Inversion method based on crustal stress field boundary load

Abstract

The invention discloses an inversion method, particularly discloses an inversion method based on a crustal stress field boundary load, and belongs to the technical field of geological survey processes. The inversion method based on the crustal stress field boundary load is relatively few in technological process and relatively fast in data acquisition. The inversion method is based on a boundary load principle, a stress measurement value array is constructed on the basis of a ground stress value measured on site, a unit boundary force load is applied to a three-dimensional model, a stress value of a measurement point position is calculated, then an overall boundary stiffness matrix is constructed on the basis of the stress value of the measurement point, and the overall boundary stiffness matrix is calculated. And finally solving the linear combination under the boundary condition to enable the stress calculation value at the measuring point position to be equal to the measured value, thereby completing the inversion work of the boundary load of the crustal stress field.

Description

Technical Field

[0001] The invention relates to an inversion method, in particular to an inversion method based on a boundary load of a ground stress field, and belongs to the technical field of geological survey technology. Background Art

[0002] The geostress field is the basic condition for the stability analysis of underground engineering. Accurate analysis of the initial geostress field plays a vital role in structural design and engineering construction plans. Generally speaking, the geostress field is determined by actual measurement + numerical inversion. The current mainstream geostress inversion methods include boundary load method, stress function method, regression analysis method, neural network algorithm, genetic algorithm, etc. Among them, the boundary load method has clear mechanical concepts and is easy to implement. It is widely used in the engineering field. However, after using the boundary load method for geostress inversion, fitting regression analysis must be performed to ensure the inversion accuracy and simplify the operation. The fitting regression analysis process is complicated, time-consuming and labor-intensive, and is not conducive to the rapid acquisition of geostress field data. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide an inversion method based on boundary load of ground stress field, which has relatively fewer process flows and relatively faster data acquisition.

[0004] The technical solution adopted to solve the above technical problems is: an inversion method based on the boundary load of the ground stress field. The inversion method is based on the boundary load principle, based on the ground stress value measured on site, to construct a stress measurement value array, apply a unit boundary force load in the three-dimensional model and calculate the stress value at the measuring point, then construct an overall boundary stiffness matrix based on the stress value of the measuring point, and finally solve the linear combination under the boundary conditions so that the calculated stress value at the measuring point is equal to the measured value to complete the inversion of the boundary load of the ground stress field, wherein the stress combination of the boundary conditions can be written as the following expression,

[0005]

[0008] In the above formula, a i is the coefficient to be determined, B i For the local boundary C i The unit distributed force load applied on the surface, n is the number of ground stress test points.

[0009] Furthermore, the following steps are followed when testing the ground stress value on site:

[0010] First, conduct ground stress tests on n points to obtain the measured stress array A 1 , A 2 , …, A n, each measured stress array contains 6 stress components, written as A 1 (s xx ,s yy ,s zz ,s xy ,s yz ,s xz ), A 2 (s xx ,s yy ,s zz ,s xy ,s yz ,s xz ),…,A n (s xx ,s yy ,s zz ,s xy ,s yz ,s xz ), where x, y, and z are the three coordinate axis directions to complete the on-site test of the ground stress value.

[0011] The preferred mode of the above scheme is that when the measured geostress parameters are constructed into a one-dimensional array in a prescribed order, the stress measurement value array is constructed according to the following formula in the order of measuring point numbers and the default order of components:

[0012]

[0013] Furthermore, before applying the boundary force load in the three-dimensional model, the artificial boundary surface of the three-dimensional model needs to be divided into regions, and then the boundary force load is applied. The specific conditions and process are as follows:

[0014] The artificial boundary of the three-dimensional model includes 1 bottom surface and 4 side surfaces. According to the surface normal vector principle, the bottom surface is named z surface, and the four side surfaces are 2 x surfaces and 2 y surfaces. When applying boundary conditions, the z surface adopts normal constraint, and the two x surfaces and the two y surfaces each adopt one side to apply boundary force load and one side to apply normal constraint.

[0015] When dividing the artificial boundary surface of the three-dimensional model into regions, the two surfaces to which the boundary force load is applied are divided into 6n regions, which are respectively denoted as C 1 ,C 2 ,C 3 ,...,C 6n .

[0016] The preferred method of the above scheme is to construct B when applying boundary force load in the three-dimensional model. 1 , B 2 , …, B 6n There are 6n linearly independent boundary conditions in total.

