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

Abstract

The invention discloses a test system for acquiring a rock high-dimensional constitutive relationship. The test system comprises six pressurizing units for applying and unloading pressure to a sample, and a detection device for correspondingly detecting the magnitude and direction of force applied to the sample by the pressurizing units, each pressurizing unit comprises three telescopic arms, a plane base and a force application block; one ends of the three telescopic arms in each pressurizing unit are respectively hinged with the plane base, the connecting lines of the three hinged central points form an equilateral triangle, and the other ends of the three telescopic arms are hinged on the force application block; the detection device detects the space azimuth angle, the length variation and the applied axial force of each telescopic arm. The invention further discloses a test method for obtaining the rock high-dimensional constitutive relation. A high-dimensional stress space rock constitutive model and a rock strength criterion model based on the neural network are constructed. According to the invention, the application and separation of the total stress tensor of the sample can be realized, and the high-dimensional constitutive relationship is obtained by obtaining the stress-strain data and the breaking strength in different principal stress spaces.

Description

Technical Field

[0001] The present invention relates to the field of rock mechanics and rock engineering research, and particularly to a test system, method and device for obtaining the high-dimensional constitutive relationship of rocks. Background Art

[0002] Rocks have characteristics such as inhomogeneity and anisotropy, and exhibit highly nonlinear mechanical behaviors, which pose great challenges to the accurate description of rock mechanical properties. Currently, the research on rock mechanical behaviors mostly focuses on the fixed three-dimensional principal stress space. However, whether rocks follow the same laws under different principal stress spaces remains an insufficiently explored issue. Moreover, under the conditions of high inhomogeneity and anisotropy of rocks, it is still unknown whether the research on rocks under fixed three-dimensional principal stresses is accurate enough. Further, whether establishing the constitutive and strength criteria of rocks in multiple principal stress spaces can more accurately describe rock mechanical behaviors is also yet to be explored. In view of this, establishing the constitutive relationship and strength criteria of rocks in a high-dimensional stress space is of crucial significance for deeply understanding and accurately predicting the mechanical behaviors of rocks under complex stress conditions.

[0003] The stress tensor of rocks is generally represented by the Cauchy stress tensor, and its corresponding stress state includes 6 elements, namely three normal stresses and three shear stresses. Traditional rock mechanics testing machines, such as the high-pressure servo dynamic true triaxial testing machine with the patent number CN 103969107 B, can conduct various tests including true triaxial tests, but can only apply normal forces and cannot apply tangential forces on rock specimens. Therefore, it cannot change the principal stress space and can only study the mechanical behaviors of rocks within a fixed principal stress space; the high-rigidity soft rock true triaxial testing machine integrated with compression-tension-electromagnetic unloading with the patent number CN 110618030 B improves the overall stiffness of the machine and can obtain the full stress-strain curve of rock specimens. However, this curve can only reflect the relationship between stress and strain 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 test mechanism with the patent number CN 110987673 B can more realistically simulate the process of in-situ rock masses being affected by disturbing forces, but it cannot explore the possibility of establishing rock constitutive and strength criteria in multiple principal stress spaces to more accurately describe rock mechanical behaviors under complex stress states. In summary, although existing testing machines can conduct true triaxial tests, due to the great technical difficulties in applying forces in the shear direction, there is currently no rock mechanics testing machine that can consider full stress separation and cannot change the principal stress space. This technical gap restricts the research on the high-dimensional constitutive relationship and strength criteria of rocks. Summary of the Invention

[0004] The purpose of the present invention is to address the problem that the existing triaxial testing machine cannot perform full stress separation and cannot explore the constitutive relationship and strength criterion of rock in high-dimensional stress space. In order to solve the technical problems existing in the known technology, the present invention provides a test system, method and equipment for obtaining the high-dimensional constitutive relationship of rock.

[0005] The technical solution adopted by the present invention to solve the technical problems existing in the known technology is:

[0006] A test system for obtaining high-dimensional constitutive relations of rocks, comprising six pressurizing units for applying and unloading pressure to rock samples, and detection devices for correspondingly detecting the magnitude and direction of the force applied by the pressurizing units to the rock samples; each pressurizing unit comprises three telescopic arms, a plane base and a force-applying block; the three telescopic arms in each pressurizing unit are respectively 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 of the three telescopic arms are hinged to the force-applying block; the detection device detects the spatial azimuth, length change and axial force applied by each telescopic arm; the force-applying block is a combination of a partial sphere and a square block; a force-applying block is detachably mounted with a A clamp C is connected to the sphere, and the bottom surface of the clamp C fits the force-applying surface of the square block; three spherical grooves A are evenly distributed on the sphere around the line connecting the center of the sphere and the center of the square block; a spherical seat is fixedly connected to the plane base; a spherical groove B is arranged in the spherical seat; a spherical end A is arranged at one end of the telescopic arm to match the spherical groove A; a spherical end B is arranged at the other end to match the spherical groove B; a clamp A is fixedly connected to the sphere to prevent the spherical end A from escaping from the spherical groove A, and a clamp B is fixedly connected to the plane base to prevent the spherical end B from escaping from the spherical groove B; both the clamps A and B are provided with through holes; the inner surfaces of the through holes of the clamps A and B correspond to 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 is the radius of the spherical end q, q=A, B.

[0007] Furthermore, the three telescopic arms in each pressurizing unit are hydraulic telescopic arms or electric telescopic arms, and the hydraulic telescopic arms include 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 in the cylinder; the angle sensor is installed on the outside of the end of the cylinder; the pressure sensor is an embedded mechanical sensor, installed in the extended end of the piston rod.

[0008] Further, the test system for obtaining the high-dimensional constitutive relationship of rocks according to claim 1 is characterized in that it further comprises a hexahedral cavity with one open side and a sealing plate for closing the hexahedral cavity. Let the sealing plate be located at the rear side of the hexahedral cavity, which is called the rear side plate, and the other side plates enclosing 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] Further, the test system for obtaining the high-dimensional constitutive relationship of rocks according to claim 3 is characterized in that it further comprises six bases, and the six bases are respectively fixedly installed at the geometric centers of the inner walls of the six side plates; among the six pressurizing units, the planar bases of five of the pressurizing units are respectively fixedly connected to the bases on the upper, lower, left, right and front side plates; the planar base of the other pressurizing unit is fixedly connected to the base on the sealing plate.

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

[0011] The present invention also provides a test method for obtaining the high-dimensional constitutive relationship of rocks by using the above-mentioned test system for obtaining the high-dimensional constitutive relationship of rocks, which is characterized in that the method comprises the following steps:

[0012] Step 1, cutting the rock sample into a cubic rock specimen and placing the rock specimen between the pressurizing units;

[0013] Step 2, establishing a spatial geometric coordinate system and an initial principal stress space:

[0014] Establish a spatial geometric coordinate system XYZ with the center of the cubic rock specimen as the coordinate origin, and at the same time establish an initial principal stress space P(S1, S2, S3); S1, S2, S3 correspond to the axes respectively parallel to the X-axis, Y-axis and Z-axis of the spatial geometric coordinate system with the center of the rock specimen as the origin.

[0015] Step 3, defining spatial transformation parameters and specifying the initial stress state of the rock specimen:

[0016] The Euler angle method in the ZXZ order is used to rotate the initial principal stress space. The angle of counterclockwise rotation of the initial principal stress space around the S3 axis is defined as φ; after rotation around the S3 axis, the angle of counterclockwise rotation of the initial principal stress space around the changed S1 axis is defined as θ; after rotation around the changed S1 axis, the angle of counterclockwise rotation of the initial principal stress space around the changed S3 axis is defined as ψ; assume that the initial principal stress space rotates counterclockwise around the S3 axis, then counterclockwise around the changed S1 axis, and then counterclockwise around the changed S3 axis, and the new principal stress space obtained is P′(S′1, S′2, S′3). In the new principal stress space P′(S′1, S′2, S′3), the initial stress state matrix of the rock specimen is given as V; assume V is expressed as follows:

[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: two principal stresses σ2 and σ3 are constant, and the other principal stress σ1 increases in a predetermined step Δσ;

[0023] Step 5, convert V into the stress tensor in the spatial geometric coordinate system through the rotation matrix; based on the stress tensor, the normal vectors and the force-bearing areas of each surface of the rock specimen, calculate the force on each surface of the rock specimen; determine the axial forces of each telescopic arm according to the mechanical equilibrium equation and the spatial azimuth angle of the telescopic arm obtained by the detection device, so as to make the confining pressure of the rock specimen reach the predetermined value;

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

[0025] Step 7, obtain the spatial azimuth angle and the length change amount of each telescopic arm according to the detection values of the detection device, and further obtain the component changes of the rock specimen in each coordinate axis direction; according to the component changes of the rock specimen in each coordinate axis, calculate the strain tensor of the rock specimen;

[0026] Step 8, reinstall a new rock specimen according to Step 1 and Step 2, change the initial stress state of the principal stress space P′ in Step 3, perform Steps 4 to 7, and establish a stress-strain and failure strength data set for multi-path failure under the principal stress space P′;

[0027] Step 9: Reinstall the new rock specimen according to Step 1 and Step 2, change φ, θ, ψ in Step 3, perform Steps 4 to 8, and obtain the stress-strain and failure strength data sets of multi-path failure under different principal stress spaces;

[0028] Step 10: Use the stress-strain and failure strength data sets of multi-path failure under different principal stress spaces obtained to build a neural network to construct a high-dimensional strength criterion;

[0029] Step 11: Use the stress-strain and failure strength data sets of multi-path failure under different principal stress spaces obtained to build a neural network to construct a high-dimensional constitutive relationship.

