Rock true triaxial aging damage mechanical model construction method

Abstract

The invention discloses a rock true triaxial aging damage mechanical model construction method, which comprises the following steps of: representing rock nonlinear rheological behaviors by adopting viscoplastic strain and aging damage, and reflecting a progressive equilibrium motion process in a rock creep process by utilizing an aging damage factor; a crack azimuth angle is considered, a damage variable is adopted to control and drive a yield surface, a rock true three-dimensional yield function is provided, and a rock true triaxial aging damage mechanical model is established; finally, an explicit nonlinear numerical integration algorithm is adopted, and creep process aging damage factor evolution is accurately calculated. The rock true triaxial aging damage mechanical model provided by the invention can accurately describe rock true triaxial instantaneous and creep mechanical response, provides a theoretical basis for long-term stability research of deep rock mass excavation engineering, and provides guarantee for 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 in particular 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 of large-scale projects such as civil engineering, water conservancy and energy. Background Art

[0002] With the increasing demand 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 excavation projects, due to the release of high ground stress, the surrounding rock will be damaged to varying degrees, forming an excavation damage zone. Under the action of high ground stress, the time-dependent deformation of the deep fractured surrounding rock gradually accumulates, showing obvious rheological characteristics. As a rate-dependent material, the mechanical properties of rock are time-dependent. Under the action of external loads, microcracks inside the rock will initiate, expand and aggregate, eventually leading to nonlinear deformation and destruction of the material. The whole process is controlled by the damage caused by microcracks.

[0003] The qualitative or quantitative description of crack propagation and progressive damage during rock deformation and failure has always been a difficult point in rock mechanics research. At present, the research results of rock damage mechanism mainly assume that the rock is isotropic, and the experimental data mainly focus on the quantitative analysis of instantaneous test results, lacking a quantitative description of the evolution of rock damage over time. 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 key to studying surrounding rock damage and failure.

[0004] In addition, the surrounding rock of the project is in an uneven three-dimensional stress state, and the intermediate principal stress has an important influence on the mechanical response of the rock. During the test, the true three-dimensional stress state of the surrounding rock of the project was simulated by using true triaxial (three-dimensional stress independence). Therefore, constructing a true triaxial time-dependent damage mechanics model of rock and accurately characterizing and describing the time-dependent damage deformation of rock are important foundations for analyzing the long-term stability of deep rock 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 and provide important basic information for analyzing the long-term stability of deep rock excavation projects.

[0006] To achieve the above object, the present invention adopts the following technical solution: a method for constructing a rock true triaxial time-dependent damage mechanics module, which comprises:

[0007] S1. Use viscoplastic strain to characterize the nonlinear rheological behavior of rock, and use time-dependent damage factor to describe the progressive equilibrium movement process of rock creep;

[0008] S1.1. Use viscoplastic strain to characterize the nonlinear rheological behavior of rocks;

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

[0010] ε=ε e +ε ip +ε vp (1)

[0011] Among them, the elastic strain ε e Calculated by Hooke's law; instantaneous plastic strain ε ip Calculated by plastic flow law; viscoplastic strain ε vp The calculation is based on Perzyna's stress theory, and its incremental form is expressed as:

[0012]

[0013] Where: represents the viscoplastic multiplier increment, and is the model control parameter, t represents time, t0 is equal to 1s to maintain dimension conservation, and the symbol <> represents a positive value. represents the yield function, G represents the potential function, and σ represents the stress tensor;

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

[0015] S1.2. Use time-dependent damage factors to describe the progressive equilibrium motion process during rock creep;

[0016] The damage of rock creep process is:

[0017] ω=ω pd +ζ(t)(3)

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

[0019]

[0020] Where: represents the steady-state aging damage value, l represents the aging factor parameter, and τ represents the [0, t] time parameter;

[0021] S1.3. Superimpose the viscoplastic strain and time-dependent damage of rock to characterize the nonlinear rheological behavior of rock;

