Method for generating stress field inversion of a grid of antagonists

Abstract

The application provides a method for generating an in-situ stress field inversion of a grid, based on the superiority of GAN data enhancement, deep learning of the distribution of lateral stress coefficients, GAN analysis of lateral stress coefficients, fine tuning of ancient lateral stress coefficients by the introduced generative adversarial network, optimization of the present in-situ stress field, and meeting the needs of engineering analysis. The advantages of uniform design can greatly reduce the number of tests and keep the training samples uniformly dispersed. After each uniform design test, GAN training can be performed, the data of the test points are input into the GAN, and the optimized lateral stress coefficients can be obtained, the optimized ancient in-situ stress field can be obtained by calculation, and the present in-situ stress field can be obtained after nonlinear elastic-plastic excavation simulation.

Description

Technical Field

[0001] The present invention relates to the field of rock and soil mechanics, and in particular to a ground stress field inversion method for generating an adversarial grid. Background Art

[0002] Quantitative research on geostress magnitude involves, on the one hand, field measurement and monitoring, and, on the other hand, inversion analysis and calculation of the initial geostress field based on limited observational data, to determine the initial geostress values ​​and distribution patterns for the entire project area. Field observation of geostress can provide relatively accurate geostress data at the measurement points. With the advancement of science and technology, observation equipment and methods are becoming increasingly advanced and accurate. However, the major drawback of field observation is its high cost. Therefore, accurately predicting and analyzing the geostress distribution across the entire project area based on limited measurement points is of paramount importance. Summary of the Invention

[0003] The main purpose of the present invention is to provide a method for inverting a geostress field by generating an adversarial grid, so as to solve the problems in the above-mentioned background technology.

[0004] To solve the above technical problems, the technical solution adopted by the present invention is: based on the superiority of GAN data enhancement, deep learning is performed on the distribution of lateral stress coefficients. The process of using GAN to analyze the lateral stress coefficients is as follows:

[0005] S1. From the field survey data, statistical analysis is performed on the stress values ​​of the measured points, and effective measuring points are selected to determine the approximate lateral stress coefficient according to formula (1):

[0006] (1);

[0007] Among them, α i and b i is the regression factor, k i is the lateral stress coefficient of the six stress components, H is the burial depth;

[0008] S2. Based on the uniform design experiment, α in formula (1) i and b i Set the floating range, so you can design multiple models with different α i and b i Paleo-stress field of the value;

[0009] S3. Based on multiple paleo-stress fields, using FLΑC 3D Excavate the stratum to obtain multiple current initial stress fields, and determine the lateral stress coefficient at the current burial depth;

[0010] S4, measuring point coordinates, current burial depth, current lateral stress coefficient and ancient regression factor are all used as real data samples; after data normalization, the data samples are input into GAN for training;

[0011] S5. After training in GAN, the optimized regression factor α of the paleolateral stress coefficient can be obtained. i and b i ; Then the optimized paleo-stress field is constructed by formula (2);

[0012] (2);

[0013] where σ1–σ6 are the stress components σ x , σ y , σ z , τ yz , τ zx and τ xy ;k i is the lateral stress coefficient of the six stress components; H is the burial depth; γ is the bulk density;

[0014] S6. Excavation of the optimized ancient geostress field can obtain the optimized current initial geostress field.

[0015] Preferably, the goal of GAN is to estimate and predict the distribution of acquired data and generate new data from the same distribution using a generator G, which converts random variables z into new data that can be forged by continuously learning the probability distribution of real data. The discriminator D is a binary classifier used to distinguish whether the input data is real or generated data.

[0016] During training, the two networks are enhanced simultaneously through mutual competition, forming a dynamic game process until the Nash equilibrium is reached. Both the generator and the discriminator can be designed in combination with the current deep neural network.

