Numerical inversion method of nonlinear stress field

Abstract

This invention discloses a numerical inversion method for nonlinear stress fields, comprising: selecting a study area and constructing a three-dimensional geological model; discretizing the boundary surface of the three-dimensional geological model into multiple surface elements, assigning a nonlinear variation coefficient to each surface element to generate the nonlinear variation coefficient of the model boundary surface; determining the stress components with significant influence on the study area based on measured geostress values ​​as linear boundary conditions applied to the model; adjusting the nonlinear coefficients of the linear boundary conditions to obtain nonlinear boundary conditions; determining the calculated stress component values ​​at measured points under preset working conditions based on the nonlinear boundary conditions; determining the regression coefficients for each preset working condition using the principle of linear superposition and the least squares method based on the measured and calculated stress component values; and generating a nonlinear geostress field based on the nonlinear boundary conditions and regression coefficients and a numerical calculation model. This method achieves the loading of nonlinear stress boundaries, thereby determining the optimal nonlinear geostress field.

Description

Technical Field

[0001] This application relates to the field of geotechnical engineering technology, and in particular to a numerical inversion method for nonlinear stress fields. Background Technology

[0002] The formation of the initial geostress field is highly complex, influenced by multiple factors. In practice, the measured geostress values ​​gradually increase with burial depth, exhibiting fluctuations or nonlinear characteristics. Existing geostress inversion methods consider linear boundary conditions, which do not reflect the actual geostress distribution in engineering sites, resulting in low accuracy of geostress inversion results. Summary of the Invention

[0003] To address the aforementioned deficiencies in existing technologies, this invention provides a numerical simulation inversion method for non-uniform geostress fields. This method solves the problem that linear boundary conditions do not adequately characterize the differences in geostress distribution at the model boundary, thus improving the accuracy of geostress field inversion. The calculated results are consistent with the geostress distribution in engineering applications.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows:

[0005] This scheme provides a numerical simulation inversion method for non-uniform stress fields, including the following steps:

[0006] S1: Select the research scope and construct a three-dimensional geological model;

[0007] S2: Collect measured ground stress data, perform coordinate transformation on the measured ground stress values, and generate the corresponding measured stress component values ​​in the calculation coordinate system;

[0008] S3: Determine the constitutive model used for inversion of the geostress field, and determine the rock mechanics parameters of the three-dimensional geological model through rock mechanics tests;

[0009] S4: Generate nonlinear boundary conditions, including the following steps:

[0010] S41: Discretize the model boundary into tiny surface elements;

[0011] S42: Assigns a progressively changing coefficient to each tiny surface element;

[0012] S43: Obtain the nonlinear variation coefficients of the model boundary;

[0013] S5: Determine the stress components that have a significant impact on the study area based on the measured values ​​of geostress as the linear boundary conditions to be applied to the model;

[0014] S6: Adjust the nonlinear coefficients of the linear boundary conditions to obtain the nonlinear boundary conditions;

[0015] S7: Calculate the stress components at the measured points under each working condition using nonlinear boundary conditions;

[0016] S8: Based on the measured and calculated values ​​of stress components, the regression coefficients for each working condition are determined using the principle of linear superposition and the least squares method.

[0017] S9: Perform a rationality test on the regression coefficients for each working condition. If the obtained regression coefficients do not conform to the actual situation, proceed to step S4 to adjust the nonlinear variation coefficients and recalculate until the final reasonable regression coefficients are obtained. Otherwise, proceed to step S10.

[0018] S10: Multiply the nonlinear boundary conditions by the final reasonable weight value and substitute them into the model calculation to obtain the irregular stress field of the overall model.

[0019] Preferably, in step S2, the measured values ​​of geostress are transformed into coordinates. Since the principal stresses at the measured points have a certain deflection angle from the coordinate axes of the established calculation coordinate system, and also for ease of calculation, it is sometimes necessary to convert the principal stresses into the six stress components in the calculation coordinate system. Specifically, using the formulas of elasticity, the formulas for converting the principal stresses into the six stress components in the calculation coordinate system are as follows:

[0020]

[0021] In the formula, α is the measured principal stress tilt angle, with elevation being + and depression being -; β is the measured principal stress azimuth angle, with true north and clockwise rotation being positive; L i M i and N i For σ i The direction cosines about the x, y, and z axes;

[0022]

[0023]

[0024] In the formula, σ x σ y σ z τ xy τ yz and τ xz There are six stress components.

