A method for measuring ground stress based on nonlinear mechanics theory

Abstract

The present application belongs to the field of ground stress measurement, and provides a ground stress measurement method based on nonlinear mechanics theory, which measures the stress-strain curve of strain hardening material to obtain mechanical parameters, and then builds a measurement platform containing a concrete cube, an elastic-plastic thick-walled cylinder and a precision range finder, the thick-walled cylinder is embedded in the through hole of the concrete and the precision range finder is built-in to monitor the change of the inner diameter. Through compression test of multiple groups of horizontal compression stress, combined with numerical simulation, a nonlinear model about horizontal pressure, mechanical parameters and geometric parameters of the thick-walled cylinder is constructed by using Bayesian neural network and data augmentation technology. The ground stress observation instrument is placed in the deep hole of the underground soft rock area or the fracture zone, and the inner diameter change of the thick-walled cylinder is continuously monitored after being coupled with the concrete, and then the maximum and minimum principal stress and direction are determined according to the nonlinear model; by the method of the present application, scientific and technical support can be provided for deep earth scientific exploration and underground engineering construction.

Description

Technical Field

[0001] This invention belongs to the field of geostress measurement, specifically relating to a geostress measurement method based on nonlinear mechanics theory. Background Technology

[0002] Currently, commonly used in-situ stress monitoring methods are typically based on linear elastic mechanics models, simplifying the rock mass into an isotropic continuous medium. This results in each commonly used in-situ stress testing method having its own applicable range and certain limitations. Currently, in-situ stress monitoring instruments mainly fall into two categories: one is the borehole radial strain in-situ stress monitoring instrument; the other is the volumetric strain in-situ stress monitoring instrument.

[0003] The working principle of a borehole radial strain in-situ stress monitoring instrument is based on the linear elasticity theory to solve the problem of radial displacement of the borehole wall in an infinitely large plane. Assuming that the surrounding rock is a linear elastic continuous medium, the radial displacement of the borehole in multiple directions is measured by multiple capacitive displacement sensors or piezomagnetic displacement sensors. Combined with the elastic modulus of the surrounding rock, the magnitude and direction of the in-situ stress can be calculated.

[0004] The volumetric strain geostress instrument is one of the earliest geostress instruments put into use, with a history of over 50 years. Benioff proposed the volumetric strain instrument based on the inspiration from measuring temperature through liquid expansion. Sacks and Evertson improved upon Benioff's volumetric strain instrument, successfully developing a borehole strain gauge. The Institute of Geomechanics successively developed the TY-1, TY-2A, and TY-2B volumetric strain geostress instruments. The former Institute of Crustal Stress of the International Seismological Bureau successfully developed the TJ series strain gauges, which are widely used in precursor observations for earthquake prediction and forecasting. Its working principle assumes the geological body is an isotropic linear elastic continuous medium, and uses the generalized Hooke's law to calculate the volumetric strain of the compressed cubic geological body, thereby calculating the sum of the geostresses borne by the geological body in three mutually perpendicular directions.

[0005] Deep Earth rocks, especially soft rocks and fractured zones, often exhibit significant nonlinear mechanical characteristics. However, current geostress observation techniques based on linear elasticity theory struggle to accurately measure geostress in these areas. Therefore, there is an urgent need to study the nonlinear stress-strain relationship of rocks under high confining pressure and to establish geostress observation methods suitable for deep soft rock areas and fractured zones, providing scientific and technological support for deep Earth scientific exploration and underground engineering construction. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a geostress measurement method based on nonlinear mechanics theory, thereby resolving the issues in the prior art. The technical solution adopted by this invention is as follows:

[0007] A method for measuring geostress based on nonlinear mechanics theory includes the following steps:

[0008] Step 1: Measure the stress-strain curve of a specific material exhibiting strain hardening characteristics to obtain its mechanical parameters;

[0009] Step 2: Construct a measurement platform, which includes a concrete cube, a thick-walled cylinder with elastoplastic mechanical characteristics, and a precision distance measuring instrument. A through-hole is provided inside the concrete cube for the thick-walled cylinder to be embedded in. The thick-walled cylinder is placed within this through-hole, and the precision distance measuring instrument is placed inside the thick-walled cylinder. The precision distance measuring instrument is used to measure changes in the inner diameter of the thick-walled cylinder to reflect its shape changes. The thick-walled cylinder is made of the specific material used in Step 1.

