Test system, method and device for obtaining high-dimensional constitutive relation of rock

Abstract

The application discloses a test system for obtaining high-dimensional constitutive relation of rock, which comprises six pressurizing units for applying and unloading pressure to a test sample and a detection device for detecting the size and direction of the force applied to the test sample by the pressurizing units; each pressurizing unit comprises three telescopic arms, a plane base and a force applying block; the three telescopic arms in each pressurizing unit are hinged to the plane base at one end and the three hinge center points are connected to form an equilateral triangle, and the other ends are hinged to the force applying block; the detection device detects the spatial azimuth angle, length change and axial force applied to each telescopic arm. The application also discloses a test method for obtaining high-dimensional constitutive relation of rock, a high-dimensional stress space rock constitutive model and a rock strength criterion model based on a neural network are constructed. The application can realize the application and separation of the full stress tensor of the test sample, and the high-dimensional constitutive relation is obtained by obtaining stress and strain data and failure strength under different principal stress spaces.

Description

Technical Field

[0001] This invention relates to the field of rock mechanics and rock engineering research, and in particular to an experimental system, method and equipment for obtaining high-dimensional constitutive relations of rocks. Background Technology

[0002] Rocks possess heterogeneity and anisotropy, exhibiting highly nonlinear mechanical behavior, which poses a significant challenge to accurately describing their mechanical properties. Current research on rock mechanical behavior largely focuses on a fixed three-dimensional principal stress space. However, whether rocks follow the same laws under different principal stress spaces remains an under-explored question. Furthermore, it is uncertain whether studying rocks under a fixed three-dimensional principal stress is sufficiently accurate given their high heterogeneity and anisotropy. Moreover, whether establishing constitutive and strength criteria for rocks in multiple principal stress spaces can more accurately describe their mechanical behavior is also under investigation. Therefore, establishing constitutive relations and strength criteria for rocks in higher-dimensional stress spaces is crucial for a deeper understanding and accurate prediction of rock mechanical behavior under complex stress conditions.

[0003] The stress tensor of rocks is generally represented by the Cauchy stress tensor, which corresponds to a stress state containing six elements: three normal stresses and three shear stresses. Traditional rock mechanics testing machines, such as the high-pressure servo-driven true triaxial testing machine with patent number CN 103969107 B, can perform various tests, including true triaxial tests, but can only apply normal forces and cannot apply tangential forces to rock samples. Therefore, they cannot change the principal stress space and can only study the mechanical behavior of rocks within a fixed principal stress space. The high-rigidity soft rock true triaxial testing machine with patent number CN 110618030 B, which integrates compression-tension-electromagnetic unloading, improves the overall rigidity of the machine and can obtain the stress-strain curve of the rock sample throughout the entire process. However, this curve can only reflect the stress-strain relationship under a fixed principal stress space and cannot obtain the stress-strain relationship of rocks under different principal stress spaces. The high-pressure hard rock low-frequency disturbance true triaxial testing mechanism with patent number CN 110987673 B can more realistically simulate the dynamic process of rock mass disturbance in the field, but it cannot explore the possibility of establishing rock constitutive and strength criteria under multiple principal stress spaces to more accurately describe the mechanical behavior of rocks under complex stress states. In summary, although existing testing machines can perform true triaxial tests, the significant technical difficulties in applying force in the shear direction mean that no rock mechanics testing machine capable of considering full stress separation has yet been developed, making it impossible to alter the principal stress space. This technological gap restricts research into the high-dimensional constitutive relations and strength criteria of rocks. Summary of the Invention

[0004] The purpose of this invention is to address the problem that existing triaxial testing machines cannot perform full stress separation and cannot explore the constitutive relationship and strength criteria of rocks in high-dimensional stress space. This invention provides a testing system, method and equipment for obtaining the high-dimensional constitutive relationship of rocks to solve the technical problems existing in the prior art.

[0005] The technical solution adopted by this invention to solve the technical problems existing in the prior art is as follows:

[0006] An experimental system for obtaining the high-dimensional constitutive relation of rocks includes six pressurizing units that apply and unload pressure to rock samples, and a detection device for detecting the magnitude and direction of the force applied by the pressurizing units to the rock samples. Each pressurizing unit includes three telescopic arms, a planar base, and a force-applying block. One end of each of the three telescopic arms is hinged to the planar base, and the three hinge centers form an equilateral triangle. The other end of each arm is hinged to the force-applying block. The detection device detects the spatial azimuth angle, length change, and applied axial force of each telescopic arm. The force-applying block is a combination of a partial sphere and a square block. A component that directly contacts the rock sample is detachably mounted on the force-applying block. A clamp C is attached to the force-applying surface of the square block; three spherical grooves A are evenly distributed around the line connecting the center of the sphere and the center of the square block on the sphere; a spherical seat is fixed to the flat base; a spherical groove B is provided inside the spherical seat; one end of the telescopic arm has a spherical end A that mates with the spherical groove A; the other end has a spherical end B that mates with the spherical groove B; a clamp A is fixed to the sphere to prevent the spherical end A from dislodging from the spherical groove A, and a clamp B is fixed to the flat base to prevent the spherical end B from dislodging from the spherical groove B; clamps A and B both have through holes; the inner surfaces of the through holes of clamps A and B correspond to the inner surfaces of the spherical grooves A and B to form spherical surfaces, and the area of ​​the formed spherical surface is greater than 2πR. q 2, R q Let q be the radius of the spherical end, where q = A and B.

[0007] Furthermore, the three telescopic arms in each pressurizing unit are either hydraulic or electric telescopic arms. The hydraulic telescopic arm includes a cylinder and a piston rod. The detection device includes the following sensors installed on each hydraulic telescopic arm: a magnetostrictive displacement sensor for detecting the displacement of the piston rod relative to the cylinder, an angle sensor for detecting the spatial angle of the cylinder, and a pressure sensor for detecting the force on the end of the piston rod. The magnetostrictive displacement sensor is installed inside the cylinder; the angle sensor is installed on the outer side of the cylinder end; and the pressure sensor is an embedded mechanical sensor installed inside the extended end of the piston rod.

[0008] Furthermore, the experimental system for obtaining high-dimensional constitutive relations of rocks according to claim 1 is characterized in that it further includes a hexahedral cavity with one side open and a sealing plate for closing the hexahedral cavity. The sealing plate is located on the rear side of the hexahedral cavity and is called the rear side plate. The other side plates surrounding the hexahedral cavity are respectively called the upper side plate, the lower side plate, the left side plate, the right side plate, and the front side plate.

[0009] Furthermore, the experimental system for obtaining high-dimensional constitutive relations of rocks according to claim 3 is characterized in that it further includes six bases, which are respectively fixedly installed at the geometric center of the inner wall of the six side plates; among the six pressurizing units, the planar bases of five pressurizing units are respectively fixedly connected to the bases on the upper, lower, left, right, and front side plates; and the planar base of the other pressurizing unit is fixedly connected to the base on the sealing plate.

[0010] Furthermore, the experimental system for obtaining high-dimensional constitutive relations of rocks according to claim 3 is characterized in that it further includes an electric drive mechanism for driving the sealing plate to close or open the hexahedral cavity, the electric drive mechanism including three or more synchronously moving electric cylinders; each electric cylinder has its fixed end fixedly connected to the front side plate and its telescopic end fixedly connected to the sealing plate.

[0011] The present invention also provides an experimental method for obtaining high-dimensional constitutive relations of rocks using the above-described experimental system for obtaining high-dimensional constitutive relations of rocks, characterized in that the method includes the following steps:

[0012] Step 1: Cut the rock sample into cubic rock specimens and place the rock specimens between the pressure units;

[0013] Step 2, establish the spatial geometric coordinate system and the initial principal stress space:

[0014] A spatial geometric coordinate system XYZ is established with the center of the cubic rock sample as the origin, and an initial principal stress space P(S1,S2,S3) is established at the same time; S1, S2, and S3 are the axes with the center of the rock sample as the origin, which are parallel to the X-axis, Y-axis, and Z-axis of the spatial geometric coordinate system, respectively.

[0015] Step 3, define the spatial transformation parameters and the initial stress state of the given rock sample:

[0016] The initial principal stress space is rotated using the ZXZ order Euler angle method. The angle of counterclockwise rotation of the initial principal stress space around the S3 axis is defined as φ; the angle of counterclockwise rotation around the changed S1 axis after rotation around the S3 axis is defined as θ; and the angle of counterclockwise rotation around the changed S3 axis after rotation around the changed S1 axis is defined as ψ. Let the new principal stress space obtained by rotating the initial principal stress space counterclockwise around the S3 axis, then counterclockwise around the changed S1 axis, and then counterclockwise around the changed S3 axis be P′(S′1,S′2,S′3). The initial stress state matrix of the given rock sample in the new principal stress space P′(S′1,S′2,S′3) is V. Let V represent the following:

[0017]

[0018] In the formula:

[0019] σ1 represents the first principal stress, and under the initial stress state, σ1 = 0 MPa;

[0020] σ2 represents the second principal stress;

[0021] σ3 represents the third principal stress;

[0022] Step 4, set the loading method as follows: the two principal stresses σ2 and σ3 are constant, and the other principal stress σ1 increases in a predetermined step size Δσ.

[0023] Step 5: Convert V into a stress tensor in a spatial geometric coordinate system using a rotation matrix; calculate the force on each surface of the rock sample based on the stress tensor, the normal vectors of each surface, and the area of ​​force application; determine the axial force of each telescopic arm according to the mechanical equilibrium equation and the spatial orientation angle of the telescopic arm obtained by the detection device, so that the confining pressure of the rock sample reaches the predetermined value.

[0024] Step 6: According to the loading method, gradually adjust the axial force of the telescopic arm to load the rock sample until the rock sample fails; collect the detection values ​​of the detection device before and after each loading step; at the same time, record the principal stresses σ1, σ2, σ3 when the rock sample fails and the stress tensor during the entire loading process.

[0025] Step 7: Obtain the spatial azimuth angle and length change of each telescopic arm based on the detection value of the detection device, and further obtain the component changes of the rock sample in each coordinate axis direction; calculate the strain tensor of the rock sample based on the component changes of the rock sample in each coordinate axis.

[0026] Step 8: Reinstall the new rock sample according to Step 1 and Step 2, change the initial stress state of the principal stress space P′ in Step 3, and perform Step 4 to Step 7 to establish a dataset of stress-strain and failure strength of multipath failure under the principal stress space P′.

[0027] Step 9: Reinstall the new rock sample according to Step 1 and Step 2, change φ, θ, and ψ in Step 3, and perform Step 4 to Step 8 to obtain the stress-strain and failure strength datasets of multipath failure under different principal stress spaces.

[0028] Step 10: Build a neural network using the obtained datasets of stress-strain and failure intensity of multipath failure under different principal stress spaces to construct a high-dimensional strength criterion;

[0029] Step 11: Using the obtained datasets of stress-strain and failure intensity of multi-path failure under different principal stress spaces, a neural network is built to construct a high-dimensional constitutive relation.

[0030] Furthermore, the stress tensor σ in the spatial geometric coordinate system is obtained from the initial stress state matrix V in the new principal stress space using the following formula. ij ;

[0031]

[0032] In the formula:

[0033] σ ij It represents the second-order stress tensor, which represents the stress state at a point in three-dimensional space;

[0034] i represents the normal direction of the stress surface, with a value range of x, y, z; x, y, and z correspond to the directions of the XYZ coordinate axes.

[0035] j represents the direction of the stress component, with a value range of x, y, z;

[0036] σ x This represents the normal stress acting on a plane perpendicular to the X-axis and along the X-axis direction;

[0037] σ y This represents the normal stress acting on a plane perpendicular to the Y-axis and along the Y-axis direction;

[0038] σ z This represents the normal stress acting on a plane perpendicular to the Z-axis and along the Z-axis direction;

[0039] τ xy This represents the shear stress acting on a plane perpendicular to the X-axis and along the Y-axis.