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

[0031]

[0032] In the formula:

[0033] σ ij represents the second-order stress tensor and represents the stress state of a point in three-dimensional space;

[0034] i represents the normal direction of the stress acting surface, and the value range is: x, y, z; x, y, z respectively represent the XYZ coordinate axis directions;

[0035] j represents the acting direction of the stress component, and the value range is: x, y, z;

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

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

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

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

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

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

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

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

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

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

[0046] Arbitrarily select a pressurizing unit. Let F be the pressure exerted by the force-applying block of this pressurizing unit on the corresponding surface of the rock specimen. Then there is:

[0047] F = (σ ij ·n)·A;

[0048] In the formula:

[0049] n: the unit normal vector on the surface of the rock specimen, with the direction pointing from the inside to the outside of the rock specimen;

[0050] A: the force-bearing area on the surface of the rock specimen;

[0051] Each surface of the rock specimen will be subjected to a normal force and two shear forces. Then there is:

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

[0053] In the formula:

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

[0055] F xy represents the shear force acting on the surface of the rock specimen along the Y-axis direction;

[0056] F xz represents the shear force acting on the surface of the rock specimen along the Z-axis direction;

[0057] Assume that the three telescopic arms in this pressurizing unit are the first telescopic arm, the second telescopic arm, and the third telescopic arm respectively;

[0058] Assume that F 轴1 represents the axial force exerted by the first telescopic arm; F 轴2 represents the axial force exerted by the second telescopic arm; F 轴3 represents the axial force exerted by the third telescopic arm;

[0059] F is obtained by solving the following equilibrium equations 轴1 , F 轴2 , F 轴3 ;

[0060]

[0061] In the formula:

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

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

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

[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, β3 are detected by the detection device;

[0069] Keep σ2 and σ3 constant in the new principal stress space P′(S′1, S′2, S′3), and increase the maximum principal stress σ1 in a predetermined step Δσ until the rock sample fails; during the loading process, adjust the axial force of each telescopic arm in the pressurizing unit in real time according to the changing principal stress; at the same time, record the principal stresses σ1, σ2, σ3 at the time of failure and solve the stress tensor σ of the rock sample during the entire loading process ij ;

[0070] The lengths of each telescopic arm of the rock sample before and after loading are detected by the detection device to determine the component changes Δx, Δy, Δz of the rock sample in each coordinate axis direction; decompose the telescopic arm length into the space geometric coordinate system, and calculate the change values of the telescopic arm length of the rock sample before and after loading in the three axes X, Y, and Z of the space geometric coordinate system; let m be the serial number of the telescopic arm in the pressurizing unit, m = 1, 2, 3;

[0071] The change values of the lengths of each telescopic arm of the pressurizing unit in each coordinate axis direction are obtained by the following formula:

[0072]

[0073] In the formula:

[0074] Δl x m represents the component of the m-th telescopic arm changing in the X-axis direction in the space geometric coordinate system;

[0075] Δl y mrepresents the component of the m-th telescopic arm's change in the Y-axis direction under the spatial geometric coordinate system;

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

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

[0078] l m '' represents 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 '' represents 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 '' represents the rotation angle of the m-th telescopic arm after loading;

[0083] Sort the telescopic arms of all pressurizing units in the order of numbers 1 to 18. After obtaining the change values of the telescopic arms of all pressurizing units in each coordinate axis direction, to reduce errors, according to the following formula, take the average value of the change values of the telescopic arms of all pressurizing units in each coordinate axis direction to obtain the change components of the rock specimen in each coordinate axis direction;

[0084]

[0085] In the formula:

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

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

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

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

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

[0091] Δl z ηIt represents the variation component of the η-th telescopic boom along the Z-axis in the spatial geometric coordinate system;

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

[0093] According to the component variations of the rock specimen in each coordinate axis, the strain tensor of the rock specimen, the strain tensor ε ij The calculation formula is as follows:

[0094]

[0095] In the formula:

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

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

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

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

[0100] γ xy 、γ yx represents the engineering shear strain of the rock specimen on the XY plane; γ xy =γ yx ;

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

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

[0103] ε xy 、ε yx represents the tensor shear strain of the rock specimen on the XY plane; ε xy =ε yx ;

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

[0105] ε yz 、εzy Denotes the tensor shear strain of the rock specimen on the YZ plane; ε yz = ε zy ;

[0106] Set the side length of the cubic rock specimen as L. Under the condition of small deformation, solve the strain tensor components according to the following formula;

[0107]

[0108] In the formula:

[0109] γ1 denotes the angle by which the rock specimen on the XY plane deviates from the Y axis;

[0110] γ2 denotes the angle by which the rock specimen on the XY plane deviates from the X axis;

[0111] γ3 denotes the angle by which the rock specimen on the XZ plane deviates from the Z axis;

[0112] γ4 denotes the angle by which the rock specimen on the XZ plane deviates from the X axis;

[0113] γ5 denotes the angle by which the rock specimen on the YZ plane deviates from the Y axis;

[0114] γ6 denotes the angle by which the rock specimen on the YZ plane deviates from the Z axis;

[0115] Δx denotes the change component of the rock specimen along the X axis in the spatial geometric coordinate system;

[0116] Δy denotes the change component of the rock specimen along the Y axis in the spatial geometric coordinate system;

[0117] Δz denotes the change component of the rock specimen along the Z axis in the spatial geometric coordinate system;

[0118] Simultaneously record the following parameter data during the multi-path failure test in 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 、σ1、σ2、σ3, where the stress-strain data set includes the following parameters: σ x 、σ y 、σ z 、τ xy 、τ yx 、τ yz 、ε x 、ε y 、εz , ε xy , ε xz , ε yz ; The failure strength data includes the following data: σ1, σ2, σ3;

[0119] Change the spatial transformation parameters φ, θ, ψ to obtain multi-path failure test data under different principal stress spaces.

[0120] Furthermore, construct a rock strength criterion model 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] Make the collected failure test data into training samples, train the rock strength criterion model, and use the trained rock strength criterion model to predict the rock failure state.

[0122] Furthermore, construct a constitutive model of rock in high-dimensional stress space based on the coupling of double neural networks. The constitutive model of rock in high-dimensional stress space 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 of the rock specimen and the spatial transformation parameters φ, θ, and ψ as inputs, and predicts the stress-strain response in the first t steps; the second neural network inputs the stress-strain time series data in the first t steps and outputs the stress-strain response in the (t + 1)-th step;

[0123] Make the collected failure test data into training samples, train the constitutive model of rock in high-dimensional stress space, and use the trained constitutive model of rock in high-dimensional stress space to predict the rock stress-strain.

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

[0125] The advantages and positive effects of the present invention are: An experimental system for obtaining the high-dimensional constitutive relationship of rock proposed by the present invention can simultaneously apply normal stress and shear stress, change the principal stress space, and obtain stress and strain data under different principal stress spaces.

[0126] An experimental method for obtaining the high-dimensional constitutive relationship of rock proposed by the present invention aims to break through the limitations of the existing technology, realize the precise application and separation of the full stress tensor of the rock specimen, and explore the constitutive relationship and strength criterion of the rock in high-dimensional space by obtaining stress-strain data and failure strength under different principal stress spaces. Description of the Drawings

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

[0128] Figure 2 It is a schematic structural diagram of a pressurizing unit according to the present invention.

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

[0130] Figure 4 It is a schematic structural diagram of a hydraulic telescopic arm according to the present invention.

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

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

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

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

[0135] Figure 9 It is a schematic diagram of the stress and shear strain directions generated by a rock specimen under force and their mutual relationship.

[0136] Figure 10 It is an analysis diagram of the pressure applied by a pressurizing unit according to the present invention.

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

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

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

[0140] In the figure, 1 - hexahedral cavity, 2 - base, 3 - pressurizing unit, 4 - electric cylinder, 5 - sealing plate, 6 - planar base, 7 - clamp B, 8 - hydraulic telescopic arm, 9 - force-applying block, 10 - clamp C, 11 - clamp A, 12 - square block, 13 - spherical groove A, 14 - angle sensor, 15 - magnetostrictive displacement sensor, 16 - cylinder barrel, 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 center of the cube of the rock specimen as the origin;

[0142] X1, Y1, and Z1 represent the three coordinate axes of a geometric coordinate system with the corner point of the cube of the rock specimen 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 on the upper surface of the planar base 6 as the origin;

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

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

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

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

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

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

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

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

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

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

[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 of the first telescopic boom before loading; β1″ represents the rotation angle of the first telescopic boom after loading;

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

[0159] The angle of counterclockwise rotation of the initial principal stress space around the S3 axis is φ; it is defined that after rotation around the S3 axis, the angle of counterclockwise rotation of the initial principal stress space around the changed S1 axis is θ; it is defined that after rotation around the changed S1 axis, the angle of counterclockwise rotation of the initial principal stress space around the changed S3 axis is ψ;

[0160] f represents the rock failure state;

[0161] ε xy represents the tensorial shear strain of the rock specimen on the xy plane;

[0162] ε xz represents the tensorial shear strain of the rock specimen on the xz plane;

[0163] ε yz represents the tensorial shear strain of the rock specimen on the yz plane;

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

[0165] T1, T2,..., T t , T t+1 correspondingly represent the stress tensors and strain tensors corresponding to the 1st, 2nd,..., t-th, and (t + 1)-th moments. Detailed implementation manners

[0166] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention and are not used to limit the present invention.