[0010] Step 3: Conduct a compression test. Apply horizontal forces of different proportions to the four sides of the concrete cube in two mutually perpendicular horizontal directions, and measure the change in the inner diameter of the thick-walled cylinder with pressure.

[0011] Step 4: Perform numerical simulation. Set the thick-walled cylinder to have elastoplastic mechanical characteristics and the concrete cube to have creep mechanical characteristics. Adjust the creep mechanical model parameters according to the compression test results until the numerical simulation results match the experimental results.

[0012] Step 5: Using machine learning, the experimental results from Step 3 and the numerical simulation results from Step 4 are studied to establish a nonlinear model of horizontal pressure and the mechanical and geometric parameters of the thick-walled cylinder.

[0013] Step 6: Place the geostress monitoring instrument in a deep hole in the underground soft rock area or fracture zone, and couple the geostress monitoring instrument to the deep hole with concrete to continuously monitor the change value of the inner diameter of the thick-walled cylinder.

[0014] Step 7: Based on the change value of the inner diameter of the thick-walled cylinder and the nonlinear model obtained in Step 5, the in-situ stress field is back-analyzed using machine learning methods to determine the maximum principal stress value, the minimum principal stress value and their direction.

[0015] Furthermore, in step 1, the stress-strain curve is represented as follows:

[0016] (1)

[0017] In the formula, For stress, The yield stress of a thick-walled cylinder. In response, For the yield strain of a thick-walled cylinder, The Young's modulus for a thick-walled cylinder. is the strain hardening index of the thick-walled cylinder.

[0018] Furthermore, in step 3, the minimum horizontal compressive stresses are set as follows:

[0019] ;

[0020] The maximum horizontal compressive stresses are set as follows:

[0021] ;

[0022] in, This represents the yield stress of a thick-walled cylinder.

[0023] Furthermore, in step 3, when measuring the change in the inner diameter of the thick-walled cylinder with pressure, it is checked whether the equivalent stress in the thick-walled cylinder exceeds [the specified value]. If the value exceeds this limit, plastic deformation occurs; otherwise, elastic deformation occurs.

[0024] During the elastic deformation stage, after the horizontal force is applied, the inner diameter of the thick-walled cylinder after deformation is elliptical, and the change in inner diameter is:

[0025] (2)

[0026] in:

[0027] (3)

[0028] (4)

[0029] (5)

[0030] In the formula: and The far-field stress experienced by the concrete cube; and These represent the inner and outer diameters of the thick-walled cylinder, respectively. The elastic modulus of a thick-walled cylinder; For a thick-walled cylinder, Poisson's ratio is given. The yield stress of a thick-walled cylinder; For average stress, This is for stress deviation; For angle variables;

[0031] For the plastic deformation stage, the finite element method is used to analyze the change in inner diameter.

[0032] Furthermore, equivalent stress Calculate using the following formula:

[0033] (6)

[0034] In the formula, It is the deviatoric stress tensor.

[0035] Further, step 5 includes: based on experimental results and numerical simulation results, combined with formulas (7) and (8), constructing a nonlinear model of the geostress inverse problem using a Bayesian neural network; using a conditional generative adversarial network method, further enhancing and expanding the actual data training set for geostress nonlinear inversion based on the augmented processing of experimental and numerical simulation data; inputting the training set into the Bayesian neural network for network training, learning the network weights of the Bayesian neural network by minimizing the KL divergence of the variational distribution and the KL divergence of the posterior distribution of the Bayesian neural network, that is, calculating the approximate value of the conditional probability of the latent variable in the sense of KL divergence under the given training data; obtaining the geostress nonlinear model;

[0036] (7)

[0037] (8)

[0038] In the formula: and The far-field stress experienced by the concrete block; and These represent the inner and outer radii of the thick-walled cylinder, respectively. and These represent the short and long semi-axis of the inner diameter of the thick-walled cylinder after deformation, respectively. The elastic modulus of a thick-walled cylinder; For a thick-walled cylinder, Poisson's ratio is given. The yield stress of a thick-walled cylinder; is the strain hardening index of the thick-walled cylinder.

[0039] Furthermore, when preparing the geostress observation instrument, a thick-walled cylinder is made of a specific material, and a precision rangefinder is built into the thick-walled cylinder; the thick-walled cylinder and the precision rangefinder together constitute the geostress observation instrument.