[0017] Preferably, the calculation process of GAN is a binary minimax game, and the objective function can be defined as:

[0018] (3);

[0019] Among them, V(D,G) is the cross entropy loss of the two categories, P dαtα(x) is the true data distribution, P g(z) is the random variable distribution, G (z) It is a generator based on random variables, and E(·) represents the calculated expected value;

[0020] When P dαtα = P gThe global optimal solution is reached when the loss functions of the generator and discriminator of GAN are expressed as log(D(G(z))) and log(D(x)) + log(1-D(G(z))).

[0021] Preferably, based on formula (1) and the measured values ​​of ground stress, the approximate lateral stress coefficient k of different stress components can be obtained: i , k i By introducing Equation (2), we can obtain an approximate ancient stress field;

[0022] Based on the approximate paleo-stress field, the present stress field was obtained by excavating the paleo-strata layer by layer through numerical simulation.

[0023] Preferably, the specific method of step S2 is: for a ground stress measurement point, it has 6 stress components, corresponding to 6 pairs of regression factors α i and b i , using uniform design experiment, design different α i and b i Various combinations of values, α i and b i The measurement point parameters under different combinations are:

[0024] (4);

[0025] (5);

[0026] (6);

[0027] (7);

[0028] (8);

[0029] (9);

[0030] Where x and y are the coordinate vectors of the measured point in the horizontal plane, n is the number of measurement points, and H p is the depth vector of the current measured point, k j is the lateral stress coefficient matrix of the current measuring point, j is the number of uniform design tests, α j and b j is the stress component σ at the ancient measuring point x ,σ y ,σ z ,τ yz ,τ zx and τ xy The regression factor matrix of .

[0031] Preferably, after each uniform design experiment, GAN training is performed, and the real data sample input to GAN can be expressed as:

[0032] (10);

[0033] After the training is completed, the data of the measurement points are input into GAN to obtain the optimized α i and b i The optimized paleo-stress field can be calculated by formula (1), and then the present-day stress field can be obtained after nonlinear elastic-plastic excavation simulation.

[0034] Preferably, the rock mass is divided into hexahedral units. Due to the existence of faults, some rock mass units are cut by faults. These units contain both rock mass and faults, forming composite units.

[0035] A set of mechanical parameters is assigned to a unit. Therefore, the mechanical parameters of the composite unit with both rock mass and fault need to be equivalent. The local coordinate system (x´y´z´) is established on the fault plane of the composite unit, and the composite unit is simplified into a transversely isotropic equivalent unit with layered distribution.

[0036] H k is the unit layer thickness, which can be expressed as:

[0037] (11);

[0038] Where subscript k is equal to 1 or 2, representing the parameters of rock mass and fault, respectively, V k is the volume of the rock mass or fault, and A is the area of ​​the contact surface between the rock mass and the fault.

[0039] Preferably, for the z' direction, the deformation and stress of the equivalent element are:

[0040] (12);

[0041] in, , σ v1 and σ v2 are the stresses applied to the equivalent unit, rock mass and fault in the z' direction, is the equivalent elastic modulus in the z´ direction;

[0042] Based on formula (12), the equivalent elastic modulus in the z´ direction is:

[0043] (13).

[0044] Preferably, for the x' and y' directions, assuming that the elongation of the rock mass and the fault in the equivalent unit is equal, then

[0045] (14);

[0046] wherein, , ε h1 and ε h2 are the strains of the equivalent element, the rock mass and the fault in the x' and y' directions, respectively, , σ h1 and σ h2 are the stresses applied in the x' and y' directions on the equivalent element, the rock mass and the fault, respectively,

[0047] Equation (14) can be written as:

[0048] (15);

[0049] According to equation (14) and equation (15), the equivalent elastic modulus is:

[0050] (16);

[0051] In combination with equation (14) and (16), the equivalent Poisson's ratio can be expressed as

[0052] (17).