[0017] The definition of linear independence of boundary conditions is that the stress field generated by any boundary condition cannot be expressed as a linear combination of the stress fields generated by the other 6n-1 boundary conditions.

[0018] Furthermore, the stress under unit boundary force load is written as,

[0019]

[0020] For any boundary condition B i , i = 1, 2, ..., 6n, at the boundary C i If a unit normal pressure P = 1 is applied on the surface, a positive stress k in the three directions of x, y, and z will be generated at the first measuring point. 1 xx , k 1 yy , k 1 zz and the corresponding shear stress k 1 xy , k 1 yz , k 1 xz , and then 6 corresponding stress components are generated at each of the n test points.

[0021] The preferred method of the above scheme is to construct the overall boundary stiffness matrix according to the following formula:

[0022] K=[K 1 K 2 ...K 6n ].

[0023] Furthermore, when solving the linear combination of boundary conditions, the following steps are followed:

[0024] Assuming that the linear combination of 6n boundary conditions and the superposition of the self-weight stress field G satisfy the measured values ​​of the existing ground stress test points, then S = G + Ka, where a = (a 1 , a 2 , …, a 6n ), then a=K- 1 (SG), the load boundary condition B obtained by inversion is:

[0025] The beneficial effects of the present invention are as follows: the technical solution provided by the present application is based on the boundary load principle, and based on the ground stress value measured on site, a stress measurement array is constructed, a unit boundary force load is applied in the three-dimensional model and the stress value at the measuring point is calculated, and then the overall boundary stiffness matrix is ​​constructed based on the stress value at the measuring point, and finally the linear combination under the boundary conditions is solved so that the calculated stress value at the measuring point is equal to the measured value, so that there is no need to perform fitting regression analysis, and the effect of improving the inversion accuracy and simplifying the operation is achieved. Thus, the invention purpose of relatively fewer process flows and relatively faster data acquisition is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of the arrangement of boundary conditions involved in the inversion method based on the boundary load of the geostress field of the present invention;

[0027] Figure 2 It is a schematic diagram of stress generated by unit load of boundary conditions involved in the inversion method of boundary load of geostress field of the present invention. DETAILED DESCRIPTION

[0028] like Figure 1 , Figure 2 The present invention provides an inversion method based on the boundary load of the geostress field, which has relatively few process steps and relatively fast data acquisition. The inversion method is based on the boundary load principle, and is based on the geostress value measured on site, to construct a stress measurement array, apply a unit boundary force load in the three-dimensional model and calculate the stress value at the measuring point, and then construct an overall boundary stiffness matrix based on the stress value at the measuring point, and finally solve the linear combination under the boundary conditions so that the calculated stress value at the measuring point is equal to the measured value to complete the inversion of the boundary load of the geostress field, where the stress combination of the boundary conditions can be written as the following expression,

[0029]

[0031] In the above formula, a i is the coefficient to be determined, B i For the local boundary C i The unit distributed force load applied on the surface, n is the number of ground stress measuring points. The technical solution provided by the present application is based on the boundary load principle. Based on the ground stress value measured on site, a stress measurement array is constructed. A unit boundary force load is applied in the three-dimensional model and the stress value at the measuring point is calculated. Then, the overall boundary stiffness matrix is ​​constructed based on the stress value at the measuring point. Finally, the linear combination under the boundary conditions is solved so that the calculated stress value at the measuring point is equal to the measured value, thereby eliminating the need for fitting regression analysis, thereby achieving the effect of improving the inversion accuracy and simplifying the operation. This achieves the purpose of the invention of relatively fewer process flows and relatively efficient data acquisition.

[0032] Accordingly, in order to further refine each step to facilitate the inversion operation, while maximizing the inversion accuracy and simplifying the operation, the present application follows the following steps when testing the ground stress value on site:

[0033] First, conduct ground stress tests on n points to obtain the measured stress array A 1 , A 2 , …, A n , each measured stress array contains 6 stress components, written as A 1 (s xx ,s yy ,s zz ,s xy ,s yz ,s xz ), A 2 (s xx ,s yy ,s zz ,s xy ,s yz ,s xz ),…,A n (s xx ,s yy ,s zz ,s xy ,s yz ,s xz ), where x, y, and z are the three coordinate axis directions to complete the field test of the geostress value. When the measured geostress parameters are constructed into a one-dimensional array in the prescribed order, the stress measurement value array is constructed according to the following formula based on the measurement point number order and the component default order,

[0034] Before applying boundary force load in the 3D model, the artificial boundary surface of the 3D model needs to be divided into regions, and then the boundary force load can be applied. The specific conditions and process are as follows:

[0035] The artificial boundary of the three-dimensional model includes 1 bottom surface and 4 side surfaces. According to the surface normal vector principle, the bottom surface is named z surface, and the four side surfaces are 2 x surfaces and 2 y surfaces. When applying boundary conditions, the z surface adopts normal constraint, and the two x surfaces and the two y surfaces each adopt one side to apply boundary force load and one side to apply normal constraint.

