A method for analyzing true triaxial tests of rock cylinder specimens

Abstract

The present invention relates to the technical field of true triaxial test of rock mechanics, and in particular to a method for analyzing true triaxial test of rock cylindrical specimens, including: applying point loads to the cylindrical surface of the cylindrical specimens, and then using the principle of linear superposition for integration to calculate the analytical solution of the stress field in the circular surface of the rock cylindrical specimens; applying symmetric surface loads to the cylindrical surface of the cylindrical specimens, and using the analytical solution to calculate the stress field in the circular surface of the cylindrical specimens under the symmetric surface loads; establishing the constraint conditions for the stress state similarity region, calculating the relationship function between the symmetric surface loads under the corresponding loading modes, and determining it as the linear gradient loading mode; performing finite element analysis on the rock cylindrical specimens to verify the feasibility of the linear gradient loading mode determined by the analytical solution. In the present invention, the true triaxial test analysis of the cylindrical specimens is realized, ensuring the similarity of the stress state in a large area of the specimens, and avoiding problems such as boundary effect, friction effect and channeling of cube specimens.

Description

Technical Field

[0001] The present invention relates to the technical field of true triaxial test of rock mechanics, and particularly to an analysis method for true triaxial test of rock cylinder specimens. Background Technique

[0002] Hydraulic fracturing technology is an important technology in the exploitation engineering of unconventional oil and gas resources and geothermal resources. Through hydraulic fracturing, the resource exploitation efficiency can be improved and the related costs can be reduced. However, the related rock mechanics mechanism of hydraulic fracturing technology has not been clarified, which is difficult to guide the actual engineering. And the development of hydraulic fracturing technology depends on the related experimental research, which requires the test instrument to be able to realize the seepage and fracturing hydraulic coupling test under different confining pressures in the true triaxial state, so as to simulate the water-thermal-mechanical multi-field coupling effect in the fracturing process under the deep-earth high in-situ stress state.

[0003] The existing true triaxial test instruments generally consist of three groups of orthogonal rigid loading mechanisms, and cooperate with the seepage loading device to realize the hydraulic coupling test. When carrying out the hydraulic coupling test, holes are usually drilled in the middle of the rock to provide water pressure. However, most of the specimen shapes are cubes. Due to the permeability of the rock, interface flow is likely to occur at the boundary edges and corners of the specimen during the test, resulting in crossflow. Friction effects are also likely to occur on the cube end faces. These effects are difficult to eliminate by changing the specimen size, making it difficult to control the fluid parameters in the test. Moreover, the on-site sampling efficiency of cube specimens is low, the cost is high, and fewer samples can be collected in the same geological area, making it difficult to evaluate the discrete differences in test results caused by the heterogeneity of rock samples in the same area. When the existing device uses cube specimens, calculating the internal stress state of the specimen only simply calculates the pressure according to the three loading units as the three principal stress components, resulting in the lack of internal stress calculation methods for other shaped specimens, which theoretically limits the development of the true triaxial loading test system for non-cube specimens. Summary of the Invention

[0004] The purpose of the present invention is to provide an analysis method for true triaxial test of rock cylinder specimens to solve the problems raised in the above background technique.

[0005] To achieve the above purpose, the present invention provides the following technical solution: An analysis method for true triaxial test of rock cylinder specimens, comprising the following steps:

[0006] Apply point loads to the cylindrical surface of the cylinder specimen, analyze the stress components in the circular surface of the cylinder specimen under the action of the point loads, and use the principle of linear superposition for integration to calculate the analytical solution of the stress field in the circular surface of the rock cylinder specimen;

[0007] Apply symmetric surface loads to the cylindrical surface of the cylinder specimen, and calculate the stress field in the circular surface of the cylinder specimen under the symmetric surface loads by using the analytical solution of the stress field in the circular surface of the cylinder specimen;

[0008] Set the constraint conditions for the similar stress state region, calculate the relationship function between the loads on each symmetry plane under the corresponding loading method, and determine it as the linear gradient loading method;

[0009] Conduct a finite element analysis on the cylindrical specimen of the rock under the linear gradient loading method, simulate the internal stress distribution of the circular surface of the cylindrical specimen, and verify the feasibility of the linear gradient loading method determined by the analytical solution.