[0053] The application provides a method for generating a stress field inversion of a grid of in-situ stresses, and introduces a generative adversarial network to fine-tune an ancient lateral stress coefficient, optimize a present in-situ stress field, and meet the needs of engineering analysis. The advantages of uniform design can greatly reduce the number of tests and keep the training samples uniformly dispersed. After each uniform design test, the training of the GAN can be performed, and after the training is completed, the data of the measuring points are input into the GAN to obtain the optimized lateral stress coefficient. The optimized ancient in-situ stress field can be obtained by calculation, and the present in-situ stress field can be obtained after nonlinear elastic-plastic excavation simulation. BRIEF DESCRIPTION OF DRAWINGS

[0054] The application will be further described below in combination with the drawings and examples:

[0055] Figure 1 is the calculation process of the GAN of the application;

[0056] Figure 2 is a schematic diagram of a fault-cutting rock mass composite element of the application;

[0057] Figure 3 is a schematic diagram of a fault-cutting rock mass equivalent element of the application;

[0058] Figure 4 is a schematic diagram of an ancient stratum denudation process of the application. DETAILED DESCRIPTION

[0059] like Figures 1-4 As shown in the figure, the inversion method of the geostress field using the generated adversarial grid shows that the ancient area was gradually shaped into steep valleys along with valley erosion, surface denudation and other geological processes. During the long-term unloading process, the rock mass continuously adjusts stress and strain to form a new local stress field. Therefore, for the inversion of the initial geostress field today, the method of excavating the ancient strata from top to bottom can be used to simulate the gradual formation of valley landform features and the release of stress. The ancient stratum denudation process is as follows: Figure 4 , and make the following assumptions:

[0060] (1) The ancient surface was a planation surface with no obvious ups and downs;

[0061] (2) The paleo-geo-stress field is composed of the self-weight stress field and the tectonic stress field, and the tectonic movement was completed in ancient times;

[0062] (3) The current geostress field evolved from the ancient stress field. Surface erosion, river erosion, etc. have gradually formed under the action of geology.

[0063] The inversion of paleostress field based on lateral stress coefficient is expressed as follows:

[0064] (2)

[0065] where σ1–σ6 are the stress components σ x , σ y , σ z , τ yz , τ zx and τ xy ;k i is the lateral stress coefficient of the six stress components; H is the burial depth; γ is the bulk density;

[0066] The current geostress field is influenced by topographic relief and the physical and mechanical properties of rock masses, resulting in significant variations in the geostress coefficient at different locations. However, in ancient times, the topography was less undulating and the geological structure was less complex. Therefore, it is more appropriate to use the lateral stress coefficient to invert the ancient geostress field.

[0067] The lateral stress coefficient at every point in the rock mass is a fixed value, which means that the stress component increases linearly with increasing burial depth. However, for deep-buried projects, the lateral stress coefficient is not linearly related to burial depth. Based on global measured ground stress data, Brown and Hoek found that the relationship between the lateral stress coefficient and burial depth is:

[0068]

[0069] Among them, σH , σ h and σ v are the maximum principal stress, minimum principal stress and vertical principal stress in the horizontal plane, respectively.

[0070] Through statistical analysis of the lateral stress coefficients of different rock masses in China, a conclusion similar to the above formula was obtained. Therefore, the relationship between the lateral stress coefficient and the burial depth is:

[0071] (1)

[0072] Among them, α i and b i is the regression factor, k i is the lateral stress coefficient of the six stress components, H is the burial depth;

[0073] Based on formula (1) and the measured values ​​of ground stress, the approximate lateral stress coefficient k of different stress components can be obtained: i . i By introducing equation (2), we can obtain an approximate ancient stress field.

[0074] Example 2

[0075] Based on the approximate paleostress field, the present-day stress field can be derived by excavating the ancient strata layer by layer through numerical simulation. However, since the paleostress field is an approximate estimate, the present-day stress field may contain significant errors. To address this issue, this example introduces a generative adversarial network (GAN) to fine-tune the ancient lateral stress coefficients and optimize the present-day stress field to meet the needs of engineering analysis.

