitative identification method of surface crack deformation based on strain tensor inversion of the present invention uses discrete points to construct triangular observation units, which has good spatial adaptability and network flexibility. It can be flexibly deployed according to the crack morphology and regional topography. At the same time, it supports a variety of high-precision data acquisition methods such as total station re-survey and GNSS three-dimensional coordinate observation. It has strong adaptability and good engineering compatibility. DETAILED DESCRIPTION The present invention is described in detail below with reference to specific embodiments.

[0014] Example 1 The quantitative identification method of surface crack deformation based on strain tensor inversion of the present invention is specifically implemented according to the following steps: Step 1: deploy several triangular observation units and observation equipment in the crack impact area; Step 2: construct a strain observation model based on side length change and a shear strain observation model based on angle change; Step 3: Periodically collect the lengths of the three sides and the included angles of the three internal angles of each triangular observation unit; Step 4, obtaining strain tensor components based on the data collected in step 3 and combined with the model constructed in step 2; Step 5, the strain tensor components obtained in step 4 are used to obtain the final strain tensor components by linear least square method; Step 6: Calculate the surface expansion, maximum shear strain value, first principal strain, second principal strain, and strain principal direction based on the final strain tensor components; Step 7: Classify the hazard level and identify the deformation of the crack area; The specific process is: Combined with the evolution trend of strain parameters within the continuous observation period, the surface expansion, maximum shear strain value, first principal strain, second principal strain, and strain main direction obtained in step 6 are compared with the surface expansion threshold, maximum shear strain threshold, first principal strain threshold, second principal strain threshold, and strain main direction threshold to divide the hazard level. The hazard level is divided into four levels: Level I is the safe zone, Level II is the mild warning zone, Level III is the obvious warning zone, and Level IV is the high-risk fracture zone. The method for determining the threshold for each level is one of the following: statistical method (background mean + multiple standard deviation), empirical calibration of the test area, or dynamic adjustment of the partition, so as to identify crack areas with rapid opening, strong shear, or significant surface expansion, thereby realizing the identification of deformation mechanism and prediction and early warning of hazard trends.

[0015] Example 2 Based on Example 1, the specific process of step 1 is as follows: The crack impact zone is determined based on the existing mining boundaries, subsidence evolution trends, and actual crack development in the field. Several triangular observation units are deployed within the crack impact zone. A laser rangefinder is set at any vertex of each triangular observation unit, and reflective targets or prisms are set at the other two vertices of each triangular observation unit to observe the internal angle and side length of the triangular observation unit. The three vertices of each triangular observation unit are set on both sides of the crack, that is, one vertex is located on one side of the crack, and the other two vertices are located on the other side of the crack.

[0016] Example 3 On the basis of Example 2, in step 2, the specific process of constructing the strain observation model based on the change of side length is: Assume that the coordinates of any point P in three-dimensional space before deformation are , the coordinates of any point P in three-dimensional space after deformation are , Indicates that point P is in the process of deformation x The displacement in the axial direction, Indicates that point P is in the process of deformation y The displacement in the axial direction, Indicates that point P is in the process of deformation z The displacement in the axial direction, the displacement vector of point P during the deformation process is for: (1) Suppose another point Q is any point in the neighborhood of point P, and the coordinates of point Q are , Indicates that point Q and point P are x The coordinate difference of the axis, Indicates that point Q and point P are x The coordinate difference of the axis, Indicates that point Q and point P are x The coordinate difference of the axis, the displacement component of point Q is expanded by the first order Taylor, and we have: (2) In formula (2), represents the displacement gradient tensor, It represents the small position increment of point Q relative to point P; in, (3) In the theory of elasticity, the strain tensor is expressed as the symmetric part of the displacement gradient tensor, that is: (4) In formula (4), is the strain tensor, represents the transpose of the displacement increment vector; strain tensor The expression is: (5) strain tensor It has 6 independent components, which can be expressed as: (6) Due to symmetry e ij = e ji ,but , , , , , ; If the unit vector If represents a certain direction, the linear elongation in that direction is expressed as: (7) In formula (7), is the linear elongation; Then, for any direction , linear elongation for: (8) Formula (8) is used as the strain observation model based on the change of edge length; At least six independent directions (edges) are required to solve the six independent strain tensor components. Since a single triangular observation unit has only three edges, a shear strain observation model based on angle changes is constructed for solution. Example 4 On the basis of Example 3, in step 2, the specific process of constructing the shear strain observation model based on angle change is as follows: In a triangulated observation unit, not only the change in side length (linear elongation) can reflect local deformation, but also the change in internal angle can reflect local changes, especially shear deformation or relative rotation; Assume that the vectors of the three sides ABC of the triangular observation unit before deformation are: (9) Then the corresponding angle θ satisfies the cosine formula: (10) Then the vectors of the three sides ABC of the deformed triangle observation unit are: , (11) In formula (11), Represents the edge vector The increment after deformation is equal to the displacement difference of point B relative to point A. Represents the edge vector The increment after deformation is equal to the displacement difference of point C relative to point A; Direction cosine variation for: (12) In formula (12), is the angle after deformation; According to the relationship between strain tensor and vector change in the small deformation theory of classical elastic mechanics, the direction cosine change By strain tensor Expressed as: (13) In formula (13), 、 is the unit direction vector, ; For a unit direction vector 、 , then formula (13) can be expanded as: (14) Formula (14) is used as the shear strain observation model based on the angle change.

