A method for constructing an equivalent deteriorated mechanical model of anisotropic rock mass

Abstract

The application provides a construction method of an anisotropic rock mass equivalent degradation mechanical model, comprising the following steps: S1, determining a mechanical model: based on the generalized Hooke's law, the basic expression form of the rock mass mechanical model can be expressed by an increment expression of a stress-strain relationship; S2, determining an elastic stiffness matrix: an elastic stiffness matrix is constructed by using a symmetrization matrix method in an inner product form; S3, determining a plastic strain increment: a yield function is determined, an expansion angle is obtained, the inner friction angle in the yield function is replaced by the expansion angle to obtain a plastic potential function, and the plastic potential function is used to solve the increment of a plastic strain tensor. On the basis of the equivalent elastoplastic theory, the anisotropic rock mass equivalent degradation mechanical model considering the synergistic effect of the intermediate principal stress and the structure surface occurrence is established, so that the model can reflect the brittle and ductile degree, the expansion characteristics, the failure mechanism and the influence mechanism of the intermediate principal stress and the structure surface.

Description

Technical Field

[0001] This invention belongs to the field of underground engineering, specifically relating to a method for constructing an equivalent deterioration mechanical model of anisotropic rock mass. Background Technology

[0002] During the construction of deep underground engineering projects, it is inevitable to encounter surrounding rock with developed structural planes. Under high ground stress and the disturbance of engineering excavation, stress-structure composite failure is easily induced. As a geological weak surface, the structural plane weakens the strength of the surrounding rock and affects the initiation, propagation, and penetration of cracks inside the rock mass. It often plays a boundary-limiting role in the failure mode of the surrounding rock. Therefore, it is very necessary to consider the characteristics of rock mass deformation strength anisotropy and rock mass failure tendency caused by the structural plane effect in the stability analysis of deep underground engineering projects.

[0003] To better describe the mechanical behavior of anisotropic rock masses in deeply buried underground engineering projects, it is essential to understand the mechanical response process of anisotropic rock masses under complex stress paths. Currently, researchers have discovered the true triaxial stress environment of deeply buried engineering projects (…). The problem is that the intermediate principal stress has a significant impact on the deformation strength characteristics of anisotropic rock masses. Therefore, the synergistic effect of the intermediate principal stress effect and the structural plane effect on the rock mass mechanical properties needs to be described in rock mechanics models. Currently, models based on the Mohr–Coulomb criterion and the Hoek-Brown criterion are the most widely used in rock mechanics model research. However, neither of these criteria considers the intermediate principal stress effect. Summary of the Invention

[0004] The purpose of this invention is to provide a method for constructing an equivalent deterioration mechanical model of anisotropic rock masses, addressing the problems mentioned above.

[0005] Therefore, the above-mentioned objective of the present invention is achieved through the following technical solution:

[0006] A method for constructing an equivalent deterioration mechanical model of anisotropic rock mass includes the following steps:

[0007] S1. Determine the mechanical model: The deformation of rock mass material is divided into two parts: elastic deformation and irreversible plastic deformation. Based on the generalized Hooke's law, the basic expression of the rock mass mechanics model is the incremental expression of the stress-strain relationship, as shown in the following formula:

[0008]

[0009] In the formula, For the increment of the stress tensor, The increment of the strain tensor; This represents the increment of the plastic strain tensor; This is the elastic stiffness matrix, whose value is determined by the intermediate principal stress. Minimum principal stress and structural surface orientation Influence;

[0010] S2. Determine the elastic stiffness matrix: Construct the elastic stiffness matrix using the symmetric matrix method in inner product form. ;

[0011] S3. Determine the plastic strain increment: Determine the yield function. Obtain expansion angle With expansion angle Alternative yield function internal friction angle To obtain the plastic potential function With plastic potential function To solve for the increment of the plastic strain tensor .

