A construction method for a true triaxial time-dependent damage mechanics model of rock

Abstract

The invention discloses a method for constructing a true triaxial time-dependent damage mechanics model of rock, that is: using viscoplastic strain and time-dependent damage to characterize the non-linear rheological behavior of rock, and using the time-dependent damage factor to reflect the progressive equilibrium movement process during the creep of rock; considering the crack azimuth angle, using the damage variable to control and drive the yield surface, proposing a true three-dimensional yield function of rock, and establishing a true triaxial time-dependent damage mechanics model of rock; finally, using an explicit non-linear numerical integration algorithm to accurately calculate the evolution of the time-dependent damage factor during the creep process. The true triaxial time-dependent damage mechanics model of rock proposed by the invention can accurately describe the true triaxial instantaneous and creep mechanical responses of rock, provide a theoretical basis for the long-term stability study of deep rock mass excavation projects, and ensure the safety and stability of deep rock engineering construction.

Description

Technical Field

[0001] The present invention relates to a method for constructing a mechanical model, and more specifically, to a method for constructing a true triaxial time-dependent damage mechanical model of rock. The present invention belongs to the technical field of rock mechanics analysis for large-scale projects such as civil engineering, water conservancy, and energy. Background Art

[0002] With the increasing demand of human beings for energy and resources, the development of deep underground space, the exploitation of energy resources, and the construction of large-scale water conservancy and hydropower projects will be promoted on a large scale. In deep rock mass excavation projects, due to the release of high in-situ stress, the surrounding rock will be damaged to varying degrees, forming an excavation damage zone. Under the action of high in-situ stress, the time-dependent deformation of deep fractured surrounding rock gradually accumulates, showing obvious rheological characteristics. As a rate-dependent material, the mechanical properties of rock have time-dependence. Under the action of external loads, microcracks inside the rock will initiate, propagate, and coalesce, eventually leading to non-linear deformation and failure of the material, and the whole process is controlled by the damage caused by microcracks.

[0003] During the process of rock deformation and failure, the qualitative or quantitative description of crack propagation and progressive damage has always been a difficult point in rock mechanics research. At present, the research results on rock damage mechanism mainly assume that rock is isotropic, and the experimental data mainly focus on the quantitative analysis of instantaneous test results, lacking the quantitative description of rock time-dependent damage evolution. Therefore, based on the deformation and failure mechanism of deep surrounding rock, selecting appropriate mechanical variables for characterization and establishing accurate mathematical description equations are the keys to studying the damage and failure of surrounding rock.

[0004] In addition, the engineering surrounding rock is in an uneven three-dimensional stress state, and the intermediate principal stress has an important influence on the mechanical response of rock. During the test process, the true triaxial (independent three-dimensional stresses) is used to simulate the true three-dimensional stress state of the engineering surrounding rock. Therefore, constructing a true triaxial time-dependent damage mechanical model of rock to accurately characterize and describe the time-dependent damage deformation of rock is an important basis for analyzing the long-term stability of deep rock mass excavation projects. Summary of the Invention

[0005] In view of the above reasons, the purpose of the present invention is to provide a method for constructing a true triaxial time-dependent damage mechanical model of rock. The constructed mechanical model can quantitatively describe the time-dependent damage deformation of rock, providing important basic information for analyzing the long-term stability of deep rock mass excavation projects.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions: A method for constructing a true triaxial time-dependent damage mechanical module of rock, which includes:

[0007] S1. Using viscoplastic strain to characterize the non-linear rheological behavior of rock, and using the time-dependent damage factor to describe the progressive equilibrium movement process during rock creep;

[0008] S1.1. Characterize the nonlinear rheological behavior of rocks using viscoplastic strain;

[0009] The total strain ε in the brittle creep deformation process of rocks includes: elastic strain ε e , instantaneous plastic strain ε ip and viscoplastic strain ε vp , that is:

[0010] ε = ε e + ε ip + ε vp (1)