[0040] The present invention has the following beneficial effects:

[0041] This invention obtains the mechanical parameters of strain-hardening materials by measuring their stress-strain curves in advance, clarifying the elastic and plastic deformation stages of thick-walled cylinders, laying a precise foundation for subsequent analysis and avoiding errors caused by ambiguity in material mechanical properties. A combined platform is constructed, consisting of a concrete cube, an elastoplastic thick-walled cylinder, and a precision rangefinder. The precision rangefinder can accurately capture changes in the inner diameter of the thick-walled cylinder in real time, while the concrete cube simulates the on-site rock environment, reducing discrepancies between the laboratory and the field. Furthermore, multiple sets of horizontal compressive stress tests with different proportions are designed to cover the entire stage from low-stress elasticity to high-stress plastic deformation, providing high-quality data support. Numerical simulations are used to expand the number of machine learning samples, and a nonlinear model is constructed using a Bayesian neural network, supplemented with conditional generative adversarial networks to augment the data and improve model fitting accuracy. In field applications, the observation instrument couples with concrete and deep underground boreholes, adapting to complex environments such as soft rock areas and fractured zones. Then, the maximum and minimum principal stresses and directions of the geostress field are analyzed, providing scientific and technological support for deep-earth scientific exploration and underground engineering construction. Attached Figure Description

[0042] Figure 1 The diagram shows the measurement platform and its stress distribution; including: 1 concrete cube, 2 thick-walled cylinder, and 3 precision rangefinder; (a) is the stress diagram of the concrete cube, and (b) is the stress diagram of its cross-section.

[0043] Figure 2 This is a nonlinear model of geostress based on neural networks. Detailed Implementation

[0044] The following will be based on embodiments of the present invention. Figures 1-2 The technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0045] A method for measuring geostress based on nonlinear mechanics theory includes the following steps:

[0046] Step 1: Measure the stress-strain curve of a specific material (metal or alloy) exhibiting strain hardening characteristics to obtain its mechanical parameters;

[0047] Step 2: Construct a measurement platform, which includes a concrete cube, a thick-walled cylinder with elastoplastic mechanical characteristics, and a precision distance measuring instrument. A through-hole is provided inside the concrete cube for the thick-walled cylinder to be inserted into. The thick-walled cylinder is placed within this through-hole, and the precision distance measuring instrument is placed inside the thick-walled cylinder. The precision distance measuring instrument is used to measure changes in the inner diameter of the thick-walled cylinder to reflect its shape changes. The thick-walled cylinder is made of the specific material used in Step 1. The thick-walled cylinder and the precision distance measuring instrument together constitute a ground stress observation instrument. The initial inner diameter of the thick-walled cylinder is 80 mm, the wall thickness is 10 mm, and the length is 1 meter. The side length of the concrete cube is 1 meter. (Reference) Figure 1 The components include: a concrete cube 1, a thick-walled cylinder 2, and a precision rangefinder 3. The precision rangefinder 3 is based on existing technology, such as an internal diameter measuring instrument.

[0048] When preparing the geostress observation instrument, a thick-walled cylinder is made of a specific material, and a precision distance measuring instrument is built into the thick-walled cylinder; the thick-walled cylinder and the precision distance measuring instrument together constitute the geostress observation instrument.

[0049] Step 3: Conduct a compression test. Apply horizontal forces of different proportions to the four sides of the concrete cube in two mutually perpendicular horizontal directions, and measure the change in the inner diameter of the thick-walled cylinder with pressure.

[0050] Step 4: Perform numerical simulation. Set the thick-walled cylinder to have elastoplastic mechanical characteristics and the concrete cube to have creep mechanical characteristics. Adjust the creep mechanical model parameters according to the compression test results until the numerical simulation results match the experimental results.

[0051] Step 5: Using machine learning, the experimental results from Step 3 and the numerical simulation results from Step 4 are studied to establish a nonlinear model of horizontal pressure and the mechanical and geometric parameters of the thick-walled cylinder.

[0052] Step 6: Place the geostress monitoring instrument in a deep hole in the underground soft rock area or fracture zone, and couple the geostress monitoring instrument to the deep hole with concrete to continuously monitor the change value of the inner diameter of the thick-walled cylinder.

[0053] Step 7: Based on the change value of the inner diameter of the thick-walled cylinder and the nonlinear model obtained in Step 5, machine learning is used to back-analyze the geostress field to determine the maximum principal stress value and the minimum principal stress value and their directions.

