Mine mining area stress-strain monitoring method based on gravity abnormal change

Abstract

The invention discloses a mining area stress-strain monitoring method based on gravity abnormal change, and the method comprises the specific steps: laying an observation network, and obtaining the gravity abnormal data of a measurement point; preprocessing the obtained gravity anomaly data of the measurement point to obtain processed gravity anomaly data; constructing a linear observation equation set, and introducing a regularization item to solve an underground disturbance density vector; obtaining a mapping relation between the underground disturbance density and the stress tensor through a relation between the stress tensor and the strain tensor, and solving the underground disturbance density through a gravity anomaly difference value between different time points so as to obtain the stress tensors at different moments; and superposing the obtained stress tensor variation result to a mining area mining map, a geological structure map and a historical deformation map to form a comprehensive analysis map, and if the stress tensor corresponding to a certain working face or fracture structure area is obviously enhanced, prompting that the area has a goaf dilatation or ground pressure display risk. According to the method, the measured space coverage degree is high, and maintenance and remeasurement are facilitated.

Description

Technical Field

[0001] The present invention belongs to the technical field of stress monitoring methods, and in particular relates to a stress-strain monitoring method in a mining area based on abnormal gravity changes. Background Art Mining activities are often accompanied by the destruction of underground rock structures, the expansion of cracks, and the redistribution of mass, which in turn causes subtle changes in the regional gravity field. Current monitoring of geological hazards in mining areas relies primarily on surface displacement observations such as GNSS, InSAR, and leveling, but lacks effective, real-time methods for acquiring changes in the underground stress-strain field.

[0002] Existing methods for monitoring underground stress in mines often rely on embedding deep stress gauges or strain gauges within the rock mass and deploying sensors through drilling to obtain in-situ information on changes in stress or deformation. However, these methods have the following significant limitations: (1) low spatial coverage, resulting in a small number of data points and poor representativeness; (2) maintenance and re-measurement are extremely inconvenient, often making it difficult to achieve high-frequency, long-term continuous observations, which limits their application in stress evolution monitoring and disaster warning.

[0003] Therefore, designing a stress-strain monitoring method for mining areas based on gravity anomaly changes has important theoretical value and engineering application prospects. Summary of the Invention

[0004] The purpose of the present invention is to provide a stress-strain monitoring method for mining areas based on gravity anomaly changes, so as to solve the problems of low spatial coverage and inconvenient maintenance and re-measurement of existing methods.

[0005] The technical solution adopted by the present invention is a stress-strain monitoring method for mining areas based on abnormal gravity changes, and the specific steps are as follows: Step 1: Deploy an observation network to obtain gravity anomaly data at the measurement points; Step 2: pre-processing the acquired gravity anomaly data of the measuring points to obtain processed gravity anomaly data; Step 3: Construct a linear observation equation system and introduce the Tikhonov regularization term to solve the underground disturbance density vector; Step 4: Obtain the mapping relationship between the underground disturbance density and the stress tensor through the relationship between the stress tensor and the strain tensor. Then, calculate the underground disturbance density by the difference in gravity anomalies between different time points to obtain the stress tensor at different times. Step 5: Superimpose the obtained stress tensor change results on the mining map, geological structure map and historical deformation map of the mining area to form a comprehensive analysis map. If the stress tensor corresponding to a certain working face or fault structure area is significantly enhanced, it indicates that there is a risk of goaf expansion or ground pressure in the area. The present invention is also characterized in that: In step 1, the distance between two adjacent measurement points is 100m~1000m.

[0006] In step 2, preprocessing includes tidal correction, pressure correction, instrument drift correction and baseline adjustment, and empirical elimination of temperature and diurnal variation effects.

[0007] The specific process of step 3 is: Step 3.1, construct the linear observation equations based on the gravity anomaly integral model; Step 3.2, organize the linear observation equations into a standard matrix form; Step 3.3, introduce the Tikhonov regularization term to construct a generalized least squares model to solve the underground disturbance density vector m, where m is the underground disturbance density voxel approximation of .