[0010] Furthermore, apply a point load to the cylindrical surface of the cylindrical specimen. The specific method for analyzing the stress components in the circular surface of the cylindrical specimen under the point load is as follows: establish a plane coordinate system oxy with the center of the circle as the origin on the circular surface of the cylindrical specimen, and analyze the stress components of any coordinate point E in the circular surface of the cylindrical specimen under the point load; rotate the point load by a set angle around the center of the circle, and at the same time rotate the plane coordinate system oxy by the set angle to generate a rotated coordinate system ox'y', and obtain the stress components of any coordinate point E in the circular surface of the cylindrical specimen under different positions of the point load.

[0011] Furthermore, the stress components of any coordinate point E in the plane coordinate system oxy under the point load:

[0012] , where x is the distance of any coordinate point E from the y-axis in the plane coordinate system oxy, y is the distance of any coordinate point E from the x-axis in the plane coordinate system oxy, σ x is the normal stress suffered by any coordinate point E in the plane coordinate system oxy along the x-axis direction, σ y is the normal stress suffered by any coordinate point E in the plane coordinate system oxy along the y-axis direction, τ xy is the shear stress suffered by any coordinate point E in the plane perpendicular to the x-axis along the y-axis direction, D is the diameter of the cylindrical specimen, a is the thickness of the cylindrical specimen, and P is the magnitude of the point load.

[0013] Furthermore, the stress components of any coordinate point E in the rotated coordinate system ox'y' under the point load:

[0014] , where σ x' is the normal stress suffered by any coordinate point E in the rotated coordinate system ox'y' along the x'-axis direction, σ y' is the normal stress suffered by any coordinate point E in the rotated coordinate system ox'y' along the y'-axis direction, τ x'y'$\tau$ is the shear stress suffered by any coordinate point E in the direction of the y'-axis on the plane perpendicular to the x'-axis, and $\theta$ is the set angle of rotation of the plane coordinate system oxy.

[0015] Furthermore, rotate the set angle around the center of the circle to adjust the position of the point load, and at the same time rotate the plane coordinate system oxy by the set angle. The specific method is as follows: Adjust the position of the point load so that the point load rotates by $\theta$ around the origin. Consider the rotation of the point load as the rotation of the plane coordinate system oxy. After rotation, a rotated coordinate system ox'y' is formed. Use the above functional relationship in the rotated coordinate system ox'y' to obtain the stress components $\sigma$ of any coordinate point E in the rotated coordinate system ox'y' x' ,$\sigma$ y' and $\tau$ x'y' , and transform x and y into new coordinates x' and y'. The relationship between the old and new coordinates is as follows:

[0016] ; .

[0017] Furthermore, use the principle of linear superposition for integration. The specific method for calculating the stress field in the circular surface of the cylindrical specimen is as follows: Replace the point load with an arc element ds and the pressure load p on the arc element ds. Combine the relationship between the pressure load p and the set angle $\theta$, and use the principle of linear superposition for integration. The distribution of the stress field in the circular surface of the cylindrical specimen under any pressure load is expressed as follows:

[0018] , where f xx (x, y, $\theta$) is the characteristic function of $\sigma$ x , f yy (x, y, $\theta$) is the characteristic function of $\sigma$ y , f xy (x, y, $\theta$) is the characteristic function of $\tau$ xy .

[0019] Furthermore, the method for applying a symmetric surface load to the cylindrical surface of the cylindrical specimen is as follows: Divide the cylindrical surface of the cylindrical specimen into 24 equal parts and divide it into 12 groups of symmetric regions. Apply symmetric surface loads p1 to p 12 to the 12 groups of symmetric regions respectively. Use the analytical solution of the stress field in the circular surface of the cylindrical specimen to calculate the stress field in the circular surface of the cylindrical specimen under the symmetric surface load as:

[0020] , where = 1, 2, 3,..., 12.

[0021] Furthermore, the constraint conditions for the established similar stress state region are as follows: the region where the shear stress component is 0 is regarded as the similar stress state region, and the similar stress state region is the region where the principal stress magnitudes of each point within the circular surface of the cylindrical specimen have a deviation ≤ 5% and the directions are the same.