[0040] τ xz This represents the shear stress acting on a plane perpendicular to the X-axis and along the Z-axis.

[0041] τ yx This represents the shear stress acting on a plane perpendicular to the Y-axis and along the X-axis.

[0042] τ yz This represents the shear stress acting on a plane perpendicular to the Y-axis and along the Z-axis.

[0043] τ zx This represents the shear stress acting on a plane perpendicular to the Z-axis and along the X-axis.

[0044] τ zy This represents the shear stress acting on a plane perpendicular to the Z-axis and along the Y-axis.

[0045] R represents the rotation matrix; R T Let R be the transpose of R;

[0046] Taking any pressure unit, let F be the pressure exerted by the force-applying block of that pressure unit on the corresponding surface of the rock sample, then we have:

[0047] F=(σ ij ·n)·A;

[0048] In the formula:

[0049] n: The unit normal vector of the rock sample surface, pointing from the inside of the rock sample to the outside;

[0050] A: The area of ​​the rock sample surface subjected to force;

[0051] Each surface of the rock sample is subjected to one normal force and two tangential forces, therefore:

[0052] F = F x +F xy +F xz ;

[0053] In the formula:

[0054] F x This represents the normal force acting on the surface of the rock sample;

[0055] F xy This represents the tangential force acting on the surface of the rock sample along the Y-axis.

[0056] F xz This represents the tangential force acting on the surface of the rock sample along the Z-axis.

[0057] Let the three telescopic arms in the pressurization unit be the first telescopic arm, the second telescopic arm, and the third telescopic arm;

[0058] Let F 轴1 F represents the axial force applied by the first telescopic arm. 轴2 F represents the axial force applied by the second telescopic arm. 轴3 This indicates the axial force applied by the third telescopic arm;

[0059] By solving the following equilibrium equation, F is obtained. 轴1 F 轴2 F 轴3 ;

[0060]

[0061] In the formula:

[0062] α1 represents the elevation angle of the first telescopic boom;

[0063] α2 represents the elevation angle of the second telescopic boom;

[0064] α3 represents the elevation angle of the third telescopic boom;

[0065] β1 represents the rotation angle of the first telescopic arm;

[0066] β2 represents the rotation angle of the second telescopic arm;

[0067] β3 represents the rotation angle of the third telescopic arm;

[0068] α1, α2, α3, β1, β2, and β3 are obtained by detection using a detection device;

[0069] Keeping σ2 and σ3 constant in the new principal stress space P′(S′1,S′2,S′3), the maximum principal stress σ1 is increased in predetermined steps Δσ until the rock specimen fails. During loading, the axial force of each telescopic arm in the pressurization unit is adjusted in real time according to the changing principal stress. At the same time, the principal stresses σ1, σ2, and σ3 at failure are recorded, and the stress tensor σ of the rock specimen during the entire loading process is solved. ij ;

[0070] The lengths of each telescopic arm before and after loading of the rock sample are obtained by the detection device to determine the component changes Δx, Δy, and Δz of the rock sample in each coordinate axis direction; the length of the telescopic arm is decomposed into a spatial geometric coordinate system, and the changes in the length of the telescopic arm in the three axes of the spatial geometric coordinate system XYZ before and after loading of the rock sample are calculated; let m be the telescopic arm number in the pressurization unit, m = 1, 2, 3.

[0071] The following formula can be used to calculate the variation of the length of each telescopic arm of the pressurizing unit in each coordinate axis direction:

[0072]

[0073] In the formula:

[0074] Δl x m This represents the component of the m-th telescopic arm's variation along the X-axis in the spatial geometric coordinate system;

[0075] Δl y mThis represents the component of the m-th telescopic arm's variation along the Y-axis in the spatial geometric coordinate system;

[0076] Δl z m This represents the component of the m-th telescopic arm's variation along the Z-axis in the spatial geometric coordinate system;

[0077] l m ′ represents the length of the m-th telescopic arm before loading;

[0078] l m "" indicates the length of the m-th telescopic arm after loading;

[0079] α m ′ represents the elevation angle of the m-th telescopic arm before loading;

[0080] α m "" indicates the elevation angle of the m-th telescopic arm after loading;

[0081] β m ′ represents the rotation angle of the m-th telescopic arm before loading;

[0082] β m "" indicates the rotation angle of the m-th telescopic arm after loading;

[0083] The telescopic arms of all pressurizing units are arranged in sequence from 1 to 18. After calculating the change values ​​of the telescopic arms of all pressurizing units in each coordinate axis direction, in order to reduce the error, the average value of the change values ​​of the telescopic arms of all pressurizing units in each coordinate axis direction is taken according to the following formula to obtain the change components of the rock sample in each coordinate axis direction.

[0084]

[0085] In the formula:

[0086] Δx represents the variation component of the rock sample along the X-axis in the spatial geometric coordinate system;

[0087] Δy represents the variation component of the rock sample along the Y-axis in the spatial geometric coordinate system;

[0088] Δz represents the variation component of the rock sample along the Z-axis in the spatial geometric coordinate system;

[0089] Δl x η This represents the variation component of the ηth telescopic arm along the X-axis in the spatial geometric coordinate system;

[0090] Δl y η This represents the variation component of the ηth telescopic arm along the Y-axis in the spatial geometric coordinate system;

[0091] Δl z ηThis represents the variation component of the ηth telescopic arm along the Z-axis in the spatial geometric coordinate system;

[0092] η represents the telescopic boom number, η = 1, 2, ..., 18;

[0093] Based on the component variations of the rock sample along each coordinate axis, the strain tensor of the rock sample is calculated. The strain tensor ε ij The calculation formula is as follows:

[0094]

[0095] In the formula:

[0096] ε ij It represents the second-order strain tensor, used to characterize the deformation state of a material in three-dimensional space;

[0097] ε x This represents the normal strain of the rock sample in the X-axis direction;

[0098] ε y This represents the normal strain of the rock sample in the Y-axis direction;

[0099] ε z This represents the normal strain of the rock sample in the Z-axis direction;

[0100] γ xy γ yx γ represents the engineering shear strain of the rock sample in the XY plane; xy =γ yx ;

[0101] γ xz γ zx γ represents the engineering shear strain of the rock sample on the XZ plane; xz =γ zx ;

[0102] γ yz γ zy γ represents the engineering shear strain of the rock sample on the YZ plane; yz =γ zy ;

[0103] ε xy ε yx ε represents the tensor shear strain of the rock sample in the XY plane; xy =ε yx ;

[0104] ε xz ε zx This represents the tensor shear strain of the rock sample on the XZ plane; εxz = ε zx ;

[0105] ε yz εzy ε represents the tensor shear strain of the rock sample on the YZ plane; yz =ε zy ;

[0106] Let the side length of the cubic rock sample be L. Under the condition of small deformation, the strain tensor components are solved according to the following formula;

[0107]

[0108] In the formula:

[0109] γ1 represents the angle by which the rock sample on the XY plane deviates from the Y-axis;

[0110] γ2 represents the angle by which the rock sample on the XY plane deviates from the X-axis;

[0111] γ3 represents the angle by which the rock sample on the XZ plane deviates from the Z-axis;

[0112] γ4 represents the angle by which the rock sample on the XZ plane deviates from the X-axis;

[0113] γ5 represents the angle by which the rock sample on the YZ plane deviates from the Y-axis;

[0114] γ6 represents the angle by which the rock sample on the YZ plane deviates from the Z-axis;

[0115] Δx represents the variation component of the rock sample along the X-axis in the spatial geometric coordinate system;

[0116] Δy represents the variation component of the rock sample along the Y-axis in the spatial geometric coordinate system;

[0117] Δz represents the variation component of the rock sample along the Z-axis in the spatial geometric coordinate system;

[0118] The following parameter data were recorded simultaneously during the multipath failure test under this principal stress space; σ x σ y σ z τ xy τ yx τ yz ε x ε y ε z ε xy ε xz ε yz The stress-strain dataset includes the following parameters: σ1, σ2, σ3. x σ y σ z τ xy τ yx τ yz ε x ε y εz ε xy ε xz ε yz The damage intensity data includes the following: σ1, σ2, σ3;

[0119] By changing the spatial transformation parameters φ, θ, and ψ, multipath failure test data were obtained under different principal stress spaces.

[0120] Furthermore, a rock strength criterion model is constructed based on a neural network. The input of the rock strength criterion model is the following parameters: φ,θ,ψ,σ1,σ2,σ3; and its output is the rock failure state.

[0121] The collected destructive test data were used to create training samples to train the rock strength criterion model. The trained rock strength criterion model was then used to predict the rock failure state.

[0122] Furthermore, a high-dimensional stress space rock constitutive model based on dual neural network coupling is constructed. The high-dimensional stress space rock constitutive model includes a first neural network and a second neural network connected in sequence. The first neural network takes the elastic modulus E, Poisson's ratio v, cohesion c, friction angle ω and spatial transformation parameters φ, θ and ψ of the rock sample as inputs to predict the stress-strain response in the first t steps. The second neural network takes the stress-strain time series data in the first t steps as input and outputs the stress-strain response in the t+1 step.

[0123] The collected destructive test data were used to create training samples to train a high-dimensional stress space rock constitutive model. The trained high-dimensional stress space rock constitutive model was then used to predict rock stress and strain.

[0124] The present invention also provides an apparatus for an experimental method for obtaining high-dimensional constitutive relations of rocks, comprising a memory and a processor, wherein the memory is used to store a computer program; and the processor is used to execute the computer program and, when executing the computer program, implement the experimental method steps for obtaining high-dimensional constitutive relations of rocks as described above.

[0125] The advantages and positive effects of this invention are: the experimental system proposed in this invention for obtaining the high-dimensional constitutive relationship of rocks can simultaneously provide the application of normal stress and shear stress, change the principal stress space, and obtain stress and strain data under different principal stress spaces.

[0126] This invention proposes an experimental method for obtaining the high-dimensional constitutive relationship of rocks, which overcomes the limitations of existing technologies and enables the precise application and separation of the full stress tensor of rock samples. By obtaining stress-strain data and failure strength under different principal stress spaces, the constitutive relationship and strength criteria of rocks in high-dimensional space can be explored. Attached Figure Description

[0127] Figure 1 This is a schematic diagram of an experimental system for obtaining high-dimensional constitutive relations of rocks according to the present invention.

[0128] Figure 2 This is a schematic diagram of the structure of a pressurization unit according to the present invention.

[0129] Figure 3 This is a schematic diagram of the structure of a force-applying block according to the present invention.

[0130] Figure 4 This is a schematic diagram of the structure of a hydraulic telescopic boom according to the present invention.

[0131] Figure 5 This is a schematic diagram of a magnetostrictive displacement sensor structure according to the present invention.

[0132] Figure 6 This is a cross-sectional view of the piston rod structure of a hydraulic telescopic arm according to the present invention.

[0133] Figure 7 This is a schematic diagram of the structure of a planar base according to the present invention.

[0134] Figure 8 It is a schematic diagram of the spatial geometric coordinate system and the initial principal stress space.

[0135] Figure 9 This is a schematic diagram showing the direction and relationship of stress and shear strain generated by the rock sample under stress.

[0136] Figure 10 This is a pressure analysis diagram of a pressurization unit according to the present invention.

[0137] Figure 11 This is a schematic diagram showing a comparative analysis of the length changes of each hydraulic telescopic arm in a pressurization unit according to the present invention.

[0138] Figure 12 This is a schematic diagram of a rock strength criterion model structure according to the present invention.

[0139] Figure 13 This is a schematic diagram of a high-dimensional stress space rock constitutive model according to the present invention.