[0017] Example 5 Based on Example 4, the specific process of step 3 is as follows: Use a total station or GNSS and a reflective target or prism to measure the lengths of the three sides and the included angles of the three internal angles of each triangular observation unit according to a set period, and obtain the initial lengths of the three sides and the initial included angles of the three internal angles of each triangular observation unit, the measured lengths of the three sides, and the measured included angles of the three internal angles; When the sedimentation is significant, the measurement period is 7 or 10 days; When the crack is in the stable period, the measurement period shall be no less than 10 days.

[0018] Example 6 Based on Example 5, the specific process of step 4 is as follows: Based on the initial length, measured length, initial angle, and measured angle obtained in step 3, the linear extension of each side (change in side length) and the direction cosine change of each internal angle (reflecting shear or rotational deformation) are calculated using formulas (1) to (7) and (9) to (12). The obtained linear extension of each side and the direction cosine change of each internal angle are substituted into formulas (8) and (14) respectively to obtain the strain tensor components. Example 7 Based on Example 6, in step 6, the surface expansion is equal to the sum of the main diagonal elements of the strain tensor; Maximum shear strain value Reflecting the degree of shear deformation in the region, the expression is: (15) In formula (15), are the strain tensor components.

[0019] The expressions for the first and second principal strains are: (16) (17) represents the first principal strain, represents the second principal strain; principal direction of strain It is used to indicate the main control direction of crack development or the movement trend of subsidence boundary. The expression is: (17).

[0020] The quantitative identification method of surface crack deformation based on strain tensor inversion in the present invention can dynamically invert the strain tensor in continuous observation, and perform deformation grade classification and risk grading in combination with the evolution trend of the principal strain direction, shear strain component and expansion amount. It has strong predictiveness and foresight, can be directly used to build a ground crack early warning system, and can be integrated into a smart mine or geological disaster monitoring platform. It has broad promotion prospects. The method of the present invention is applicable to a variety of engineering scenarios that require crack deformation identification, such as coal mine subsidence areas, ground crack active zones, ground building settlement risk areas, etc. It has engineering deployability and algorithm portability, and is expected to become a key technical module in smart mine construction and geological disaster monitoring systems.

[0021] The method of the present invention has comprehensive advantages such as strong recognition ability, rigorous model construction, good engineering adaptability, and strong scalability. It can significantly improve the current level of surface crack monitoring from "qualitative description" to "quantitative identification", and has important technical promotion value and practical application significance in the fields of intelligent monitoring, risk prevention and control, and geological disaster early warning.

Claims

1. A quantitative identification method for surface crack deformation based on strain tensor inversion, characterized by: The specific steps are as follows: Step 1: deploy several triangular observation units and observation equipment in the crack impact area; Step 2: construct a strain observation model based on side length change and a shear strain observation model based on angle change; Step 3: Periodically collect the lengths of the three sides and the included angles of the three internal angles of each triangular observation unit; Step 4, obtaining strain tensor components based on the data collected in step 3 and combined with the model constructed in step 2; Step 5, the strain tensor components obtained in step 4 are used to obtain the final strain tensor components by linear least square method; Step 6: Calculate the surface expansion, maximum shear strain value, first principal strain, second principal strain, and strain principal direction based on the final strain tensor components; Step 7: Classify the hazard level and identify the deformation in the crack area.

2. The method for quantitatively identifying surface crack deformation based on strain tensor inversion according to claim 1, characterized in that: The specific process of step 1 is: The crack impact zone is determined based on the existing mining boundaries, subsidence evolution trends, and actual crack development in the field. Several triangular observation units are deployed within the crack impact zone. A laser rangefinder is set at any vertex of each triangular observation unit, and reflective targets or prisms are set at the other two vertices of each triangular observation unit to observe the internal angle and side length of the triangular observation unit. The three vertices of each triangular observation unit are set on both sides of the crack, that is, one vertex is located on one side of the crack, and the other two vertices are located on the other side of the crack.