[0012] While adopting the above technical solutions, the present invention may also adopt or combine the following technical solutions:

[0013] As a preferred technical solution of the present invention: in step S2, the elastic stiffness matrix The formula is as follows:

[0014]

[0015] In the formula, It is the elastic modulus of the rock mass sample in the three principal stress directions; It is the Poisson's ratio of the rock mass sample; It is the shear modulus of the rock mass sample in the three principal stress directions.

[0016] As a preferred technical solution of the present invention: shear modulus of rock mass sample Expressed using the following formula:

[0017]

[0018] In the formula, It is the elastic modulus of the rock mass sample in the three principal stress directions; It is the shear modulus of the rock mass sample in the three principal stress directions. It can be 1, 2, or 3; It is the Poisson's ratio of the rock mass sample.

[0019] As a preferred embodiment of the present invention: the elastic modulus E of the rock mass sample j Expressed using the following formula:

[0020]

[0021]

[0022] In the formula, It is the elastic modulus of the rock mass sample in the three principal stress directions. The elastic modulus of the rock mass sample in the three principal stress directions was characterized. The rate of weakening in the residual phase; It is the rate at which the elastic modulus of the rock mass sample weakens with respect to the plastic intrinsic variable k in the three principal stress directions. These are the fitting parameters.

[0023] As a preferred technical solution of the present invention: in step S3, the yield function The yield function is determined as follows: The expression is as follows:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] In the formula, , and For material constants, The stress Lode angle has a value range of 0-60°. This represents the shear stress in octahedral space. It represents the normal stress in octahedral space.

[0031] As a preferred technical solution of the present invention: yield function The key to determining this lies in the shape function. The expression is determined by the following formula:

[0032]

[0033]

[0034]

[0035] In the formula, It is a shape function; The generalized triaxial tensile-compressive strength ratio is defined as the axisymmetric tensile strength ( ) and axisymmetric compressive strength ( The ratio of ) to the stress Lod angle under axisymmetric tension. =0°, at this point, the shape function Under axisymmetric compression, the Lod angle of stress =60°, at this point, the shape function .

[0036] As a preferred technical solution of the present invention: in step S3, the shear dilatation angle... The shear expansion angle is determined as follows: The expression is as follows:

[0037]

[0038]

[0039] In the formula, The peak shear dilatation angle of the sample; The absolute value of the plastic volumetric strain corresponding to the peak shear dilatation angle of the specimen; The plastic volumetric strain of the specimen; These are empirical constants; It is a plastic internal variable; It is a brittleness index.

[0040] As a preferred technical solution of the present invention: in step S3, the plastic potential function With the increment of the plastic strain tensor The relationship is as follows:

[0041]

[0042] In the formula, An index used to describe the magnitude of the plastic strain increment; Let be the plastic potential function. By expanding the angle Alternative yield function internal friction angle The determination is made while other parameters remain unchanged.

[0043] Compared with existing technologies, this invention has the following advantages: Based on the equivalent elastoplastic theory, this invention establishes an equivalent deterioration mechanical model of anisotropic rock mass that considers the synergistic effect of intermediate principal stress and structural plane orientation. This model can reflect the material's brittleness-ductility degree, dilatation characteristics, failure mechanism, and the influence mechanism of intermediate principal stress and structural planes. Furthermore, using a programming language, the established mechanical model is embedded into numerical simulation analysis software to analyze the anisotropic characteristics of the deformation and failure process of rock mass containing structural planes, providing a basis for the design and construction of underground engineering projects. Attached Figure Description

[0044] Figure 1 The graph shows the evolution of the elastic modulus of the rock mass sample in the three principal stress directions as a function of the internal plasticity.

[0045] Figure 2 This is a three-dimensional yield function diagram of the mechanical model.

[0046] Figure 3a This is a typical curve showing the variation of the shear dilatation angle of a rock mass sample.

[0047] Figure 3b This is a typical curve showing the rate of weakening of the shear dilatation angle of a rock mass sample.