[0140] In the diagram, 1-hexahedral cavity, 2-base, 3-pressurizing unit, 4-electric cylinder, 5-sealing plate, 6-flat base, 7-clamp B, 8-hydraulic telescopic arm, 9-force application block, 10-clamp C, 11-clamp A, 12-square block, 13-spherical groove A, 14-angle sensor, 15-magnetostrictive displacement sensor, 16-cylinder, 17-piston rod, 18-electronic transmitter, 19-waveguide wire, 20-magnetically movable part, 21-piston, 22-rod, 23-waveguide wire groove, 24-mechanical sensor, 25-spherical seat.

[0141] X, Y, and Z represent the three coordinate axes of a geometric coordinate system with the body center of the rock sample cube as the origin;

[0142] X1, Y1, and Z1 represent the three coordinate axes of a geometric coordinate system with the corner points of the rock sample cube as the origin;

[0143] X2, Y2, and Z2 represent the three coordinate axes of a geometric coordinate system with the hinge center point where the first telescopic arm is hinged to the planar base as the origin.

[0144] X3, Y3, and Z3 represent the three coordinate axes of a geometric coordinate system with the corner point of the upper surface of the planar base 6 as the origin;

[0145] S1, S2, and S3 correspond to the axes of the spatial geometric coordinate system, which are parallel to the X-axis, Y-axis, and Z-axis, respectively, with the center of the rock sample as the origin.

[0146] σ x This represents the normal stress acting on a plane perpendicular to the X-axis and along the X-axis direction;

[0147] σ y This represents the normal stress acting on a plane perpendicular to the Y-axis and along the Y-axis direction;

[0148] σ z This represents the normal stress acting on a plane perpendicular to the Z-axis and along the Z-axis direction;

[0149] τ xy This represents the shear stress acting on a plane perpendicular to the X-axis and along the Y-axis.

[0150] τ xz This represents the shear stress acting on a plane perpendicular to the X-axis and along the Z-axis.

[0151] τ yx This represents the shear stress acting on a plane perpendicular to the Y-axis and along the X-axis.

[0152] τ yz This represents the shear stress acting on a plane perpendicular to the Y-axis and along the Z-axis.

[0153] τ zx This represents the shear stress acting on a plane perpendicular to the Z-axis and along the X-axis.

[0154] τ zy This represents the shear stress acting on a plane perpendicular to the Z-axis and along the Y-axis.

[0155] l1′ represents the length of the first telescopic arm before loading; l1″ represents the length of the first telescopic arm after loading.

[0156] α1′ represents the elevation angle of the first telescopic boom before loading; α1″ represents the elevation angle of the first telescopic boom after loading.

[0157] β1′ represents the rotation angle before the first telescopic arm is loaded; β1″ represents the rotation angle after the first telescopic arm is loaded.

[0158] σ1 represents the first principal stress; σ2 represents the second principal stress; σ3 represents the third principal stress;

[0159] The initial principal stress space is rotated counterclockwise around the S3 axis by an angle φ; after rotating around the S3 axis, the initial principal stress space is rotated counterclockwise around the changed S1 axis by an angle θ; after rotating around the changed S1 axis, the initial principal stress space is rotated counterclockwise around the changed S3 axis by an angle ψ.

[0160] f represents the rock failure state;

[0161] ε xy This represents the tensor shear strain of the rock sample on the xy plane;

[0162] ε xz This represents the tensor shear strain of the rock sample on the xz plane;

[0163] ε yz This represents the tensor shear strain of the rock sample on the yz plane;

[0164] E represents the elastic modulus; v represents Poisson's ratio; c represents cohesion; ω represents the angle of friction.

[0165] T1, T2, ..., T t T t+1 The corresponding stress tensor and strain tensor are represented at time 1, 2, ..., t, and t+1. Detailed Implementation

[0166] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0167] The Chinese definitions of the following English words, abbreviations, and phrases are as follows:

[0168] Hidden layer: The hidden layer.

[0169] Input: Input.

[0170] Output: Output.

[0171] TensorFlow: TensorFlow is a symbolic mathematics system based on dataflow programming, which is widely used in the programming implementation of various machine learning algorithms.

[0172] PyTorch is an open-source deep learning framework for machine learning and deep learning, released by Facebook in 2016. It mainly implements automatic differentiation and introduces dynamic computation graphs to make model building more flexible.

[0173] In the description of this invention, the terms "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," and "bottom," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and do not require the invention to be constructed and operated in a specific orientation; therefore, they should not be construed as limitations on the invention. The terms "connected" and "linked" used in this invention should be interpreted broadly. For example, they can refer to a fixed connection or a detachable connection; a direct connection or an indirect connection through intermediate components; or an electrical connection or signal transmission. Those skilled in the art can understand the specific meaning of the above terms according to the specific circumstances.

[0174] Please see Figures 1 to 13 An experimental system for obtaining the high-dimensional constitutive relationship of rocks is disclosed. The system includes six pressurizing units 3 for applying and unloading pressure onto rock samples, and a detection device for detecting the magnitude and direction of the force applied by the pressurizing units 3 to the rock samples. Each pressurizing unit 3 includes three telescopic arms, a planar base 6, and a force-applying block 9. One end of each of the three telescopic arms is hinged to the planar base 6, and the three hinge centers form an equilateral triangle. The other end of each arm is hinged to the force-applying block 9. The detection device detects the spatial azimuth angle, length change, and applied axial force of each telescopic arm. The force-applying block 9 is a combination of a partial sphere and a square block 12. A clamp C10, which directly contacts the rock sample, is detachably mounted on the force-applying block 9. The bottom surface of C10 is attached to the force-applying surface of the square block 12; three spherical grooves A13 are evenly distributed around the line connecting the center of the sphere and the center of the square block 12 on the sphere; a spherical seat 25 is fixedly connected to the flat base 6; a spherical groove B is provided inside the spherical seat 25; one end of the telescopic arm is provided with a spherical end A that mates with the spherical groove A13; the other end is provided with a spherical end B that mates with the spherical groove B; a clamp A11 is fixedly connected to the sphere to prevent the spherical end A from falling out of the spherical groove A13; a clamp B7 is fixedly connected to the flat base 6 to prevent the spherical end B from falling out of the spherical groove B; both clamps A11 and clamp B7 have through holes; the inner surfaces of the through holes of clamps A11 and clamp B7 correspond to the inner surfaces of the spherical grooves A13 and B to form a spherical surface, and the area of ​​the formed spherical surface is greater than 2πR. q 2, R q Let q be the radius of the spherical end, where q = A and B.

[0175] Preferably, the three telescopic arms in each pressurizing unit 3 can be hydraulic telescopic arms 8 or electric telescopic arms. The hydraulic telescopic arm 8 includes a cylinder 16 and a piston rod 17. The detection device may include the following sensors installed on each hydraulic telescopic arm 8: a magnetostrictive displacement sensor 15 for detecting the displacement of the piston rod 17 relative to the cylinder 16, an angle sensor 14 for detecting the spatial angle of the cylinder 16, and a pressure sensor for detecting the force on the end of the piston rod 17. The magnetostrictive displacement sensor 15 is installed inside the cylinder 16; the angle sensor 14 is installed on the outer side of the end of the cylinder 16; and the pressure sensor is an embedded mechanical sensor 24, installed inside the extended end of the piston rod 17.

[0176] Preferably, the test system may further include a hexahedral cavity 1 with one open side and a sealing plate 5 for closing the hexahedral cavity 1. The sealing plate 5 may be located on the rear side of the hexahedral cavity 1 and is called the rear side plate. The other side plates surrounding the hexahedral cavity 1 are respectively called the upper side plate, lower side plate, left side plate, right side plate and front side plate.

[0177] Preferably, the test system may further include six bases 2, which can be fixedly installed at the geometric center of the inner wall of the six side plates respectively; among the six pressurizing units 3, the planar bases 6 of five pressurizing units 3 are fixedly connected to the bases 2 on the upper, lower, left, right and front side plates respectively; the planar base 6 of the other pressurizing unit 3 is fixedly connected to the base 2 on the sealing plate 5.

[0178] Preferably, the test system may further include an electric drive mechanism for driving the sealing plate 5 to close or open the hexahedral cavity 1. The electric drive mechanism may include three or more synchronously moving electric cylinders; each electric cylinder 4 has its fixed end fixedly connected to the front side plate and its telescopic end fixedly connected to the sealing plate 5.

[0179] The present invention also provides an experimental method for obtaining high-dimensional constitutive relations of rocks using the above-described experimental system for obtaining high-dimensional constitutive relations of rocks, the method comprising the following steps:

[0180] Step 1: Cut the rock sample into cubic rock specimens and place the rock specimens between the pressure units 3;

[0181] Step 2, establish the spatial geometric coordinate system and the initial principal stress space:

[0182] A spatial geometric coordinate system XYZ is established with the center of the cubic rock sample as the origin. At the same time, an initial principal stress space P(S1,S2,S3) is established, which is abbreviated as P. S1, S2, and S3 correspond to the axes with the center of the rock sample as the origin, which are parallel to the X-axis, Y-axis, and Z-axis of the spatial geometric coordinate system, respectively.

[0183] Step 3, define the spatial transformation parameters and the initial stress state of the given rock sample:

[0184] The initial principal stress space is rotated using the ZXZ order Euler angle method. The angle of counterclockwise rotation of the initial principal stress space around the S3 axis is defined as φ; the angle of counterclockwise rotation around the changed S1 axis after rotation around the S3 axis is defined as θ; and the angle of counterclockwise rotation around the changed S3 axis after rotation around the changed S1 axis is defined as ψ. Let the new principal stress space obtained by rotating the initial principal stress space counterclockwise around the S3 axis, then counterclockwise around the changed S1 axis, and then counterclockwise around the changed S3 axis be P′(S′1,S′2,S′3), abbreviated as P′. The initial stress state matrix of the given rock sample in the new principal stress space P′(S′1,S′2,S′3) is denoted as V. Let V represent the following:

[0185]

[0186] In the formula:

[0187] σ1 represents the first principal stress, and under the initial stress state, σ1 = 0 MPa;

[0188] σ2 represents the second principal stress;

[0189] σ3 represents the third principal stress;

[0190] Step 4, set the loading method as follows: the two principal stresses σ2 and σ3 are constant, and the other principal stress σ1 increases in a predetermined step size Δσ.

[0191] Step 5: Convert V into a stress tensor in a spatial geometric coordinate system using a rotation matrix; calculate the force on each surface of the rock sample based on the stress tensor, the normal vectors of each surface, and the area of ​​force application; determine the axial force of each telescopic arm according to the mechanical equilibrium equation and the spatial orientation angle of the telescopic arm obtained by the detection device, so that the confining pressure of the rock sample reaches the predetermined value.

[0192] Step 6: According to the loading method, gradually adjust the axial force of the telescopic arm to load the rock sample until the rock sample fails; collect the detection values ​​of the detection device before and after each loading step; at the same time, record the principal stresses σ1, σ2, σ3 when the rock sample fails and the stress tensor during the entire loading process.

[0193] Step 7: Obtain the spatial azimuth angle and length change of each telescopic arm based on the detection value of the detection device, and further obtain the component changes of the rock sample in each coordinate axis direction; calculate the strain tensor of the rock sample based on the component changes of the rock sample in each coordinate axis.

[0194] Step 8: Reinstall the new rock sample according to Step 1 and Step 2, change the initial stress state of the principal stress space P′ in Step 3, and perform Step 4 to Step 7 to establish a dataset of stress-strain and failure strength of multipath failure under the principal stress space P′.

[0195] Step 9: Reinstall the new rock sample according to Step 1 and Step 2, change φ, θ, and ψ in Step 3, and perform Step 4 to Step 8 to obtain the stress-strain and failure strength datasets of multipath failure under different principal stress spaces.

[0196] Step 10: Build a neural network using the obtained datasets of stress-strain and failure intensity of multipath failure under different principal stress spaces to construct a high-dimensional strength criterion;

[0197] Step 11: Using the obtained datasets of stress-strain and failure intensity of multi-path failure under different principal stress spaces, a neural network is built to construct a high-dimensional constitutive relation.