[0054] Furthermore, in step 1, the stress-strain curve is represented as follows:

[0055] (1)

[0056] In the formula, For stress, The yield stress of a thick-walled cylinder. In response, For the yield strain of a thick-walled cylinder, The Young's modulus for a thick-walled cylinder. is the strain hardening index of the thick-walled cylinder.

[0057] Furthermore, in step 3, the minimum horizontal compressive stresses are set as follows:

[0058] ;

[0059] The maximum horizontal compressive stresses are set as follows:

[0060] ;

[0061] in, This represents the yield stress of a thick-walled cylinder.

[0062] Furthermore, in step 3, when measuring the change in the inner diameter of the thick-walled cylinder with pressure, it is checked whether the equivalent stress of the thick-walled cylinder exceeds [the specified value]. If the value exceeds this limit, plastic deformation occurs; otherwise, elastic deformation occurs.

[0063] During the elastic deformation stage, after the horizontal force is applied, the inner diameter of the thick-walled cylinder after deformation is elliptical, and the change in inner diameter is:

[0064] (2)

[0065] in:

[0066] (3)

[0067] (4)

[0068] (5)

[0069] In the formula: and The far-field stress experienced by the concrete cube; and These represent the inner and outer diameters of the thick-walled cylinder, respectively. The elastic modulus of a thick-walled cylinder; For a thick-walled cylinder, Poisson's ratio is given. The yield stress of a thick-walled cylinder; For average stress, This is for stress deviation; For angle variables; because Includes The inner diameter of the item after deformation is elliptical.

[0070] For the plastic deformation stage, the finite element method is used to analyze the change in inner diameter; that is, the compression process of the concrete cube can be simplified into a two-dimensional plane strain problem along a horizontal cross-section. The bottom and left sides of the plane are fixed, while the right and top sides of the plane bear uniformly distributed loads. A triangular mesh is used for computation. An elastoplastic model is used for the thick-walled cylinder, and a creep model is used for the concrete cube. Numerical simulation results show that under the action of external forces, the cross-section of the thick-walled cylinder changes from a circle to an ellipse.

[0071] Furthermore, equivalent stress Calculate using the following formula:

[0072] (6)

[0073] In the formula, It is the deviatoric stress tensor. Considering that the stress and deformation of the cross-section are symmetrical about the x-axis and y-axis, the numerical analysis results show that the inner diameter cross-section of the deformed thick-walled cylinder is elliptical.

[0074] Further, step 5 includes: based on experimental results and numerical simulation results, combined with formulas (7) and (8), constructing a nonlinear model of the geostress inverse problem using a Bayesian neural network; using a conditional generative adversarial network method, further enhancing and expanding the actual data training set for geostress nonlinear inversion based on the augmented processing of experimental and numerical simulation data; inputting the training set into the Bayesian neural network for network training, learning the network weights of the Bayesian neural network by minimizing the KL divergence of the variational distribution and the KL divergence of the posterior distribution of the Bayesian neural network, that is, calculating the approximate value of the conditional probability of the latent variable in the sense of KL divergence under the given training data; obtaining the geostress nonlinear model, the input value of the nonlinear model is The output value is ;

[0075] (7)

[0076] (8)

[0077] In the formula: and The far-field stress experienced by the concrete block; and These represent the inner and outer radii of the thick-walled cylinder, respectively. and These represent the short and long semi-axis of the inner diameter of the thick-walled cylinder after deformation, respectively. The elastic modulus of a thick-walled cylinder; For a thick-walled cylinder, Poisson's ratio is given. The yield stress of a thick-walled circular cylinder; is the strain hardening index of the thick-walled cylinder.