[0022] Furthermore, when ensuring that the shear stress component at the center of the circle is 0, substituting x = 0 and y = 0 into the stress field distribution formula within the circular surface of the cylindrical specimen, the shear stress at the center of the circle can be obtained as follows:

[0023] , it can be seen from the formula that the maximum constraint condition for satisfying the similar stress state region is to ensure that the change gradient of τ xy is the smallest.

[0024] Furthermore, the relationship function between the loads on each symmetry plane is as follows:

[0025] ; , where σ n is the principal stress component of any point in the similar stress state region along the x-axis direction, and σ m is the principal stress component of any point in the similar stress state region along the y-axis direction. Therefore, when adopting the linear gradient loading method, the similar stress state region within the circular surface of the cylindrical specimen is the largest.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] 1. A true triaxial test analysis method for a rock cylindrical specimen provided by the present invention changes the specimen shape to a cylinder, which can effectively avoid boundary effects and channeling during the test. By using an analytical method, the analytical solution of the stress field within the circular surface of the cylindrical specimen is obtained, and a numerical analysis method of finite element analysis is used to simulate the distribution of the stress field within the circular surface of the cylindrical specimen, providing a theoretical basis for realizing different true triaxial states of the cylindrical specimen by applying multiple groups of different loads on the cylindrical surface. It can achieve true triaxial loading of non-cubic specimens, and can avoid problems such as corner stress concentration and channeling that are prone to occur in cubic specimens. Cubic specimens are more susceptible to end friction effects, while the cylindrical specimen can effectively prevent end friction by adjusting the height-diameter ratio, improving the test efficiency and accuracy. Moreover, the stress components at any point within the cylinder can be calculated based on the diameter of the cylindrical specimen and the magnitude of the pressure load at different parts of the cylindrical surface. The cylindrical specimen has higher symmetry, which is convenient to use more mechanical means and assumptions in the research. At the same time, the cylindrical specimen is easier to sample and process on-site rock samples, improving the sampling efficiency, reducing costs, increasing the test sample size, and thus improving the credibility of the test results.

[0028] 2. The true triaxial test analysis method for rock cylinder specimens provided by the present invention uses the obtained stress field calculation method to calculate the shear stress at the center of the specimen after the specimen reaches the required stress state. By ensuring that the area with the same principal stress direction is the largest, the area with similar stress state is ensured to be the largest, that is, by successively reducing p1 to p7 in equal proportion to ensure that the modulus of the shear stress gradient is the smallest. Finally, this loading method is verified by finite element simulation. By obtaining the size of the area where the shear stress is 0 under different loading methods, the reliability of this method is verified. The boundary conditions of the verification model are consistent with the loading method, and a loading method that satisfies the similar stress state in the research area is proposed, filling the gaps in related theories and technologies. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a schematic flow chart of the loading method of the present invention;

[0030] Figure 2 is a schematic loading diagram of the cylinder specimen in the loading method of the present invention;

[0031] Figure 3 is a schematic diagram when the cylinder specimen in the loading method of the present invention is subjected to surface load;

[0032] Figure 4 is a schematic diagram of the coordinate system in the circular cross-section of the cylinder specimen under point load in the loading method of the present invention;

[0033] Figure 5 is a schematic diagram of the new coordinate system after the rotation of the point load position in the loading method of the present invention;

[0034] Figure 6 is a stress field diagram inside the cylinder specimen of the loading method of the present invention;

[0035] Figure 7 is a stress field diagram inside the cylinder specimen of the present invention using the direct loading method. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0036] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0037] In the description of the following invention, it should be noted that the orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "inner", "outer", 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 simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation. The term "connection" only represents the connection between devices and has no special meaning.