[0011] Among them, the elastic strain ε e is calculated by Hooke's law; the instantaneous plastic strain ε ip is calculated by the plastic flow rule; the viscoplastic strain ε vp is calculated according to Perzyna's stress theory, and its incremental form is expressed as:

[0012]

[0013] In the formula: represents the incremental viscoplastic multiplier, and are model control parameters, t represents time, t0 is equal to 1 s to maintain dimensional consistency, the symbol <> represents taking the positive value, represents the yield function, G represents the potential function, and σ represents the stress tensor;

[0014] The increment of viscoplastic strain is obtained by calculating according to formula (2), then, the viscoplastic strain is obtained by superposition, and finally, the nonlinear rheological behavior of rocks is characterized by the viscoplastic strain;

[0015] S1.2. Describe the progressive equilibrium movement process during rock creep using the aging damage factor;

[0016] The damage during rock creep is:

[0017] ω = ω pd + ζ(t)(3)

[0018] In the formula: ω represents the damage during rock creep; ω pd represents the damage induced by nonlinear deformation, which is solved by the elasto-plastic damage coupling consistency condition; ζ(t) represents the progressive equilibrium movement process of the rheological process of rock materials, and is expressed by the formula:

[0019]

[0020] In the formula: Denote the steady-state aging damage value, \(l\) denote the aging factor parameter, and \(\tau\) denote the time parameter within \([0, t]\);

[0021] S1.3. Superpose the viscoplastic strain and aging damage of the rock to characterize the nonlinear rheological behavior of the rock;

[0022] S2. Considering the crack azimuth angle, adopt the damage variable to control the expansion and contraction of the yield surface, and construct the true three-dimensional yield function of the rock;

[0023] True three-dimensional yield function of rock considering crack azimuth angle is:

[0024]

[0025] In the formula: \(\sigma_1\), \(\sigma_2\), and \(\sigma_3\) respectively denote the major principal stress, intermediate principal stress, and minor principal stress, \(\theta\) denotes the angle between the local coordinate axis \(z'\) of the crack and the global coordinate axis \(z\), \(\sigma\) c denotes the uniaxial strength, \(m\) is a model parameter to be determined; \(\omega\) denotes the damage during the creep process of the rock, and \(\alpha(\omega)\) is the hardening / softening function;

[0026] S3. Adopt the exponential damage evolution criterion to systematically describe the progressive damage deterioration behavior of the rock;

[0027] Characterize the stiffness degradation of the rock by damage, and represent the deterioration behavior of the rock by the exponential damage evolution criterion:

[0028]

[0029] In the formula: The parameter \(\omega\) c is used to control the maximum damage degree, the parameter \(\beta\) is used to control the damage deterioration rate, \(Y\) d is the damage driving force, \(Y_0\) is the damage threshold, and \(\omega\) denotes the damage during the creep process of the rock;

[0030] Considering that there is a potential mechanism of mutual enhancement between damage and viscoplasticity, assume that both occur simultaneously, and the damage increment induced by nonlinear deformation is expressed as:

[0031]

[0032] In the formula: \(\lambda\) pd denotes the damage multiplier, denotes the damage multiplier increment;

[0033] S4. Construct a true triaxial aging damage model of the rock, adopt an explicit nonlinear numerical integration algorithm to realize the numerical solution of the mechanical model, and accurately calculate the evolution of the aging damage factor during the creep process;

[0034] S4.1. Incremental expression form of the true three-dimensional aging damage mechanical model of the rock

[0035] For any rock, the general constitutive relationship during the entire creep process is expressed in the following form:

[0036]

[0037] where: represents the total strain increment, is the stress increment, is the increment of the aging damage factor, represents the fourth-order elastoplastic damage stiffness tensor, and ψ represents the creep deformation tensor affected by the aging damage factor;