[0022] S2. Considering the crack azimuth, damage variables are used to control the expansion and contraction of the driven yield surface to construct the true three-dimensional yield function of rock;

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

[0024]

[0025] Where: σ1, σ2 and σ3 represent the major principal stress, the intermediate principal stress and the 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, m is the model parameter to be determined; ω represents the damage of rock creep process, α(ω) is the hardening / softening function;

[0026] S3. Using the exponential damage evolution criterion, the progressive damage degradation behavior of rock is systematically described;

[0027] The stiffness degradation of rock is characterized by damage, and the rock degradation behavior is expressed by the exponential damage evolution criterion:

[0028]

[0029] Where: parameter ω c is used to control the maximum damage degree, and parameter β is used to control the damage degradation rate. d is the damage driving force, Y0 is the damage threshold, and ω represents the damage during rock creep;

[0030] Considering the potential mechanism of mutual reinforcement between damage and viscoplasticity, assuming that both occur simultaneously, the nonlinear deformation-induced damage increment It is expressed as:

[0031]

[0032] Where: pd represents the damage multiplier, represents the damage multiplier increment;

[0033] S4. Construct a true triaxial time-dependent damage model for rock, use an explicit nonlinear numerical integration algorithm to achieve numerical solution of the mechanical model, and accurately calculate the evolution of time-dependent damage factors during creep;

[0034] S4.1. Incremental expression of true three-dimensional time-dependent damage mechanics model for rock;

[0035] For any rock, the general constitutive relation for the entire creep process is expressed as follows:

[0036]

[0037] Where: represents the total strain increment, Stress increment, Time-dependent damage factor increment, represents the fourth-order elastic-plastic damage stiffness tensor, ψ represents the creep deformation tensor affected by the time-dependent damage factor;

[0038] The entire creep deformation and failure process of rock is divided into two stages: instantaneous loading and creep deformation. The strain calculations at different stages meet the following conditions:

[0039] (1) The known conditions in the transient 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, Stress increment, represents the fourth-order elastoplastic damage stiffness tensor, represents the instantaneous plastic deformation increment, represents the damage increment caused by instantaneous nonlinear deformation, and ω represents the damage during rock creep;

[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, Indicates the damage increment caused by aging deformation and aging damage factor;

[0045] S4.2. Use explicit nonlinear numerical integration algorithm to solve the numerical evolution of time-dependent damage factor.

[0046] Preferably, the step S2 considers the crack azimuth, uses damage variables to control the expansion and contraction of the driven yield surface, and constructs the true three-dimensional yield function of the rock by:

[0047] S2.1. Considering the crack azimuth of the rock, a true three-dimensional Hoek-Brown strength criterion is constructed to describe the strength characteristics of the rock under true three-dimensional stress conditions;

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

[0049]

[0050] Where: σ1, σ2 and σ3 represent the major principal stress, the intermediate principal stress and the 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, using damage variables to control the expansion and contraction of the driven yield surface and construct the true three-dimensional yield function of rock;

[0052] The damage ω in 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 is obtained.

[0053] Preferably, the step S2 introduces a hardening / softening function α(ω) to control the contraction and expansion of the yield surface, reflecting the nonlinear 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 Indicates the constant that needs to be obtained;

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

[0057] ω cri represents the critical damage variable, and ω c Indicates a constant that needs to be 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, and better describes the three-stage deformation characteristics of rock brittle creep through time-dependent damage: attenuated creep, steady-state creep and accelerated creep. The present invention also considers the influence of stress level on the evolution of rock damage, and starts from the mechanism of rock time-dependent damage degradation, and explains the intrinsic physical mechanism of rock creep deformation and destruction in more depth, providing a comprehensive theoretical framework for research extending to other physical fields. The present invention can provide theoretical support for the proposal of reasonable and effective disaster prevention and mitigation measures to ensure the safety and stability of deep rock engineering construction. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0061] Figure 2B A true triaxial stress state diagram of the surrounding rock of an underground cavern excavated according to an embodiment of the present invention;