[0008] The specific process of step 3.1 is: According to Newton's law of universal gravitation, the measuring point Gravity anomaly at for: (1) In formula (1), is the underground disturbance density; G is the gravitational constant; V is the integration area where the disturbance body is located; Represents the position vector of a small volume unit in the disturbance body; is the position vector of the gravity measurement point; The mining area is divided into x 、 y 、 z Divide into N voxels in three directions, and assume that the underground disturbance density in each voxel is a constant , the number of gravity measurement points is M, then the formula (1) is discretized to obtain the linear observation equations, which are expressed as follows: (2) In formula (2), is the gravity anomaly at the i-th measurement point; is the response coefficient of the j-th voxel to the i-th gravity measurement point.

[0009] In step 3.2, the standard matrix form is: (3) In formula (3), is the gravity anomaly vector, ; A is the response coefficient matrix, ; m is the underground disturbance density vector, .

[0010] In step 3.3, the expression for the underground disturbance density vector m is: (4) In formula (4), is the regularization coefficient; L is the regularization matrix.

[0011] The specific process of step 4 is: Step 4.1, establish the relationship between subsurface disturbance density and local volume strain; Step 4.2, establish the relationship between stress tensor and strain tensor; Step 4.3, establishing a mapping relationship between underground disturbance density and stress tensor based on steps 4.1 and 4.2; Step 4.4: Calculate the underground disturbance density by taking the difference in gravity anomalies between different time points to obtain the change in strain tensor.

[0012] The expression for step 4.1 is: According to the principle of mass conservation, underground disturbance density and local volume strain The relationship is: (5) In formula (5), is the original density of the medium; is the displacement field, is the volume strain, which represents the local volume change rate, It is the divergence calculation symbol in higher mathematics; The specific process of step 4.2 is: According to the linear elastic theory, the strain tensor is defined as for: (6) Defining the stress tensor for: (7) In formula (7), is the strain tensor component, which represents the coordinates in the unit volume Direction and Deformation response in direction; is the fourth-order elastic modulus tensor; Assuming the rock mass in the mining area is an isotropic elastic body, simplify formula (7) to the Lame form, thereby eliminating the fourth-order elastic modulus tensor The explicit dependency of is expressed as: (8) In formula (8), is the Lamé parameter; is the Kronecker symbol.

[0013] In step 4.3, the mapping relationship between the underground disturbance density and the stress tensor is obtained by combining formula (5) and formula (8), and the expression is: (9) In formula (9) The value of is the subsurface perturbation density vector m obtained in step 3.3.

[0014] The specific process of step 4.4 is as follows: Assume that the underground disturbance density at time t is , then the difference in gravity anomaly between the two time points is: (10) In formula (10), is the difference in gravity anomalies between two time points, which is used to capture the time-varying trend of underground density disturbances; is the time interval between two consecutive gravity measurements; For spatial location The gravity anomaly at time t; For the same location , the gravity anomaly value in the next observation period; The underground disturbance density vector at different times is obtained by using formula (10) and formula (1); Substituting the underground disturbance density at different times into formula (9) and formula (11), the stress tensor change can be obtained: ; (11) In formula (11), , at different times 、 The stress tensor difference reflects the evolution trend of the underground stress field.

[0015] The beneficial effects of the present invention are: (1) The present invention is based on a stress-strain monitoring method for mining areas based on anomaly gravity changes. By observing the anomaly changes in surface gravity, the underground disturbance density distribution is inverted, and the stress-strain field is derived. This method achieves the acquisition of underground stress field information without the need to deploy stress or deformation sensors underground. High-risk areas can be predicted based on stress change trends, which helps to early identify and control risks of disasters such as mine tremors, ground pressure manifestations, and goaf collapses. (2) The present invention is based on a stress-strain monitoring method for mining areas based on gravity anomaly changes. It uses a combination of forward integration and inversion to model the disturbance density field, breaking through the previous limitation that gravity anomalies can only be explained qualitatively. It can construct a three-dimensional density model and a stress field spatial distribution map with physical significance, providing an intuitive and quantitative basis for mining area safety evaluation and engineering design. (3) The stress changes obtained by the stress-strain monitoring method of the mining area based on gravity anomaly changes are coupled with the surface deformation data such as GNSS, InSAR, and leveling to improve the deformation mechanism identification ability. DETAILED DESCRIPTION

[0016] The present invention is described in detail below with reference to specific embodiments.