[0038] In addition, the technical fields and installation methods involved in the embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0039] Specific embodiment: Please refer to Figures 1-7 , a true triaxial test analysis method for rock cylindrical specimens, comprising the following steps:

[0040] Apply a point load to the cylindrical surface of the cylindrical specimen, analyze the stress components in the circular surface of the cylindrical specimen under the action of the point load, and use the principle of linear superposition for integration to calculate the analytical solution of the stress field in the circular surface of the rock cylindrical specimen;

[0041] Apply a symmetric surface load to the cylindrical surface of the cylindrical specimen, and calculate the stress field in the circular surface of the cylindrical specimen under the symmetric surface load by using the analytical solution of the stress field in the circular surface of the cylindrical specimen;

[0042] Establish the constraint conditions for the stress state similarity region, calculate the relationship function between the symmetric surface loads under the corresponding loading methods, and determine it as the linear gradient loading method;

[0043] Conduct a finite element analysis on the rock cylindrical specimen in the linear gradient loading method, simulate the stress distribution inside the circular surface of the cylindrical specimen, and verify the feasibility of the linear gradient loading method determined by the analytical solution.

[0044] Furthermore, apply a surface load p0 to the upper bottom surface of the cylindrical specimen at a set loading speed to provide axial compression; since the axial compression is fixed in the axial direction, the stress component in this direction is the magnitude of the surface load p0. Therefore, the calculation of the stress distribution is actually the calculation of the stress magnitudes in the x and y directions on the xoy plane. Using the plane stress assumption, calculate the stress distribution of a cylinder with a diameter of D and a thickness of a under the boundary condition of non-uniform load applied to the circumference. The specific steps are as follows:

[0045] When applying a point load to the cylindrical surface, select a circular cross-section at the point where the cylindrical surface of the cylindrical specimen is subjected to the point load, establish a plane coordinate system oxy with the center of the circle as the coordinate origin, the direction parallel to the point load as the y-axis, and the direction perpendicular to the point load as the x-axis. With Figure 4For example, select an arbitrary coordinate point within the coordinate system, that is, any coordinate point E. Use the Airy function method to calculate the stress components of any coordinate point E in the plane coordinate system oxy under the action of a point load, as follows:

[0046] (1), where x is the distance of any coordinate point E from the y-axis in the plane coordinate system oxy, y is the distance of any coordinate point E from the x-axis in the plane coordinate system oxy, σ x is the normal stress on any coordinate point E in the plane coordinate system oxy along the x-axis direction, σ y is the normal stress on any coordinate point E in the plane coordinate system oxy along the y-axis direction, τ xy is the shear stress on any coordinate point E in the plane perpendicular to the x-axis along the y-axis direction, D is the diameter of the cylindrical specimen, a is the thickness of the cylindrical specimen, and P is the magnitude of the point load.

[0047] Furthermore, adjust the position of the point load so that the point load rotates by θ around the origin. Consider the rotation of the point load as the rotation of the plane coordinate system oxy. After rotation, a rotated coordinate system ox'y' is formed. Use formula (1) in the rotated coordinate system ox'y' to obtain the stress components σ x' , σ y' and τ x'y' of any coordinate point E in the rotated coordinate system ox'y', and transform x and y into the new coordinates x' and y'. The relationship between the old and new coordinates is as follows:

[0048] ; (2), and after obtaining σ x' , σ y' and τ x'y' , transform the stress components in the rotated coordinate system ox'y' into the stress components in the plane coordinate system oxy, that is, transform σ x' , σ y' and τ x'y' into σ x , σ y and τ xy , then the stress components of any coordinate point E in the rotated coordinate system ox'y' under the action of the point load can be obtained:

[0049] (3), where σ x' is the normal stress on any coordinate point E in the rotated coordinate system ox'y' along the x'-axis direction, σ y'is the normal stress acting on any coordinate point E in the y'-axis direction within the rotating coordinate system ox'y', and τ x'y' is the shear stress acting on any coordinate point E in the y'-axis direction on the plane perpendicular to the x'-axis. Finally, the stress components under different point load positions can be obtained:

[0050]

[0051]

[0052] (4).

[0053] Furthermore, by replacing the point load with an arc element ds and the pressure load p on the arc element ds, and considering the relationship between the pressure load p and the set angle θ, the following can be obtained:

[0054] (5). According to the principle of linear superposition, the stress field distribution within the circular surface of the cylindrical specimen under any pressure load is expressed as follows:

[0055]

[0056]

[0057] (6), where f xx (x, y, θ) is the eigenfunction of σ x , f yy (x, y, θ) is the eigenfunction of σ y , f xy (x, y, θ) is the eigenfunction of τ xy .