[0198] Preferably, the stress tensor σ in the spatial geometric coordinate system can be obtained from the initial stress state matrix V in the new principal stress space using the following formula. ij ;

[0199]

[0200] In the formula:

[0201] σ ij It represents the second-order stress tensor, which represents the stress state at a point in three-dimensional space;

[0202] i represents the normal direction of the stress surface, with a value range of x, y, z; x, y, and z correspond to the directions of the XYZ coordinate axes.

[0203] j represents the direction of the stress component, with a value range of x, y, z;

[0204] σ x This represents the normal stress acting on a plane perpendicular to the X-axis and along the X-axis direction;

[0205] σ y This represents the normal stress acting on a plane perpendicular to the Y-axis and along the Y-axis direction;

[0206] σ z This represents the normal stress acting on a plane perpendicular to the Z-axis and along the Z-axis direction;

[0207] τ xy This represents the shear stress acting in a plane perpendicular to the axis and along the Y-axis direction;

[0208] τ xz This represents the shear stress acting on a plane perpendicular to the X-axis and along the Z-axis.

[0209] τ yx This represents the shear stress acting on a plane perpendicular to the Y-axis and along the X-axis.

[0210] τ yz This represents the shear stress acting on a plane perpendicular to the Y-axis and along the Z-axis.

[0211] τ zx This represents the shear stress acting on a plane perpendicular to the Z-axis and along the X-axis.

[0212] τ zy This represents the shear stress acting on a plane perpendicular to the Z-axis and along the Y-axis.

[0213] R represents the rotation matrix; R T Let R be the transpose of R;

[0214] We can choose any pressurizing unit 3, and let F be the pressure applied by the force-applying block 9 of the pressurizing unit 3 to the corresponding surface of the rock sample. Then we have:

[0215] F=(σ ij ·n)·A;

[0216] In the formula:

[0217] n: The unit normal vector of the rock sample surface, pointing from the inside of the rock sample to the outside;

[0218] A: The area of ​​the rock sample surface subjected to force;

[0219] Each surface of the rock sample is subjected to one normal force and two tangential forces, therefore:

[0220] F = F x +F xy +F xz ;

[0221] In the formula:

[0222] F x This represents the normal force acting on the surface of the rock sample;

[0223] F xy This represents the tangential force acting on the surface of the rock sample along the Y-axis.

[0224] F xz This represents the tangential force acting on the surface of the rock sample along the Z-axis.

[0225] Let the three telescopic arms in the pressurization unit 3 be the first telescopic arm, the second telescopic arm, and the third telescopic arm;

[0226] Let F 轴1F represents the axial force applied by the first telescopic arm. 轴2 F represents the axial force applied by the second telescopic arm. 轴3 This indicates the axial force applied by the third telescopic arm;

[0227] F can be obtained by solving the following equilibrium equation. 轴1 F 轴2 F 轴3 ;

[0228]

[0229] In the formula:

[0230] α1 represents the elevation angle of the first telescopic arm; α2 represents the elevation angle of the second telescopic arm; α3 represents the elevation angle of the third telescopic arm; β1 represents the turning angle of the first telescopic arm; β2 represents the turning angle of the second telescopic arm; β3 represents the turning angle of the third telescopic arm.

[0231] α1, α2, α3, β1, β2, and β3 are obtained by detection using a detection device;

[0232] The system maintains constant σ2 and σ3 in the new principal stress space P′(S′1,S′2,S′3), and increases the maximum principal stress σ1 in predetermined steps Δσ until the rock sample fails. During loading, the axial force of each telescopic arm in the pressurization unit 3 is adjusted in real time according to the changing principal stress. Simultaneously, the principal stresses σ1, σ2, and σ3 at failure are recorded, and the stress tensor σ of the rock sample during the entire loading process is solved. ij ;

[0233] The lengths of each telescopic arm before and after loading of the rock sample can be detected by the detection device to determine the component changes Δx, Δy, and Δz of the rock sample in each coordinate axis direction; the length of the telescopic arm is decomposed into a spatial geometric coordinate system, and the changes in the length of the telescopic arm in the three axes of the spatial geometric coordinate system XYZ before and after loading of the rock sample are calculated; let m be the telescopic arm number in the pressurization unit 3, m = 1, 2, 3;

[0234] The variation of the length of each telescopic arm of the pressurizing unit 3 in each coordinate axis direction can be calculated using the following formula:

[0235]

[0236] In the formula:

[0237] Δl x m This represents the component of the m-th telescopic arm's variation along the X-axis in the spatial geometric coordinate system;

[0238] Δl y m This represents the component of the m-th telescopic arm's variation along the Y-axis in the spatial geometric coordinate system;

[0239] Δl z m This represents the component of the m-th telescopic arm's variation along the Z-axis in the spatial geometric coordinate system;

[0240] l m ′ represents the length of the m-th telescopic arm before loading;

[0241] l m "" indicates the length of the m-th telescopic arm after loading;

[0242] α m ′ represents the elevation angle of the m-th telescopic arm before loading;

[0243] α m "" indicates the elevation angle of the m-th telescopic arm after loading;

[0244] β m ′ represents the rotation angle of the m-th telescopic arm before loading;

[0245] β m "" indicates the rotation angle of the m-th telescopic arm after loading;

[0246] All the telescopic arms of the pressurizing unit 3 can be sorted according to serial numbers 1 to 18. After obtaining the change values ​​of all the telescopic arms of the pressurizing unit 3 in each coordinate axis direction, in order to reduce the error, the average value of the change values ​​of all the telescopic arms of the pressurizing unit 3 in each coordinate axis direction is taken according to the following formula to obtain the change components of the rock sample in each coordinate axis direction.

[0247]

[0248] In the formula:

[0249] Δx represents the variation component of the rock sample along the X-axis in the spatial geometric coordinate system;

[0250] Δy represents the variation component of the rock sample along the Y-axis in the spatial geometric coordinate system;

[0251] Δz represents the variation component of the rock sample along the Z-axis in the spatial geometric coordinate system;

[0252] Δl x η This represents the variation component of the ηth telescopic arm along the X-axis in the spatial geometric coordinate system;

[0253] Δl y η This represents the variation component of the ηth telescopic arm along the Y-axis in the spatial geometric coordinate system;

[0254] Δl z ηThis represents the variation component of the ηth telescopic arm along the Z-axis in the spatial geometric coordinate system;

[0255] η represents the telescopic boom number, η = 1, 2, ..., 18;

[0256] The strain tensor ε of the rock sample can be obtained from the component variations of the rock sample along each coordinate axis. ij The calculation formula is as follows:

[0257]

[0258] In the formula:

[0259] ε ij It represents the second-order strain tensor, used to characterize the deformation state of a material in three-dimensional space;

[0260] ε x This represents the normal strain of the rock sample in the X-axis direction;

[0261] ε y This represents the normal strain of the rock sample in the Y-axis direction;

[0262] ε z This represents the normal strain of the rock sample in the Z-axis direction;

[0263] γ xy γ yx γ represents the engineering shear strain of the rock sample in the XY plane; xy =γ yx ;

[0264] γ xz γ zx γ represents the engineering shear strain of the rock sample on the XZ plane; xz =γ zx ;

[0265] γ yz γ zy γ represents the engineering shear strain of the rock sample on the YZ plane; yz =γ zy ;

[0266] ε xy ε yx ε represents the tensor shear strain of the rock sample in the XY plane; xy =ε yx ;

[0267] ε xz ε zx ε represents the tensor shear strain of the rock sample on the XZ plane; xz =ε zx ;

[0268] εyz ε zy ε represents the tensor shear strain of the rock sample on the YZ plane; yz =ε zy ;

[0269] Let the side length of the cubic rock sample be L. Under the condition of small deformation, the strain tensor components can be solved according to the following formula.

[0270]

[0271] In the formula:

[0272] γ1 represents the angle by which the rock sample on the XY plane deviates from the Y-axis;

[0273] γ2 represents the angle by which the rock sample on the XY plane deviates from the X-axis;

[0274] γ3 represents the angle by which the rock sample on the XZ plane deviates from the Z-axis;

[0275] γ4 represents the angle by which the rock sample on the XZ plane deviates from the X-axis;

[0276] γ5 represents the angle by which the rock sample on the YZ plane deviates from the Y-axis;

[0277] γ6 represents the angle by which the rock sample on the YZ plane deviates from the Z-axis;

[0278] Δx represents the variation component of the rock sample along the X-axis in the spatial geometric coordinate system;

[0279] Δy represents the variation component of the rock sample along the Y-axis in the spatial geometric coordinate system;

[0280] Δz represents the variation component of the rock sample along the Z-axis in the spatial geometric coordinate system;

[0281] The following parameter data can be recorded simultaneously during the multipath failure test under this principal stress space; σ x σ y σ z τ xy τ yx τ yz ε x ε y ε z ε xy ε xz ε yz The stress-strain dataset includes the following parameters: σ1, σ2, σ3. x σ y σ z τ xy τ yx τ yz ε xε y ε z ε xy ε xz ε yz The damage intensity data includes the following data: σ1, σ2, σ3.

[0282] Preferably, the spatial transformation parameters φ, θ, and ψ can be changed to obtain multipath failure test data under different principal stress spaces.

[0283] Preferably, a rock strength criterion model can be constructed based on a neural network. The input of the rock strength criterion model is the following parameters: φ,θ,ψ,σ1,σ2,σ3; and its output is the rock failure state.

[0284] The collected destructive test data can be used to create training samples to train the rock strength criterion model, and the trained rock strength criterion model can be used to predict the rock failure state.

[0285] Preferably, a high-dimensional stress space rock constitutive model based on dual neural network coupling can be constructed. The high-dimensional stress space rock constitutive model may include a first neural network and a second neural network connected in sequence. The first neural network takes the elastic modulus E, Poisson's ratio v, cohesion c, friction angle ω and spatial transformation parameters φ, θ and ψ of the rock sample as inputs to predict the stress-strain response in the first t steps. The second neural network takes the stress-strain time series data in the first t steps as input and outputs the stress-strain response in the t+1 step.

[0286] The collected destructive test data can be used to create training samples to train a high-dimensional stress space rock constitutive model, and the trained high-dimensional stress space rock constitutive model can be used to predict rock stress and strain.

[0287] An apparatus for an experimental method of obtaining high-dimensional constitutive relations of rocks includes a memory and a processor, the memory being used to store a computer program; the processor being used to execute the computer program and, when executing the computer program, to implement the experimental method steps for obtaining high-dimensional constitutive relations of rocks as described above.

[0288] The structure and working principle of the present invention will be further illustrated below with reference to a preferred embodiment:

[0289] like Figures 1-7As shown, an experimental system for obtaining the high-dimensional constitutive relationship of rocks is characterized by comprising six pressurizing units 3 for applying and unloading pressure to rock samples, and a detection device for detecting the magnitude and direction of the force applied to the rock samples by the pressurizing units 3; each pressurizing unit 3 includes three telescopic arms, a planar base 6, and a force-applying block 9; one end of each of the three telescopic arms in each pressurizing unit 3 is hinged to the planar base 6, and the three hinge center points form an equilateral triangle, and the other end of each arm is hinged to the force-applying block 9; the detection device detects the spatial azimuth angle, length change, and applied axial force of each telescopic arm; the force-applying block 9 is a combination of a partial sphere and a square block 12; a clamp C10 that directly contacts the rock sample is detachably mounted on the force-applying block 9. The sphere has a C10 bottom surface that fits against the square block 12. Three spherical grooves A13 are evenly distributed around the line connecting the center of the sphere and the center of the square block 12. A spherical seat 25 is fixed to the flat base 6. A spherical groove B is provided inside the spherical seat 25. One end of the telescopic arm has a spherical end A that mates with the spherical groove A13; the other end has a spherical end B that mates with the spherical groove B. A clamp A11 is fixed to the sphere to prevent the spherical end A from dislodging from the spherical groove A13, and a clamp B7 is fixed to the flat base 6 to prevent the spherical end B from dislodging from the spherical groove B. Both clamps A11 and B7 have through holes. The inner surfaces of the through holes of clamps A11 and B7 correspond to the inner surfaces of the spherical grooves A13 and B to form a spherical surface, and the area of ​​the formed spherical surface is greater than 2πR. q 2, R q Let q be the radius of the spherical end, where q = A and B.