[0036] When dividing the artificial boundary surface of the three-dimensional model into regions, the two surfaces to which the boundary force load is applied are divided into 6n regions, which are respectively denoted as C 1 ,C 2 ,C 3 ,...,C 6n When applying boundary force loads in a three-dimensional model, it is necessary to construct B1 , B 2 , …, B 6n There are 6n linearly independent boundary conditions in total.

[0037] The definition of linear independence of boundary conditions is that the stress field generated by any boundary condition cannot be expressed as a linear combination of the stress fields generated by the other 6n-1 boundary conditions. The stress under unit boundary force load can be written as,

[0038]

[0039] For any boundary condition B i , i = 1, 2, ..., 6n, at the boundary C i If a unit normal pressure P = 1 is applied on the surface, a positive stress k in the three directions of x, y, and z will be generated at the first measuring point. 1 xx , k 1 yy , k 1 zz and the corresponding shear stress k 1 xy , k 1 yz , k 1 xz , and then 6 corresponding stress components are generated at each of the n test points. When constructing the overall boundary stiffness matrix, it is constructed according to the following formula:

[0040] K=[K 1 K 2 ...K 6n ]. When solving the linear combination of boundary conditions, the following steps are followed:

[0041] Assuming that the linear combination of 6n boundary conditions and the superposition of the self-weight stress field G satisfy the measured values ​​of the existing ground stress test points, then S = G + Ka, where a = (a 1 , a 2 , …, a 6n ), then a=K- 1 (SG), the load boundary condition B obtained by inversion is:

[0042] The technical solution of the present application is further described below through specific embodiments:

[0043] Embodiment 1

[0044] 1. Conduct ground stress tests at n points: A 1 , A 2 , …, A nThere are 6 ground stress components measured at each ground stress measuring point: A 1 (s xx ,s yy ,s zz ,s xy ,s yz ,s xz ), A 2 (s xx ,s yy ,s zz ,s xy ,s yz ,s xz ),…,A n (s xx ,s yy ,s zz ,s xy ,s yz ,s xz ). Among them, x, y, z are the directions of the three coordinate axes;

[0045] 2. For the above 6n known stress values, construct a 1D array in a certain order. Taking the order of measuring point numbers and the default order of components in step 1 as an example, the constructed stress measurement value array is:

[0046]

[0047] 3. Artificial boundary surface division of 3D model: The artificial boundary of 3D model includes 1 bottom surface and 4 side surfaces. According to the surface normal vector principle, the bottom surface is named z surface, and the four side surfaces are 2 x surfaces and 2 y surfaces. When applying boundary conditions, the z surface adopts normal constraint. The two x surfaces adopt one side to apply boundary force load and the other side to apply normal constraint, and the same is true for the two y surfaces;

[0048] 4. In the previous step of applying the boundary force load, B should be constructed 1 , B 2 , …, B 6n There are a total of 6n mutually linearly independent boundary conditions to ensure that the subsequent linear equations can be solved. The definition of linear independence of boundary conditions is as follows: the stress field generated by any boundary condition cannot be expressed as a linear combination of the stress fields generated by the remaining 6n-1 boundary conditions. Figure 1 As shown;

[0049] 5. Calculate the stress under unit boundary conditions. For any boundary condition B i , i = 1, 2, ..., 6n, at the boundary C i If a unit normal pressure P = 1 is applied on the surface, a positive stress k in the three directions of x, y, and z will be generated at the first measuring point. 1 xx , k 1yy , k 1 zz and the corresponding shear stress k 1 xy , k 1 yz , k 1 xz , and then 6 corresponding stress components are generated at each of the n test points;

[0050] 6. Construct the boundary stiffness matrix. For all 6n boundary conditions, construct the overall boundary stiffness matrix K;