[0025] Preferably, in step S5, the linear boundary conditions applied to the model are obtained, and the geostress field within the calculation area is regarded as a linear superposition of the self-weight stress field and the tectonic stress field. Through decomposition, the self-weight stress field and the tectonic stress field are simulated, and finally the geostress field is formed based on the superposition principle.

[0026] Preferably, in step S8, the regression coefficients for each working condition are determined based on the measured and calculated values ​​of the stress components, using the principle of linear superposition and the least squares method. Specifically, using the principle of linear superposition, the regression model expression for the initial stress field is as follows:

[0027]

[0028] In the formula, This represents the measured value of the j-th stress component at the k-th measuring point; n represents the total number of preset working conditions; C i (i = 1, 2, ..., n) represents the regression coefficient for the i-th working condition; This represents the calculated value of the j-th stress component at the k-th measuring point under the i-th working condition; ε represents the model error.

[0029] When using the multiple regression method to invert the geostress field, the expression for the sum of squared residuals from the measured and calculated values ​​is as follows:

[0030]

[0031] In the formula, Q is the sum of squared residuals; m represents the total number of measured points; and L represents the total number of stress components.

[0032] According to the least squares method, the sum of squared residuals is minimized, i.e., Q ≤ C. i Taking the partial derivative and setting it to zero, then

[0033] According to equation (2), we obtain information about C. i The normal equations of (i = 1, 2, ..., n) are solved to obtain the regression coefficients for each preset working condition.

[0034] The beneficial effects of this invention are as follows: The numerical inversion method for nonlinear stress fields provided by this invention, based on the concept of differentiation, discretizes the model boundary into small surface elements. Each small surface element is assigned an asymptotic variation coefficient, resulting in the nonlinear variation coefficients of the model boundary. A set of nonlinear variation coefficients is selected to adjust a boundary condition, constructing a nonlinear boundary condition to achieve nonlinear stress boundary loading. Compared with the widely used geostress field inversion methods based on linear boundary conditions (stress boundaries or displacement boundaries), this invention solves the problem that linear boundary conditions do not adequately represent the characteristics of the differential distribution of geostress at the model boundary, improves the accuracy of geostress inversion, and the obtained calculation results conform to the engineering geostress distribution.

[0035] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0036] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 A flowchart of a numerical inversion method for a nonlinear stress field according to an embodiment of the present invention is shown;

[0038] Figure 2 A schematic diagram of a three-dimensional geological model is shown in an embodiment of the present invention;

[0039] Figure 3 A set of nonlinear variation coefficients on the boundary surface perpendicular to the x-axis in an embodiment of the present invention is shown;

[0040] Figure 4 A schematic diagram of the self-weight load boundary conditions in an embodiment of the present invention is shown;

[0041] Figure 5 A schematic diagram of the horizontal x-direction load boundary conditions in an embodiment of the present invention is shown;

[0042] Figure 6 A schematic diagram of the horizontal y-direction load boundary conditions in an embodiment of the present invention is shown;

[0043] Figure 7 This illustrates the schematic diagram of the horizontal shear load boundary conditions in an embodiment of the present invention;

[0044] Figure 8 A flowchart illustrating the creation of nonlinear boundary conditions in an embodiment of the present invention is shown;

[0045] Figure 9 The maximum horizontal principal stress of the overall model in this embodiment of the invention is shown;

[0046] Figure 10 The minimum horizontal principal stress of the overall model in an embodiment of the present invention is shown;

[0047] Figure 11 The vertical principal stress of the overall model in an embodiment of the present invention is shown. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] Example 1:

[0050] like Figure 1 As shown, this invention provides a numerical inversion method for nonlinear geostress fields, which includes the following steps:

[0051] S1: Select the research scope and construct a three-dimensional geological model;

[0052] S2: Collect measured ground stress data, perform coordinate transformation on the measured ground stress values, and generate the corresponding measured stress component values ​​in the calculation coordinate system;

[0053] S3: Determine the constitutive model used for inversion of the geostress field, and determine the rock mechanics parameters of the three-dimensional geological model through rock mechanics tests;

[0054] S4: Generate nonlinear boundary conditions, including the following steps:

[0055] S41: Discretize the model boundary into tiny surface elements;

[0056] S42: Assigns a progressively changing coefficient to each tiny surface element;

[0057] S43: Obtain the nonlinear variation coefficients of the model boundary;

[0058] S5: Determine the stress components that have a significant impact on the study area based on the measured values ​​of geostress as the linear boundary conditions to be applied to the model;

[0059] S6: Adjust the nonlinear coefficients of the linear boundary conditions to obtain the nonlinear boundary conditions;

[0060] S7: Calculate the stress components at the measured points under each working condition using nonlinear boundary conditions;

[0061] S8: Based on the measured and calculated values ​​of stress components, the regression coefficients for each working condition are determined using the principle of linear superposition and the least squares method.