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

[0168] Hidden layer: Hidden layer.

[0169] Input: Input.

[0170] Output: Output.

[0171] TensorFlow: TensorFlow is a symbolic mathematical system based on data flow programming and is widely used in the programming implementation of various machine learning algorithms.

[0172] PyTorch: An open-source deep learning framework for machine learning and deep learning, released by Facebook in 2016. It mainly implements automatic differentiation and introduces a dynamic computational graph to make model building more flexible.

[0173] In the description of the present invention, the orientation or positional relationship indicated by the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and does not require the present invention to be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation to the present invention. The terms "connected" and "joined" used in the present invention should be understood in a broad sense. For example, it can be a fixed connection or a detachable connection; it can be directly connected or indirectly connected through an intermediate component; it can also be an electrical connection or a signal transmission; for those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0174] Please refer to Figures 1 to 13 , a test system for obtaining the high-dimensional constitutive relationship of rocks. The test system includes six pressurizing units 3 for applying and unloading pressure to a rock specimen, and a detection device for correspondingly detecting the magnitude and direction of the force applied by the pressurizing unit 3 to the rock specimen; each pressurizing unit 3 includes three telescopic arms, a planar base 6 and a force-applying block 9; for the three telescopic arms in each pressurizing unit 3, one end of each of the three is respectively hinged to the planar base 6 and the connecting lines of the three hinge centers form an equilateral triangle, and the other ends of the three are hinged to the force-applying block 9; the detection device detects the spatial azimuth angle, the length change amount and the 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 is in direct contact with the rock specimen is detachably installed on the force-applying block 9, and the bottom surface of the clamp C10 fits the force-applying surface of the square block 12; three spherical grooves A13 are evenly distributed on the sphere around the connection line between the center of the sphere and the center of the square block 12; a spherical seat 25 is fixedly connected to the planar base 6; a spherical groove B is provided in the spherical seat 25; one end of the telescopic arm is provided with a spherical end A that cooperates with the spherical groove A13; the other end is provided with a spherical end B that cooperates with the spherical groove B; a clamp A11 for preventing the spherical end A from disengaging from the spherical groove A13 is fixedly connected to the sphere, and a clamp B7 for preventing the spherical end B from disengaging from the spherical groove B is fixedly connected to the planar base 6; through holes are provided in both the clamp A11 and the clamp B7; the inner surfaces of the through holes of the clamp A11 and the clamp B7 cooperate with the inner surfaces of the spherical groove A13 and the spherical groove B respectively to form a spherical surface, and the spherical surface area formed is greater than 2πR q 2, R q is the radius of the spherical end q, where q = A, 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 barrel 16 and a piston rod 17. The detection device can 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 barrel 16, an angle sensor 14 for detecting the spatial angle of the cylinder barrel 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 barrel 16; the angle sensor 14 is installed outside the end of the cylinder barrel 16; the pressure sensor is an embedded mechanical sensor 24 and is installed inside the extended end of the piston rod 17.

[0176] Preferably, the test system can 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 can be arranged at the rear side of the hexahedral cavity 1 and is called the rear side plate. The other side plates enclosing the hexahedral cavity 1 are respectively called: the upper side plate, the lower side plate, the left side plate, the right side plate, and the front side plate.

[0177] Preferably, the test system can further include six bases 2, and the six bases 2 can be respectively fixedly installed at the geometric centers of the inner walls of the six side plates. Among the six pressurizing units 3, the planar bases 6 of five of the pressurizing units 3 are respectively fixedly connected to the bases 2 on the upper, lower, left, right, and front side plates; 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 can further include an electric drive mechanism for driving the sealing plate 5 to close or open the hexahedral cavity 1. The electric drive mechanism can include more than 3 synchronously moving electric cylinders. For each electric cylinder 4, its fixed end is fixedly connected to the front side plate, and its telescopic end is fixedly connected to the sealing plate 5.

[0179] The present invention also provides a test method for obtaining the high-dimensional constitutive relationship of rocks by using the above test system for obtaining the high-dimensional constitutive relationship of rocks. The method includes the following steps:

[0180] Step 1, cut the rock sample into cubic rock specimens and place the rock specimens between the pressurizing units 3.

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

[0182] Establish a spatial geometric coordinate system XYZ with the center of the cubic rock specimen as the coordinate origin. At the same time, establish an initial principal stress space P(S1, S2, S3), and P(S1, S2, S3) is simply called P. S1, S2, and S3 correspond to the axes respectively parallel to the X-axis, Y-axis, and Z-axis of the spatial geometric coordinate system with the center of the rock specimen as the origin.

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

[0184] The Euler angle method in the ZXZ order is used to rotate the initial principal stress space. The angle of counterclockwise rotation of the initial principal stress space around the S3 axis is defined as φ; after rotation around the S3 axis, the angle of counterclockwise rotation of the initial principal stress space around the changed S1 axis is defined as θ; after rotation around the changed S1 axis, the angle of counterclockwise rotation of the initial principal stress space around the changed S3 axis is defined as ψ; assume that the initial principal stress space rotates counterclockwise around the S3 axis, then counterclockwise around the changed S1 axis, and then counterclockwise around the changed S3 axis, and the obtained new principal stress space is P′(S′1, S′2, S′3), and P′(S′1, S′2, S′3) is simply referred to as P′. In the new principal stress space P′(S′1, S′2, S′3), the initial stress state matrix of the rock specimen is given as V; assume that V is expressed as follows:

[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: two principal stresses σ2 and σ3 are constant, and the other principal stress σ1 increases in a predetermined step Δσ;

[0191] Step 5, convert V into the stress tensor in the spatial geometric coordinate system through the rotation matrix; based on the stress tensor and the normal vectors and force-bearing areas of each surface of the rock specimen, calculate the force on each surface of the rock specimen; determine the axial forces of each telescopic arm according to the mechanical equilibrium equation and the spatial azimuth angle of the telescopic arm obtained by the detection device, so as to make the confining pressure of the rock specimen reach the predetermined value;

[0192] Step 6, according to the loading method, gradually adjust the axial forces of the telescopic arms to load the rock specimen until the rock specimen fails; collect the detection values of the detection device before and after each step of loading; at the same time, record the principal stresses σ1, σ2, σ3 at the time of rock specimen failure and the stress tensor during the entire loading process;

[0193] Step 7, obtain the spatial azimuth angle and length change amount of each telescopic arm according to the detection values of the detection device, and further obtain the component changes of the rock specimen in each coordinate axis direction; according to the component changes of the rock specimen in each coordinate axis, calculate the strain tensor of the rock specimen;

[0194] Step 8: Reinstall the new rock specimen according to Step 1 and Step 2, change the initial stress state of the principal stress space P' in Step 3, perform Steps 4 to 7, and establish a stress-strain and failure strength data set for multi-path failure in the principal stress space P'.

[0195] Step 9: Reinstall the new rock specimen according to Step 1 and Step 2, change φ, θ, ψ in Step 3, perform Steps 4 to 8, and obtain a stress-strain and failure strength data set for multi-path failure under different principal stress spaces.

[0196] Step 10: Use the obtained stress-strain and failure strength data set for multi-path failure under different principal stress spaces to build a neural network to construct a high-dimensional strength criterion.

[0197] Step 11: Use the obtained stress-strain and failure strength data set for multi-path failure under different principal stress spaces to build a neural network to construct a high-dimensional constitutive relationship.