3. The method for quantitatively identifying surface crack deformation based on strain tensor inversion according to claim 1, characterized in that: In step 2, the specific process of constructing the strain observation model based on edge length change is as follows: Assume that the coordinates of any point P in three-dimensional space before deformation are , the coordinates of any point P in three-dimensional space after deformation are , Indicates that point P is in the process of deformation x The displacement in the axial direction, Indicates that point P is in the process of deformation y The displacement in the axial direction, Indicates that point P is in the process of deformation z The displacement in the axial direction, the displacement vector of point P during the deformation process is for: （1） Suppose another point Q is any point in the neighborhood of point P, and the coordinates of point Q are , Indicates that point Q and point P are x The coordinate difference of the axis, Indicates that point Q and point P are x The coordinate difference of the axis, Indicates that point Q and point P are x The coordinate difference of the axis, the displacement component of point Q is expanded by the first order Taylor, and we have: （2） In formula (2), represents the displacement gradient tensor, It represents the small position increment of point Q relative to point P; in, （3） In the theory of elasticity, the strain tensor is expressed as the symmetric part of the displacement gradient tensor, that is: （4） In formula (4), is the strain tensor, represents the transpose of the displacement increment vector; strain tensor It has 6 independent components, which can be expressed as: （6） Due to symmetry ε ij = ε ji ,but , , , , , ; If the unit vector If represents a certain direction, the linear elongation e in that direction can be expressed as: （7） Then, for any direction , linear elongation for: （8） Formula (8) is used as the strain observation model based on the change of edge length.

4. The method for quantitatively identifying surface crack deformation based on strain tensor inversion according to claim 3 is characterized in that: In step 2, the specific process of constructing the shear strain observation model based on angle change is as follows: Assume that the vectors of the three sides ABC of the triangular observation unit before deformation are: （9） Then the corresponding angle θ satisfies the cosine formula: （10） Then the vectors of the three sides ABC of the deformed triangle observation unit are: ， （11） In formula (11), Represents the edge vector The increment after deformation is equal to the displacement difference of point B relative to point A. Represents the edge vector The increment after deformation is equal to the displacement difference of point C relative to point A; Direction cosine variation for: （12） In formula (12), is the angle after deformation; According to the relationship between strain tensor and vector change in the small deformation theory of classical elastic mechanics, the direction cosine change By strain tensor Expressed as: （13） In formula (13), 、 is the unit direction vector, ; For a unit direction vector 、 , then formula (13) can be expanded as: （14） Formula (14) is used as the shear strain observation model based on the angle change.

5. The method for quantitatively identifying surface crack deformation based on strain tensor inversion according to claim 4, characterized in that: The specific process of step 3 is: use a total station or GNSS and a reflective target or prism to measure the lengths of the three sides and the angles of the three internal angles of each triangular observation unit according to a set period, and obtain the initial lengths of the three sides and the initial angles of the three internal angles of each triangular observation unit, the measured lengths of the three sides, and the measured angles of the three internal angles.

6. The method for quantitatively identifying surface crack deformation based on strain tensor inversion according to claim 5, characterized in that: The specific process of step 4 is as follows: according to the initial length, measured length, initial angle and measured angle obtained in step 3, the linear extension of each side and the direction cosine change of each internal angle are calculated by formulas (1) to (7) and formulas (9) to (12), and the obtained linear extension of each side and the direction cosine change of each internal angle are substituted into formulas (8) and (14) respectively to obtain the strain tensor components.

7. The method for quantitatively identifying surface crack deformation based on strain tensor inversion according to claim 5, characterized in that: In step 6, the surface expansion is equal to the sum of the main diagonal elements of the strain tensor; Maximum shear strain value The expression is: （15） The expressions for the first and second principal strains are: （16） （17） represents the first principal strain, represents the second principal strain; principal direction of strain The expression is: （17）。 8. The method for quantitatively identifying surface crack deformation based on strain tensor inversion according to claim 1, characterized in that: The specific process of step 7 is as follows: the surface expansion, maximum shear strain value, first principal strain, second principal strain, and strain main direction obtained in step 6 are compared with the surface expansion threshold, maximum shear strain threshold, first principal strain threshold, second principal strain threshold, and strain main direction threshold, respectively, to divide the hazard level. The hazard level is divided into four levels: Level I is a safe area, Level II is a mild warning area, Level III is a significant warning area, and Level IV is a high-risk fracture area; the method for determining the threshold for each level is one of statistical methods, empirical calibration of the test area, or dynamic adjustment of the partition.

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