[0062] S9: Perform a rationality test on the regression coefficients for each working condition. If the obtained regression coefficients do not conform to the actual situation, proceed to step S4 to adjust the nonlinear variation coefficients and recalculate until the final reasonable regression coefficients are obtained. Otherwise, proceed to step S10.

[0063] S10: Multiply the nonlinear boundary conditions by the final reasonable weight value and substitute them into the model calculation to obtain the irregular stress field of the overall model.

[0064] Preferably, in step S2, the measured values ​​of geostress are transformed into coordinates. Since the principal stresses at the measured points have a certain deflection angle from the coordinate axes of the established calculation coordinate system, and also for ease of calculation, it is sometimes necessary to convert the principal stresses into the six stress components in the calculation coordinate system. Specifically, using the formulas of elasticity, the formulas for converting the principal stresses into the six stress components in the calculation coordinate system are as follows:

[0065]

[0066] In the formula, α is the measured principal stress tilt angle, with elevation being + and depression being -; β is the measured principal stress azimuth angle, with true north and clockwise rotation being positive; L i M i and N i For σ i The direction cosines about the x, y, and z axes;

[0067]

[0068] In the formula, σ x σ y σ z τ xy τ yz and τ xz There are six stress components.

[0069] Preferably, in step S5, the linear boundary conditions applied to the model are obtained, and the geostress field within the calculation area is regarded as a linear superposition of the self-weight stress field and the tectonic stress field. Through decomposition, the self-weight stress field and the tectonic stress field are simulated, and finally the geostress field is formed based on the superposition principle.

[0070] Preferably, in step S8, the regression coefficients for each working condition are determined based on the measured and calculated values ​​of the stress components, using the principle of linear superposition and the least squares method. Specifically, using the principle of linear superposition, the regression model expression for the initial stress field is as follows:

[0071]

[0072] In the formula, This represents the measured value of the j-th stress component at the k-th measuring point; n represents the total number of preset working conditions; C i (i = 1, 2, ..., n) represents the regression coefficient for the i-th working condition; This represents the calculated value of the j-th stress component at the k-th measuring point under the i-th working condition; ε represents the model error.

[0073] When using the multiple regression method to invert the geostress field, the expression for the sum of squared residuals from the measured and calculated values ​​is as follows:

[0074]

[0075] In the formula, Q is the sum of squared residuals; m represents the total number of measured points; and L represents the total number of stress components.

[0076] According to the least squares method, the sum of squared residuals is minimized, i.e., Q ≤ C. i Taking the partial derivative and setting it to zero, then

[0077] According to equation (2), we obtain information about C. i The normal equations of (i = 1, 2, ..., n) are solved to obtain the regression coefficients for each preset working condition.

[0078] In a practical example of the present invention:

[0079] Taking a mining project as an example, the applicability of the method of the present invention is discussed.

[0080] Based on the geological report, a three-dimensional geological model was established, encompassing the entire area affected by the project and taking into full account the regional tectonic development. The orientations of the X, Y, and Z coordinates are as follows: the X-axis runs along the strike of the ore body, the Y-axis dips the ore body, and the Z-axis points vertically upwards. The three-dimensional geological model is shown below. Figure 2 As shown.

[0081] Measured in-situ stress data for the mine were collected. Analysis of the measured values ​​showed good consistency in the direction of the maximum principal stress, aligning with the regional maximum principal stress direction NWW. Based on the conversion formula between principal stress and total stress components, the measured principal stress values ​​for the engineering area were converted into corresponding stress components for the numerical calculation model. Table 1 shows the three-dimensional principal stresses at the collected measured points, and Table 2 shows the in-situ stress components at the measured points in the calculation coordinate system. The model coordinate origin is (0,0,0), the relative coordinates of measuring point 1 are (900,1150,-860), and the relative coordinates of measuring point 2 are (1080,1311,-1160).

