Rock cylinder sample true triaxial test analysis method

Abstract

The invention relates to the technical field of rock mechanics true triaxial tests, in particular to a rock cylinder sample true triaxial test analysis method which comprises the following steps: applying a point load to the cylindrical surface of a cylinder sample, performing integration by using a linear superposition principle, and calculating an analytical solution of an internal stress field in the circular surface of the rock cylinder sample; applying a symmetry plane load to the cylindrical surface of the cylinder sample, and calculating an internal stress field of the circular surface of the cylinder sample under the symmetry plane load by using an analytical solution; setting a constraint condition of a stress state similar region, calculating a relation function between symmetrical surface loads in a corresponding loading mode, and determining the relation function as a linear gradient loading mode; and performing finite element analysis on the cylindrical sample of the rock, and verifying the feasibility of the linear gradient loading mode determined by the analytical solution. According to the invention, true triaxial test analysis of the cylinder sample is realized, the internal stress state of a larger area of the sample is ensured to be similar, and the problems of boundary effect, friction effect, fluid channeling and the like of a cubic sample are avoided.

Description

Technical Field

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

[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, making it difficult to guide engineering practice. The development of hydraulic fracturing technology depends on relevant 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 to simulate the multi-field coupling effect of water-thermal-mechanical during the fracturing process under the deep ground high in-situ stress state.

[0003] Existing true triaxial test instruments generally consist of three groups of orthogonal rigid loading mechanisms, which are combined with a seepage loading device to realize the hydraulic coupling test. When conducting the hydraulic coupling test, a hole is 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. Frictional 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 during the test. In addition, 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 current device uses cube specimens, calculating the internal stress state of the specimen only requires simply calculating 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, theoretically limiting 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 cylindrical specimens to solve the problems raised in the above background art.

[0005] To achieve the above purpose, the present invention provides the following technical solution: An analysis method for true triaxial test of rock cylindrical specimens, comprising the following steps: Apply point loads 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 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 cylindrical specimen; Apply symmetric surface loads 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 loads using the analytical solution of the stress field in the circular surface of the cylindrical specimen; 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; 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.

[0006] Furthermore, the specific method for applying point loads to the cylindrical surface of the cylindrical specimen and analyzing the stress components in the circular surface of the cylindrical specimen under the action of the point loads 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 action of 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.

[0007] Furthermore, 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, σ x is the normal stress exerted on any coordinate point E in the x-axis direction in the plane coordinate system oxy, σ y is the normal stress exerted on any coordinate point E in the y-axis direction in the plane coordinate system oxy, τ xy is the shear stress exerted 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.

[0008] Furthermore, 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 exerted on any coordinate point E in the x'-axis direction in the rotated coordinate system ox'y', σ y' is the normal stress exerted on any coordinate point E in the y'-axis direction in the rotated coordinate system ox'y', τ x'y' is the shear stress exerted 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.

[0009] Further, 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. 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 function 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', and transform x and y into new coordinates x' and y'. The relationship between the old and new coordinates is as follows: .

[0010] Further, use the principle of linear superposition for integration to calculate the stress field in the circular surface of the cylindrical specimen. The specific method 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 θ, and use the principle of linear superposition for integration. The stress field distribution in the circular surface of the cylindrical specimen under any pressure load is expressed as follows: , where f xx (x, y, θ) is the eigenfunction of σ x , f yy (x, y, θ) is the eigenfunction of σ y , and f xy (x, y, θ) is the eigenfunction of τ xy .

[0011] Further, the method of 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 follows: , where = 1, 2, 3, ……, 12.

[0012] Further, the constraint condition for setting up the stress state similarity region is: The region where the shear stress component is 0 is regarded as the stress state similarity region. The stress state similarity region is the region where the deviation of the principal stress magnitude at each point in the circular surface of the cylindrical specimen is ≤ 5% and the directions are the same.

[0013] Furthermore, when ensuring that the shear stress component at the center of the circle is 0, substituting x = 0 and y = 0 into the formula for the stress field distribution within the circular surface of the cylindrical specimen, the shear stress at the center of the circle can be obtained as follows: , as can be seen from the formula, the constraint condition for maximizing the similar stress state region is to ensure that the change gradient of τ xy is minimized.