[0038] The entire creep deformation and failure process of the rock is divided into two stages: the instantaneous loading stage and the creep deformation stage. The calculation of the strain in different stages satisfies the following conditions:

[0039] (1) The known conditions in the instantaneous loading stage are: dζ = 0, and The strain in the instantaneous stage can be expressed as:

[0040]

[0041] where: represents the total strain increment, σ represents the stress, is the stress increment, represents the fourth-order elastoplastic damage stiffness tensor, represents the increment of instantaneous plastic deformation, represents the damage increment caused by instantaneous non-linear deformation, and ω represents the damage during the rock creep process;

[0042] (2) The known conditions in the creep stage are: The strain in the creep stage is expressed as:

[0043]

[0044] where: represents the total strain increment, σ represents the stress, represents the fourth-order elastoplastic damage stiffness tensor, represents the viscoplastic strain increment, represents the damage increment caused by aging deformation and aging damage factor;

[0045] S4.2. Use the explicit non-linear numerical integration algorithm to solve the numerical evolution of the aging damage factor.

[0046] Preferably, the method for constructing the true three-dimensional yield function of the rock by considering the crack azimuth angle and using the damage variable to control the expansion and contraction of the yield surface in step S2 is as follows:

[0047] S2.1. Consider the crack azimuth angle of the rock, construct the true three-dimensional Hoek-Brown strength criterion, and describe the strength characteristics of the rock under true three-dimensional stress conditions;

[0048] According to the theories of elasticity and fracture mechanics, the true three-dimensional Hoek-Brown strength criterion considering the crack azimuth angle can be obtained. Its formula is as follows:

[0049]

[0050] In the formula: σ1, σ2, and σ3 represent the major principal stress, intermediate principal stress, and minor principal stress respectively, θ represents the angle between the local coordinate axis z' of the crack and the global coordinate axis z, σ c represents the uniaxial strength, and m is a model parameter to be determined;

[0051] S2.2. Adopt the damage variable to control the expansion and contraction of the yield surface, and construct the true three-dimensional yield function of the rock.

[0052] Introduce the damage ω during the creep process of the rock into the true three-dimensional Hoek-Brown strength criterion, and obtain the true three-dimensional yield function of the rock considering the crack azimuth angle.

[0053] Preferably, the step S2 introduces a hardening / softening function α(ω) to control the contraction and expansion of the yield surface, reflecting the non-linear mechanical behavior of rock failure. The hardening / softening function α(ω) is expressed as:

[0054]

[0055] Among them, η(ω) max represents the maximum value of the function η(ω), and ω c represent constants to be determined and obtained;

[0056] Based on the method of finding the extreme value of the function derivative, take the derivative of the function η(ω) to determine the critical damage variable.

[0057] ω cri represents the critical damage variable, and ω c represent constants to be determined and obtained.

[0058] The true three-dimensional time-dependent damage mechanics model of rock proposed in the present invention reflects the intermediate principal stress effect of rock by introducing the crack azimuth angle, and describes the three-stage deformation characteristics of brittle creep of rock, namely, attenuation creep, steady-state creep, and accelerating creep, through time-dependent damage. The present invention also considers the influence of stress level on the damage evolution of rock, starting from the mechanism of time-dependent damage deterioration of rock, and more deeply explains the internal physical mechanism of rock creep deformation and failure, providing a comprehensive theoretical framework for the research extended to other physical fields. The present invention can provide theoretical support for proposing reasonable and effective disaster prevention and mitigation measures to ensure the safety and stability of deep rock engineering construction. Description of the Drawings

[0059] Figure 1 It is a flow chart for constructing the true triaxial time-dependent damage mechanics model of rock of the present invention;

[0060] Figure 2A It is the excavation damage diagram of the surrounding rock of the underground cavern excavated in the embodiment of the present invention;

[0061] Figure 2B It is the true triaxial stress state diagram of the surrounding rock of the underground cavern excavated in the embodiment of the present invention;