[0082] Table 1

[0083]

[0084] Table 2

[0085] Measurement point number <![CDATA[σ x (Mpa)]]> <![CDATA[σ y (Mpa)]]> <![CDATA[σ z (Mpa)]]> <![CDATA[τ xy (Mpa)]]> <![CDATA[τ yz (Mpa)]]> <![CDATA[τ xz (Mpa)]]> Measurement point 1 -14.5 -32.4 -21.7 0.127 1.69 -1.49 Measurement point 2 -25.4 -40.7 -29.1 4.28 3.02 -0.687

[0086] An elastic constitutive model was selected as the constitutive model for the inversion of the geostress field in this project. Table 3 shows the rock mass mechanical parameters corresponding to different rock mass types in the three-dimensional geological model.

[0087] Table 3

[0088] Rock mass type Elastic modulus E / Gpa Poisson's ratio <![CDATA[Density kg / m 3 > Ore body 1 28.54 0.28 2690 Ore body 2 26.87 0.28 2690 Surrounding rock 18.76 0.29 2650

[0089] This application, based on the concept of differential calculus, discretizes the boundary surface of a three-dimensional geological model into multiple micro-element elements, assigning an asymptotic variation coefficient to each element to obtain the nonlinear variation coefficients of the model boundary surface. In this embodiment, the size of each micro-element is set to 50m × 50m, and 40, 60, and 33 micro-element elements are divided along the x-axis, y-axis, and z-axis of the three-dimensional geological model, respectively. Ten sets of nonlinear variation coefficients are generated for each boundary surface. The reason for choosing to generate ten sets of nonlinear variation coefficients is that it was found in trial calculations that using ten sets of nonlinear coefficients can precisely simulate the nonlinear characteristics of the geostress field. Figure 3 As shown, this is a set of nonlinear variation coefficients on the boundary surface perpendicular to the x-axis.

[0090] Based on measured in-situ stress values, the stress components with the greatest impact on the study area are determined as linear boundary conditions applied to the model. The in-situ stress field within the computational area is considered as a linear superposition of the self-weight stress field and the tectonic stress field. Through decomposition, the self-weight stress field and the tectonic stress field are simulated, and finally, the in-situ stress field is formed based on the superposition principle. The following four boundary conditions are selected as influencing factors of the in-situ stress field of this project: Self-weight stress field: Considering the unit weight of the rock mass, the stress field under self-weight is calculated, and the boundary conditions are as follows: Figure 4 As shown. Tectonic stress field: (1) East-west horizontal uniform compression tectonic movement (along the x-axis), as shown. Figure 5 For example; (2) North-south horizontal uniform compression tectonic movement (along the y-axis), such as Figure 6 As shown; (3) Uniform shearing structural motion in the horizontal plane (xy and yz planes), such as Figure 7 As shown.

[0091] Nonlinear boundary conditions are obtained by adjusting the nonlinear coefficients of linear boundary conditions. A set of nonlinear variation coefficients is selected to adjust a linear boundary condition; that is, the nonlinear variation coefficient of the micro-element at the same location is multiplied by the linear stress component value to obtain the nonlinear stress component value at each micro-element. The same method is used to obtain the nonlinear boundary conditions for each boundary of the numerical calculation model. Ten sets of nonlinear variation coefficients are selected to adjust seven types of linear structural stress boundary conditions, resulting in 70 nonlinear boundary conditions. For example... Figure 8 The diagram shown illustrates the flowchart for creating nonlinear boundary conditions.

[0092] Nonlinear boundary conditions were used to calculate the stress components at the measured points under each working condition. Since the collected measured in-situ stress values ​​are secondary stress values ​​caused by the disturbance of mining I# ore body 1, it is necessary to excavate I# ore body 1 first and then perform inversion of the in-situ stress field.

[0093] Based on the measured and calculated values ​​of stress components, the regression coefficients for each working condition are determined using the principle of linear superposition and the least squares method.

[0094] By testing the rationality of the regression coefficients for each working condition, it was found that the obtained regression coefficients are consistent with the actual situation.

[0095] The nonlinear boundary conditions used are multiplied by the final, reasonable weight values ​​and substituted into the model calculation to obtain the overall irregular stress field of the model. For example... Figures 9 to 11 The diagram shows the maximum horizontal principal stress contour plot, minimum horizontal principal stress contour plot, and vertical principal stress contour plot of the overall model's geostress field. Table 4 shows the measured geostress values, regression values, and relative errors at the measuring points in the calculation coordinate system. The multiple correlation coefficient R0 of the regression values ​​is also shown. 2 =0.9997, indicating that the regression formula has a good correlation.