[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 through the following formula ij ;

[0199]

[0200] In the formula:

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

[0202] i represents the normal direction of the stress acting surface, with a value range of x, y, z; x, y, z respectively represent the XYZ coordinate axis directions;

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

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

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

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

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

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

[0209] τ yx represents the shear stress acting on the plane perpendicular to the Y-axis and in the X-axis direction;

[0210] τ yz represents the shear stress acting on the plane perpendicular to the Y-axis and in the Z-axis direction;

[0211] τ zx represents the shear stress acting on the plane perpendicular to the Z-axis and in the X-axis direction;

[0212] τ zy represents the shear stress acting on the plane perpendicular to the Z-axis and in the Y-axis direction;

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

[0214] Any one of the pressurizing units 3 can be selected. Let F be the pressure applied by the force-applying block 9 of the pressurizing unit 3 to the corresponding surface of the rock specimen. Then, there is:

[0215] F = (σ ij ·n)·A;

[0216] In the formula:

[0217] n: the unit normal vector on the surface of the rock specimen, with the direction pointing from the inside to the outside of the rock specimen;

[0218] A: the force-bearing area on the surface of the rock specimen;

[0219] Each surface of the rock specimen will be subjected to a normal force and two shear forces. Then, there can be:

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

[0221] In the formula:

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

[0223] F xy represents the shear force acting on the surface of the rock specimen in the Y-axis direction;

[0224] F xz represents the shear force acting on the surface of the rock specimen in the Z-axis direction;

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

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

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

[0232] It is possible to keep σ2 and σ3 constant in the new principal stress space P′(S′1, S′2, S′3), increase the maximum principal stress σ1 by a predetermined step Δσ until the rock specimen fails; during the loading process, adjust the axial force of each telescopic arm in the pressure application unit 3 in real time according to the changing principal stress; at the same time, record the principal stresses σ1, σ2, σ3 at the time of failure and solve the stress tensor σ of the rock specimen during the entire loading process ij ;

[0233] It is possible to determine the component changes Δx, Δy, Δz of the rock specimen in the directions of each coordinate axis by detecting the lengths of each telescopic arm of the rock specimen before and after loading with a detection device; decompose the length of the telescopic arm into the spatial geometric coordinate system and calculate the change values of the length of the telescopic arm of the rock specimen before and after loading on the three axes X, Y, and Z of the spatial geometric coordinate system; let m be the serial number of the telescopic arm in the pressure application unit 3, m = 1, 2, 3;

[0234] The change values of the lengths of each telescopic arm of the pressure application unit 3 in the directions of each coordinate axis can be obtained by the following formula:

[0235]

[0236] In the formula:

[0237] Δl x m Denote the component of the m-th telescopic arm changing in the X-axis direction in the spatial geometric coordinate system;

[0238] Δl y m Denote the component of the m-th telescopic arm changing in the Y-axis direction in the spatial geometric coordinate system;

[0239] Δl z m Represents the component of the m-th telescopic arm's change in the Z-axis direction under the spatial geometric coordinate system;

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

[0241] l m ″ represents 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 ″ represents 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 ″ represents the rotation angle of the m-th telescopic arm after loading;

[0246] The telescopic arms of all the pressurizing units 3 can be sorted according to the serial numbers 1 to 18. After obtaining the change values of the telescopic arms of all the pressurizing units 3 in the directions of each coordinate axis, to reduce the error, according to the following formula, the average value of the change values of the telescopic arms of all the pressurizing units 3 in the directions of each coordinate axis is taken to obtain the change components of the rock specimen in the directions of each coordinate axis;

[0247]

[0248] In the formula:

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

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

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

[0252] Δl x η Represents the change component of the η-th telescopic arm along the X-axis in the spatial geometric coordinate system;

[0253] Δl y η Represents the change component of the η-th telescopic arm along the Y-axis in the spatial geometric coordinate system;

[0254] Δl z ηIt represents the variation component of the η-th telescopic boom along the Z-axis in the space geometric coordinate system;

[0255] η represents the serial number of the telescopic boom, η = 1, 2, …, 18;

[0256] Based on the variation of the components of the rock specimen along each coordinate axis, the strain tensor of the rock specimen, ε ij can be obtained, and the calculation formula is as follows:

[0257]

[0258] In the formula:

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

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

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

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

[0263] γ xy and γ yx represent the engineering shear strain of the rock specimen on the XY plane; γ xy = γ yx ;

[0264] γ xz and γ zx represent the engineering shear strain of the rock specimen on the XZ plane; γ xz = γ zx ;

[0265] γ yz and γ zy represent the engineering shear strain of the rock specimen on the YZ plane; γ yz = γ zy ;

[0266] ε xy and ε yx represent the tensor shear strain of the rock specimen on the XY plane; ε xy = ε yx ;

[0267] ε xz and ε zx represent the tensor shear strain of the rock specimen on the XZ plane; ε xz = ε zx ;

[0268] εyz , ε zy represents the tensorial shear strain of the rock specimen on the YZ plane; ε yz = ε zy ;

[0269] The side length of the cubic rock specimen can be set as L. In the case 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 specimen on the XY plane deviates from the Y axis;

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

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

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

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

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

[0278] Δx represents the change component of the rock specimen along the X axis in the spatial geometric coordinate system;

[0279] Δy represents the change component of the rock specimen along the Y axis in the spatial geometric coordinate system;

[0280] Δz represents the change component of the rock specimen along the Z axis in the spatial geometric coordinate system;

[0281] The following parameter data during the multi-path failure test in this principal stress space can be synchronously recorded; σ x , σ y , σ z , τ xy , τ yx , τ yz , ε x , ε y , ε z , ε xy , ε xz , ε yz , σ1, σ2, σ3, where the stress-strain data set includes the following parameters: 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 failure strength data includes the following data: σ1, σ2, σ3.

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

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

[0284] The collected failure test data can be made into 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 the coupling of double neural networks can be constructed. The high-dimensional stress space rock constitutive model can 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 of the rock specimen, and spatial transformation parameters φ, θ, and ψ as input to predict the stress-strain response in the first t steps; the second neural network inputs the stress-strain time series data in the first t steps and outputs the stress-strain response in the (t + 1)th step.

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

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

[0288] The following further illustrates the structure and working principle of the present invention with a preferred embodiment of the present invention:

[0289] As Figures 1 to 7As shown in the figure, a test system for obtaining the high-dimensional constitutive relationship of rocks is characterized in that it includes six pressurizing units 3 for applying and unloading pressure to the rock specimen, and a detection device for correspondingly detecting the magnitude and direction of the force applied by the pressurizing unit 3 to the rock specimen; each pressurizing unit 3 includes three telescopic arms, a flat base 6 and a force application block 9; for the three telescopic arms in each pressurizing unit 3, one ends of the three are respectively hinged to the flat base 6 and the connecting lines of the three hinge centers form an equilateral triangle, and the other ends of the three are hinged to the force application block 9; the detection device detects the spatial azimuth angle, the length change amount and the applied axial force of each telescopic arm; the force application block 9 is a combination of a partial sphere and a square block 12; a fixture C10 that is in direct contact with the rock specimen is detachably installed on the force application block 9, and the bottom surface of the fixture C10 fits the force application surface of the square block 12; three spherical grooves A13 are evenly distributed on the sphere around the connecting line between the center of the sphere and the center of the square block 12; a spherical seat 25 is fixedly connected to the flat base 6; a spherical groove B is provided in the spherical seat 25; one end of the telescopic arm is provided with a spherical end A that cooperates with the spherical groove A13; the other end is provided with a spherical end B that cooperates with the spherical groove B; a fixture A11 for preventing the spherical end A from slipping out of the spherical groove A13 is fixedly connected to the sphere, and a fixture B7 for preventing the spherical end B from slipping out of the spherical groove B is fixedly connected to the flat base 6; through holes are opened in both the fixture A11 and the fixture B7; the inner surfaces of the through holes of the fixture A11 and the fixture B7 cooperate with the inner surfaces of the spherical groove A13 and the spherical groove B respectively to form a spherical surface, and the spherical surface area formed is greater than 2πR q 2, R q is the radius of the spherical end q, q = A, B.

[0290] A fixture C10 is installed on the force application block 9. The fixture C10 is a U-shaped steel with holes on both sides. The bottom surface fits the force application surface of the square block 12 and is fixed to the square block 12 by bolts and can be disassembled. The fixture C10 is used to clamp the specimen and can be replaced.

[0291] The system also includes a hexahedron cavity 1 with one open side and a sealing plate 5 for closing the hexahedron cavity 1. Let the sealing plate 5 be located at the rear side of the hexahedron cavity 1 and be called the rear side plate, and the other side plates enclosing the hexahedron cavity 1 are respectively called: the upper side plate, the lower side plate, the left side plate, the right side plate and the front side plate;

[0292] The system also includes six bases 2, and the six bases 2 are respectively welded at the geometric centers of the inner walls of the upper side plate, the right side plate and the rear side plate; among the six pressurizing units 3, the flat bases 6 of five of the pressurizing units 3 are respectively fixedly connected to the bases 2 on the upper, lower, left, right and front side plates; the flat base 6 of the other pressurizing unit 3 is fixedly connected to the base 2 on the sealing plate 5.

[0293] The system further includes an electric drive mechanism for driving the sealing plate 5 to close or open the hexahedral cavity 1. The electric drive mechanism includes more than 3 electric cylinders 4 that move synchronously; for each electric cylinder 4, its fixed end is fixedly connected to the front side plate, and its telescopic end is fixedly connected to the sealing plate 5.

[0294] The hexahedral cavity 1 can be integrally cast using high-strength alloy steel and formed by machining. The materials of the upper side plate, lower side plate, left side plate, right side plate, front side plate, and rear side plate are all high-strength alloys. When the hexahedral cavity 1 is in the closed state, the distances inside the hexahedral cavity 1 in the up-down, left-right, and front-back directions are all 500 mm; 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 100 mm and a height of 10 mm, and the material is high-strength alloy, and it is respectively fastened to the geometric centers of the inner walls of the upper, lower, left, right, and front side plates by screws; the base 2 can also be welded to the geometric centers of the side walls. The pressurizing unit 3 is fastened to the base 2 by screws.