[0290] The force-applying block 9 is equipped with a clamp C10, which is a U-shaped steel material with holes on both sides. The bottom surface of the clamp is attached to the force-applying surface of the square block 12 and is fixed to the square block 12 with bolts. It can be disassembled. The clamp C10 is used to clamp the sample and is replaceable.

[0291] The system also includes a hexahedral cavity 1 with one open side and a sealing plate 5 for closing the hexahedral cavity 1. The sealing plate 5 is located on the rear side of the hexahedral cavity 1 and is called the rear side plate. The other side plates surrounding the hexahedral cavity 1 are respectively called the upper side plate, lower side plate, left side plate, right side plate and front side plate.

[0292] The system also includes six bases 2, which are welded to the geometric center of the inner wall of the upper side plate, the right side plate and the rear side plate respectively; of the six pressurizing units 3, the planar bases 6 of five pressurizing units 3 are fixed to the bases 2 on the upper, lower, left, right and front side plates respectively; the planar base 6 of the other pressurizing unit 3 is fixed to the base 2 on the sealing plate 5.

[0293] The system also includes an electric drive mechanism for driving the sealing plate 5 to close or open the hexahedral cavity 1. The electric drive mechanism includes three or more synchronously moving electric cylinders 4. Each electric cylinder 4 has its fixed end fixedly connected to the front side plate and its telescopic end fixedly connected to the sealing plate 5.

[0294] The hexahedral cavity 1 can be integrally cast from high-strength alloy steel and machined. The upper, lower, left, right, front, and rear side plates are all made of high-strength alloy. When the hexahedral cavity 1 is in a closed state, the internal vertical, horizontal, and front-rear distances are all 500mm. The fixed end of the electric cylinder 4 is welded to the front side plate, and the telescopic end is fixedly connected to the rear side plate. The base 2 is disc-shaped with a diameter of 100mm and a height of 10mm, made of high-strength alloy, and is fastened to the geometric center of the inner wall of the upper, lower, left, right, and front side plates with screws. The base 2 can also be welded to the geometric center of each side wall. The pressurizing unit 3 is fastened to the base 2 with screws.

[0295] The force-applying block 9 is a combination of a partial sphere and a square block 12; the force-applying block 9 is equipped with a clamp C10, which is a U-shaped steel with holes on both sides, with its bottom surface in contact with the force-applying surface of the square block 12, and is fixed to the square block 12 by bolts, and can be disassembled. Three spherical grooves A13 are evenly distributed around the line connecting the center of the sphere and the center of the square block 12 on the sphere; a spherical seat 25 is fixedly connected to the flat base 6; a spherical groove B is provided inside the spherical seat 25; one end of the telescopic arm is provided with a spherical end A that mates with the spherical groove A13; the other end is provided with a spherical end B that mates with the spherical groove B; a clamp A11 is fixedly connected to the sphere to prevent the spherical end A from falling out of the spherical groove A13, and a clamp B7 is fixedly connected to the flat base 6 to prevent the spherical end B from falling out of the spherical groove B; both clamps A11 and clamps B7 have through holes; the inner surfaces of the through holes of clamps A11 and clamps B7 correspond to the inner surfaces of the spherical grooves A13 and B to form a spherical surface, and the area of ​​the formed spherical surface is greater than 2πR. q 2, R q Let q be the radius of the spherical end, where q = A and B.

[0296] The planar base 6 includes a square plate with dimensions of 170mm × 170mm × 10mm, made of high-strength alloy steel. Three spherical seats 25 are welded to the surface of the planar base 6, arranged in a ring at equal angles within the planar base 6 with the geometric center of the base plate as the center. The spherical seats 25 have spherical grooves B with a diameter of 20mm. The force-applying block 9 is integrally cast and includes a square block 12 and a part of a sphere. The sphere has three spherical grooves A13 evenly distributed in a ring, with a diameter of 10mm.

[0297] Each pressurizing unit 3 has three telescopic arms, which are hydraulic telescopic arms 8. Each hydraulic telescopic arm 8 includes a cylinder 16 and a piston rod 17. The detection device includes the following sensors installed on each hydraulic telescopic arm 8: a magnetostrictive displacement sensor 15 for detecting the displacement of the piston rod 17 relative to the cylinder 16, an angle sensor 14 for detecting the spatial angle of the cylinder 16, and a pressure sensor for detecting the force on the end of the piston rod 17. The magnetostrictive displacement sensor 15 is installed inside the cylinder 16. The angle sensor 14 is installed on the outer side of the end of the cylinder 16. The pressure sensor is an embedded mechanical sensor 24, which is installed inside the extended end of the piston rod 17.

[0298] The cylinder 16 is made of high-strength alloy steel, with an inner diameter of 8mm and a length of 100mm. It houses a CH series magnetostrictive displacement sensor 15. An LCA326T type angle sensor 14 is clamped near the outer end of the cylinder 16. The end of the cylinder 16 has a 19.8mm diameter sphere that forms a clearance fit with the groove B on the base plate and is fixed by a clamp B7, also made of high-strength alloy steel, which is bolted to the flat base 6. The piston rod 17 is also made of high-strength alloy steel and includes a rod 22 and a piston 21 welded to it. The rod 22 has a diameter of 6mm and a length of 80mm. A waveguide wire groove 23 is provided inside the rod 22, and an HBM (Hyper- ... The U2B series mechanical sensor 24 has a spherical end A of piston rod 17 with a diameter of 9.8 mm. The spherical end A is clearance-fitted with the spherical groove A13 and fixed by clamp A11. The clamp A11 is made of high-strength alloy material and is fastened to the force application block 9 by bolts. The magnetostrictive displacement sensor 15 includes an electronic transmitter 18, a waveguide wire 19, and a magnetic movable part 20. The electronic transmitter 18 is fixedly installed at the end of cylinder 16 by bolts. The magnetic movable part 20 is embedded in piston 21. The waveguide wire 19 is located in waveguide wire groove 23 and connected to the electronic transmitter 18.

[0299] like Figures 8-13 As shown, an experimental method for obtaining high-dimensional constitutive relations of rocks using the above-described experimental system for obtaining high-dimensional constitutive relations of rocks includes the following steps:

[0300] (1) Rock sample clamping:

[0301] ① Start electric cylinder 4 to drive the rear side panel to open to the maximum degree;

[0302] ② Chamfer the 50mm×50mm×50mm rock sample, with a chamfer distance of 2.5mm;

[0303] ③ Place the treated rock sample between the pressurization units 3;

[0304] ④ By controlling the electric cylinder 4 to close the sealing plate 5, a closed loading cavity is formed.

[0305] (2) Establish the spatial geometric coordinate system and the initial principal stress space:

[0306] like Figure 6 As shown, a spatial geometric coordinate system XYZ is established with the center of the cubic rock sample as the origin. At the same time, an initial principal stress space P(S1,S2,S3), abbreviated as P, is established, where the S1 axis coincides with the X-axis, the S2 axis coincides with the Y-axis, and the S3 axis coincides with the Z-axis.

[0307] (3) Define the spatial transformation parameters and specify the initial stress state of the rock sample:

[0308] The initial principal stress space is rotated using the ZXZ sequence Euler angle method. The angle of counterclockwise rotation of the initial principal stress space P(S1,S2,S3) around the S3 axis is defined as φ, where φ ∈ [0°, 360°), and initially φ = 0°. The angle of counterclockwise rotation of the initial principal stress space around the changed S1 axis after rotation around the S3 axis is defined as θ, where θ ∈ [0°, 180°], and initially θ = 0°. The angle of counterclockwise rotation of the initial principal stress space around the changed S3 axis after rotation around the changed S1 axis is defined as ψ, where ψ ∈ [0°, 360°), and initially ψ = 0°. Rotating the initial principal stress space counterclockwise around axis S3, then counterclockwise around the modified axis S1, and then counterclockwise again around the modified axis S3, yields a new principal stress space P′(S′1,S′2,S′3), abbreviated as P′. The initial stress state V of the rock sample is then defined within this new principal stress space P′(S′1,S′2,S′3), where V is:

[0309]

[0310] In the formula: σ1 represents the first principal stress, and σ1 = 0 MPa under the initial stress state; σ2 represents the second principal stress; and σ3 represents the third principal stress.

[0311] (4) Set the loading method:

[0312] The loading method is set as follows: the two principal stresses σ2 and σ3 are constant, and the other principal stress σ1 increases in a predetermined step of Δσ = 0.1 MPa.

[0313] (5) Load to the predetermined confining pressure:

[0314] ① Adjust all the pressurizing units 3 so that the center of gravity of the force-applying block 9 is coaxial with the center of gravity of the flat base 6;

[0315] ② Based on the initial stress state V under the new principal stress space, adjust the axial force of different telescopic arms in the pressurization unit 3 to make the rock sample meet the predetermined confining pressure:

[0316] Step 1: Convert the initial stress state V in the new principal stress space into the stress tensor σ in the spatial geometric coordinate system using equation (2). ij ;

[0317]

[0318] In the formula:

[0319] σ ij It represents the second-order stress tensor, which represents the stress state at a point in three-dimensional space;

[0320] i represents the normal direction of the stress surface, with a value range of x, y, z; x, y, and z correspond to the directions of the XYZ coordinate axes.

[0321] j represents the direction of the stress component, with a value range of x, y, z;

[0322] σ x This represents the normal stress acting on a plane perpendicular to the x-axis and along the x-axis direction;

[0323] σ y This represents the normal stress acting on a plane perpendicular to the y-axis and along the y-axis direction;

[0324] σ z This represents the normal stress acting on a plane perpendicular to the Z-axis and along the Z-axis direction;

[0325] τ xy This represents the shear stress acting on a plane perpendicular to the X-axis and along the Y-axis.

[0326] τ xz This represents the shear stress acting on a plane perpendicular to the X-axis and along the Z-axis.

[0327] τ yx This represents the shear stress acting on a plane perpendicular to the y-axis and along the x-axis.

[0328] τ yz This represents the shear stress acting on a plane perpendicular to the Y-axis and along the z-axis.

[0329] τ zx This represents the shear stress acting on a plane perpendicular to the Z-axis and along the X-axis.

[0330] τ zy This represents the shear stress acting on a plane perpendicular to the Z-axis and along the Y-axis.

[0331] R represents the rotation matrix; R T Let R be the transpose of R;

[0332] Step 2: Based on the stress tensor σ ijGiven the normal vector n and the force-bearing area A of each surface of the rock sample, and arbitrarily choosing a pressure unit 3, let F be the pressure exerted by the force-applying block 9 of the pressure unit 3 on the corresponding surface of the rock sample, including normal and tangential components; then we have:

[0333] F=(σ ij ·n)·A (4)

[0334] In the formula: n: the unit normal vector of the rock sample surface, with the direction pointing from the inside of the rock sample to the outside;

[0335] A: The surface area of ​​the rock sample subjected to force.

[0336] Step 3: Obtain the spatial azimuth angles (α, β) of cylinder 16 using angle sensor 14, and simultaneously solve the mechanical equilibrium equations to determine the axial forces in each cylinder 16. The stress condition of the rock sample is as follows: Figure 9 As shown, each surface of the rock sample is subjected to one normal force and two tangential forces, the specific magnitudes of which can be determined by equation (4). For the pressure unit 3 installed on the right side plate, the force F it applies is the vector sum of the forces on the right side surface of the rock sample, as shown in equation (5).