[0058] Furthermore, the cylindrical surface of the cylindrical specimen is divided into 24 equal parts, with each 15° interval defining a region. Symmetric surface loads are applied to 12 groups of symmetric regions, namely loads p1 to p 12 . Since the loading method is to apply different pressure loads p1 to p 12 in 12 groups of regions respectively, integration by parts and linear superposition can be performed. Finally, the stress field distribution within the circular surface of the cylindrical specimen is:

[0059]

[0060]

[0061] (7), where = 1, 2, 3, ……, 12. Changing the shape of the specimen to a cylinder can effectively avoid boundary effects and channeling during the test. Cubic specimens are more susceptible to end friction effects, while cylindrical specimens can effectively prevent end friction by adjusting the height-diameter ratio. Moreover, cylindrical specimens have higher symmetry, making it more convenient to use more mechanical means and assumptions in the study. At the same time, cylindrical specimens are easier to sample and process on-site rock samples, improving the sampling efficiency, reducing costs, increasing the test sample size, and thus enhancing the credibility of the test results. By using a loading device to load on the cylindrical surface, the true triaxial state of the specimen can be achieved. According to different loading methods, the internal stress field of the specimen is obtained using both analytical and numerical methods, and the loading method that makes the stress state in a larger area inside the specimen similar is determined according to the above method, thus realizing the true triaxial loading test on the cylindrical specimen, avoiding problems such as boundary effects, friction effects, and channeling of cubic specimens. By applying multiple groups of different loads on the cylindrical surface, different true triaxial states of the cylindrical specimen 2 are achieved, realizing the true triaxial loading of non-cubic specimens, avoiding problems such as corner stress concentration and channeling that are prone to occur in cubic specimens, improving the test efficiency and accuracy, and the stress components at any point inside the cylinder can be calculated based on the diameter of the cylindrical specimen and the magnitude of the pressure load at different parts of the cylindrical surface.

[0062] Further, f in formula (4) xx (x, y, θ), f yy (x, y, θ), f xy (x, y, θ) are specifically expressed as follows:

[0063] (8).

[0064] Further, to meet the test requirements, it is necessary to ensure that the area with similar internal stress state in the cylindrical specimen during the test is the largest. Therefore, a special loading method is required, and the specific steps are as follows:

[0065] Among the three principal stress components, the magnitude of one principal stress component is applied by axial loading on the cylinder, and its magnitude is the load pressure. The magnitudes of the other two principal stress components are applied by combined loading on the cylindrical surface. Therefore, assume that the x-axis and y-axis directions are the directions of the other two principal stress components, and the x-axis direction is p1 and p 12The direction of the angular bisector between them, and the y-axis direction is the direction of the angular bisector between p6 and p7. The region where the shear stress component is approximately 0 can be regarded as the region with similar stress states. The region with similar stress states is the region where the deviation of the principal stress magnitude at each point within the circular surface of the cylindrical specimen is ≤ 5% and the directions are the same;

[0066] Taking the center coordinates as an example, substituting x = 0 and y = 0 into formula (7), we can get:

[0067] (9), Assume that the load is equal everywhere, that is, p1 = p2 = … = p 12 = p. At this time, the stress components at the center of the circle can be obtained as σ ox = σ oy = p, which is the same as the result of the conventional triaxial test, proving the accuracy of the stress field distribution within the circular surface of the obtained cylindrical specimen;

[0068] After determining the stress state of the cylindrical specimen under different load combinations by formula (9), when ensuring that the shear stress component at the center of the circle is 0, substituting x = 0 and y = 0 into the stress field distribution formula of the circular surface of the cylindrical specimen obtained, the shear stress at the center of the circle can be obtained as:

[0069] (10). Therefore, it is necessary to ensure that the loading is symmetric, further verifying the accuracy of the symmetric loading in zones of this method. According to formula (10), the maximum constraint condition for satisfying the region with similar stress states is: spreading outwards from the center position to ensure that ∇τ xy is the smallest; for different principal stresses, the linearly decreasing method can generally approximately meet ∇τ xy , where ∇τ xy represents the change gradient of τ xy . Substituting τ oxy = 0 into formula (10) for calculation, the relationship function between the loads on each symmetric plane can be obtained as:

[0070] ; (11), where σ n is the principal stress component along the x-axis direction at any point in the region with similar stress states, and σ m is the principal stress component along the y-axis direction at any point in the region with similar stress states. Therefore, when adopting the linear gradient loading method, the region with the largest similar stress state within the circular surface of the cylindrical specimen can be satisfied.