[0051] 7. Solve the linear combination of boundary conditions. Assuming that the linear combination of 6n boundary conditions and the superposition of the self-weight stress field G satisfy the measured values ​​of the existing ground stress test points, we have:

[0052] S=G+Ka,

[0053] Among them, a=(a 1 , a 2 , …, a 6n ),but:

[0054] a=K -1 (SG),

[0055] The load boundary condition B obtained by the final inversion can be written as:

[0056]

Claims

1. The inversion method based on the boundary load of the ground stress field is characterized by: The inversion method is based on the boundary load principle. Based on the ground stress value measured on site, a stress measurement array is constructed. A unit boundary force load is applied in the three-dimensional model and the stress value at the measuring point is calculated. Then, the overall boundary stiffness matrix is ​​constructed based on the stress value at the measuring point. Finally, the linear combination under the boundary conditions is solved so that the calculated stress value at the measuring point is equal to the measured value to complete the inversion of the boundary load of the ground stress field. The stress combination of the boundary conditions can be written as the following expression: In the above formula, a i is the coefficient to be determined, B i For the local boundary C i The unit distributed force load applied on the surface, n is the number of ground stress test points.

2. The inversion method based on boundary load of geostress field according to claim 1, characterized in that: When testing the ground stress value on site, the following steps are followed: First, carry out ground stress test on n points to obtain the measured stress arrays A1, A2, ..., A n , each measured stress array contains 6 stress components, written as A1(s xx ,s yy ,s zz ,s xy ,s yz ,s xz )、A2(s xx ,s yy ,s zz ,s xy ,s yz ,s xz ),…,A n (s xx ,s yy ,s zz ,s xy ,s yz ,s xz ), where x, y, and z are the three coordinate axis directions to complete the field test of the ground stress value.

3. The inversion method based on boundary load of geostress field according to claim 2 is characterized in that: When the measured geostress parameters are constructed into a one-dimensional array in a specified order, the stress measurement value array is constructed according to the following formula based on the measurement point number order and the component default order:

4. The inversion method based on boundary load of geostress field according to claim 1, 2 or 3, characterized in that: Before applying boundary force load in the 3D model, the artificial boundary surface of the 3D model needs to be divided into regions, and then the boundary force load can be applied. The specific conditions and process are as follows: The artificial boundary of the three-dimensional model includes 1 bottom surface and 4 side surfaces. According to the surface normal vector principle, the bottom surface is named z surface, and the four side surfaces are 2 x surfaces and 2 y surfaces. When applying boundary conditions, the z surface adopts normal constraint, and the two x surfaces and the two y surfaces each adopt one side to apply boundary force load and one side to apply normal constraint. When dividing the artificial boundary surface of the three-dimensional model into regions, the two surfaces to which the boundary force load is applied are divided into 6n regions, which are recorded as C1, C2, C3, ..., C 6n .

5. The inversion method based on boundary load of geostress field according to claim 4 is characterized in that: When applying boundary force loads in a three-dimensional model, it is necessary to construct B1, B2, ..., B 6n There are 6n linearly independent boundary conditions in total. The definition of linear independence of boundary conditions is that the stress field generated by any boundary condition cannot be expressed as a linear combination of the stress fields generated by the other 6n-1 boundary conditions.

6. The inversion method based on boundary load of geostress field according to claim 5 is characterized in that: The stress under unit boundary force load is written as, For any boundary condition B i , i = 1, 2, ..., 6n, at the boundary C i If a unit normal pressure P = 1 is applied on the surface, a positive stress k in the three directions of x, y, and z will be generated at the first measuring point. 1 xx , k 1 yy , k 1 zz and the corresponding shear stress k 1 xy , k 1 yz , k 1 xz , and then 6 corresponding stress components are generated at each of the n test points.

7. The inversion method based on boundary load of geostress field according to claim 6 is characterized in that: When constructing the overall boundary stiffness matrix, it is constructed according to the following formula: K=[K1 K2...K 6n ]。 8. The inversion method based on boundary load of geostress field according to claim 7 is characterized in that: When solving the linear combination of boundary conditions, the following steps are followed: Assuming that the linear combination of 6n boundary conditions and the superposition of the self-weight stress field G satisfy the measured values ​​of the existing geostress test points, then S = G + Ka, where a = (a1, a2, ..., a 6n ), then a=K- 1 (SG), the load boundary condition B obtained by inversion is:

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