[0048] Figure 4a This is a typical true triaxial stress-strain curve of a rock mass sample with a structural plane dip angle of 0°.

[0049] Figure 4b This is a typical true triaxial stress-strain curve of a rock mass specimen with a structural plane dip angle of 40°.

[0050] Figure 4c This is a typical true triaxial stress-strain curve of a rock mass specimen with a structural plane dip angle of 78°.

[0051] Figure 5a This is a typical curve showing the relationship between the deformation modulus and the plastic internal variable of a rock mass sample with a structural plane dip angle of 0°.

[0052] Figure 5b This is a typical curve showing the relationship between the deformation modulus and the plastic internal variable of a rock mass sample with a structural plane dip angle of 40°.

[0053] Figure 5c This is a typical curve showing the relationship between the deformation modulus and the plastic internal variable of a rock mass sample with a structural plane dip angle of 78°.

[0054] Figure 6 This is a typical result of the true triaxial strength of rock mass specimens containing structural planes.

[0055] Figure 7a This is the result of the stress-strain curve fitting.

[0056] Figure 7b Simulation of the sample failure results. Detailed Implementation

[0057] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0058] A method for constructing an equivalent deterioration mechanical model of anisotropic rock mass includes the following steps:

[0059] S1. Determine the mechanical model: The deformation of rock mass materials can be divided into two parts: elastic deformation and irreversible plastic deformation. Based on the generalized Hooke's law, the basic expression of the rock mass mechanics model can be expressed by the incremental expression of the stress-strain relationship, as follows:

[0060]

[0061] In the formula, For the increment of the stress tensor, For the increment of the strain tensor, rock engineering typically uses compressive strain and compressive stress as positive values; This represents the increment of the plastic strain tensor; This is the elastic stiffness matrix, used to describe the elastic modulus in the three principal strain directions of the rock mass. Its value is determined by the intermediate principal stress. Minimum principal stress and structural surface orientation The influence, and varies with the internal variables of plasticity. It changes as a result of the increase.

[0062] Therefore, the determination of the rock mechanics model can be divided into the elastic stiffness matrix. Determination of the plastic strain tensor increment The determination consists of two parts.

[0063] S2. Determine the elastic stiffness matrix: Construct the elastic stiffness matrix using the symmetric matrix method in inner product form. ;

[0064] Elastic stiffness matrix The formula is as follows:

[0065] (2)

[0066] In the formula, It is the elastic modulus of the rock mass sample in the three principal stress directions; It is the Poisson's ratio of the rock mass sample; It is the shear modulus of the rock mass sample in the three principal stress directions;

[0067] rock mass sample shear modulus Expressed using the following general formula:

[0068]

[0069] In the formula, It is the elastic modulus of the rock mass sample in the three principal stress directions; It is the shear modulus of the rock mass sample in the three principal stress directions. It can be 1, 2, or 3; It is the Poisson's ratio of the rock mass sample;

[0070] like Figure 1 As shown, under specific stress levels and structural plane orientations... Elastic modulus of rock mass specimen in three principal stress directions With plasticity internal variable The typical evolution curve, for which the elastic stiffness matrix The key to determining this lies in clarifying the elastic modulus. The expression for the elastic modulus of rock mass specimens. Based on the results of numerous true triaxial tests on rock mass specimens, the elastic modulus of the rock mass specimens is... It can be expressed by the following general formula:

[0071]

[0072]

[0073] In the formula, It is the elastic modulus of the rock mass sample in the three principal stress directions. The elastic modulus of the rock mass sample in the three principal stress directions was characterized. The rate of weakening in the residual phase; It is the rate at which the elastic modulus of the rock mass sample weakens with respect to the plastic intrinsic variable k in the three principal stress directions. For the fitting parameters, equation (5) gives and plastic internal variables The empirical quantitative relationship between them, and their fitting parameters Stress level and structural plane orientation The impact.