[0062] Figure 2C 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 The true three-dimensional stress state of the coin-shaped crack in the underground cavern excavated by the embodiment of the present invention;

[0064] Figure 4 The strength criterion profile of the surrounding rock of the underground cavern excavated for the embodiment of the present invention varies with θ on the π plane;

[0065] Figure 5 The hardening / softening function η of the embodiment of the present invention varies with the damage variable;

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

[0067] Figure 7 The comparison between the real 3D test results and the simulation results of marble in the embodiment of the present invention;

[0068] Fig. 8A The true triaxial transient mechanical response constitutive simulation results of marble with σ2=50MPa and σ3=40MPa in the embodiment of the present invention are compared with the test data;

[0069] Figure 8BThe true triaxial transient mechanical response constitutive simulation results of marble with σ2=200MPa and σ3=40MPa in the embodiment of the present invention are compared with the test data;

[0070] Fig. 9 The true triaxial creep mechanical response constitutive simulation results of marble in the embodiment of the present invention are compared with the experimental data. DETAILED DESCRIPTION

[0071] The structure and features of the present invention are described in detail below in conjunction with the accompanying drawings and embodiments. It should be noted that various modifications can be made to the embodiments disclosed herein, and therefore, the embodiments disclosed in the specification should not be regarded as limiting the present invention, but are merely examples of embodiments, the purpose of which is to make the features of the present invention obvious.

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

[0073] S1. Viscoplastic strain is used to characterize the nonlinear rheological behavior of rock, and the time-dependent damage factor is used to describe the progressive equilibrium movement process of rock creep.

[0074] S1.1. Use viscoplastic strain to characterize the nonlinear rheological behavior of rock.

[0075] See also Figure 2A-2C As shown in the figure, the rock brittle creep deformation and failure process includes three stages: attenuation creep stage, steady-state creep stage and accelerated creep stage. The total strain ε in each stage of creep deformation process includes: elastic strain ε e , instantaneous plastic strain ε ip and viscoplastic strain ε vp , which can be expressed as:

[0076] ε=ε e +ε ip +ε vp (1)

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

[0078]

[0079] Where: represents the viscoplastic multiplier increment, and is the model control parameter, t represents time, t0 is equal to 1s to maintain dimension conservation, and the symbol <> represents a positive value. represents the yield function, G represents the potential function, and σ represents the stress tensor.

[0080] According to formula (2), the increment of viscoplastic strain can be calculated, and then the viscoplastic strain can be obtained by superposition. Finally, the nonlinear rheological behavior of rock can be characterized by the viscoplastic strain.

[0081] S1.2. Use time-dependent damage factors 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 time-dependent damage, the damage in the rock creep failure process can be calculated by the following formula:

[0083] ω=ω pd +ζ(t)(3)

[0084] Where: ω represents the damage in the rock creep process; ω pd represents the damage induced by nonlinear deformation, which can be solved by the elastic-plastic damage coupling consistency condition; ζ(t) represents the progressive equilibrium motion process of the rheological process of rock materials, which can be expressed by the formula:

[0085]

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

[0087] S1.3. Superimpose the viscoplastic strain and time-dependent damage of rock to characterize the nonlinear rheological behavior of rock.

[0088] The nonlinear rheological behavior of rock includes irreversible deformation and stiffness degradation. The present invention uses viscoplastic strain to characterize irreversible deformation and time-dependent damage to reflect stiffness degradation, and then adds the two together to characterize the nonlinear rheological behavior of rock.

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

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

[0091] The deformation and failure of rock is affected by the extension of internal microcracks. Therefore, when describing the true three-dimensional strength function of rock, the influence of microcracks needs to be considered. In this invention, it is assumed that coin-shaped microcracks are randomly distributed inside the rock, such as Figure 3 As shown. Ignoring the interaction between cracks, according to the theory of elasticity and fracture mechanics, the true three-dimensional Hoek-Brown strength criterion considering the crack orientation can be obtained through theoretical derivation The formula is as follows:

[0092]

[0093] Where: σ1, σ2 and σ3 represent the major principal stress, the intermediate principal stress and the 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 uniaxial strength.