[0017] Example 1 The stress-strain monitoring method for a mining area based on abnormal gravity changes of the present invention is specifically implemented according to the following steps: Step 1: Deploy an observation network to obtain gravity anomaly data at the measurement points; The specific process is as follows: according to the geological structure of the mining area, the distribution of goaf areas and the mining dynamics, measurement points are arranged within the mining area, and periodic measurements are carried out using relative gravimeters to obtain gravity anomaly data at the measurement points; The distance between two adjacent measurement points is 100m~1000m to take into account both spatial resolution and measurement efficiency; The layout of gravity measurement points must cover the mining working face, structural weak zones and historical subsidence areas; Step 2: pre-processing the acquired gravity anomaly data of the measuring points to obtain processed gravity anomaly data; Step 3: Construct a linear observation equation system and introduce the Tikhonov regularization term to solve the underground disturbance density vector; Step 4: Obtain the mapping relationship between the underground disturbance density and the stress tensor through the relationship between the stress tensor and the strain tensor. Then, calculate the underground disturbance density by the difference in gravity anomalies between different time points to obtain the stress tensor at different times. Step 5: Superimpose the obtained stress tensor change results on the mining map, geological structure map and historical deformation map of the mining area to form a comprehensive analysis map. If the stress tensor corresponding to a certain working face or fault structure area is significantly enhanced, it indicates that there is a risk of goaf expansion or ground pressure in the area.

[0018] Example 2 On the basis of Example 1, in step 2, the preprocessing includes tidal correction (using a long-period tidal model), pressure correction (based on local weather station data), instrument drift correction and baseline adjustment, and empirical elimination of temperature effects and diurnal variation effects.

[0019] Example 3 Based on Example 2, the specific process of step 3 is as follows: Step 3.1, construct the linear observation equations based on the gravity anomaly integral model; According to Newton's law of universal gravitation, the measuring point Gravity anomaly at for: (1) In formula (1), is the underground disturbance density; G is the gravitational constant; V is the integration area where the disturbance body is located; Represents the position vector of a small volume unit in the disturbance body and is an integral variable; is the position vector of the gravity measurement point, and the integral kernel function represents the gravitational coupling between the measurement point and the disturbance body; The mining area is divided into x 、 y 、 z Divide into N voxels in three directions, that is, x 、 y 、 z The three spatial directions are divided at a fixed interval so that each voxel has the same size after division, and the underground disturbance density in each voxel is set to be a constant. , the number of gravity measurement points is M, then the formula (1) is discretized to obtain the linear observation equations, which are expressed as follows: (2) In formula (2), is the gravity anomaly at the i-th measurement point; is the response coefficient of the jth voxel to the i-th gravity measurement point, which can be calculated by the integral kernel of formula (1); Step 3.2: Arrange the linear observation equations (Formula (2)) into a standard matrix form, which is expressed as follows: (3) In formula (3), is the gravity anomaly vector, ; A is the response coefficient matrix, ; m is the underground disturbance density vector, ; Step 3.3, introduce the Tikhonov regularization term to construct a generalized least squares model to solve the underground disturbance density vector m (that is, the underground disturbance density The voxel approximation of ), is expressed as: (4) In formula (4), is the regularization coefficient; L is the regularization matrix (such as the identity matrix, first-order derivative or second-order difference matrix).