[0014] Furthermore, the relationship function between the loads on each symmetry plane is: , where σ n is the principal stress component in the x-axis direction at any point within the similar stress state region, and σ m is the principal stress component in the y-axis direction at any point within the similar stress state region. Therefore, when adopting the linear gradient loading method, the similar stress state region within the circular surface of the cylindrical specimen is the largest.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. A true triaxial test analysis method for rock cylindrical specimens 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 avoid problems such as corner stress concentration and channeling that are prone to occur in cubic specimens. Cubic specimens are more susceptible to the influence of end friction effects, while cylindrical specimens 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 loads at different parts of the cylindrical surface. In addition, the cylindrical specimen has a higher symmetry, which is convenient for using more mechanical means and assumptions in the research. At the same time, it is easier to sample and process on-site rock samples for cylindrical specimens, improving the sampling efficiency, reducing costs, increasing the test sample size, and thus improving the credibility of the test results.

[0016] 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 a similar stress state is ensured to be the largest. That is, by sequentially reducing p1 to p7 in equal proportion, the modulus of the shear stress gradient is minimized. Finally, this loading method is verified through 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 within the research area is proposed, filling the gaps in relevant theories and technologies. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a schematic flow chart of the loading method of the present invention; Figure 2 is a schematic loading diagram of the cylinder specimen in the loading method of the present invention; Figure 3 is a schematic diagram when the cylinder specimen in the loading method of the present invention is subjected to surface load; Figure 4 is a schematic diagram of the coordinate system within the circular cross-section of the cylinder specimen under point load in the loading method of the present invention; 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; Figure 6 is the stress field diagram inside the cylinder specimen with the loading method of the present invention; Figure 7 is the stress field diagram inside the cylinder specimen with the direct loading method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0018] 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 of 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.

[0019] In the following description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "upper", "lower", "left", "right", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings, and 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.

[0020] In addition, in the embodiments of the present invention described below, the technical fields and installation methods involved can be combined with each other as long as they do not conflict with each other.

[0021] Specific embodiment: Please refer to Figures 1-7 , a true triaxial test analysis method for rock cylindrical specimens, comprising the following steps: Apply point loads 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 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 cylindrical specimen; Apply symmetric surface loads to the cylindrical surface of the cylindrical specimen, and 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 loads; 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; Perform 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.

[0022] Furthermore, apply a surface load p0 to the upper bottom surface of the cylindrical specimen at a set loading speed to provide axial pressure; since the axial pressure 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 loads applied to the circumference, and the specific steps are as follows: When applying point loads 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 loads, establish a plane coordinate system oxy with the center of the circle as the coordinate origin, the direction parallel to the point load direction as the y-axis, and the direction perpendicular to the point load direction as the x-axis. Taking Figure 4 as an example, select an arbitrary coordinate point in the coordinate system, that is, any coordinate point E, and 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 the point loads, as follows: (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 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 xyτ is the shear stress exerted on any coordinate point E in the y-axis direction on a 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.

[0023] 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, and a rotated coordinate system ox'y' is formed. In the rotated coordinate system ox'y', use formula (1) 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'. And transform x and y into the new coordinates x' and y'. The relationship between the old and new coordinates is as follows: (2). 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: (3), where σ x' is the normal stress exerted on any coordinate point E in the x'-axis direction in the rotated coordinate system ox'y', σ y' is the normal stress exerted on any coordinate point E in the y'-axis direction in the rotated coordinate system ox'y', τ x'y' is the shear stress exerted on any coordinate point E in the y'-axis direction on a plane perpendicular to the x'-axis. Finally, the stress components under different point load positions can be obtained: (4).

[0024] Furthermore, replace the point load with an arc element ds and the pressure load p on the arc element ds, and consider the relationship between the pressure load p and the set angle θ, then we can get: (5). According to the principle of linear superposition, the stress field distribution in the circular surface of the cylindrical specimen under the action of any pressure load is expressed as follows: (6), where fxx (x, y, θ) is the characteristic function of σ x , and f yy (x, y, θ) is the characteristic function of σ y , and f xy (x, y, θ) is the characteristic function of τ xy .