[0094] Depend on Figure 4 It can be seen that with the change of θ, the strength criterion profile changes in the π plane. Therefore, formula (5) can be used to describe the strength characteristics of rock under true three-dimensional stress conditions.

[0095] S2.2. Use damage variables to control the expansion and contraction of the driven yield surface and construct a true three-dimensional yield function of rock.

[0096] The present invention controls the contraction and expansion of the yield surface by introducing the hardening / softening function α(ω) of the damage variable to reflect the nonlinear mechanical behavior of rock failure, which can be expressed as follows:

[0097]

[0098] Among them, η(ω) max Represents the maximum value of the function η(ω). and ω c Indicates a constant that needs to be obtained.

[0099] The invention introduces the hardening / softening function α(ω) in that the damage has only one maximum value in the range of 0-1 (see Figure 5 ), the critical damage value ω at the material peak failure can be further derived cri , and then through normalization processing, the parameters of the true three-dimensional Hoek-Brown strength criterion obtained based on the test data can be directly used in the elastic-plastic damage coupling calculation.

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

[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 The expression is as follows:

[0102]

[0103] In addition, the plastic deformation adopts the non-associative plastic potential function Determine that the function G(σ,ω) is obtained by introducing the parameter and The inhibitory effect of intermediate principal stress on deformation and the effect of brittleness enhancement are considered.

[0104] S3. The exponential damage evolution criterion is used to systematically describe the progressive damage degradation behavior of rock.

[0105] The present invention uses damage to characterize the stiffness degradation of rock, and the rock degradation behavior is represented by the exponential damage evolution criterion:

[0106]

[0107] Where: parameter ω c is used to control the maximum damage degree, parameter β is used to control the damage degradation rate, ω d is the damage driving force, Y0 is the damage threshold, and ω represents the damage during rock creep.

[0108] Considering the potential mechanism of mutual enhancement between damage and plasticity, the present invention assumes that the two occur simultaneously, similar to the associated flow law in plasticity theory, and nonlinear deformation induces damage increment It can be expressed as:

[0109]

[0110] Where: pd represents the damage multiplier, Indicates its increment.

[0111] S4. Construct a true triaxial time-dependent damage model for rock, use an explicit nonlinear numerical integration algorithm to achieve the numerical solution of the mechanical model, and accurately calculate the evolution of the time-dependent damage factor in the creep process.

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

[0113] For any rock, the general constitutive relation of the entire creep process can be expressed as follows:

[0114]

[0115] Where: represents the fourth-order elastic-plastic damage stiffness tensor, ψ represents the creep deformation tensor affected by the time-dependent damage factor;

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

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

[0118]

[0119] Where: represents the instantaneous plastic deformation increment, It represents the damage increment caused by instantaneous nonlinear deformation.

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

[0121]

[0122] Where: Represents the damage increment caused by aging deformation and aging damage factor.

[0123] S4.2. Numerical calculation method for evolution of time-dependent damage factors.

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

[0125]

[0126] Where: k represents the incremental step, dt k Represents the time increment step.

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

[0128]

[0129] Wherein: the parameter χ is used to consider the influence of stress level on aging damage, which is expressed as χ = χ0exp[-B(Δσ / Δσ0)], χ0 and B are two control parameters, Δσ represents the difference between the current stress level and the threshold and the difference between the failure stress level and the threshold Δσ0.