[0295] The force-applying block 9 is a combination of a partial sphere and a square block 12; a clamp C10 is installed on the force-applying block 9. The clamp C10 is a U-shaped steel with holes drilled on both sides. The bottom surface fits 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 center line connecting the center of the sphere of the sphere and the center of the square block 12; a spherical seat 25 is fixedly connected to the flat base 6; a spherical groove B is provided in the spherical seat 25; one end of the telescopic arm is provided with a spherical end A that cooperates with the spherical groove A13; the other end is provided with a spherical end B that cooperates with the spherical groove B; a clamp A11 for preventing the spherical end A from slipping out of the spherical groove A13 is fixedly connected to the sphere, and a clamp B7 for preventing the spherical end B from slipping out of the spherical groove B is fixedly connected to the flat base 6; through holes are provided in both the clamp A11 and the clamp B7; the inner surfaces of the through holes of the clamp A11 and the clamp B7 respectively cooperate with the inner surfaces of the spherical grooves A13 and B to form a spherical surface, and the formed spherical surface area is greater than 2πR q 2, R q is the radius of the spherical end q, q = A, B.

[0296] The flat base 6 includes a square plate with dimensions of 170 mm × 170 mm × 10 mm, and the material is high-strength alloy steel. Three spherical seats 25 are welded on the surface of the flat base 6, which are evenly distributed in an annular shape with the geometric center of the bottom plate as the center in the flat base 6; a spherical groove B is provided in the spherical seat 25; the diameter of the spherical groove B is 20 mm; the force-applying block 9 is integrally cast and formed, including a square block 12 and a partial sphere, and three spherical grooves A13 are annularly and evenly distributed on the sphere, and the diameter of the spherical groove A13 is 10 mm.

[0297] Each of the three telescopic arms in each pressurizing unit 3 is a hydraulic telescopic arm 8, and the hydraulic telescopic arm 8 includes a cylinder barrel 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 barrel 16, an angle sensor 14 for detecting the spatial angle of the cylinder barrel 16, and a pressure sensor for detecting the force at the end of the piston rod 17; the magnetostrictive displacement sensor 15 is installed inside the cylinder barrel 16; the angle sensor 14 is installed outside the end of the cylinder barrel 16; the pressure sensor is an embedded mechanical sensor 24 and is installed inside the extended end of the piston rod 17.

[0298] The material of the cylinder barrel 16 is high-strength alloy steel. The inner diameter of the cylinder barrel 16 is 8 mm, the length is 100 mm, and the CH series magnetostrictive displacement sensor 15 is installed inside. An LCA326T type angle sensor 14 is clamped outside near the end of the cylinder barrel 16. The end of the cylinder barrel 16 is a sphere with a diameter of 19.8 mm and forms a clearance fit with the groove B of the bottom plate, and is fixed by a clamp B7. The material of the clamp B7 is high-strength alloy steel and is fastened to the flat base 6 by bolts; the material of the piston rod 17 is high-strength alloy steel. The piston rod 17 includes a rod 22 and a piston 21 welded to the rod 22. The diameter of the rod 22 is 6 mm and the length is 80 mm. A waveguide wire groove 23 is provided inside the rod 22. An HBM U2B series mechanical sensor 24 along the axis direction of the piston rod 17 is embedded inside near the top end of the piston rod 17. The spherical end A of the piston rod 17 is a sphere with a diameter of 9.8 mm, and the spherical end A forms a clearance fit with the spherical groove A13 and is fixed by a 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 the cylinder barrel 16 by bolts. The magnetic movable part 20 is embedded in the piston 21. The waveguide wire 19 is located in the waveguide wire groove 23 and is connected to the electronic transmitter 18.

[0299] As Figures 8 to 13 shown, a test method for obtaining the high-dimensional constitutive relationship of rock using the above-mentioned test system for obtaining the high-dimensional constitutive relationship of rock includes the following steps:

[0300] (1) Clamping of the rock specimen:

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

[0302] ② Chamfer the 50 mm×50 mm×50 mm rock specimen, and the chamfering distance is 2.5 mm;

[0303] ③ Place the processed rock specimen between the pressurizing units 3;

[0304] ④Close the sealing plate 5 by controlling the electric cylinder 4 to form a closed loading cavity.

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

[0306] As Figure 6 shown, establish a spatial geometric coordinate system XYZ with the center of the cube rock specimen as the coordinate origin, and at the same time establish an initial principal stress space P(S1, S2, S3), abbreviated as P, 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 spatial transformation parameters and specify the initial stress state of the rock specimen:

[0308] Use the Euler angle method in the ZXZ order to rotate the initial principal stress space. Define the angle of counterclockwise rotation of the initial principal stress space P(S1, S2, S3) around the S3 axis as φ, φ ∈ [0°, 360°), and the initial φ = 0°. Define that after rotation around the S3 axis, the angle of counterclockwise rotation of the initial principal stress space around the changed S1 axis is θ, θ ∈ [0°, 180°], and the initial θ = 0°. Define that after rotation around the changed S1 axis, the angle of counterclockwise rotation of the initial principal stress space around the changed S3 axis is ψ, ψ ∈ [0°, 360°), and the initial ψ = 0°. Rotate 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 to obtain a new principal stress space P'(S'1, S'2, S'3), abbreviated as P', and specify the initial stress state V of the rock specimen in the 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; σ3 represents the third principal stress.

[0311] (4) Set the loading method:

[0312] Set the loading method as follows: 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] ①Adjust all the pressurizing units 3 so that the center of the force-applying block 9 is coaxial with the center of the plane base 6;

[0315] ②According to the initial stress state V in the new principal stress space, adjust the axial forces of different telescopic arms in the pressurizing unit 3 to make the rock specimen 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 through Equation (2). ij ;

[0317]

[0318] Where:

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

[0320] i represents the normal direction of the stress acting surface, with a value range of x, y, z; x, y, z respectively represent the XYZ coordinate axis directions;

[0321] j represents the acting direction of the stress component, with a value range of x, Y, Z;

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

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

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

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

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

[0327] τ yx represents the shear stress acting on the plane perpendicular to the y-axis and along the X-axis direction;

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

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

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

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

[0332] Step 2: Based on the stress tensor σ ijand the normal vector n and the force-bearing area A of each surface of the rock specimen. Arbitrarily select a pressurizing unit 3. Let F be the pressure exerted by the force-applying block 9 of the pressurizing unit 3 on the corresponding surface of the rock specimen, 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 surface of the rock specimen, with the direction pointing from the inside of the rock specimen to the outside;

[0335] A: the force-bearing area of the surface of the rock specimen.

[0336] Step 3: Obtain the spatial azimuth angles (α, β) of the cylinder barrel 16 according to the angle sensor 14, and simultaneously solve the mechanical equilibrium equation to determine the axial forces of each cylinder barrel 16. The force-bearing condition of the rock specimen is as Figure 9 shown. Each surface of the rock specimen will be subjected to a normal force and two tangential forces, and the specific magnitudes can be known from Equation (4). For the pressurizing unit 3 installed on the right side plate, the force F it exerts is the vector sum of the forces on the right surface of the rock specimen. See Equation (5),

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

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

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

[0340] Let F 轴1 represent the axial force exerted by the first telescopic arm; F 轴2 represent the axial force exerted by the second telescopic arm; F 轴3 represent the axial force exerted by the third telescopic arm.

[0341] Conduct a force analysis on this, as shown in Figure 10 shown. The equilibrium equation can be listed as Equation (6). By solving the equilibrium equation, the axial forces F 轴1 , F 轴2 , F 轴3 that each cylinder barrel 16 in the pressurizing unit 3 installed on the right side plate should exert can be obtained;

[0342]

[0343] In the formula:

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

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

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

[0347] According to the loading method, and in combination with Equations (2) to (6), gradually adjust the axial force of the telescopic arm to load the rock specimen until the rock specimen fails. The axially force adjusted in steps will be output through the embedded mechanical sensor 24; collect the detection values of the detection device before and after each step of loading; at the same time, record the principal stresses σ1, σ2, and σ3 when the rock specimen fails and the stress tensor σ during the entire loading process ij .

[0348] (7) Obtaining the strain tensor

[0349] Based on the spatial azimuth angles of each telescopic arm of the rock specimen before and after loading obtained by the angle sensor 14 and the lengths of the telescopic arm 8 of the rock specimen before and after loading obtained by the electronic transmitter 18, determine the component changes (Δx, Δy, Δz) of the rock specimen in the directions of each coordinate axis. As Figure 11 shown, decompose the length of the telescopic arm into the three orthogonal axis directions of the spatial geometric coordinate system, and then calculate the change values (Δl x m , Δl y m , Δl z m ) of the lengths of each telescopic arm of the pressurizing unit in the directions of each coordinate axis. For a certain pressurizing unit 3, the change values of the lengths of each telescopic arm of the pressurizing unit in the directions of each coordinate axis can be obtained through Equation (7):

[0350]

[0351] In the formula:

[0352] Δl x m represents the component of the m-th telescopic arm changing in the X-axis direction in the spatial geometric coordinate system;

[0353] Δl y m represents the component of the m-th telescopic arm changing in the Y-axis direction in the spatial geometric coordinate system;

[0354] Δl z m represents the component of the m-th telescopic arm changing in the Z-axis direction in the spatial geometric coordinate system;

[0355] l m ′ represents the length of the m-th telescopic arm before loading; l m ″ represents 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 ″ represents 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 ″ represents the rotation angle of the m-th telescopic arm after loading.