[0076] GAN consists of a generator and a discriminator trained on an adversarial learning mechanism, such as Figure 1 As shown in the figure, the goal of GAN is to estimate and predict the distribution of acquired data and generate new data from the same distribution using the generator G. The generator G transforms the random variable z into new data that can be forged by continuously learning the probability distribution of real data. The discriminator D is a binary classifier used to distinguish whether the input data is real or generated. During training, the two networks compete with each other and are enhanced simultaneously, forming a dynamic game process until a Nash equilibrium is reached. Both the generator and the discriminator can be designed in combination with current deep neural networks. The computational process of GAN can be summarized as a binary minimax game, and the objective function can be defined as:

[0077] (3)

[0078] Among them, V(D,G) is the cross entropy loss of the two categories, P dαtα(x)is the true data distribution, P g(z) is the random variable distribution, G (z) is a generator based on random variables, E(·) represents the calculated expected value; when P dαtα = P g The global optimal solution is reached when the loss functions of the generator and discriminator of GAN are expressed as log(D(G(z))) and log(D(x)) + log(1-D(G(z))).

[0079] Example 3

[0080] In this example, based on the superiority of GAN data enhancement, deep learning is performed on the distribution of lateral stress coefficients. The process of using GAN to analyze the lateral stress coefficients is as follows:

[0081] S1. From the field survey data, statistical analysis is performed on the stress values ​​of the measured points, and effective measuring points are selected to determine the approximate lateral stress coefficient according to formula (1):

[0082] (1)

[0083] Among them, α i and b i is the regression factor, k i is the lateral stress coefficient of the six stress components, H is the burial depth;

[0084] S2. Based on the uniform design experiment, α in formula (1) i and b i By setting the floating range, multiple paleo-stress fields with different αi and bi values ​​can be designed;

[0085] S3. Based on multiple paleo-stress fields, FLAC3D is used to excavate the strata to obtain multiple present-day initial stress fields, thereby determining the lateral stress coefficient at the present-day burial depth;

[0086] S4, measuring point coordinates, current burial depth, current lateral stress coefficient and ancient regression factor are all used as real data samples; after data normalization, the data samples are input into GAN for training;

[0087] S5. After training in GAN, the optimized regression factor α of the paleolateral stress coefficient can be obtained. i and b i ; Then the optimized paleo-stress field is constructed by formula (2);

[0088] (2)

[0089] where σ1–σ6 are the stress components σ x , σ y , σz , τ yz , τ zx and τ xy ; k i is the lateral stress coefficient of 6 stress components; H is the buried depth; γ is the bulk density;

[0090] S6, the optimized ancient geostress field is excavated, and an optimized present initial geostress field can be obtained.

[0091] For the selection of α i and b i values, uniform design test is adopted. The advantage of uniform design is that it can greatly reduce the number of tests while keeping the training samples uniformly dispersed. In the uniform design test, various combinations of α i and b i i values can be designed. The measured point parameters under different combinations of α i and b i are as follows:

[0092] (4)

[0093] (5)

[0094] (6)

[0095] (7)

[0096] (8)

[0097] (9)

[0098] wherein x and y are the coordinate vectors of the measured point in the horizontal plane, n is the number of measurement points, H p is the buried depth vector of the present measured point, k j is the lateral stress coefficient matrix of the present measurement point, j is the number of uniform design tests, α j and b j are the regression factor matrices of the stress components σ x , σ y , σ z , τ yz , τ zx and τ xy of the ancient measurement point.

[0099] After each uniform design test, the training of GAN is carried out. The real data samples input to the GAN can be expressed as:

[0100] (10)

[0101] After the training is completed, the data of the measurement points are input into GAN to obtain the optimized α i and b i The optimized paleo-stress field can be calculated by formula (1), and then the present-day stress field can be obtained after nonlinear elastic-plastic excavation simulation.