[0025] Furthermore, the cylindrical surface of the cylindrical specimen is equally divided into 24 parts, and a region is distinguished every 15°. The same symmetric surface load is applied to 12 groups of symmetric regions respectively, that is, the loads p1 to p 12 . Since the loading method is to apply different pressure loads p1 to p in 12 groups of regions respectively 12 , it is possible to perform partial integration and linear superposition. Finally, the stress field distribution in the circular surface of the cylindrical specimen is as follows: (7), where = 1, 2, 3,..., 12. Changing the specimen shape 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, which is convenient for using more mechanical means and assumptions in the research. 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 improving the credibility of the test results. The loading device is used to load on the cylindrical surface to achieve the true triaxial state of the specimen. According to different loading methods, the internal stress field of the specimen is obtained by using analytical methods and numerical methods at the same time, and the loading method that makes the stress states in a larger area inside the specimen similar is determined according to the above method, so as to realize the true triaxial loading test of the cylindrical specimen, avoiding problems such as boundary effects, friction effects, and channeling of cubic specimens. Different true triaxial states of the cylindrical specimen are realized by applying multiple groups of different loads on the cylindrical surface, achieving 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 loads at different parts of the cylindrical surface.

[0026] Furthermore, f xx (x, y, θ), f yy (x, y, θ), f xy (x, y, θ) are specifically expressed as follows: (8).

[0027] Furthermore, to meet the test requirements, it is necessary to ensure that the maximum similar region of the internal stress state of the cylindrical specimen during the test. Therefore, a special loading method is required, and the specific steps are as follows: 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 cylinder surface. Therefore, assuming that the x-axis and y-axis directions are the directions of the other two principal stress components, the x-axis direction is the bisector direction between p1 and p 12 The direction of the bisector between p6 and p7, then the region where the shear stress component is approximately 0 can be regarded as the similar region of the stress state. The similar region of the stress state 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; Taking the center coordinates as an example, substituting x = 0 and y = 0 into formula (7), we can obtain: (9), assuming 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; 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 within the circular surface of the obtained cylindrical specimen, the shear stress at the center of the circle can be obtained as: (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 constraint condition for meeting the maximum similar region of the stress state is: spreading outwards from the center position, ensuring that ▽τ xy is the smallest; for different principal stresses, the linearly decreasing method can usually 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: (11), where σ n is the principal stress component along the x-axis direction at any point within the similar region of the stress state, and σ mis the principal stress component in the y-axis direction at any point in the similar stress state region. Therefore, when adopting the linear gradient loading method, the maximum similar stress state region in the circular surface of the cylindrical specimen can be satisfied.

[0028] Furthermore, establish a finite element model of the cylindrical specimen, establish boundary conditions according to the symmetric plane load relationships of direct loading and linear gradient loading respectively, conduct numerical simulation of finite element tests to simulate the internal stress distribution of the cylindrical specimen. Taking p1 = 8MPa and p7 = 20MPa as examples, when loading in the direct way, p1 = p2 = p3 = p 12 = p 11 = p 10 = 8MPa, p4 = p5 = p6 = p7 = p8 = p9 = 20MPa. When loading in the linear gradient way, according to the calculation of formula (11), p1 = 8MPa, p2 = p 12 = 10MPa, p3 = p 11 = 12MPa, p4 = p 10 = 14MPa, p5 = p9 = 16MPa, p6 = p8 = 18MPa, p7 = 20Mpa. Respectively take the corresponding values of p1 to p 12 as input parameters, compare the finally output stress distribution of the two loading methods to verify the feasibility of the linear gradient loading method determined by the analytical solution; 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 similar stress state region, proving the feasibility of the loading method of the present invention. Using the obtained stress field calculation method, first calculate the magnitude of the principal stress 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 similar stress state 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 with shear stress of 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 similar stress state in the research region, filling the relevant theoretical and technical gaps.