[0337] F = F x +F xy +F xz (5)

[0338] In the formula: F x F represents the normal force acting on the surface of the rock sample; xy F represents the tangential force acting on the surface of the rock sample along the Y-axis. xz This represents the tangential force acting on the surface of the rock sample along the Z-axis.

[0339] Let the three telescopic arms in the pressurization unit 3 be the first telescopic arm, the second telescopic arm, and the third telescopic arm;

[0340] Let F 轴1 F represents the axial force applied by the first telescopic arm. 轴2 F represents the axial force applied by the second telescopic arm. 轴3 This indicates the axial force applied by the third telescopic arm.

[0341] For a force analysis of this, see Figure 10 As shown, the equilibrium equation can be listed as equation (6). By solving the equilibrium equation, the axial force F that should be applied to each cylinder 16 in the pressurization unit 3 installed on the right side plate can be obtained. 轴1 F 轴2 F 轴3 ;

[0342]

[0343] In the formula:

[0344] α1, α2, and α3 represent the elevation angles of the first, second, and third telescopic booms, respectively.

[0345] β1, β2, and β3 represent the rotation angles of the first, second, and third telescopic arms, respectively.

[0346] (6) Obtaining stress tensor and failure strength

[0347] According to the loading method, and in combination with equations (2) to (6), the axial force of the telescopic arm is gradually adjusted to load the rock sample until the rock sample fails. The axial force adjusted step by step will be output through the embedded mechanical sensor 24; the detection values ​​of the detection device before and after each loading step are collected; at the same time, the principal stresses σ1, σ2, σ3 at the time of rock sample failure and the stress tensor σ during the entire loading process are recorded. ij .

[0348] (7) Obtaining the strain tensor

[0349] Based on the spatial azimuth angles of each telescopic arm before and after loading of the rock sample obtained by angle sensor 14 and the lengths of the telescopic arm 8 before and after loading of the rock sample obtained by electronic transmitter 18, the component changes (Δx, Δy, Δz) of the rock sample in each coordinate axis direction are determined. Figure 11 The telescopic arm length is decomposed into three orthogonal axes in a spatial geometric coordinate system, and then the changes in the telescopic arm length along the three orthogonal axes before and after loading the rock sample are calculated (Δl). x m ,Δl y m ,Δl z m ), m=1, 2, 3; For a certain pressurizing unit 3, the variation of the length of each telescopic arm of the pressurizing unit in each coordinate axis direction can be obtained by equation (7):

[0350]

[0351] In the formula:

[0352] Δl x m This represents the component of the m-th telescopic arm's variation along the X-axis in the spatial geometric coordinate system;

[0353] Δl y m This represents the component of the m-th telescopic arm's variation along the Y-axis in the spatial geometric coordinate system;

[0354] Δl z m This represents the component of the m-th telescopic arm's variation along the Z-axis in the spatial geometric coordinate system;

[0355] l m ′ represents the length of the m-th telescopic arm before loading; l m "" indicates the length of the m-th telescopic arm after loading;

[0356] α m ′ represents the elevation angle of the m-th telescopic arm before loading; α m "" indicates the elevation angle of the m-th telescopic arm after loading;

[0357] β m ′ represents the rotation angle of the m-th telescopic arm before loading; β m "" indicates the rotation angle after the m-th telescopic arm is loaded.

[0358] All the telescopic arms 8 of the pressurizing unit 3 are sorted according to serial number 1-18. After obtaining the change value of all the telescopic arms 8 of the pressurizing unit 3 in each coordinate axis direction, in order to reduce the error, according to the following formula (8), the average value of the change value of all the telescopic arms 8 of the pressurizing unit 3 in each coordinate axis direction is taken to obtain the change component of the rock sample in each coordinate axis direction.

[0359]

[0360] In the formula:

[0361] Δx represents the variation component of the rock sample along the X-axis in the spatial geometric coordinate system;

[0362] Δy represents the variation component of the rock sample along the Y-axis in the spatial geometric coordinate system;

[0363] Δz represents the variation component of the rock sample along the Z-axis in the spatial geometric coordinate system;

[0364] Δl x η This represents the variation component of the ηth telescopic arm along the X-axis in the spatial geometric coordinate system;

[0365] Δl y η This represents the variation component of the ηth telescopic arm along the Y-axis in the spatial geometric coordinate system;

[0366] Δl z η This represents the variation component of the ηth telescopic arm along the Z-axis in the spatial geometric coordinate system;

[0367] η represents the telescopic boom number, η = 1, 2, ..., 18.

[0368] Based on the component variations (Δx, Δy, Δz) of the rock sample along each coordinate axis, the strain tensor ε of the rock sample is calculated. ij , ε ij The expression for is shown in equation (9).

[0369]

[0370] In the formula:

[0371] In the formula:

[0372] ε ij It represents the second-order strain tensor, used to characterize the deformation state of a material in three-dimensional space;

[0373] ε x This represents the normal strain of the rock sample in the X-axis direction;

[0374] ε y This represents the normal strain of the rock sample in the Y-axis direction;

[0375] ε z This represents the normal strain of the rock sample in the Z-axis direction;

[0376] γ xy γ yx γ represents the engineering shear strain of the rock sample in the XY plane; xy =γ yx ;

[0377] γ xz γ zx γ represents the engineering shear strain of the rock sample on the XZ plane; xz =γ zx ;

[0378] γ yz γ zy γ represents the engineering shear strain of the rock sample on the YZ plane; yz =γ zy ;

[0379] ε xy ε yx ε represents the tensor shear strain of the rock sample in the XY plane; xy =ε yx ;

[0380] ε xz ε zx ε represents the tensor shear strain of the rock sample on the XZ plane; xz =ε zx ;

[0381] ε yz ε zy ε represents the tensor shear strain of the rock sample on the YZ plane; yz =ε zy ;

[0382] like Figure 9As shown, the length of the cubic rock sample in each direction is L. Under small deformation, the strain tensor components are solved according to equation (10).

[0383]

[0384] In the formula:

[0385] γ1 represents the angle by which the rock sample on the XY plane deviates from the Y-axis;

[0386] γ2 represents the angle by which the rock sample on the XY plane deviates from the X-axis;

[0387] γ3 represents the angle by which the rock sample on the XZ plane deviates from the Z-axis;

[0388] γ4 represents the angle by which the rock sample on the XZ plane deviates from the X-axis;

[0389] γ5 represents the angle by which the rock sample on the YZ plane deviates from the Y-axis;

[0390] γ6 represents the angle by which the rock sample on the YZ plane deviates from the Z-axis;

[0391] Δx represents the variation component of the rock sample along the X-axis in the spatial geometric coordinate system;

[0392] Δy represents the variation component of the rock sample along the Y-axis in the spatial geometric coordinate system;

[0393] Δz represents the variation component of the rock sample along the Z-axis in the spatial geometric coordinate system.

[0394] (8) Conduct multipath failure tests by changing the initial stress state of the new principal stress space:

[0395] Reinstall the new rock sample according to steps 1 and 2, modify the initial stress state in the new principal stress space in step (3), and perform steps (4) to (7) to establish the stress-strain dataset {σ} for multipath failure under this principal stress space. x , σ y , σ z , τ xy , τ yx , τ yz ,ε,ε y , ε z , ε xy , ε xz , ε yz} and the damage intensity dataset {σ1, σ2, σ3}.

[0396] (9) Global Data Acquisition:

[0397] Reinstall the specimen according to steps 1 and 2, change φ, θ, and ψ in step (3), and perform steps (4) to (8) to achieve multipath failure testing and data acquisition under different principal stress spaces. The traversal process of φ, θ, and ψ parameters is as follows:

[0398] ① Fix φ and θ, iterate through ψ: Keep the current φ and θ unchanged, and let ψ start from the initial value and gradually increase it in steps of Δψ = 5° until the final value of ψ is reached;

[0399] ② Fix φ, iterate through θ: After completing the ψ traversal under the current φ and θ, keep φ unchanged, increase θ by Δθ = 5° to obtain a new θ value, and repeat step ① for the new θ value until θ reaches the termination value;

[0400] ③ Traverse φ: After completing the traversal of all θ and ψ under the current φ, increase φ by Δφ = 5° to obtain a new φ value. Repeat step ② for the new φ value until φ reaches the termination value, and the traversal ends.

[0401] (10) Constructing a rock strength criterion model based on neural networks:

[0402] like Figure 12 The following describes the construction of a deep neural network with 6 parameters (φ, θ, ψ, σ1, σ2, σ3) as input and a corrupted state f as output.

[0403] Step 1: Build the input layer. The input layer receives 6 parameters (φ, θ, ψ, σ1, σ2, σ3). In practice, these input parameters are first standardized using Z-scores to eliminate the differences in dimensions between different features, thereby improving the model's training performance and generalization ability. The specific implementation is as follows:

[0404] Collect experimental data, including spatial transformation parameters φ, θ, and ψ, as well as intensity parameters σ1, σ2, and σ3.

[0405] Calculate the mean u and standard deviation for each variable.

[0406] Z-score standardization is performed on each input variable g:

[0407]

[0408] In the formula: g represents the input variable; g norm This represents the standardized variables; u represents the mean of each variable; This represents the standard deviation of each variable.

[0409] The standardized parameters are input into the input layer of the neural network, which contains 6 neurons, corresponding to φ, θ, ψ, σ1, σ2 and σ3 respectively.

[0410] Step 2: Construct the hidden layers. The hidden layers are designed as three fully connected layers with 64, 128, and 64 neurons respectively. The ReLU activation function is chosen. The specific implementation is as follows:

[0411] ReLU(h) = max(0,h) (12)

[0412] In the formula: h represents the input variable of the activation function; ReLU() represents the activation function.

[0413] Use deep learning frameworks (such as TensorFlow or PyTorch) to define neural network structures.

[0414] The first fully connected layer has an input dimension of 6 and an output dimension of 64.

[0415] The second fully connected layer has an input dimension of 64 and an output dimension of 128.

[0416] The third fully connected layer has an input dimension of 128 and an output dimension of 64.

[0417] Each fully connected layer is followed by a ReLU activation function to enhance the network's ability to represent nonlinearities.

[0418] Step 3: Construct the output layer. The output layer represents the rock state corresponding to different parameters, where 1 indicates rock failure, 0 indicates the rock is in a critical state of failure, and -1 indicates the rock is not failed. The output layer contains one neuron, and the output is mapped to the range [-1, 1] using the Tanh function.

[0419]

[0420] In the formula: b represents the input variable of the Tanh function. tanh() represents the activation function.

[0421] Step 4: Network training and optimization, implemented as follows:

[0422] Dataset partitioning: The data is divided into a training set and a test set in a ratio of 8:2.

[0423] Optimizer selection: The Adam backpropagation algorithm was used to optimize the network weights, with a learning rate of 0.001.

[0424] Loss function selection: Mean Squared Error (MSE) loss function:

[0425]

[0426] In the formula: L s For training loss; f d f is the network prediction value for the d-th sample; true,dd represents the true value of the d-th sample; N is the number of samples.

[0427] Training stop condition: The training network will stop training when it reaches the preset number of training rounds, 1000 rounds.

[0428] Model validation: The model's performance is validated using a test set. The mean squared error (MSE) on the test set is calculated to evaluate the model's performance and generalization ability. Based on the validation results, the model's hyperparameters can be tuned and optimized to improve the model's predictive performance.

[0429] Step 5: Model application. The trained neural network model is applied to rock failure prediction. New stress state parameters (φ,θ,ψ,σ1,σ2,σ3) are input, and the state f of the rock in the stress space is output.

[0430] (11) Construct a high-dimensional stress space rock constitutive model based on dual neural network coupling.