[0062] Figure 2C It is the three-stage creep failure diagram of the surrounding rock of the underground cavern excavated in the embodiment of the present invention;

[0063] Figure 3 It is the true three-dimensional stress state of the coin-shaped crack of the underground cavern excavated in the embodiment of the present invention;

[0064] Figure 4 It is the change of the strength criterion contour of the surrounding rock of the underground cavern excavated in the embodiment of the present invention with θ on the π plane;

[0065] Figure 5 It is the change of the hardening / softening function η with the damage variable in the embodiment of the present invention;

[0066] Figure 6 It is the fitting of the conventional triaxial peak strength envelope of marble based on the proposed Hoek-Brown yield function of rock in the embodiment of the present invention;

[0067] Figure 7 It is the comparison between the true three-dimensional test results and the simulation results of marble in the embodiment of the present invention;

[0068] Figure 8A It is the comparison between the constitutive simulation results and the test data of the true triaxial instantaneous mechanical response of marble with σ2 = 50 MPa and σ3 = 40 MPa in the embodiment of the present invention;

[0069] Figure 8BComparison between the constitutive simulation results and experimental data of the true triaxial instantaneous mechanical response of marble with σ2 = 200 MPa and σ3 = 40 MPa in the embodiments of the present invention;

[0070] Figure 9 Comparison between the constitutive simulation results and experimental data of the true triaxial creep mechanical response of marble in the embodiments of the present invention. Specific Embodiments

[0071] The structure and features of the present invention will be described in detail below with reference to the drawings and embodiments. It should be noted that various modifications can be made to the embodiments disclosed herein. Therefore, the embodiments disclosed in the specification should not be regarded as limitations of the present invention, but only as examples of the embodiments, the purpose of which is to make the features of the present invention obvious.

[0072] As Figure 1 shown, the method for constructing the true triaxial time-dependent damage mechanics module of the present invention is as follows:

[0073] S1. Characterize the non-linear rheological behavior of rocks using viscoplastic strain, and describe the progressive equilibrium movement process during the creep of rocks using the time-dependent damage factor.

[0074] S1.1. Characterize the non-linear rheological behavior of rocks using viscoplastic strain.

[0075] See Figure 2A - Figure 2C shown, the brittle creep deformation and failure process of rocks includes three stages: the decaying creep stage, the steady-state creep stage, and the accelerating creep stage. The total strain ε during the creep deformation process of each stage includes: elastic strain ε e , instantaneous plastic strain ε ip and viscoplastic strain ε vp , which can be expressed by the formula:

[0076] ε = ε e + ε ip + ε vp (1)

[0077] Among them, the elastic strain ε e can be calculated by Hooke's law; the instantaneous plastic strain ε ip can be calculated through the plastic flow rule; the viscoplastic strain ε vp can be calculated according to Perzyna's stress theory, and its incremental form can be expressed as:

[0078]

[0079] In the formula: represents the incremental viscoplastic multiplier, and is the model control parameter, t represents time, t0 equals 1 s to maintain dimensional consistency, and the symbol <> represents taking the positive value. represents the yield function, G represents the potential function, and σ represents the stress tensor.

[0080] According to the calculation of formula (2), the increment of viscoplastic strain can be obtained. Then, the viscoplastic strain is obtained by superposition, and finally, the nonlinear rheological behavior of rock is characterized by the viscoplastic strain.

[0081] S1.2. Use the aging damage factor to describe the progressive equilibrium movement process during rock creep.

[0082] The nonlinear behavior of rock materials is manifested as stiffness degradation, which can be characterized by damage. Considering the damage induced by nonlinear deformation and aging damage, the damage during the rock creep failure process can be calculated by the following formula:

[0083] ω = ω pd + ζ(t)(3)

[0084] In the formula: ω represents the damage during rock creep; ω pd represents the damage induced by nonlinear deformation, which can be solved by the elastoplastic damage coupling consistency condition; ζ(t) represents the progressive equilibrium movement process during the rheological process of rock materials, and is expressed by the formula:

[0085]

[0086] In the formula: represents the steady-state aging damage value, l represents the aging factor parameter, and τ represents the time parameter of [0, t].