[0102] Example 4

[0103] The parameters between faults and rock masses are very different. If the influence of faults is not considered in the inversion of the current stress field, large errors will occur. Therefore, before simulating the excavation of ancient strata, the fault parameters should be assigned to the corresponding units. In numerical simulation analysis, they are often simplified to thin units, but faults and underground caves usually do not intersect in an orthogonal form. Due to the limited thickness of the faults and the complex intersection relationship, this method of handling faults may bring difficulties to the mesh generation of the model. In this example, the rock mass is divided into hexahedral units. Due to the existence of faults, some rock mass units are cut by faults. These units contain both rock mass and faults, forming composite units, such as Figure 2 As shown in Figure 2. For a unit, only one set of mechanical parameters can be assigned. Therefore, the mechanical parameters of the composite unit with both rock mass and fault need to be equivalent. The local coordinate system (x´y´z´) established on the fault plane of the composite unit simplifies the composite unit into a layered, transversely isotropic equivalent unit with parameters such as Figure 3 As shown. k is the unit layer thickness, which can be expressed as:

[0104] (11)

[0105] Where subscript k is equal to 1 or 2, representing the parameters of rock mass and fault, respectively, V k is the volume of the rock mass or fault, and A is the area of ​​the contact surface between the rock mass and the fault.

[0106] For the z´ direction, the deformation and stress of the equivalent element are:

[0107] (12)

[0108] in, , σ v1 and σ v2 are the stresses applied to the equivalent unit, rock mass and fault in the z' direction, is the equivalent elastic modulus in the z´ direction;

[0109] Based on formula (12), the equivalent elastic modulus in the z´ direction is:

[0110] . (13)

[0111] For the x' and y' directions, assuming that the elongation of the rock mass and the fault in the equivalent unit is equal, then

[0112] (14)

[0113] in, , ε h1 and ε h2 are the strains of the equivalent unit, rock mass and fault in the x' and y' directions, respectively, , σ h1 and σ h2 are the stresses applied to the equivalent element, rock mass and fault in the x' and y' directions, respectively,

[0114] Formula (14) can be written as:

[0115] (15)

[0116] According to equations (14) and (15), the equivalent elastic modulus is:

[0117] (16)

[0118] Combining equations (14) and (16), the equivalent Poisson's ratio It can be expressed as

[0119] (17).

[0120] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions set forth in the claims, including equivalent alternatives to the technical features of the technical solutions set forth in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. The inversion method of the ground stress field for generating the adversarial grid is as follows: Based on the superiority of GAN data enhancement, deep learning is performed on the distribution of lateral stress coefficients. The process of using GAN to analyze lateral stress coefficients is as follows: S1. From the field survey data, statistical analysis is performed on the stress values ​​of the measured points, and effective measuring points are selected to determine the approximate lateral stress coefficient according to formula (1): （1）； in, α i and b i is the regression factor, k i is the lateral stress coefficient of the six stress components, H is the burial depth; S2. Based on the uniform design experiment, α in formula (1) i and b i Set the floating range, thus designing multiple models with different α i and b i The paleo-stress field of the value; S3, according to multiple paleo-stress fields, using FLΑC 3D Excavate the stratum to obtain multiple current initial stress fields, and determine the lateral stress coefficient at the current burial depth; S4, measuring point coordinates, present-day burial depth, present-day lateral stress coefficient, and ancient regression factor are all taken as real data samples; After data normalization, the data samples are input into GAN for training; S5. After training in GAN, the regression factor α of the optimized paleolateral stress coefficient is obtained. i and b i ; Then the optimized paleo-stress field is constructed by formula (2); （2）； Where σ1 –σ6 are stress components σ x , σ y , σ z , τ yz , τ zx and τ xy ;k i is the lateral stress coefficient of the six stress components; H is the burial depth; γ is the bulk density; S6. Excavation of the optimized ancient geostress field can obtain the optimized current initial geostress field.

2. The inverse method for geostress field using adversarial grid generation according to claim 1, wherein: The goal of GAN is to estimate and predict the distribution of acquired data and generate new data from the same distribution using a generator G that transforms random variables z into new data forged by continuously learning the probability distribution of real data. The discriminator D is a binary classifier used to distinguish whether the input data is real or generated data. During training, the two networks are enhanced simultaneously through mutual competition, forming a dynamic game process until the Nash equilibrium is reached. Both the generator and the discriminator can be designed in combination with the current deep neural network.