[0431] like Figure 13 As shown, a high-dimensional stress-space rock constitutive model based on dual neural network coupling is constructed. The second neural network uses the stress-strain time series data of the previous t steps as input to predict the stress-strain response of the t+1 step. The first neural network uses the elastic modulus E, Poisson's ratio v, cohesion c, friction angle ω, and spatial transformation parameters φ, θ, and ψ as input to predict the stress-strain response of the previous t steps. The first neural network provides input data to the second neural network, which is then used to predict the later stress-strain response of the rock. The specific implementation process is as follows:

[0432] 1) Construct a second neural network with the stress-strain data of step t as input and the stress-strain data of step t+1 as output:

[0433] Step 1: Building the input layer. First, the stress-strain data is Z-score standardized to eliminate dimensional differences between different features, improving the model's training effect and generalization ability. Then, the stress-strain data is split according to the step size to form sequential data. Each sequence contains strain and stress component data for t steps, which serves as the input to the second neural network. The specific implementation is as follows:

[0434] Step 1: Collect experimental data, including 6 strain components and 6 stress components at each step of the loading process;

[0435] Step 2: Calculate the mean and standard deviation for each variable;

[0436] Step 3: Perform Z-score standardization on each input variable;

[0437] Step 4: The standardized data is divided into sequences by step size. Each sequence contains strain and stress data for t steps, which serve as input to the neural network. Each step contains 12 features, 6 of which are strain components and 6 are stress components. The input data has a shape of (t, 12) and is passed to subsequent LSTM layers for processing.

[0438] Step 2: Construct an LSTM layer. The Long Short-Term Memory (LSTM) network is used to process time-series data. LSTM layers can effectively capture temporal dependencies and long-term memory features in the data. The LSTM layer is designed as a two-layer structure, with 128 and 64 neurons in each layer, respectively. The ReLU activation function is chosen. The specific implementation is as follows:

[0439] The first LSTM layer has an input dimension of 12 and an output dimension of 128.

[0440] The second LSTM layer has an input dimension of 128 and an output dimension of 64.

[0441] Each LSTM layer is followed by a ReLU activation function to enhance the network's ability to represent nonlinearities.

[0442] The third step involves building the output layer. The strain and stress data at step t+1 of each sequence are used as the output target for training the neural network. The output dimension is 12, including 6 strain components and 6 stress components at step t+1. The output is implemented through a fully connected layer to predict the strain and stress at step t+1. The specific implementation is as follows:

[0443] The input dimension of the output layer is 64 (from the output of the second LSTM layer), and the output dimension is 12.

[0444] The output of the LSTM layer is mapped to the strain and stress components at step t+1 using a fully connected layer.

[0445] Step 4: Network training and optimization, implemented as follows:

[0446] Dataset partitioning: The collected dataset is randomly divided into a training set and a test set in an 8:2 ratio. The training set is used to train the neural network model, and the test set is used to evaluate the model's performance and generalization ability.

[0447] Optimizer and learning rate: The Adam optimizer is used to update and optimize the model parameters, and the learning rate is set to 0.001.

[0448] Loss function: The mean squared error (MSE) is used as the loss function to measure the difference between the model's predicted value and the true value.

[0449] Training stop condition: Training will stop when the preset number of training rounds of 1000 is reached.

[0450] Model validation: The trained model is validated using a test set. The mean squared error (MSE) on the test set is calculated to evaluate the model's performance and generalization ability. Based on the validation results, the model's hyperparameters can be adjusted and optimized to improve the model's predictive performance.

[0451] 2) Construct a first neural network with rock mechanical parameters (elastic modulus E, Poisson's ratio v, cohesion c, friction angle ω, and spatial transformation parameters φ, θ, and φ) as inputs and the previous t-step stress-strain data as output:

[0452] Step 1: Build the input layer. The input layer receives 7 parameters (E, v, c, ω, φ, θ, ψ). In practice, these input parameters are first standardized using Z-scores to eliminate the differences in dimensions between different features, thereby improving the model's training performance and generalization ability. The specific implementation is as follows:

[0453] Collect experimental data, including spatial transformation parameters φ, θ, and φ, as well as rock mechanics parameters E, v, c, and ω.

[0454] Calculate the mean and standard deviation for each variable.

[0455] Z-score standardization is performed on each input variable:

[0456] The standardized parameters are input into the input layer of the neural network, which contains 7 neurons, corresponding to E, v, c, ψ, φ, θ, and ψ, respectively.

[0457] Step 2: Construct hidden layers. The hidden layers are designed as three fully connected layers with 64, 256, and 512 neurons respectively.

[0458] The activation function chosen is ReLU. The specific implementation is as follows:

[0459] Use deep learning frameworks (such as TensorFlow or PyTorch) to define neural network structures.

[0460] The first fully connected layer has an input dimension of 7 and an output dimension of 64.

[0461] The second fully connected layer has an input dimension of 64 and an output dimension of 256.

[0462] The third fully connected layer has an input dimension of 256 and an output dimension of 512.

[0463] Each fully connected layer is followed by a ReLU activation function to enhance the network's ability to represent nonlinearities.

[0464] Step 3: Build the output layer, flatten the data from the previous t steps as the output, and the output layer contains t×12 neurons.

[0465] Step 4: Network training and optimization, implemented as follows:

[0466] Dataset partitioning: The data is divided into a training set and a test set in a ratio of 8:2.

[0467] Optimizer selection: The Adam backpropagation algorithm was used to optimize the network weights, with a learning rate of 0.001.

[0468] Loss function selection: Mean Squared Error (MSE) loss function.

[0469] Training stop condition: The training network will stop training when it reaches the preset number of training rounds, 1000 rounds.

[0470] Model validation: The model's performance is validated using a test set. The mean squared error (MSE) on the test set is calculated to evaluate the model's performance and generalization ability. Based on the validation results, the model's hyperparameters can be tuned and optimized to improve the model's predictive performance.

[0471] 3) Model Application: The first neural network outputs stress-strain data for the first t steps by inputting rock mechanics parameters and spatial transformation parameters (E,ν,c,ω,φ,θ,ψ). This stress-strain data from the first t steps is then used as input to the second neural network to predict the stress-strain data for the t+1 step. By progressively inputting new data, the strain and stress state of subsequent steps are continuously predicted, achieving dynamic prediction of rock mechanics behavior. The specific steps are as follows:

[0472] Step 1: Predict the initial t-step data using the first neural network.

[0473] The second step: Using the initial t-step data as input, the strain and stress at step t+1 are predicted through the second neural network.

[0474] Step 3: Add the predicted data from step t+1 to the sequence, remove the earliest step data, and form a new t-step sequence data, which is used as the input to the second neural network.

[0475] Step 4: Repeat the above steps to gradually predict the strain and stress state of subsequent steps, thereby achieving dynamic prediction of rock mechanical behavior.

[0476] The first neural network, the second neural network, the backpropagation algorithm, the Adam optimizer, the Z-score normalization, and the Long Short-Term Memory (LSTM) layer mentioned above can all adopt existing functional modules and software, or be constructed using existing functional modules and software and conventional technical means.

[0477] The above embodiments are only used to illustrate the technical ideas and features of the present invention. Their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The patent scope of the present invention should not be limited by these embodiments. That is, all equivalent changes or modifications made in accordance with the spirit of the present invention still fall within the patent scope of the present invention.

Claims

1. An experimental system for obtaining high-dimensional constitutive relations of rocks, characterized in that, The system includes six pressurizing units that apply and unload pressure to rock samples, and a detection device to measure the magnitude and direction of the force applied by each pressurizing unit to the rock sample. Each pressurizing unit includes three telescopic arms, a flat base, and a force-applying block. One end of each of the three telescopic arms is hinged to the flat base, and the three hinge centers form an equilateral triangle. The other end of each arm is hinged to the force-applying block. The detection device measures the spatial azimuth angle, length change, and applied axial force of each telescopic arm. The force-applying block is a combination of a partial sphere and a square block. A clamp C, which directly contacts the rock sample, is detachably mounted on the force-applying block. The bottom of clamp C... The force-applying surface of the square block is fitted with the surface of the sphere. Three spherical grooves A are evenly distributed around the line connecting the center of the sphere and the center of the square block. A spherical seat is fixed to the flat base. A spherical groove B is provided inside the spherical seat. One end of the telescopic arm has a spherical end A that mates with the spherical groove A. The other end has a spherical end B that mates with the spherical groove B. A clamp A is fixed to the sphere to prevent the spherical end A from falling out of the spherical groove A. A clamp B is fixed to the flat base to prevent the spherical end B from falling out of the spherical groove B. Both clamps A and B have through holes. The inner surfaces of the through holes of clamps A and B mate with the inner surfaces of the spherical grooves A and B to form a spherical surface, and the area of ​​the formed spherical surface is greater than 2πR. q 2, R q Let q be the radius of the spherical end, where q = A and B.

2. The experimental system for obtaining high-dimensional constitutive relations of rocks according to claim 1, characterized in that, The three telescopic arms in each pressurization unit are either hydraulic or electric. The hydraulic telescopic arm includes a cylinder and a piston rod. The detection device includes the following sensors installed on each hydraulic telescopic arm: a magnetostrictive displacement sensor for detecting the displacement of the piston rod relative to the cylinder, an angle sensor for detecting the spatial angle of the cylinder, and a pressure sensor for detecting the force on the end of the piston rod. The magnetostrictive displacement sensor is installed inside the cylinder; the angle sensor is installed on the outside of the cylinder end; and the pressure sensor is an embedded mechanical sensor installed inside the extended end of the piston rod.

3. The experimental system for obtaining high-dimensional constitutive relations of rocks according to claim 1, characterized in that, It also includes a hexahedral cavity with one open side and a sealing plate for closing the hexahedral cavity. The sealing plate is located on the rear side of the hexahedral cavity and is called the rear side plate. The other side plates surrounding the hexahedral cavity are respectively called the upper side plate, lower side plate, left side plate, right side plate and front side plate.

4. The experimental system for obtaining high-dimensional constitutive relations of rocks according to claim 3, characterized in that, It also includes six bases, which are fixedly installed at the geometric center of the inner wall of the six side plates respectively; of the six pressurizing units, the flat bases of five pressurizing units are fixedly connected to the bases on the upper, lower, left, right and front side plates respectively; the flat base of the other pressurizing unit is fixedly connected to the base on the sealing plate.

5. The experimental system for obtaining high-dimensional constitutive relations of rocks according to claim 3, characterized in that, It also includes an electric drive mechanism for driving the sealing plate to close or open the hexahedral cavity, the electric drive mechanism comprising three or more synchronously moving electric cylinders; each electric cylinder has its fixed end fixedly connected to the front side plate and its telescopic end fixedly connected to the sealing plate.