[0087] S1.3. Superpose the viscoplastic strain and aging damage of the rock to characterize the nonlinear rheological behavior of the rock.

[0088] The nonlinear rheological behavior of rock includes irrecoverable deformation and stiffness degradation. In the present invention, the viscoplastic strain is respectively used to characterize the irrecoverable deformation and the aging damage reflects the stiffness degradation part, and then the nonlinear rheological behavior of the rock is characterized by adding the two.

[0089] S2. Considering the crack azimuth angle, use the damage variable to control the expansion and contraction of the driving yield surface, and construct the true three-dimensional yield function of rock.

[0090] S2.1. Considering the crack azimuth angle of the rock, construct the true three-dimensional Hoek - Brown strength criterion to describe the strength characteristics of the rock under true three-dimensional stress conditions.

[0091] The deformation and failure of rock are affected by the propagation of internal microcracks. Therefore, when describing the true three-dimensional strength function of rock, the influence of microcracks needs to be considered. In the present invention, it is assumed that penny-shaped microcracks are randomly distributed inside the rock, such asFigure 3 As shown. Ignoring the interaction between cracks, based on the theories of elasticity and fracture mechanics, the true three-dimensional Hoek-Brown strength criterion considering the crack azimuth angle can be obtained through theoretical derivation. Its formula is as follows:

[0092]

[0093] In the formula: σ1, σ2, and σ3 represent the major principal stress, intermediate principal stress, and minor principal stress respectively, θ represents the angle between the local coordinate axis z' of the crack and the global coordinate axis z, and σ c represents the uniaxial strength.

[0094] From Figure 4 it can be seen that as θ changes, the contour of the strength criterion varies in the π plane. Therefore, the strength characteristics of rocks under true three-dimensional stress conditions can be described using formula (5).

[0095] S2.2. Using the damage variable to control the expansion and contraction of the yield surface, a true three-dimensional yield function of rock is constructed.

[0096] In the present invention, the hardening / softening function α(ω) of the damage variable is introduced to control the contraction and expansion of the yield surface, reflecting the non-linear mechanical behavior of rock failure, which can be expressed by the formula:

[0097]

[0098] Among them, η(ω) max represents the maximum value of the function η(ω). and ω c represent constants to be determined.

[0099] The innovation of introducing the hardening / softening function α(ω) in the present invention lies in that there is only one extreme value of the damage within the range of 0-1 (see Figure 5 ), and the critical damage value ω cri at the peak failure of the material can be further derived. Through normalization, the parameters obtained from the true three-dimensional Hoek-Brown strength criterion based on test data can be directly used for elastoplastic damage coupling calculation.

[0100] Based on the method of finding the extreme value of the function derivative, by taking the derivative of the function η(ω), the critical damage variable is determined. When the damage variable is greater than ω cri , it means that damage failure occurs. Therefore, ω cri can be used as the damage criterion for engineering rock masses.

[0101] Furthermore, the present invention introduces damage into the true three-dimensional Hoek-Brown strength criterion to obtain the true three-dimensional yield function of rock considering the microcrack azimuth angle. The expression is as follows:

[0102]

[0103] In addition, non-associated plastic potential function is adopted for plastic deformation. It is determined that the function G(σ,ω) considers the inhibitory effect of the intermediate principal stress on deformation and the influence of brittle enhancement by introducing parameters and S3. The exponential damage evolution criterion is adopted to systematically describe the progressive damage deterioration behavior of rock.