[0074] Therefore, by conducting true triaxial tests on rock mass samples, different stress levels can be obtained. and structural surface orientation Elastic modulus of lower rock mass sample Compared to Poisson The data is used to fit the parameters of formula (5). With residual stage weakening rate By combining formulas (2) to (5), the elastic stiffness matrix of the specimen can be obtained. .

[0075] S3. Determine the plastic strain increment: Determine the yield function. Obtain expansion angle With expansion angle Alternative yield function internal friction angle To obtain the plastic potential function With plastic potential function To solve for the increment of the plastic strain tensor .

[0076] Plastic potential function It is used to describe the magnitude and direction of the change in plastic strain increment. In this invention, the flow rule of plastic potential used for rock mass samples is the non-associated flow rule, and the formula of plastic potential function is as follows:

[0077]

[0078] In the formula, An index used to describe the magnitude of the plastic strain increment; Given the plastic potential function, due to the adoption of the non-associated flow rule, the yield surface and the plastic strain increment of the mechanical model are not orthogonal; that is, the plastic potential function... Not completely consistent with the yield function Similarly, considering the expansion effect of brittle rock masses, and drawing on the definition of the plastic potential function in the Mohr-Coulomb ideal elastoplastic model, the plastic potential function... It can be expanded by angle Alternative yield function internal friction angle The other parameters remain constant to determine the plastic strain increment. The key to determining this lies in the yield function. and shear expansion angle Determining the expression.

[0079] Yield function Based on true triaxial test data of rock mass, it was determined that a hyperbolic function can be used to fit the relationship between octahedral shear stress and normal stress. Therefore, the yield function... The expression is as follows:

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] In the formula, , and Let g( be a material constant, if the hyperbolic function follows the Mohr-Coulomb criterion under axisymmetric compression (g( If the function of (=60°)=1) is the asymptote equation, then the fitting parameters can be obtained. , and ) and cohesion and internal friction angle The relationship (Formulas (11) and (12)); The stress Lode angle has a value range of 0-60°. This represents the shear stress in octahedral space. It represents the normal stress in octahedral space.

[0087] The shape function must possess the following three important characteristics: a) continuity, smoothness, and convexity; b) it is a closed curve; and c) it is symmetric about the three principal stress axes. Therefore, this invention uses an elliptic function to describe it, with K as the key variable:

[0088] The key to determining the yield function F lies in the shape function. The expression is determined by the following formula:

[0089]

[0090]

[0091]

[0092] In the formula, It is a shape function; The generalized triaxial tensile-compressive strength ratio is defined as the axisymmetric tensile strength ( ) and axisymmetric compressive strength ( The ratio of ) to the stress Lod angle under axisymmetric tension. =0°, at this point, the shape function Under axisymmetric compression, the Lod angle of stress =60°, at this point, the shape function .

[0093] Combining formulas (7) to (15), the three-dimensional form of the yield function is as follows: Figure 2 As shown.

[0094] like Figures 3a-3bAs shown, a typical curve of the shear dilatation angle of a rock mass specimen under a true triaxial test as plastic volumetric strain increases is given. Plastic volumetric strain is a component of the plastic intrinsic variable (Equation (17)). It can be seen that the relationship between the shear dilatation angle and plastic volumetric strain of the rock mass specimen has obvious stage characteristics, and the peak shear dilatation angle is the dividing point of this stage. Before the peak shear dilatation angle, as the plastic volumetric strain of the specimen increases, the shear dilatation angle of the specimen rapidly increases from a small value to its peak value, that is, the specimen reaches the maximum shear dilatation angle with very little damage accumulation; after the peak shear dilatation angle, the shear dilatation angle of the specimen decreases slowly with the increase of plastic volumetric strain. In order to generalize the relationship between the shear dilatation angle and plastic volumetric strain, it can be considered that: before the peak shear dilatation angle, the shear dilatation angle of the specimen is linearly related to the plastic volumetric strain, while after the peak shear dilatation angle, the shear dilatation angle of the specimen decreases exponentially with the increase of plastic volumetric strain. The expression is as follows:

[0095]

[0096]

[0097] In the formula, The peak shear dilatation angle of the sample; The absolute value of the plastic volumetric strain corresponding to the peak shear dilatation angle of the specimen; The plastic volumetric strain of the specimen is negative, indicating that the specimen volume is expanding. It is an empirical constant that reflects the weakening rate of the shear dilatation angle of the specimen; It is a plastic internal variable; It is a brittleness index, which is the cumulative plastic volumetric strain corresponding to the moment when the specimen reaches the residual stage.