3. The inverse method for geostress field using adversarial grid generation according to claim 2, wherein: The calculation process of GAN is a binary minimax game, and the objective function is defined as: （3）； Among them, V(D,G) is the cross entropy loss of the two categories, P dαtα(x) is the true data distribution, P g(z) is the random variable distribution, G (z) It is a generator based on random variables, and E(·) represents the calculated expected value; When P dαtα = P g The global optimal solution is reached when the loss functions of the generator and discriminator of GAN are expressed as log(D(G(z))) and log(D(x)) + log(1-D(G(z))).

4. The inverse method for geostress field using adversarial grid generation according to claim 1, wherein: Based on formula (1) and the measured values ​​of ground stress, the approximate lateral stress coefficient k of different stress components is obtained i , k i Introduced into equation (2), the approximate paleo-stress field is obtained; Based on the approximate paleo-stress field, the present stress field was obtained by excavating the paleo-strata layer by layer through numerical simulation.

5. The inverse method for geostress field by generating an adversarial grid according to claim 1, characterized in that: The specific method of step S2 is to use uniform design experiment to design different α i and b i Various combinations of values, α i and b i The measurement point parameters under different combinations are: （4）； （5）； （6）； （7）； （8）； （9）； Where x and y are the coordinate vectors of the measured point in the horizontal plane, n is the number of measurement points, and H p is the depth vector of the current measured point, k j is the lateral stress coefficient matrix of the current measuring point, j is the number of uniform design tests, α j and b j is the stress component σ at the ancient measuring point x ,σ y ,σ z ,τ yz ,τ zx and τ xy The regression factor matrix of .

6. The inverse method for geostress field by generating an adversarial grid according to claim 1, characterized in that: After each uniformly designed experiment, GAN is trained and the real data sample input to GAN is expressed as: （10）； After the training is completed, the data of the measurement points are input into GAN to obtain the optimized α i and b i The optimized paleo-stress field is calculated by formula (1), and then the present-day stress field is obtained after nonlinear elastic-plastic excavation simulation.

7. The inverse method for geostress field using adversarial grid generation according to claim 1, wherein: The rock mass is divided into hexahedral units. Due to the existence of faults, some rock mass units are cut by faults. These units contain both rock mass and faults, forming composite units. A set of mechanical parameters is assigned to a unit. Therefore, the mechanical parameters of the composite unit with both rock mass and fault need to be equivalent. The local coordinate system (x´y´z´) is established on the fault plane of the composite unit, and the composite unit is simplified into a transversely isotropic equivalent unit with layered distribution. H k is the unit layer thickness, which can be expressed as: （11）； Where subscript k is equal to 1 or 2, representing the parameters of rock mass and fault, respectively, V k is the volume of the rock mass or fault, and A is the area of ​​the contact surface between the rock mass and the fault.

8. The inverse method for geostress field using adversarial grid generation according to claim 7, wherein: For the z´ direction, the deformation and stress of the equivalent element are: （12）； in, , σ v1 and σ v2 are the stresses applied to the equivalent unit, rock mass and fault in the z' direction, is the equivalent elastic modulus in the z´ direction; Based on formula (12), the equivalent elastic modulus in the z´ direction is: （13）。 9. The inverse method for geostress field using adversarial grid generation according to claim 7, wherein: For the x´ and y´ directions, assuming that the elongation of the rock mass and the fault in the equivalent unit is equal, then: （14）； in, , ε h1 and ε h2 are the strains of the equivalent unit, rock mass and fault in the x' and y' directions, respectively, , σ h1 and σ h2 are the stresses applied to the equivalent element, rock mass and fault in the x' and y' directions, respectively, Formula (14) is written as: （15）； According to equations (14) and (15), the equivalent elastic modulus is: （16）； Combining equations (14) and (16), the equivalent Poisson's ratio It can be expressed as （17）。

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