[0358] Sort the telescopic arms 8 of all pressurizing units 3 according to the serial numbers 1 - 18. After obtaining the change values of the telescopic arms 8 of all pressurizing units 3 in each coordinate axis direction, in order to reduce errors, according to the following formula (8), take the average value of the change values of the telescopic arms 8 of all pressurizing units 3 in each coordinate axis direction to obtain the change components of the rock specimen in each coordinate axis direction;

[0359]

[0360] In the formula:

[0361] Δx represents the change component of the rock specimen along the X-axis in the space geometric coordinate system;

[0362] Δy represents the change component of the rock specimen along the Y-axis in the space geometric coordinate system;

[0363] Δz represents the change component of the rock specimen along the Z-axis in the space geometric coordinate system;

[0364] Δl x η represents the change component of the η-th telescopic arm along the X-axis in the space geometric coordinate system;

[0365] Δl y η represents the change component of the η-th telescopic arm along the Y-axis in the space geometric coordinate system;

[0366] Δl z η represents the change component of the η-th telescopic arm along the Z-axis in the space geometric coordinate system;

[0367] η represents the serial number of the telescopic arm, η = 1, 2, …, 18.

[0368] According to the component changes (Δx, Δy, Δz) of the rock specimen in each coordinate axis, obtain the strain tensor ε ij , ε ij The expression of is shown in formula (9).

[0369]

[0370] In the formula:

[0371] In the formula:

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

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

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

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

[0376] γ xy and γ yx represent the engineering shear strain of the rock specimen on the XY plane; γ xy =γ yx ;

[0377] γ xz and γ zx represent the engineering shear strain of the rock specimen on the XZ plane; γ xz =γ zx ;

[0378] γ yz and γ zy represent the engineering shear strain of the rock specimen on the YZ plane; γ yz =γ zy ;

[0379] ε xy and ε yx represent the tensor shear strain of the rock specimen on the XY plane; ε xy =ε yx ;

[0380] ε xz and ε zx represent the tensor shear strain of the rock specimen on the XZ plane; ε xz =ε zx ;

[0381] ε yz and ε zy represent the tensor shear strain of the rock specimen on the YZ plane; ε yz =ε zy ;

[0382] For example Figure 9As shown, the length of the known cubic rock specimen in each direction is L. In the case of small deformation, the strain tensor components are solved according to Equation (10).

[0383]

[0384] Where:

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

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

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

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

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

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

[0391] Δx represents the change component of the rock specimen along the X axis in the spatial geometric coordinate system;

[0392] Δy represents the change component of the rock specimen along the Y axis in the spatial geometric coordinate system;

[0393] Δz represents the change component of the rock specimen along the Z axis in the spatial geometric coordinate system.

[0394] (8) Conduct multi-path failure tests by changing the initial stress state in the new principal stress space:

[0395] Reinstall the new rock specimen according to Steps 1 and 2, change the initial stress state in the new principal stress space in Step (3), and conduct Steps (4) to (7) to establish the stress-strain data set {σ x , σ y , σ z , τ xy , τ yx , τ yz , ε, ε y , ε z , ε xy , ε xz , ε yz} and the failure strength data set {σ1, σ2, σ3} under this principal stress space.

[0396] (9) Global data acquisition:

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

[0398] ① Fix φ and θ, and traverse ψ: Keep the current φ and θ unchanged, start from the initial value of ψ, and increment it step by step with Δψ = 5° until the termination value of ψ is reached;

[0399] ② Fix φ and traverse θ: After completing the traversal of ψ 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, and repeat Step ② for the new φ value until φ reaches the termination value, and the traversal ends.

[0401] (10) Construct a rock strength criterion model based on a neural network:

[0402] As Figure 12 shown, construct a deep neural network with six parameters (φ, θ, ψ, σ1, σ2, σ3) as inputs and the failure state f as the output. The specific process is as follows:

[0403] The first step: Build the input layer. The input layer receives six parameters (φ, θ, ψ, σ1, σ2, σ3). In actual operation, first perform Z-score standardization on these input parameters to eliminate the dimensional differences between different features and improve the training effect and generalization ability of the model. The specific implementation is as follows:

[0404] Collect experimental data, including the spatial transformation parameters φ, θ, and ψ, and the strength parameters σ1, σ2, and σ3.

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

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

[0407]

[0408] where: g represents the input variable; g norm represents the standardized variable; u represents the mean of each variable; represents the standard deviation of each variable.

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

[0410] Step 2: Build the hidden layer. The hidden layer is designed as three fully connected layers with 64, 128, and 64 neurons respectively. The ReLU activation function is selected. 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] Define the neural network structure using a deep learning framework (such as TensorFlow or PyTorch).

[0414] The first fully connected layer: The input dimension is 6, and the output dimension is 64.

[0415] The second fully connected layer: The input dimension is 64, and the output dimension is 128.

[0416] The third fully connected layer: The input dimension is 128, and the output dimension is 64.

[0417] The ReLU activation function is used after each fully connected layer to enhance the network's non-linear representation ability.

[0418] Step 3: Build the output layer. The output layer represents the rock state corresponding to different parameters, where 1 indicates rock failure, 0 indicates the critical state of rock failure, and -1 indicates the rock is not damaged. The output layer contains 1 neuron, and the output is mapped to the range [-1, 1] through 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. The specific implementation is as follows:

[0422] Dataset division: Divide the data into a training set and a test set with a ratio of 8:2.

[0423] Optimizer selection: Use the Adam optimization algorithm for backpropagation to optimize the network weights, and set the learning rate to 0.001.

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

[0425]

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

[0427] Training stop condition: Train the network and stop training when the preset number of training epochs reaches 1000 epochs.

[0428] Model validation: Use the test set to validate the performance of the model, calculate the mean squared error (MSE) on the test set, and evaluate the performance and generalization ability of the model. According to the validation results, the hyperparameters of the model can be adjusted and optimized to improve the prediction performance of the model.

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

[0430] (11) Construct a constitutive model of rock in high-dimensional stress space based on the coupling of double neural networks

[0431] As Figure 13 shown, construct a constitutive model of rock in high-dimensional stress space based on the coupling of double neural networks. The second neural network takes the stress-strain time series data of the previous t steps as input and predicts the stress-strain response of the t+1 step; 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 as input and predicts the stress-strain response of the previous t steps. The first neural network provides input data for the second neural network, and uses the second neural network to predict the stress-strain response of the rock in the later stage. The specific implementation process is as follows:

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

[0433] Step 1: Build the input layer. First, perform Z-score standardization on the stress-strain data to eliminate the dimensional differences between different features, improve the training effect and generalization ability of the model, and then divide the stress-strain data by step size to form sequence data. Each sequence contains the strain and stress component data of t steps as the input of 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 during the loading process;

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

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

[0437] Step 4: Divide the standardized data by a step size to form sequence data. Each sequence contains strain and stress data for t steps, serving as the input to the neural network. Each step contains 12 features, with 6 being strain components and 6 being stress components. The shape of the input data is (t, 12), and it is passed to the subsequent LSTM layer for processing.

[0438] Step 2: Build the LSTM layer. The long short-term memory (LSTM) layer is used to process time series data. The LSTM layer can effectively capture the temporal dependence and long-term memory features in the data. The LSTM layer is designed with 2 layers, with the number of neurons in each layer being 128 and 64 respectively. The ReLU activation function is selected. The specific implementation is as follows:

[0439] The first LSTM layer: The input dimension is 12, and the output dimension is 128.

[0440] The second LSTM layer: The input dimension is 128, and the output dimension is 64.

[0441] The ReLU activation function is used after each LSTM layer to enhance the network's non-linear representation ability.

[0442] Step 3: Build the output layer. The strain and stress data for the (t + 1)-th step corresponding to each sequence are used as the output targets for training the neural network. The output dimension is 12, including 6 strain components and 6 stress components for the (t + 1)-th step. The output is implemented through a fully connected layer and is used to predict the strain and stress for the (t + 1)-th step. The specific implementation is as follows:

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

[0444] The output of the LSTM layer is mapped to the strain and stress components for the (t + 1)-th step through a fully connected layer.

[0445] Step 4: Network training and optimization. The specific implementation is as follows:

[0446] Dataset division: Randomly divide the collected dataset into a training set and a test set with a ratio of 8:2. 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 values and the true values.

[0449] Training stop condition: Stop training when the preset number of training epochs reaches 1000.

[0450] Model verification: Use the test set to verify the trained model, calculate the mean squared error (MSE) on the test set, and evaluate the performance and generalization ability of the model. According to the verification results, the hyperparameters of the model can be adjusted and optimized to improve the prediction performance of the model.