[0020] Example 4 Based on Example 3, the specific process of step 4 is as follows: Step 4.1, establish the relationship between subsurface disturbance density and local volume strain; According to the principle of mass conservation, underground disturbance density and local volume strain The relationship is: (5) In formula (5), is the original density of the medium; is the displacement field, is the volume strain, which represents the local volume change rate, It is the divergence calculation symbol in higher mathematics; Step 4.2, establish the relationship between stress tensor and strain tensor; According to the linear elastic theory, the strain tensor is defined as for: (6) Defining the stress tensor for: (7) In formula (7), is the strain tensor component, which represents the coordinates in the unit volume Direction and Deformation response in direction; is the fourth-order elastic modulus tensor; Assuming the rock mass in the mining area is an isotropic elastic body, simplify formula (7) to the Lame form, thereby eliminating the fourth-order elastic modulus tensor The explicit dependency of is expressed as: (8) In formula (8), is the Lamé parameter; is the Kronecker symbol; Step 4.3, establish the mapping relationship between underground disturbance density and stress tensor; Step 4.4: Calculate the underground disturbance density by taking the difference in gravity anomalies between different time points to obtain the change in strain tensor.

[0021] Example 5 Based on Example 4, in step 4.3, the mapping relationship between underground disturbance density and stress tensor is obtained by combining formula (5) and formula (8), and the specific relationship is: (9) In formula (9) The value of is the subsurface perturbation density vector m obtained in step 3.3.

[0022] Example 6 Based on Example 5, the specific process of step 4.4 is as follows: Assume that the underground disturbance density at time t is , then the difference in gravity anomaly between the two time points is: (10) In formula (10), is the difference in gravity anomalies between two time points, which is used to capture the time-varying trend of underground density disturbances; is the time interval between two consecutive gravity measurements; For spatial location The gravity anomaly at time t, from periodic measurements; For the same location , the gravity anomaly value in the next observation period; The underground disturbance density vector at different times is obtained by using formula (10) and formula (1); Substituting the underground disturbance density at different times into formula (9) and formula (11), the stress tensor change can be obtained: ; (11) In formula (11), , at different times 、 The stress tensor difference reflects the evolution trend of the underground stress field.

[0023] Changes in stress tensor at different times It is used to characterize the dynamic evolution of local stress state and is an important indicator for analyzing the trend of mine pressure and predicting the risk of sudden disasters. The underground disturbance density values ​​involved in step 4 are all the underground disturbance density vector m obtained in step 3.3.

[0024] The present invention is a stress-strain monitoring method for mining areas based on gravity anomaly changes. With gravity anomaly changes as the core, the underground disturbance density is inverted through a model to obtain the strain field. From network design to data acquisition, processing, modeling, and interpretation, it has a complete operational process. The method is mature, the calculation is controllable, and it has good versatility and scalability, which is convenient for application and promotion in actual projects. It can be flexibly applied to various types of underground projects such as coal mines, metal mines, salt caverns, and oil and gas mining areas. It is also suitable for complex geological background areas with dense faults and cracks and large lithology differences.

Claims

1. A stress-strain monitoring method for mining areas based on gravity anomaly changes, characterized in that: The specific steps are as follows: Step 1: Deploy an observation network to obtain gravity anomaly data at the measurement points; Step 2: pre-processing the acquired gravity anomaly data of the measuring points to obtain processed gravity anomaly data; Step 3: Construct a linear observation equation system and introduce the Tikhonov regularization term to solve the underground disturbance density vector; Step 4: Obtain the mapping relationship between the underground disturbance density and the stress tensor through the relationship between the stress tensor and the strain tensor. Then, calculate the underground disturbance density by the difference in gravity anomalies between different time points to obtain the stress tensor at different times. Step 5: Superimpose the obtained stress tensor change results on the mining map, geological structure map and historical deformation map of the mining area to form a comprehensive analysis map. If the stress tensor corresponding to a certain working face or fault structure area is significantly enhanced, it indicates that there is a risk of goaf expansion or ground pressure in the area.

2. The stress-strain monitoring method for mining areas based on gravity anomaly changes according to claim 1 is characterized in that: In step 1, the distance between two adjacent measurement points is 100m~1000m.

3. The stress-strain monitoring method for mining areas based on gravity anomaly changes according to claim 1 is characterized in that: In step 2, preprocessing includes tidal correction, pressure correction, instrument drift correction and baseline adjustment, and empirical elimination of temperature and diurnal variation effects.