6. A test method for obtaining high-dimensional constitutive relations of rocks using the test system for obtaining high-dimensional constitutive relations of rocks according to any one of claims 1 to 5, characterized in that, The method includes the following steps: Step 1: Cut the rock sample into cubic rock specimens and place the rock specimens between the pressure units; Step 2, establish the spatial geometric coordinate system and the initial principal stress space: A spatial geometric coordinate system XYZ is established with the center of the cubic rock sample as the origin, and an initial principal stress space P(S1,S2,S3) is established at the same time; S1, S2, and S3 are the axes with the center of the rock sample as the origin, which are parallel to the X-axis, Y-axis, and Z-axis of the spatial geometric coordinate system, respectively. Step 3, define the spatial transformation parameters and the initial stress state of the given rock sample: The initial principal stress space is rotated using the ZXZ order Euler angle method. The angle of counterclockwise rotation of the initial principal stress space around the S3 axis is defined as φ; the angle of counterclockwise rotation around the changed S1 axis after rotation around the S3 axis is defined as θ; and the angle of counterclockwise rotation around the changed S3 axis after rotation around the changed S1 axis is defined as ψ. Let the new principal stress space obtained by rotating the initial principal stress space counterclockwise around the S3 axis, then counterclockwise around the changed S1 axis, and then counterclockwise around the changed S3 axis be P′(S1′,S2′,S3′). The initial stress state matrix of the given rock sample in the new principal stress space P′(S1′,S2′,S3′) is V. Let V represent the following: In the formula: σ1 represents the first principal stress, and under the initial stress state, σ1 = 0 MPa; σ2 represents the second principal stress; σ3 represents the third principal stress; Step 4, set the loading method as follows: the two principal stresses σ2 and σ3 are constant, and the other principal stress σ1 increases in a predetermined step size Δσ. Step 5: Convert V into a stress tensor in a spatial geometric coordinate system using a rotation matrix; Based on the stress tensor and the normal vector and force-bearing area of ​​each surface of the rock sample, the force on each surface of the rock sample is calculated; the axial force of each telescopic arm is determined according to the mechanical equilibrium equation and the spatial orientation angle of the telescopic arm obtained by the detection device, so that the confining pressure of the rock sample reaches the predetermined value. Step 6: According to the loading method, gradually adjust the axial force of the telescopic arm to load the rock sample until the rock sample fails; collect the detection values ​​of the detection device before and after each loading step; at the same time, record the principal stresses σ1, σ2, σ3 when the rock sample fails and the stress tensor during the entire loading process. Step 7: Obtain the spatial azimuth angle and length change of each telescopic arm based on the detection value of the detection device, and further obtain the component changes of the rock sample in each coordinate axis direction; calculate the strain tensor of the rock sample based on the component changes of the rock sample in each coordinate axis. Step 8: Reinstall the new rock sample according to Step 1 and Step 2, change the initial stress state of the principal stress space P′ in Step 3, and perform Step 4 to Step 7 to establish a dataset of stress-strain and failure strength of multipath failure under the principal stress space P′. Step 9: Reinstall the new rock sample according to Step 1 and Step 2, change φ, θ, and ψ in Step 3, and perform Step 4 to Step 8 to obtain the stress-strain and failure strength datasets of multipath failure under different principal stress spaces. Step 10: Build a neural network using the obtained datasets of stress-strain and failure intensity of multipath failure under different principal stress spaces to construct a high-dimensional strength criterion; Step 11: Using the obtained datasets of stress-strain and failure intensity of multi-path failure under different principal stress spaces, a neural network is built to construct a high-dimensional constitutive relation.

7. The experimental method for obtaining high-dimensional constitutive relations of rocks according to claim 6, characterized in that, The stress tensor σ in the spatial geometric coordinate system is obtained from the initial stress state matrix V in the new principal stress space by the following formula. ij ; In the formula: σ ij It represents the second-order stress tensor, which represents the stress state at a point in three-dimensional space; i represents the normal direction of the stress surface, with a value range of x, y, z; x, y, and z correspond to the directions of the XYZ coordinate axes. j represents the direction of the stress component, with a value range of x, y, z; σ x This represents the normal stress acting on a plane perpendicular to the X-axis and along the X-axis direction; σ y This represents the normal stress acting on a plane perpendicular to the Y-axis and along the Y-axis direction; σ z This represents the normal stress acting on a plane perpendicular to the Z-axis and along the Z-axis direction; τ xy This represents the shear stress acting on a plane perpendicular to the X-axis and along the Y-axis. τ xz This represents the shear stress acting on a plane perpendicular to the X-axis and along the Z-axis. τ yx This represents the shear stress acting on a plane perpendicular to the Y-axis and along the X-axis. τ yz This represents the shear stress acting on a plane perpendicular to the Y-axis and along the Z-axis. τ zx This represents the shear stress acting on a plane perpendicular to the Z-axis and along the X-axis. τ zy This represents the shear stress acting on a plane perpendicular to the Z-axis and along the Y-axis. R represents the rotation matrix; R T Let R be the transpose of R; Taking any pressure unit, let F be the pressure exerted by the force-applying block of that pressure unit on the corresponding surface of the rock sample, then we have: F=(σ ij ·n)·A; In the formula: n: The unit normal vector of the rock sample surface, pointing from the inside of the rock sample to the outside; A: The area of ​​the rock sample surface subjected to force; Each surface of the rock sample is subjected to one normal force and two tangential forces, therefore: F=F x +F xy +F xz ; In the formula: F x This represents the normal force acting on the surface of the rock sample; F xy This represents the tangential force acting on the surface of the rock sample along the Y-axis. F xz This represents the tangential force acting on the surface of the rock sample along the Z-axis. Let the three telescopic arms in the pressurization unit be the first telescopic arm, the second telescopic arm, and the third telescopic arm; Let F 轴1 F represents the axial force applied by the first telescopic arm. 轴2 F represents the axial force applied by the second telescopic arm. 轴3 This indicates the axial force applied by the third telescopic arm; By solving the following equilibrium equation, F is obtained. 轴1 F 轴2 F 轴3 ; In the formula: α1 represents the elevation angle of the first telescopic boom; α2 represents the elevation angle of the second telescopic boom; α3 represents the elevation angle of the third telescopic boom; β1 represents the rotation angle of the first telescopic arm; β2 represents the rotation angle of the second telescopic arm; β3 represents the rotation angle of the third telescopic arm; α1, α2, α3, β1, β2, and β3 are obtained by detection using a detection device; Keeping σ2 and σ3 constant in the new principal stress space P′(S′1,S′2,S′3), the maximum principal stress σ1 is increased in predetermined steps Δσ until the rock specimen fails. During loading, the axial force of each telescopic arm in the pressurization unit is adjusted in real time according to the changing principal stress. At the same time, the principal stresses σ1, σ2, and σ3 at failure are recorded, and the stress tensor σ of the rock specimen during the entire loading process is solved. ij ; The lengths of each telescopic arm before and after loading of the rock sample are obtained by the detection device to determine the component changes Δx, Δy, and Δz of the rock sample in each coordinate axis direction; the length of the telescopic arm is decomposed into a spatial geometric coordinate system, and the changes in the length of the telescopic arm in the three axes of the spatial geometric coordinate system XYZ before and after loading of the rock sample are calculated; let m be the telescopic arm number in the pressurization unit, m = 1, 2, 3. The following formula can be used to calculate the variation of the length of each telescopic arm of the pressurizing unit in each coordinate axis direction: In the formula: Δl x m This represents the component of the m-th telescopic arm's variation along the X-axis in the spatial geometric coordinate system; Δl y m This represents the component of the m-th telescopic arm's variation along the Y-axis in the spatial geometric coordinate system; Δl z m This represents the component of the m-th telescopic arm's variation along the Z-axis in the spatial geometric coordinate system; l m ′ represents the length of the m-th telescopic arm before loading; l m "" indicates the length of the m-th telescopic arm after loading; α m ′ represents the elevation angle of the m-th telescopic arm before loading; α m "" indicates the elevation angle of the m-th telescopic arm after loading; β m ′ represents the rotation angle of the m-th telescopic arm before loading; β m "" indicates the rotation angle of the m-th telescopic arm after loading; The telescopic arms of all pressurizing units are arranged in sequence from 1 to 18. After calculating the change values ​​of the telescopic arms of all pressurizing units in each coordinate axis direction, in order to reduce the error, the average value of the change values ​​of the telescopic arms of all pressurizing units in each coordinate axis direction is taken according to the following formula to obtain the change components of the rock sample in each coordinate axis direction. In the formula: Δx represents the variation component of the rock sample along the X-axis in the spatial geometric coordinate system; Δy represents the variation component of the rock sample along the Y-axis in the spatial geometric coordinate system; Δz represents the variation component of the rock sample along the Z-axis in the spatial geometric coordinate system; Δl x η This represents the variation component of the ηth telescopic arm along the X-axis in the spatial geometric coordinate system; Δl y η This represents the variation component of the ηth telescopic arm along the Y-axis in the spatial geometric coordinate system; Δl z η This represents the variation component of the ηth telescopic arm along the Z-axis in the spatial geometric coordinate system; η represents the telescopic boom number, η = 1, 2, ..., 18; Based on the component variations of the rock sample along each coordinate axis, the strain tensor of the rock sample is calculated. The strain tensor ε ij The calculation formula is as follows: In the formula: ε ij It represents the second-order strain tensor, used to characterize the deformation state of a material in three-dimensional space; ε x This represents the normal strain of the rock sample in the X-axis direction; ε y This represents the normal strain of the rock sample in the Y-axis direction; ε z This represents the normal strain of the rock sample in the Z-axis direction; γ xy γ yx γ represents the engineering shear strain of the rock sample in the XY plane; xy =γ yx ; γ xz γ zx γ represents the engineering shear strain of the rock sample on the XZ plane; xz =γ zx ; γ yz γ zy γ represents the engineering shear strain of the rock sample on the YZ plane; yz =γ zy ; ε xy ε yx ε represents the tensor shear strain of the rock sample in the XY plane; xy =ε yx ; ε xz ε zx ε represents the tensor shear strain of the rock sample on the XZ plane; xz =ε zx ; ε yz ε zy ε represents the tensor shear strain of the rock sample on the YZ plane; yz =ε zy ; Let the side length of the cubic rock sample be L. Under the condition of small deformation, the strain tensor components are solved according to the following formula; In the formula: γ1 represents the angle by which the rock sample on the XY plane deviates from the Y-axis; γ2 represents the angle by which the rock sample on the XY plane deviates from the X-axis; γ3 represents the angle by which the rock sample on the XZ plane deviates from the Z-axis; γ4 represents the angle by which the rock sample on the XZ plane deviates from the X-axis; γ5 represents the angle by which the rock sample on the YZ plane deviates from the Y-axis; γ6 represents the angle by which the rock sample on the YZ plane deviates from the Z-axis; Δx represents the variation component of the rock sample along the X-axis in the spatial geometric coordinate system; Δy represents the variation component of the rock sample along the Y-axis in the spatial geometric coordinate system; Δz represents the variation component of the rock sample along the Z-axis in the spatial geometric coordinate system; The following parameter data were recorded simultaneously during the multipath failure test under this principal stress space; σ x σ y σ z τ xy τ yx τ yz ε x ε y ε z ε xy ε xz ε yz The stress-strain dataset includes the following parameters: σ1, σ2, σ3. x σ y σ z τ xy τ yx τ yz ε x ε y ε z ε xy ε xz ε yz The damage intensity data includes the following: σ1, σ2, σ3; By changing the spatial transformation parameters φ, θ, and ψ, multipath failure test data were obtained under different principal stress spaces.

8. The experimental method for obtaining high-dimensional constitutive relations of rocks according to claim 6, characterized in that, A rock strength criterion model is constructed based on a neural network. The input of the rock strength criterion model is the following parameters: φ,θ,ψ,σ1,σ2,σ3; and the output is the rock failure state. The collected destructive test data were used to create training samples to train the rock strength criterion model. The trained rock strength criterion model was then used to predict the rock failure state.

9. The experimental method for obtaining high-dimensional constitutive relations of rocks according to claim 6, characterized in that, A high-dimensional stress space rock constitutive model based on dual neural network coupling was constructed. The high-dimensional stress space rock constitutive model includes a first neural network and a second neural network connected in sequence. The first neural network takes the elastic modulus E, Poisson's ratio v, cohesion c, friction angle ω and spatial transformation parameters φ, θ and ψ of the rock sample as inputs to predict the stress-strain response in the first t steps. The second neural network takes the stress-strain time series data in the first t steps as input and outputs the stress-strain response in the t+1 step. The collected destructive test data were used to create training samples to train a high-dimensional stress space rock constitutive model. The trained high-dimensional stress space rock constitutive model was then used to predict rock stress and strain.

10. An apparatus for obtaining experimental methods of high-dimensional constitutive relations of rocks, comprising a memory and a processor, characterized in that, The memory is used to store a computer program; the processor is used to execute the computer program and, when executing the computer program, implement the experimental method steps for obtaining the high-dimensional constitutive relation of rocks as described in any one of claims 6 to 9.

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