[0104] In the present invention, the stiffness degradation of rock is characterized by damage, and the deterioration behavior of rock is represented by the exponential damage evolution criterion:

[0105] In the formula: The parameter ω

[0106]

[0107] is used to control the maximum damage degree, the parameter β is used to control the damage deterioration rate, ω c is the damage driving force, Y0 is the damage threshold, and ω represents the damage during the creep process of rock. d Considering the potential mechanism of mutual enhancement between damage and plasticity, in the present invention, it is assumed that they occur simultaneously. Similar to the associated flow rule in plastic theory, the damage increment induced by non-linear deformation

[0108] can be expressed as: In the formula: λ

[0109]

[0110] represents the damage multiplier, pd and represents its increment.

[0111] S4. A true triaxial time-dependent damage model of rock is constructed, and an explicit non-linear numerical integration algorithm is adopted to realize the numerical solution of the mechanical model and accurately calculate the evolution of the time-dependent damage factor during the creep process.

[0112] S4.1 Incremental expression form of the true three-dimensional time-dependent damage mechanics model of rock;

[0113] For any rock, the general constitutive relationship during the entire creep process can be expressed in the following form:

[0114]

[0115] In the formula: represents the fourth-order elastoplastic damage stiffness tensor, and ψ represents the creep deformation tensor affected by the aging damage factor;

[0116] The entire creep deformation and failure process of the rock is divided into two stages: the instantaneous loading stage and the creep deformation stage. The strain calculations for different stages satisfy the following conditions:

[0117] (1) The known conditions for the instantaneous loading stage are: dζ = 0, and The strain in the instantaneous stage can be expressed as:

[0118]

[0119] In the formula: represents the increment of instantaneous plastic deformation, represents the damage increment caused by instantaneous non-linear deformation.

[0120] (2) The known conditions for the creep stage are: The strain in the creep stage can be expressed as:

[0121]

[0122] In the formula: represents the damage increment caused by aging deformation and the aging damage factor.

[0123] S4.2, Numerical calculation method for the evolution of the aging damage factor.

[0124] The aging damage ζ(t) is in the form of an integral with respect to time. The evolution of damage over time determines the accuracy of the simulation results. In the present invention, the evolution of aging damage over time is solved using an explicit non-linear numerical integration algorithm, and the calculation formula is as follows:

[0125]

[0126] In the formula: k represents the increment step, and dt k represents the time increment step size.

[0127] The creep test results of the rock show that during the creep process, the damage rate is affected by the current stress level. Creep deformation only occurs when the stress level is higher than a certain threshold condition, and when the stress level is lower than a certain threshold, the specimen will not fail. Stress-induced creep deformation and failure only occur when the stress level exceeds a certain threshold condition:

[0128]

[0129] In the formula: The parameter χ is used to consider the influence of the stress level on the aging damage, and its expression form is χ = χ0exp[-B(Δσ / Δσ0)], where χ0 and B are two control parameters, and Δσ represents the difference between the current stress level and the threshold value and the difference between the failure stress level and the threshold value Δσ0.

[0130] Specific example:

[0131] Apply the above method to the true triaxial instantaneous and creep test analysis of Jinping marble. The main mineral components of the marble are dolomite and calcite. The true triaxial sample is a cuboid with dimensions of 50mm×50mm×100mm, the uniaxial compressive strength is 193.2MPa, the elastic modulus is 57.8GPa, and the Poisson's ratio is 0.3.

[0132] The specific steps are as follows:

[0133] (1) Determine the true three-dimensional strength criterion parameters based on the conventional triaxial peak strength of the marble, as Figure 6 shown, and the result is m = 11.26;

[0134] (2) Determine the relationship between θ and the stress state based on the true triaxial peak strength of the marble. Here, the exponential form θ = θ0exp(-s1b) can better reflect the influence of the intermediate principal stress of the marble, as Figure 7 shown, and the parameter fitting results are θ0 = 36° and

[0135] (3) ω max represents the maximum damage degree. Since it is affected by the stress state, it is not a fixed value under different confining pressures or intermediate principal stress states. Through trial calculations, it is found that ω max = Aexp(Bσ3)+Cln(σ2 / σ3) can better reflect the variation law of ω max with the stress state;

[0136] (4) The remaining model parameters are obtained through parameter sensitivity analysis to obtain their influence laws on the constitutive behavior. By comparing the constitutive simulation results with the test data, they are indirectly obtained according to the test results. The parameters of this marble can be taken as: ω c = 0.2 and β = 75.0.