[0096] Table 4

[0097]

[0098] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A numerical simulation inversion method for non-uniform stress fields, characterized in that, Includes the following steps: S1: Select the research scope and construct a three-dimensional geological model; S2: Collect measured ground stress data, perform coordinate transformation on the measured ground stress values, and generate the corresponding measured stress component values ​​in the calculation coordinate system; S3: Determine the constitutive model used for inversion of the geostress field, and determine the rock mechanics parameters of the three-dimensional geological model through rock mechanics tests; S4: Generate nonlinear boundary conditions, including the following steps: S41: Discretize the boundaries of the three-dimensional geological model into tiny surface elements; S42: Assigns a progressively changing coefficient to each tiny surface element; S43: Obtain the nonlinear variation coefficients of the model boundary; S5: Determine the stress components that have a significant impact on the study area based on the measured values ​​of geostress as the linear boundary conditions to be applied to the model; S6: Adjust the nonlinear coefficients of the linear boundary conditions to obtain the nonlinear boundary conditions; S7: Calculate the stress components at the measured points under each working condition using nonlinear boundary conditions; S8: Based on the measured and calculated values ​​of stress components, the regression coefficients for each working condition are determined using the principle of linear superposition and the least squares method. S9: Perform a rationality test on the regression coefficients for each working condition. If the obtained regression coefficients do not conform to the actual situation, proceed to step S4 to adjust the nonlinear variation coefficients and recalculate until the final reasonable regression coefficients are obtained. Otherwise, proceed to step S10. S10: Multiply the nonlinear boundary conditions by the final reasonable weight value and substitute them into the model calculation to obtain the irregular stress field of the overall model.

2. The numerical simulation and inversion method for non-uniform stress fields according to claim 1, characterized in that, In step S2, coordinate transformation is performed on the measured values ​​of geostress. Since the principal stresses at the measured points have a certain deflection angle from the coordinate axes of the established calculation coordinate system, and also for ease of calculation, it is sometimes necessary to convert the principal stresses into the six stress components in the calculation coordinate system. Specifically, using the formulas of elasticity, the formulas for converting the principal stresses into the six stress components in the calculation coordinate system are as follows: （1） In the formula, the subscript i marks the principal stress, and its value of 1, 2, and 3 corresponds to the maximum principal stress, intermediate principal stress, and minimum principal stress, respectively. The measured principal stress inclination angles are positive (elevation) and negative (depression). To measure the azimuth of the principal stresses, clockwise rotation from true north is taken as positive. , and They are respectively The direction cosines about the x, y, and z axes; （2） In the formula, , , , , and There are six stress components.

3. The numerical simulation and inversion method for non-uniform stress fields according to claim 1, characterized in that, In step S5, the linear boundary conditions applied to the model are obtained. The geostress field in the calculation area is regarded as a linear superposition of the self-weight stress field and the tectonic stress field. Through decomposition, the self-weight stress field and the tectonic stress field are simulated. Finally, the geostress field is formed based on the superposition principle.

4. The numerical simulation and inversion method for non-uniform stress fields according to claim 1, characterized in that, In step S8, based on the measured and calculated values ​​of the stress components, the regression coefficients for each working condition are determined using the principle of linear superposition and the least squares method. Specifically, using the principle of linear superposition, the regression model expression for the initial stress field is as follows: （3） In the formula, This represents the measured value of the j-th stress component at the k-th measuring point; n represents the total number of preset working conditions. (i=1,2,......,n) represents the regression coefficients for the i-th working condition; This represents the calculated value of the j-th stress component at the k-th measuring point under the i-th working condition; Indicates model error; When using the multiple regression method to invert the geostress field, the expression for the sum of squared residuals from the measured and calculated values ​​is as follows: （4） In the formula, Q is the sum of squared residuals; m represents the total number of measured points; and L represents the total number of stress components. According to the least squares method, the sum of squared residuals is minimized, i.e., Q ≤ C. i Taking the partial derivative and setting it to zero, then (i=1, 2, ..., n); According to equation (2), we obtain information about C. i Solve the system of normal equations (i=1, 2, ..., n) to obtain the regression coefficients for each preset working condition.

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