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

[0452] The first step: Build the input layer. The input layer receives 7 parameters (E, v, c, ω, φ, θ, ψ). In actual operation, first perform Z-score standardization on these input parameters to eliminate the dimensional differences between different features and improve the training effect and generalization ability of the model. The specific implementation is as follows:

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

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

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

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

[0457] The second step: Build the hidden layer. The hidden layer is designed as 3 fully connected layers, and the number of neurons is 64, 256, and 512 respectively.

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

[0459] Use a deep learning framework (such as TensorFlow or PyTorch) to define the neural network structure.

[0460] The first fully connected layer: The input dimension is 7, and the output dimension is 64.

[0461] The second fully connected layer: The input dimension is 64, and the output dimension is 256.

[0462] The third fully connected layer: The input dimension is 256, and the output dimension is 512.

[0463] The ReLU activation function is used after each fully connected layer to enhance the non-linear representation ability of the network.

[0464] Step 3: Build the output layer. Flatten the data of the previous t steps as the output. The output layer contains t × 12 neurons.

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

[0466] Dataset division: Divide the data into a training set and a test set in a ratio of 8:2.

[0467] Optimizer selection: Use the Adam optimization algorithm for backpropagation to optimize the network weights, and set the learning rate to 0.001.

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

[0469] Training stop condition: Train the network and stop training when the preset number of training epochs, 1000 epochs, is reached.

[0470] Model validation: Use the test set to validate the performance of the model. Calculate the Mean Square Error (MSE) on the test set to evaluate the performance and generalization ability of the model. According to the validation results, the hyperparameters of the model can be adjusted and optimized to improve the prediction performance of the model.

[0471] 3) Model application: Use the first neural network to output the stress-strain data of the previous t steps by inputting rock mechanics parameters and spatial transformation parameters (E, ν, c, ω, φ, θ, ψ). Use the stress-strain data of the previous t steps as the input of the second neural network to predict the stress-strain data of the t + 1 step. By gradually inputting new data, continuously predict the strain and stress states of subsequent steps to achieve dynamic prediction of rock mechanics behavior. The specific steps are as follows:

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

[0473] Step 2: Use the second neural network to predict the strain and stress of the t + 1 step with the initial t-step data as the input.

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

[0475] Step 4: Repeat the above steps to gradually predict the strain and stress states of subsequent steps to achieve dynamic prediction of rock mechanics behavior.

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

[0477] The above embodiments are only used to illustrate the technical idea and features of the present invention, and the 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 cannot be limited only by these embodiments. That is, any equivalent changes or modifications made in accordance with the spirit disclosed by the present invention still fall within the patent scope of the present invention.

Claims

1. An experimental system for obtaining the high-dimensional constitutive relationship of rocks, characterized in that, It includes six pressurizing units for applying and unloading pressure to a rock specimen, and a detection device for correspondingly detecting the magnitude and direction of the force applied by the pressurizing units to the rock specimen; each pressurizing unit includes three telescopic arms, a flat base and a force application block; for the three telescopic arms in each pressurizing unit, one end of each of the three is hinged to the flat base and the connecting lines of the three hinge centers form an equilateral triangle, and the other ends of the three are hinged to the force application block; the detection device detects the spatial azimuth angle, the length change amount and the applied axial force of each telescopic arm; the force application block is a combination of a partial sphere and a square block; a clamp C that is in direct contact with the rock specimen is detachably installed on the force application block, and the bottom surface of the clamp C fits the force application surface of the square block; three spherical grooves A are evenly distributed on the sphere around the connection line of the sphere center of the sphere and the body center of the square block; a spherical seat is fixedly connected to the flat base; a spherical groove B is arranged in the spherical seat; one end of the telescopic arm is provided with a spherical end A that cooperates with the spherical groove A; the other end is provided with a spherical end B that cooperates with the spherical groove B; a clamp A for preventing the spherical end A from disengaging from the spherical groove A is fixedly connected to the sphere, and a clamp B for preventing the spherical end B from disengaging from the spherical groove B is fixedly connected to the flat base; through holes are opened in both the clamp A and the clamp B; the inner surfaces of the through holes of the clamp A and the clamp B respectively cooperate with the inner surfaces of the spherical grooves A and B to form a spherical surface, and the formed spherical surface area is greater than 2πR q 2, R q is the radius of the spherical end q, q = A, B.

2. The test system for obtaining the high-dimensional constitutive relationship of rocks according to claim 1, characterized in that, Each of the three telescopic arms in each pressurizing unit is a hydraulic telescopic arm or an electric telescopic arm. The hydraulic telescopic arm includes a cylinder barrel 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 barrel, an angle sensor for detecting the spatial angle of the cylinder barrel, and a pressure sensor for detecting the force on the end of the piston rod. The magnetostrictive displacement sensor is installed inside the cylinder barrel; the angle sensor is installed outside the end of the cylinder barrel; the pressure sensor is an embedded mechanical sensor and is installed inside the extended end of the piston rod.

3. The test system for obtaining the high-dimensional constitutive relationship of rocks according to claim 1, characterized in that It further includes a hexahedron cavity with one open side and a sealing plate for closing the hexahedron cavity. Let the sealing plate be located at the rear side of the hexahedron cavity, which is called the rear side plate, and the other side plates enclosing the hexahedron 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.

4. The test system for obtaining the high-dimensional constitutive relationship of rocks according to claim 3, characterized in that, It further includes six bases, and the six bases are respectively fixedly installed at the geometric centers of the inner walls of the six side plates. Among the six pressurizing units, the planar bases of five of the pressurizing units are respectively fixedly connected to the bases on the upper, lower, left, right, and front side plates; the planar base of the other pressurizing unit is fixedly connected to the base on the sealing plate.

5. The test system for obtaining the high-dimensional constitutive relationship of rocks according to claim 3, wherein It further includes an electric drive mechanism for driving the sealing plate to close or open the hexahedron cavity. The electric drive mechanism includes more than 3 synchronously moving electric cylinders. For each electric cylinder, its fixed end is fixedly connected to the front side plate, and its telescopic end is fixedly connected to the sealing plate.

6. A test method for obtaining the high-dimensional constitutive relationship of rock using the test system for obtaining the high-dimensional constitutive relationship of rock 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 a cubic rock specimen and place the rock specimen between the pressurizing units. Step 2: Establish a spatial geometric coordinate system and an initial principal stress space: Establish a spatial geometric coordinate system XYZ with the center of the cubic rock specimen as the coordinate origin, and at the same time establish an initial principal stress space P(S1, S2, S3). S1, S2, and S3 respectively correspond to the axes parallel to the X-axis, Y-axis, and Z-axis of the spatial geometric coordinate system with the center of the rock specimen as the origin. Step 3: Define the spatial transformation parameters and specify the initial stress state of the rock specimen: Use the Euler angle method in the ZXZ order to rotate the initial principal stress space. Define the angle of counterclockwise rotation of the initial principal stress space around the S3 axis as φ; define the angle of counterclockwise rotation of the initial principal stress space around the changed S1 axis after rotating around the S3 axis as θ; define the angle of counterclockwise rotation of the initial principal stress space around the changed S3 axis after rotating around the changed S1 axis as ψ. Assume that the initial principal stress space rotates counterclockwise around the S3 axis, then counterclockwise around the changed S1 axis, and then counterclockwise around the changed S3 axis, and the obtained new principal stress space is P′(S1′, S2′, S3′). In the new principal stress space P′(S1′, S2′, S3′), the initial stress state matrix of the rock specimen is V. Let V be expressed as follows: In the formula: σ1 represents the first principal stress, and in 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: Two principal stresses σ2 and σ3 are constant, and the other principal stress σ1 increases in a predetermined step Δσ. Step 5: Convert V into the stress tensor in the spatial geometric coordinate system through the rotation matrix; Based on the stress tensor, the normal vectors and the force-bearing areas of each surface of the rock specimen, calculate the force on each surface of the rock specimen; determine the axial forces of each telescopic arm according to the mechanical equilibrium equation and the spatial azimuth angles of the telescopic arms obtained by the detection device, so as to make the confining pressure of the rock specimen reach the predetermined value; Step 6: According to the loading method, gradually adjust the axial forces of the telescopic arms to load the rock specimen until the rock specimen fails; collect the detection values of the detection device before and after each step of loading; simultaneously record the principal stresses σ1, σ2, σ3 when the rock specimen fails and the stress tensor during the entire loading process; Step 7: Obtain the spatial azimuth angles and the length change amounts of each telescopic arm according to the detection values of the detection device, and further obtain the component changes of the rock specimen in the directions of each coordinate axis; according to the component changes of the rock specimen in each coordinate axis, calculate the strain tensor of the rock specimen; Step 8: Reinstall a new rock specimen according to Steps 1 and 2, change the initial stress state of the principal stress space P′ in Step 3, and perform Steps 4 to 7 to establish a stress-strain and failure strength data set for multi-path failure in the principal stress space P′; Step 9: Reinstall a new rock specimen according to Steps 1 and 2, change φ, θ, ψ in Step 3, and perform Steps 4 to 8 to obtain a stress-strain and failure strength data set for multi-path failure under different principal stress spaces; Step 10: Use the obtained stress-strain and failure strength data sets for multi-path failure under different principal stress spaces to build a neural network to construct a high-dimensional strength criterion; Step 11: Use the obtained stress-strain and failure strength data sets for multi-path failure under different principal stress spaces to build a neural network to construct a high-dimensional constitutive relationship.