[0137] (5) The comparison between the constitutive simulation results and the test data of the true triaxial instantaneous mechanical response of the marble under the conditions of σ2 = 50MPa and σ3 = 40MPa and σ2 = 200MPa and σ3 = 40MPa is as Figure 8A 、 Figure 8B shown; the comparison between the constitutive simulation results and the test data of the true triaxial creep mechanical response of the marble under the condition of σ2 = 120MPa and σ3 = 20MPa is as Figure 9 shown.

[0138] The results show that the constructed true three-dimensional time-dependent damage model can better reflect the true triaxial instantaneous and creep mechanical responses of marble.

[0139] The true triaxial time-dependent damage mechanical model of rock proposed in the present invention can accurately describe the true triaxial instantaneous and creep mechanical responses of rock, provide a theoretical basis for the long-term stability study of deep rock mass excavation engineering, and provide guarantee for the safety and stability of deep rock engineering construction.

[0140] Finally, it should be noted that the above-mentioned embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing a true triaxial time-dependent damage mechanics model of rock, characterized in that: It includes: S1. Characterize the non - linear rheological behavior of rocks by viscoplastic strain, and use the aging damage factor to describe the progressive equilibrium movement process during rock creep; S1.

1. Characterize the non - linear rheological behavior of rocks by viscoplastic strain; The total strain ε during the brittle creep deformation process of the rock includes: elastic strain ε e , instantaneous plastic strain ε ip and viscoplastic strain ε vp , that is: ε = ε e + ε ip + ε vp (1) Among them, the elastic strain ε e is calculated by Hooke's law; the instantaneous plastic strain ε ip is calculated by the plastic flow rule; the viscoplastic strain ε vp is calculated according to Perzyna’s stress theory, and its incremental form is expressed as: In the formula: represents the increment of the viscoplastic multiplier, and are model control parameters, t represents time, t0 is equal to 1 s for dimensional conservation, and the symbol <> represents taking the positive value, represents the yield function, G represents the potential function, and σ represents the stress tensor; Calculate the increment of viscoplastic strain according to formula (2), then obtain the viscoplastic strain by superposition, and finally characterize the non - linear rheological behavior of rocks by viscoplastic strain; S1.

2. Use the aging damage factor to describe the progressive equilibrium movement process during rock creep; The damage during rock creep is: ω = ω pd + ζ(t) (3) Where: ω represents the damage during the rock creep process; ω pd represents the damage induced by non-linear deformation, which is solved through the elastoplastic damage coupling consistency condition; ζ(t) represents the progressive equilibrium movement process of the rock material during the rheological process, and is expressed by the formula as: In the formula: represents the steady-state aging damage value, represents the aging factor parameter, and τ represents the time parameter in [0, t]; S1.