4. The stress-strain monitoring method for mining areas based on gravity anomaly changes according to claim 1 is characterized in that: The specific process of step 3 is: Step 3.1, construct the linear observation equations based on the gravity anomaly integral model; Step 3.2, organize the linear observation equations into a standard matrix form; Step 3.3, introduce the Tikhonov regularization term to construct a generalized least squares model to solve the underground disturbance density vector m, where m is the underground disturbance density voxel approximation of .

5. The method for monitoring stress and strain in mining areas based on abnormal gravity changes according to claim 1, characterized in that: The specific process of step 3.1 is: According to Newton's law of universal gravitation, the measuring point Gravity anomaly at for: （1） In formula (1), is the underground disturbance density; G is the gravitational constant; V is the integration area where the disturbance body is located; Represents the position vector of a small volume unit in the disturbance body; is the position vector of the gravity measurement point; The mining area is divided into x 、 y 、 z Divide into N voxels in three directions, and assume that the underground disturbance density in each voxel is a constant , the number of gravity measurement points is M, then the formula (1) is discretized to obtain the linear observation equations, which are expressed as follows: （2） In formula (2), is the gravity anomaly at the i-th measurement point; is the response coefficient of the j-th voxel to the i-th gravity measurement point.

6. The method for monitoring stress and strain in mining areas based on abnormal gravity changes according to claim 5, characterized in that: In step 3.2, the standard matrix form is: （3） In formula (3), is the gravity anomaly vector, ; A is the response coefficient matrix, ; m is the underground disturbance density vector, ; In step 3.3, the expression for the underground disturbance density vector m is: （4） In formula (4), is the regularization coefficient; L is the regularization matrix.

7. The method for monitoring stress and strain in mining areas based on abnormal gravity changes according to claim 5, characterized in that: The specific process of step 4 is: Step 4.1, establish the relationship between subsurface disturbance density and local volume strain; Step 4.2, establish the relationship between stress tensor and strain tensor; Step 4.3, establishing a mapping relationship between underground disturbance density and stress tensor based on steps 4.1 and 4.2; Step 4.4: Calculate the underground disturbance density by taking the difference in gravity anomalies between different time points to obtain the change in strain tensor.

8. The method for monitoring stress and strain in mining areas based on abnormal gravity changes according to claim 5, characterized in that: The expression for step 4.1 is: According to the principle of mass conservation, underground disturbance density and local volume strain The relationship is: （5） In formula (5), is the original density of the medium; is the displacement field, is the volume strain, which represents the local volume change rate, It is the divergence calculation symbol in higher mathematics; The specific process of step 4.2 is: According to the linear elastic theory, the strain tensor is defined as for: （6） Defining the stress tensor for: （7） In formula (7), is the strain tensor component, which represents the coordinates in the unit volume Direction and Deformation response in direction; is the fourth-order elastic modulus tensor; Assuming the rock mass in the mining area is an isotropic elastic body, simplify formula (7) to the Lame form, thereby eliminating the fourth-order elastic modulus tensor The explicit dependency of is expressed as: （8） In formula (8), is the Lamé parameter; is the Kronecker symbol.

9. The method for monitoring stress and strain in mining areas based on abnormal gravity changes according to claim 5, characterized in that: In step 4.3, the mapping relationship between the underground disturbance density and the stress tensor is obtained by combining formula (5) and formula (8), and the expression is: （9） In formula (9) The value of is the subsurface perturbation density vector m obtained in step 3.

3.

10. The method for monitoring stress and strain in mining areas based on abnormal gravity changes according to claim 5, characterized in that: The specific process of step 4.4 is as follows: Assume that the underground disturbance density at time t is , then the difference in gravity anomaly between the two time points is: （10） In formula (10), is the difference in gravity anomalies between two time points, which is used to capture the time-varying trend of underground density disturbances; is the time interval between two consecutive gravity measurements; For spatial location The gravity anomaly at time t; For the same location , the gravity anomaly value in the next observation period; The underground disturbance density vector at different times is obtained by using formula (10) and formula (1); Substituting the underground disturbance density at different times into formula (9) and formula (11), the stress tensor change can be obtained: ; （11） In formula (11), , at different times 、 The stress tensor difference reflects the evolution trend of the underground stress field.

Images