[0071] Further, a finite element model of the cylindrical specimen is established. Boundary conditions are established respectively according to the symmetric plane load relationship of direct loading and linear gradient loading, and a numerical simulation of the finite element test is carried out to simulate the internal stress distribution of the cylindrical specimen. Taking p1 = 8 MPa and p7 = 20 MPa as examples, when loaded in the direct way, p1 = p2 = p3 = p 12 = p 11 = p 10 = 8 MPa, p4 = p5 = p6 = p7 = p8 = p9 = 20 MPa. When loaded in the linear gradient way, it can be calculated according to formula (11) that p1 = 8 MPa, p2 = p 12 = 10 MPa, p3 = p 11 = 12 MPa, p4 = p 10 = 14 MPa, p5 = p9 = 16 MPa, p6 = p8 = 18 MPa, p7 = 20 Mpa. The corresponding values of p1 to p 12 are used as input parameters respectively, and the stress distribution finally output by the two loading methods is compared to verify the feasibility of the linear gradient loading determined by the analytical solution;

[0072] The comparison of the shear stress nephograms of the two loading methods is as Figure 6 and Figure 7 shown. The loading method of the present invention significantly increases the area of the stress state similarity region, proving the feasibility of the loading method of the present invention. Using the obtained stress field calculation method, first calculate the principal stress magnitude at the center of the specimen to ensure that the specimen reaches the required stress state, then calculate the shear stress at the center of the specimen, ensure the maximum of the region with the same principal stress direction to ensure the maximum of the stress state similarity region, then successively reduce p1 to p7 in equal proportion to ensure the minimum modulus of the shear stress gradient, and finally verify this loading method through finite element simulation. Verify the reliability of this method by obtaining the size of the region where the shear stress is 0 under different loading methods, verify that the boundary conditions of the model are consistent with the loading method, and propose a loading method that satisfies the stress state similarity in the research area, filling the relevant theoretical and technical gaps.

Claims

1. A true triaxial test analysis method for rock cylinder specimens, characterized in that: The steps are as follows: Apply a point load to the cylindrical surface of the cylindrical specimen, analyze the stress components within the circular surface of the cylindrical specimen under the action of the point load, and use the principle of linear superposition for integration to calculate the analytical solution of the stress field within the circular surface of the rock cylindrical specimen; Apply a symmetric surface load to the cylindrical surface of the cylindrical specimen, and use the analytical solution of the stress field within the circular surface of the cylindrical specimen to calculate the stress field within the circular surface of the cylindrical specimen under the symmetric surface load; Establish the constraint conditions for the stress state similarity region, calculate the relationship function between the symmetric surface loads under the corresponding loading mode, and determine it as the linear gradient loading mode; Conduct a finite element analysis on the cylindrical specimen of the rock in the linear gradient loading mode, simulate the internal stress distribution within the circular surface of the cylindrical specimen, and verify the feasibility of the linear gradient loading mode determined by the analytical solution; The method of applying symmetric surface loads to the cylindrical surface of a cylindrical specimen is as follows: The cylindrical surface of the cylindrical specimen is equally divided into 24 parts and divided into 12 groups of symmetric regions, and symmetric surface loads p1 to p are applied to the 12 groups of symmetric regions respectively. 12 ; The constraint conditions for the established stress state similarity region are: the region where the shear stress component is 0 is regarded as the stress state similarity region, and the stress state similarity region is the region where the deviation of the principal stress magnitudes at each point within the circular surface of the cylindrical specimen is ≤ 5% and the directions are the same; The relationship function between the symmetric surface loads is: ； ， where σ n is the principal stress component in the x-axis direction at any point in the similar region of the stress state, and σ m is the principal stress component in the y-axis direction at any point in the similar region of the stress state. Therefore, when using the linear gradient loading method, the maximum similar region of the stress state is in the circular surface of the cylindrical specimen.