Claims

1. A true triaxial test analysis method for a rock cylindrical specimen, characterized by: The steps include: Apply point load to the cylindrical surface of the cylindrical sample, analyze the stress components in the cylindrical surface of the cylindrical sample under the point load, and integrate using the linear superposition principle to calculate the analytical solution of the stress field in the cylindrical surface of the rock sample; A symmetrical surface load is applied to the cylindrical surface of the cylindrical specimen, and the stress field inside the cylindrical surface of the cylindrical specimen under the symmetrical surface load is calculated using the analytical solution of the stress field inside the cylindrical surface of the cylindrical specimen; Set up constraint conditions for areas with similar stress states, calculate the relationship function between the loads on each symmetry surface under the corresponding loading mode, and determine it as a linear gradient loading mode; Finite element analysis was performed on the cylindrical rock specimens using linear gradient loading to simulate the internal stress distribution on the cylindrical surface of the cylindrical specimens and verify the feasibility of the linear gradient loading method determined by the analytical solution.

2. A true triaxial test analysis method for a rock cylinder specimen according to claim 1, characterized in that: A point load is applied to the cylindrical surface of the cylindrical specimen and a specific method for analyzing the stress component in the circular surface of the cylindrical specimen under the action of the point load is as follows: a plane coordinate system oxy is established on the circular surface of the cylindrical specimen with the center of the circle as the origin, and the stress component of an arbitrary coordinate point E in the circular surface of the cylindrical specimen under the action of the point load is analyzed; the position of the point load is adjusted by rotating a set angle around the center of the circle, and at the same time, the plane coordinate system oxy is rotated by a set angle to generate a rotating coordinate system ox'y', and the stress component of an arbitrary coordinate point E in the circular surface of the cylindrical specimen under different point load positions is obtained.

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

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

5. A true triaxial test analysis method for a rock cylinder specimen according to claim 2, characterized in that: The position of the point load is adjusted by rotating the set angle around the center of the circle, and the plane coordinate system oxy is rotated by the set angle. The specific method is: adjust the position of the point load so that the point load rotates around the origin by θ, and the rotation of the point load is regarded as the rotation of the plane coordinate system oxy. After the rotation, the rotating coordinate system ox'y' is formed. In the rotating coordinate system ox'y', the above function relationship is used to obtain the stress component σ of any coordinate point E in the rotating coordinate system ox'y' x' , σ y' With τ x'y' , and transform x, y into new coordinates x', y'. The new and old coordinates have the following relationship: 。 6. A true triaxial test analysis method for a rock cylinder specimen according to claim 4, characterized in that: The specific method of calculating the stress field on the circular surface of the cylindrical specimen by integrating the linear superposition principle is as follows: replace the point load with the 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 integrate using the linear superposition principle. The distribution of the stress field on the circular surface of the cylindrical specimen under any pressure load is expressed as follows: , where f xx (x,y,θ) is σ x The characteristic function, f yy (x,y,θ) is σ y The characteristic function, f xy (x,y,θ) is τ xy The characteristic function of .

7. A true triaxial test analysis method for a rock cylinder specimen according to claim 6, characterized in that: The method of applying symmetrical surface load to the cylindrical surface of the cylindrical specimen is as follows: the cylindrical surface of the cylindrical specimen is divided into 24 equal parts, which are divided into 12 groups of symmetrical areas, and symmetrical surface loads p1 to p2 are applied to the 12 groups of symmetrical areas respectively. 12 , using the analytical solution of the stress field in the cylindrical surface of the cylindrical specimen, the stress field in the cylindrical surface of the cylindrical specimen under symmetrical surface load is calculated as: ,in =1,2,3,……,12.

8. A true triaxial test analysis method for a rock cylinder specimen according to claim 1, characterized in that: The constraint condition of the established stress state similarity region is: the region with shear stress component of 0 is regarded as the stress state similarity region, and the stress state similarity region is the region where the principal stress magnitude deviation of each point in the circular surface of the cylindrical specimen is ≤5% and the direction is consistent.

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

10. A true triaxial test analysis method for a rock cylinder specimen according to claim 7, characterized in that: The relationship function between the loads on each symmetry surface is: , where σ n is the principal stress component along the x-axis at any point in the region with similar stress states, σ m It is the principal stress component along the y-axis direction at any point in the stress state similarity area. Therefore, when the linear gradient loading method is adopted, the stress state similarity area in the circular surface of the cylindrical specimen is the largest.

Images