[0098] Specifically, the construction method of the above-mentioned equivalent deterioration mechanical model of anisotropic rock mass is implemented in the following manner:

[0099] like Figures 4a-4c As shown, typical true triaxial test stress-strain curves for rock mass specimens with structural planes are presented. The construction process of the equivalent degradation mechanical model of anisotropic rock mass proposed in this invention is as follows:

[0100] (1) Determine the elastic stiffness matrix (i.e., determine formula (5))

[0101] like Figures 5a-5c As shown, the deformation modulus of a specimen with a structural surface under true triaxial compression is given. With plastic internal variables A set of relationship curves between them shows the evolution law of deformation modulus in the three directions ( – The relationship is very different, and, – The relationship is affected by the stress level and the orientation of the structural planes.

[0102] By describing the weakening law of the deformation modulus of the specimen with respect to the internal plastic variables in the three principal stress directions, the anisotropy of the deformation parameters is quantified. The specific expressions are as follows:

[0103]

[0104]

[0105]

[0106] In the formula, It is the deformation modulus of the specimen in the three principal stress directions; and These are the elastic modulus and Poisson's ratio of the sample, respectively; from Figures 5a-5c The fitting results show that formula (5) can well describe and quantify the evolution process of deformation modulus.

[0107] (2) Determination of the yield function (i.e., determination of formula (7))

[0108] The key to determining formula (7) lies in determining formula (11), formula (12), and formula (15).

[0109] Determination of Formula (15): Yield Function Shape functions on the partial plane There is only one parameter, namely, the generalized triaxial tensile-compressive strength ratio. Furthermore, the generalized triaxial tensile-compressive strength ratio The value is simultaneously subjected to octahedral normal stress. and structural surface orientation The impact, that is, If the generalized triaxial tensile-compressive strength ratio Generalized triaxial tensile-compressive strength ratio under the Mohr-Coulomb criterion Then the yield function The fitting parameters will be from four ( , , and ) changed into three ( , and Furthermore, all three simplified fitting parameters are affected by the orientation of the structural planes. At this point, the generalized triaxial tensile-compressive strength ratio can be calculated using the shape function based on the Mohr-Coulomb criterion. :

[0110]

[0111] At this point, the key to determining formula (7) lies in determining the four fitting parameters ( , , and Based on formulas (11), (12), and (15), the four fitting parameters can be simplified to three ( , and ).

[0112] The yield function established in this invention There are four parameters representing the generalized triaxial tensile-compressive strength ratio. Characterizing the degree of approximation to the Mohr-Coulomb criterion on the meridional plane. and material constants and , where the parameters The precise values ​​require at least a set of true triaxial generalized tensile and compressive tests to determine; however, the parameters... The approximate value and the internal friction angle of the material The relevant parameters can be determined using formula (18). , and Cohesion with materials and internal friction angle The relevant factors can be determined according to formulas (11) and (12), while the cohesion of the material... and internal friction angle This can be obtained through a set of conventional triaxial compression tests; parameters The value of can be determined through a uniaxial compression test, and the specific expression is as follows:

[0113]

[0114] In the formula, It is the compressive strength of the specimen under uniaxial compression. Therefore, based on formulas (11), (12), and (15), the yield function is... The four fitting parameters can be determined by fitting cohesion, internal friction angle, and uniaxial compressive strength data from a series of conventional triaxial compression tests, while the yield function... The relationship between the four fitting parameters and the attitude of the structural surface is fitted as follows:

[0115]

[0116]

[0117]

[0118]

[0119] like Figure 6 As shown, dots represent experimental results, and dashed lines represent function fitting results. The evolution of intermediate principal stresses is represented by black, red, and blue dashed lines, while the minimum principal stress is represented by the two pink dashed lines. Figure 6 A set of true triaxial strength test results and fitting results for rock mass specimens with structural planes are presented. It can be seen that the yield function established in this invention can well describe the evolution of the true triaxial strength of the test with the intermediate principal stress and the minimum principal stress. On the one hand, the yield function can well describe the trend of the true triaxial strength of the specimen first increasing and then decreasing with the increase of the intermediate principal stress. On the other hand, the yield function can well describe the trend of the true triaxial strength of the specimen increasing with the increase of the minimum principal stress.

[0120] (3) Determine the shear expansion angle (i.e., determine formula (16))

[0121] The key to determining formula (16) lies in the peak shear dilatation angle of the sample. and empirical constants The determination.

[0122] For the quantification of the peak shear dilatation angle of the specimen in formula (16), this invention fits the quantification formula of the relationship between the peak shear dilatation angle, the peak internal friction angle and the confining pressure, so that the fitted formula can also reflect the influence of the intermediate principal stress on the peak shear dilatation angle. The specific expression is as follows:

[0123]

[0124] In the formula, This is the internal friction angle corresponding to the peak strength of the specimen, i.e., the internal friction angle in the fitting result of the yield function to the peak strength. ; Let be the uniaxial compressive strength of the specimen. For the weakening rate of the specimen shear dilatation angle in formula (16)... The present invention believes that Only affected by the orientation of structural planes, such as Figure 3b As shown, the relationship curves between the weakening rate of the shear dilatation angle of the specimen and the orientation of the structural planes are presented. It can be found that... and The relationship follows a Gaussian function, and the specific expression is as follows:

[0125]

[0126] In the formula, the orientation of the structural planes The unit is radians.

[0127] Formula (21) is the square of the correlation coefficient of the fitting results of the sample parameters. All are greater than 0.9 (e.g.) Figures 3a-3b As shown in the figure, this indicates that the quantization formula has a very good fitting effect.

[0128] (4) Model numericalization and validation

[0129] Typical fitting results of mechanical models are as follows Figures 7a-7b As shown.

[0130] The mechanical model established by this invention can be embedded into numerical simulation analysis software through a programming language to simulate the deformation and failure process of rock masses with structural planes. Figure 7a Typical fitting results of the mechanical model are presented. It can be seen that the stress-strain curves generated by the numerical simulation have a high degree of overlap with the corresponding true triaxial test results in all three principal stress directions. This demonstrates that the model can effectively simulate the elastic, plastic, ductile, and brittle segments of the curve, indicating that the mechanical model established in this invention is also well-suited for true triaxial test results of rock mass specimens. Furthermore, as... Figure 7b As shown, the final failure diagram of the specimen obtained by numerical simulation is in high agreement with the results of the true triaxial test. The numerical simulation can reflect the shear failure, slip shear failure along the structural plane, and composite failure of intact marble material. Furthermore, the failure surface of the numerical simulation is parallel to the direction of the intermediate principal stress, indicating that the mechanical model established in this invention can well reflect the test results of tests with different orientation structural planes under the true triaxial test.