2. The true triaxial test analysis method for a rock cylinder specimen according to claim 1, wherein: The specific method for applying a point load to the cylindrical surface of the cylindrical specimen and analyzing the stress components within the circular surface of the cylindrical specimen under the action of the point load is: establish a plane coordinate system oxy with the center of the circle as the origin on the circular surface of the cylindrical specimen, and analyze the stress components of any coordinate point E within the circular surface of the cylindrical specimen under the action of the point load; rotate the point load by a set angle around the center of the circle to adjust its position, and at the same time rotate the plane coordinate system oxy by the set angle to generate a rotated coordinate system ox'y', and obtain the stress components of any coordinate point E within the circular surface of the cylindrical specimen at different point load positions.

3. A true triaxial test analysis method for rock cylinder specimens according to claim 2, characterized in that: The stress components of any coordinate point E in the plane coordinate system oxy under the action of the point load: ， where x is the distance of any coordinate point E from the y-axis in the plane coordinate system oxy, y is the distance of any coordinate point E from the x-axis in the plane coordinate system oxy, and σ x is the normal stress acting on any coordinate point E in the x-axis direction in the plane coordinate system oxy, and σ y is the normal stress acting on any coordinate point E in the y-axis direction in the plane coordinate system oxy, τ xy is the shear stress acting on any coordinate point E in the y-axis direction on the plane perpendicular to the x-axis, D is the diameter of the cylindrical specimen, a is the thickness of the cylindrical specimen, and P is the magnitude of the point load.

4. The true triaxial test analysis method for a rock cylinder specimen according to claim 3, characterized in that: The stress components of any coordinate point E in the rotated coordinate system ox'y' under the action of the point load: ， where σ x' is the normal stress acting on any coordinate point E in the x'-axis direction within the rotating coordinate system ox'y', and σ y' is the normal stress acting on any coordinate point E in the y'-axis direction within the rotating coordinate system ox'y'. τ x'y' is the shear stress acting on any coordinate point E in the y'-axis direction on the plane perpendicular to the x'-axis, and θ is the set angle of rotation of the plane coordinate system oxy.

5. The true triaxial test analysis method for a rock cylinder specimen according to claim 2, characterized in that: Rotate the point load around the center of the circle by a set angle to adjust its position. At the same time, rotate the plane coordinate system oxy by a set angle. The specific method is as follows: Adjust the position of the point load so that the point load rotates by θ around the origin. Consider the rotation of the point load as the rotation of the plane coordinate system oxy. After rotation, a rotated coordinate system ox'y' is formed. Use the above functional relationship in the rotated coordinate system ox'y' to obtain the stress components σ x' , σ y' and τ x'y' at any coordinate point E in the rotated coordinate system ox'y'. Then transform x and y into the new coordinates x' and y'. The relationship between the old and new coordinates is as follows: ； 。 6. A true triaxial test analysis method for a rock cylinder specimen according to claim 4, characterized in that: The specific method for using the principle of linear superposition for integration to calculate the stress field within the circular surface of the cylindrical specimen is: replace the point load with an arc element ds and the pressure load p on the arc element ds, combine the relationship between the pressure load p and the set angle θ, and use the principle of linear superposition for integration. The stress field distribution within the circular surface of the cylindrical specimen under the action of any pressure load is expressed as follows: , where f xx (x, y, θ) is the characteristic function of σ x , f yy (x, y, θ) is the characteristic function of σ y , f xy (x, y, θ) is the characteristic function of τ xy is the characteristic function.

7. A true triaxial test analysis method for a rock cylinder specimen according to claim 6, characterized in that: Using the analytical solution of the stress field within the circular surface of the cylindrical specimen to calculate the stress field within the circular surface of the cylindrical specimen under the symmetric surface load is: , where = 1, 2, 3, ……, 12.

8. A true triaxial test analysis method for a rock cylinder specimen according to claim 1, characterized in that: When ensuring that the shear stress component at the center of the circle is 0, substitute x = 0 and y = 0 into the stress field distribution formula obtained for the circular surface of the cylindrical specimen, and the shear stress at the center of the circle can be obtained: , according to the formula, the maximum constraint condition for the region with similar stress state is: diffusing outward from the center position to ensure the minimum change gradient of τ xy .

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