7. The test method for obtaining the high-dimensional constitutive relationship of rocks according to claim 6, wherein: 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 represents the second-order stress tensor, representing the stress state at a point in three-dimensional space; i represents the normal direction of the stress acting surface, and the value range is: x, y, z; x, y, z respectively represent the XYZ coordinate axis directions; j represents the acting direction of the stress component, and the value range is: x, y, z; σ x represents the normal stress acting on the plane perpendicular to the X-axis and in the positive X-axis direction; σ y represents the normal stress acting on the plane perpendicular to the Y-axis and along the Y-axis direction; σ z represents the normal stress acting on the plane perpendicular to the Z-axis and in the Z-axis direction; τ xy represents the shear stress acting on the plane perpendicular to the X-axis and in the Y-axis direction; τ xz represents the shear stress acting on the plane perpendicular to the X-axis and in the Z-axis direction; τ yx represents the shear stress acting on the plane perpendicular to the Y-axis and in the X-axis direction; τ yz represents the shear stress acting on the plane perpendicular to the Y-axis and in the Z-axis direction; τ zx represents the shear stress acting on a plane perpendicular to the Z-axis and in the X-axis direction; τ zy represents the shear stress acting on a plane perpendicular to the Z-axis and in the Y-axis direction; R represents the rotation matrix; R T is the transpose matrix of R; Arbitrarily select a pressurizing unit. Let F be the pressure exerted by the force-applying block of the pressurizing unit on the corresponding surface of the rock specimen, then there is: F = (σ ij · n) · A; In the formula: n: the unit normal vector of the surface of the rock specimen, and the direction points from the inside of the rock specimen to the outside; A: the force-bearing area of the surface of the rock specimen; Each surface of the rock specimen will be subjected to a normal force and two shear forces, then there is: F = F x + F xy + F xz ; In the formula: F x represents the normal force acting on the surface of the rock specimen; F xy represents the tangential force acting on the surface of the rock specimen along the Y-axis direction; F xz represents the tangential force acting on the surface of the rock specimen along the Z-axis direction; Suppose the three telescopic arms in this pressurizing unit are the first telescopic arm, the second telescopic arm, and the third telescopic arm respectively; Let F 轴1 represent the axial force applied by the first telescopic arm; F 轴2 represent the axial force applied by the second telescopic arm; F 轴3 represent the axial force applied by the third telescopic arm; F is obtained by solving the following balance equation 轴1 and F 轴2 and F 轴3 ; In the formula: 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 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, β3 are detected by the detection device; Keep σ2 and σ3 constant in the new principal stress space P′(S′1, S′2, S′3), and increase the maximum principal stress σ1 by a predetermined step Δσ until the rock specimen fails; during the loading process, adjust the axial force of each telescopic arm in the pressurizing unit in real time according to the changing principal stresses; meanwhile, record the principal stresses σ1, σ2, and σ3 at failure and solve the stress tensor σ of the rock specimen during the entire loading process ij ; The lengths of each telescopic arm before and after loading the rock specimen are detected by a detection device to determine the component changes Δx, Δy, and Δz of the rock specimen in the directions of each coordinate axis; the lengths of the telescopic arms are decomposed into a spatial geometric coordinate system, and the change values of the lengths of the telescopic arms before and after loading the rock specimen on the three axes X, Y, and Z of the spatial geometric coordinate system are calculated; let m be the serial number of the telescopic arm in this pressurizing unit, m = 1, 2, 3; The change values of the lengths of each telescopic arm of this pressurizing unit in the directions of each coordinate axis are obtained by the following formula: In the formula: Δl x m represents the component of the change of the m-th telescopic arm in the X-axis direction under the spatial geometric coordinate system; Δl y m represents the component of the change of the m-th telescopic arm in the Y-axis direction in the space geometric coordinate system; Δl z m represents the component of the change of the m-th telescopic arm in the Z-axis direction in the space geometric coordinate system; l m ′ represents the length of the m-th telescopic boom before loading; l m ″ represents the length after the m-th telescopic arm is loaded; α m ′ represents the elevation angle before the m-th telescopic boom is loaded; α m ″ represents the elevation angle after the m-th telescopic boom is loaded; β m ′ represents the rotation angle before the m-th telescopic boom is loaded; β m ″ represents the rotation angle after the m-th telescopic boom is loaded; The telescopic arms of all pressurizing units are sorted according to the serial numbers from 1 to 18. After obtaining the change values of the telescopic arms of all pressurizing units in the directions of each coordinate axis, in order to reduce errors, according to the following formula, the average value of the change values of the telescopic arms of all pressurizing units in the directions of each coordinate axis is taken to obtain the change components of the rock specimen in the directions of each coordinate axis; In the formula: Δx represents the change component of the rock specimen along the X-axis in the spatial geometric coordinate system; Δy represents the change component of the rock specimen along the Y-axis in the spatial geometric coordinate system; Δz represents the change component of the rock specimen along the Z-axis in the spatial geometric coordinate system; Δl x η represents the variation component of the η-th telescopic arm along the X-axis in the space geometric coordinate system; Δl y η represents the variation component of the η-th telescopic arm along the Y-axis in the space geometric coordinate system; Δl z η It represents the variation component of the η-th telescopic boom along the Z-axis in the space geometric coordinate system; η represents the serial number of the telescopic arm, η = 1, 2,..., 18; According to the component changes of the rock specimen in each coordinate axis, the strain tensor of the rock specimen is obtained, and the strain tensor ε ij has the following calculation formula: In the formula: ε ij represents the second-order strain tensor and is used to characterize the deformation state of materials in three-dimensional space; ε x represents the positive strain of the rock specimen in the X-axis direction; ε y represents the positive strain of the rock specimen in the Y-axis direction; ε z represents the positive strain of the rock specimen in the Z-axis direction; γ xy , γ yx represent the engineering shear strain of the rock specimen on the XY plane; γ xy = γ yx ; γ xz and γ zx represent the engineering shear strain of the rock specimen on the XZ plane; γ xz = γ zx ; γ yz and γ zy represent the engineering shear strain of the rock specimen on the YZ plane; γ yz = γ zy ; ε xy , ε yx represent the tensorial shear strain of the rock specimen on the XY plane; ε xy = ε yx ; ε xz and ε zx represent the tensorial shear strain of the rock specimen on the XZ plane; ε xz = ε zx ; ε yz , ε zy represent the tensorial shear strain of the rock specimen on the YZ plane; ε yz = ε zy ; Let the side length of the cubic rock specimen be L. In the case 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 specimen on the XY plane deviates from the Y-axis; γ2 represents the angle by which the rock specimen on the XY plane deviates from the X-axis; γ3 represents the angle by which the rock specimen on the XZ plane deviates from the Z-axis; γ4 represents the angle by which the rock specimen on the XZ plane deviates from the X-axis; γ5 represents the angle by which the rock specimen on the YZ plane deviates from the Y-axis; γ6 represents the angle by which the rock specimen on the YZ plane deviates from the Z-axis; Δx represents the change component of the rock specimen along the X-axis in the spatial geometric coordinate system; Δy represents the change component of the rock specimen along the Y-axis in the spatial geometric coordinate system; Δz represents the change component of the rock specimen along the Z-axis in the spatial geometric coordinate system; Synchronously record the following parameter data during the multi-path failure test in 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 、σ1, σ2, σ3, where the stress-strain data set includes the following parameters: 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 failure strength data includes the following data: σ1, σ2, σ3; Change the spatial transformation parameters φ, θ, ψ to obtain multi-path failure test data under different principal stress spaces.

8. The test method for obtaining the high-dimensional constitutive relationship of rocks according to claim 6, characterized in that Construct a rock strength criterion model based on a neural network. The rock strength criterion model has the following parameters as input: φ, θ, ψ, σ1, σ2, σ3; and its output is the rock failure state; Make the collected failure test data into training samples, train the rock strength criterion model, and use the trained rock strength criterion model to predict the rock failure state.

9. The test method for obtaining the high-dimensional constitutive relationship of rocks according to claim 6, characterized in that, Construct a high-dimensional stress space rock constitutive model based on the coupling of double neural networks. 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 specimen as input and predicts the stress-strain response in the first t steps; the second neural network inputs the stress-strain time series data in the first t steps and outputs the stress-strain response in the (t + 1)-th step; Make the collected failure test data into training samples, train the high-dimensional stress space rock constitutive model, and use the trained high-dimensional stress space rock constitutive model to predict the rock stress-strain.

10. An apparatus for an experimental method for obtaining a high-dimensional constitutive relationship of a rock, 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 steps of the test method for obtaining the high-dimensional constitutive relationship of rocks as described in any one of claims 6 to 9.

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