3. Superpose the viscoplastic strain and aging damage of rocks to characterize the non - linear rheological behavior of rocks; S2. Consider the crack azimuth angle, use the damage variable to control the expansion and contraction of the yield surface, and construct a true three - dimensional yield function for rocks; True three-dimensional yield function of rock considering crack azimuth angle is as follows: In the formula: σ1, σ2 and σ3 respectively represent the major principal stress, intermediate principal stress and minor principal stress, θ represents the angle between the local coordinate axis z' of the crack and the global coordinate axis z, σ c represents the uniaxial strength, m is a model parameter to be determined; ω represents the damage during the rock creep process, and α(ω) is the hardening / softening function; S3. Adopt the exponential damage evolution criterion to systematically describe the progressive damage degradation behavior of rocks; Characterize the stiffness degradation of rocks by damage, and represent the degradation behavior of rocks by the exponential damage evolution criterion: In the formula: parameter ω c is used to control the maximum damage degree, parameter β is used to control the damage degradation rate, Y d is the damage driving force, Y0 is the damage threshold, and ω represents the damage during the rock creep process; Considering the potential mechanism of mutual enhancement between damage and viscoplasticity, it is assumed that both occur simultaneously, and the damage increment induced by non-linear deformation is expressed as: where: λ pd represents the damage multiplier, represents the increment of the damage multiplier; S4. Construct a true triaxial aging damage model for rocks, adopt an explicit non - linear numerical integration algorithm to achieve the numerical solution of the mechanical model, and accurately calculate the evolution of the aging damage factor during creep; S4.

1. Incremental expression form of the true three - dimensional aging damage mechanical model of rocks; For any rock, the general constitutive relationship during the entire creep process is expressed in the following form: In the formula: represents the total strain increment, the stress increment, the increment of the aging damage factor, represents the fourth-order elastoplastic damage stiffness tensor, and ψ represents the creep deformation tensor affected by the aging damage factor; The entire creep deformation and failure process of rocks is divided into two stages: instantaneous loading and creep deformation stage. The calculation of strain in different stages satisfies the following conditions: (1) The known conditions in the instantaneous loading stage are: dζ = 0, and The strain in the instantaneous stage can be expressed as: In the formula: represents the total strain increment, σ represents the stress, the stress increment, represents the fourth-order elastoplastic damage stiffness tensor, represents the instantaneous plastic deformation increment, represents the damage increment caused by the instantaneous nonlinear deformation, and ω represents the damage during the rock creep process; (2) The known conditions in the creep stage are as follows: The strain in the creep stage is expressed as: In the formula: represents the total strain increment, σ represents the stress, represents the fourth-order elastoplastic damage stiffness tensor, represents the viscoplastic strain increment, represents the damage increment caused by the aging deformation and aging damage factor; S4.

2. Solve the numerical evolution of the aging damage factor by using an explicit non - linear numerical integration algorithm.

2. The method for constructing a true triaxial time-dependent damage mechanics model of rock according to claim 1, characterized in that: The method in step S2 for considering the crack azimuth angle, using the damage variable to control the expansion and contraction of the yield surface, and constructing a true three - dimensional yield function for rocks is: S2.

1. Consider the crack azimuth angle of rocks, construct a true three - dimensional Hoek - Brown strength criterion to describe the strength characteristics of rocks under true three - dimensional stress conditions; According to the theories of elasticity and fracture mechanics, the true three-dimensional Hoek-Brown strength criterion considering the crack azimuth angle can be obtained. Its formula is as follows: Where: σ1, σ2 and σ3 represent the major principal stress, intermediate principal stress and minor principal stress respectively, θ represents the angle between the local coordinate axis z' of the crack and the global coordinate axis z, σ c represents the uniaxial strength, and m is a model parameter to be determined; S2.

2. Use the damage variable to control the expansion and contraction of the yield surface, and construct a true three - dimensional yield function for rocks; The damage ω during the rock creep process is introduced into the true three-dimensional Hoek-Brown strength criterion, and the true three-dimensional yield function of the rock considering the crack azimuth angle is obtained.

3. The method for constructing a true triaxial time-dependent damage mechanics model of rock according to claim 2, characterized in that: The step S2 introduces a hardening / softening function α(ω) to control the contraction and expansion of the yield surface, reflecting the non - linear mechanical behavior of rock failure. The hardening / softening function α(ω) is expressed as: where, η(ω) max represents the maximum value of the function η(ω), and ω c represent constants to be determined and obtained; Based on the method of finding the extreme value by the derivative of the function, the derivative of the function η(ω) is calculated to determine the critical damage variable ω cri represents the critical damage variable, and ω c represents the constant to be determined.

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