[0078] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, alterations, substitutions, or variations made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention shall fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for measuring geostress based on nonlinear mechanics theory, characterized in that, Includes the following steps: Step 1: Measure the stress-strain curve of a specific material exhibiting strain hardening characteristics to obtain its mechanical parameters; Step 2: Construct a measurement platform, which includes a concrete cube, a thick-walled cylinder with elastoplastic mechanical characteristics, and a precision distance measuring instrument. A through-hole is provided inside the concrete cube for the thick-walled cylinder to be inserted into, and the thick-walled cylinder is placed within this through-hole. The precision distance measuring instrument is placed inside the thick-walled cylinder. The precision distance measuring instrument is used to measure the change in the inner diameter of the thick-walled cylinder to reflect its shape change. The thick-walled cylinder is made of the specific material used in Step 1. Step 3: Conduct a compression test. Apply horizontal forces of different proportions to the four sides of the concrete cube in two mutually perpendicular horizontal directions, and measure the change in the inner diameter of the thick-walled cylinder with pressure. Step 4: Perform numerical simulation. Set the thick-walled cylinder to have elastoplastic mechanical characteristics and the concrete cube to have creep mechanical characteristics. Adjust the creep mechanical model parameters according to the compression test results until the numerical simulation results match the experimental results. Step 5: Using machine learning, the experimental results from Step 3 and the numerical simulation results from Step 4 are studied to establish a nonlinear model of horizontal pressure and the mechanical and geometric parameters of the thick-walled cylinder. Step 6: Place the geostress monitoring instrument in a deep hole in the underground soft rock area or fracture zone, and couple the geostress monitoring instrument to the deep hole with concrete to continuously monitor the change value of the inner diameter of the thick-walled cylinder. Step 7: Based on the change value of the inner diameter of the thick-walled cylinder and the nonlinear model obtained in Step 5, the in-situ stress field is back-analyzed using machine learning methods to determine the maximum principal stress value, the minimum principal stress value and their direction.

2. The geostress measurement method based on nonlinear mechanics theory according to claim 1, characterized in that, In step 1, the stress-strain curve is represented as follows: （1） In the formula, For stress, The yield stress of a thick-walled cylinder. In response, For the yield strain of a thick-walled cylinder, The Young's modulus for a thick-walled cylinder. is the strain hardening index of the thick-walled cylinder.

3. The geostress measurement method based on nonlinear mechanics theory according to claim 1, characterized in that, In step 3, the minimum horizontal compressive stresses are set as follows: ； The maximum horizontal compressive stresses are set as follows: ； in, This represents the yield stress of a thick-walled cylinder.

4. The geostress measurement method based on nonlinear mechanics theory according to claim 3, characterized in that, In step 3, when measuring the change in the inner diameter of the thick-walled cylinder with pressure, check whether the equivalent stress in the thick-walled cylinder exceeds [the specified value]. If the value exceeds this limit, plastic deformation occurs; otherwise, elastic deformation occurs. During the elastic deformation stage, after the horizontal force is applied, the inner diameter of the thick-walled cylinder after deformation is elliptical, and the change in inner diameter is: （2） in: （3） （4） （5） In the formula: and The far-field stress experienced by the concrete cube; and These represent the inner and outer diameters of the thick-walled cylinder, respectively. The elastic modulus of a thick-walled cylinder; For a thick-walled cylinder, Poisson's ratio is given. The yield stress of a thick-walled cylinder; For average stress, This is for stress deviation; For angle variables; For the plastic deformation stage, the finite element method is used to analyze the change in inner diameter.

5. The geostress measurement method based on nonlinear mechanics theory according to claim 4, characterized in that, Equivalent stress Calculate using the following formula: （6） In the formula, It is the deviatoric stress tensor.

6. The geostress measurement method based on nonlinear mechanics theory according to claim 1, characterized in that, Step 5 includes: based on experimental results and numerical simulation results, combined with formulas (7) and (8), constructing a nonlinear model of the geostress inverse problem using a Bayesian neural network; using a conditional generative adversarial network method, further enhancing and expanding the actual data training set for geostress nonlinear inversion based on the augmented processing of experimental and numerical simulation data; inputting the training set into the Bayesian neural network for network training, learning the network weights of the Bayesian neural network by minimizing the KL divergence of the variational distribution and the KL divergence of the posterior distribution of the Bayesian neural network, that is, calculating the approximate value of the conditional probability of the latent variable in the sense of KL divergence under the given training data; obtaining the geostress nonlinear model. (7) (8) In the formula: and The far-field stress experienced by the concrete block; and These represent the inner and outer radii of the thick-walled cylinder, respectively. and These represent the short and long semi-axis of the inner diameter of the thick-walled cylinder after deformation, respectively. The elastic modulus of a thick-walled cylinder; For a thick-walled cylinder, Poisson's ratio is given. The yield stress of a thick-walled cylinder; is the strain hardening index of the thick-walled cylinder.

7. The geostress measurement method based on nonlinear mechanics theory according to claim 1, characterized in that, When preparing the geostress observation instrument, a thick-walled cylinder is made of a specific material, and a precision distance measuring instrument is built into the thick-walled cylinder; the thick-walled cylinder and the precision distance measuring instrument together constitute the geostress observation instrument.

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