[0131] The technical solution of the present invention has been described in conjunction with the specific experimental procedures shown in the accompanying drawings. However, the scope of protection of the present invention is not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions resulting from such changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A method for constructing an equivalent deterioration mechanical model of anisotropic rock mass, characterized in that, Includes the following steps: S1. Determine the mechanical model: The deformation of rock mass material is divided into two parts: elastic deformation and irreversible plastic deformation. Based on the generalized Hooke's law, the basic expression of the rock mass mechanics model is the incremental expression of the stress-strain relationship, as shown in the following formula: In the formula, For the increment of the stress tensor, The increment of the strain tensor; E represents the increment of the plastic strain tensor. a is the elastic stiffness matrix, whose value is affected by the intermediate principal stress σ2, the minimum principal stress σ3 and the orientation of the structural plane β, and k is the plastic internal variable; S2. Determine the elastic stiffness matrix: Construct the elastic stiffness matrix E using the symmetric matrix method in inner product form. a ; S3. Determine the plastic strain increment: Determine the yield function F, obtain the expansion angle Ψ, and replace the internal friction angle in the yield function F with the expansion angle Ψ. To obtain the plastic potential function G, we can use the plastic potential function G to solve for the increment of the plastic strain tensor.

2. The method according to claim 1, characterized in that: In step S2, the elastic stiffness matrix E a The formula is as follows: In the formula, E1, E2, and E3 are the elastic moduli of the rock mass sample in the three principal stress directions; v is the Poisson's ratio of the rock mass sample; and G1, G2, and G3 are the shear moduli of the rock mass sample in the three principal stress directions.

3. The method according to claim 2, characterized in that: rock mass sample shear modulus G j Expressed using the following formula: In the formula, E j It is the elastic modulus of the rock mass sample in the three principal stress directions; G j is the shear modulus of the rock mass sample in the three principal stress directions, where j is 1, 2, or 3; v is the Poisson's ratio of the rock mass sample.

4. The method according to claim 3, characterized in that: Rock mass sample elastic modulus E j Expressed using the following formula: E j =E0d j (σ2,σ3,β,k) d j =R j +(1-R j )e -Ak In the formula, E j R is the elastic modulus of the rock mass sample in the three principal stress directions. j The elastic modulus E of the rock mass sample in the three principal stress directions was characterized. j The weakening rate in the residual phase; d j is the rate of weakening of the elastic modulus of the rock mass sample in the three principal stress directions as a function of the plastic internal variable k, where A is the fitting parameter; E0 is the elastic modulus of the sample.

5. The method according to claim 1, characterized in that: In step S3, the yield function F is determined as follows, and the expression for the yield function F is as follows: s oct =(σ1+σ2+σ3) / 3 In the formula, a, b, and d are material constants, and θ σ The stress Lode angle, with a value ranging from 0 to 60°; τ oct For the shear stress in octahedral space, σ oct It represents the normal stress in octahedral space.

6. The method according to claim 1 or 5, characterized in that: The key to determining the yield function F lies in the shape function g(θ) σ The expression is determined by the following formula: R=2(1-K 2 )cosθ σ In the formula, g(θ) σ ) is a shape function; K is the generalized triaxial tensile-compressive strength ratio, defined as the axisymmetric tensile strength (τ) oct,ae ) and axisymmetric compressive strength (τ) oct,ac The ratio of ) to the stress Lod angle θ in axisymmetric tension. σ =0°, at this point, the shape function g(θ) σ =K; Under axisymmetric compression, the Lode angle θ is... σ =60°, at this point, the shape function g(θ) σ ) = 1.

7. The method according to claim 1, characterized in that: In step S3, the shear dilatation angle Ψ is determined as follows, and the expression for the shear dilatation angle Ψ is as follows: In the formula, Ψ peak The peak shear dilatation angle of the sample; The absolute value of the plastic volumetric strain corresponding to the peak shear dilatation angle of the specimen; ρ is the plastic volumetric strain of the specimen; M is an empirical constant; k is the internal plastic variable; B I It is a brittleness index.

8. The method according to claim 1, characterized in that: In step S3, the plastic potential function G and the increment of the plastic strain tensor are... The relationship is as follows: In the formula, The plastic strain increment is an index describing the magnitude of the plastic strain increment; G is the plastic potential function, which replaces the internal friction angle in the yield function F with the expansion angle Ψ. The determination is made while other parameters remain unchanged.

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