[0130] Specific examples:

[0131] The above method is applied to the analysis of the true triaxial transient and creep tests of Jinping marble. The main mineral components of marble are dolomite and calcite. The true triaxial sample is a cuboid with a size of 50mm×50mm×100mm, a uniaxial compressive strength of 193.2MPa, an elastic modulus of 57.8GPa and a Poisson's ratio of 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 marble, such as Figure 6 As shown, the result is m=11.26;

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

[0135] (3)ω max Indicates the maximum degree of damage. 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 calculation, it is found that ω max =Aexp(Bσ3)+Cln(σ2 / σ3) can better reflect ω max Variation law with stress state;

[0136] (4) The remaining model parameters are analyzed through parameter sensitivity to obtain their influence on the constitutive behavior, and the constitutive simulation results are compared with the test data, and the marble parameters can be obtained indirectly based on the test results. ω c =0.2 and β=75.0.

[0137] (5) Comparison of constitutive simulation results of true triaxial transient mechanical response of marble with σ2 = 50 MPa and σ3 = 40 MPa and σ2 = 200 MPa and σ3 = 40 MPa with experimental data. Fig. 8A , Figure 8B As shown in the figure, the true triaxial creep mechanical response constitutive simulation results of marble with σ2 = 120MPa and σ3 = 20MPa are compared with the experimental data. Fig. 9 shown.

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

[0139] The rock true triaxial time-dependent damage mechanics model 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 research of deep rock excavation engineering, and provide guarantee for the safety and stability of deep rock engineering construction.

[0140] Finally, it should be noted that the above-described embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing a rock true triaxial time-dependent damage mechanics module, characterized by: It includes: S1. Use viscoplastic strain to characterize the nonlinear rheological behavior of rock, and use time-dependent damage factor to describe the progressive equilibrium movement process of rock creep; S1.

1. Use viscoplastic strain to characterize the nonlinear rheological behavior of rocks; The total strain ε in the brittle creep deformation process of rock includes: elastic strain ε e , instantaneous plastic strain ε ip and viscoplastic strain ε vp ,Right now: e=e e +e ip +e vp (1) Among them, the elastic strain ε e Calculated by Hooke's law; instantaneous plastic strain ε ip Calculated by plastic flow law; viscoplastic strain ε vp The calculation is based on Perzyna's stress theory, and its incremental form is expressed as: Where: represents the viscoplastic multiplier increment, and is the model control parameter, t represents time, t0 is equal to 1s to maintain dimension conservation, and the symbol <> represents a positive value. represents the yield function, G represents the potential function, and σ represents the stress tensor; The increment of viscoplastic strain is calculated according to formula (2), and then the viscoplastic strain is obtained by superposition, and finally the nonlinear rheological behavior of rock is characterized by the viscoplastic strain. S1.

2. Use time-dependent damage factors to describe the progressive equilibrium motion process during rock creep; The damage of rock creep process is: oh = oh pd +ζ(t) (3) Where: ω represents the damage in the rock creep process; ω pd represents the damage induced by nonlinear deformation, which is solved by the elastic-plastic damage coupling consistency condition; ζ(t) represents the progressive equilibrium motion process of the rheological process of rock materials, which is expressed by the formula: Where: represents the steady-state aging damage value, l represents the aging factor parameter, and τ represents the [0, t] time parameter; S1.

3. Superimpose the viscoplastic strain and time-dependent damage of rock to characterize the nonlinear rheological behavior of rock; S2. Considering the crack azimuth, damage variables are used to control the expansion and contraction of the driven yield surface to construct the true three-dimensional yield function of rock; True three-dimensional yield function of rock considering crack azimuth for: Where: σ1, σ2 and σ3 represent the major principal stress, the intermediate principal stress and the 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, m is the model parameter to be determined; ω represents the damage of rock creep process, α(ω) is the hardening / softening function; S3. Using the exponential damage evolution criterion, the progressive damage degradation behavior of rock is systematically described; The stiffness degradation of rock is characterized by damage, and the rock degradation behavior is expressed by the exponential damage evolution criterion: Where: parameter ω c is used to control the maximum damage degree, and parameter β is used to control the damage degradation rate. d is the damage driving force, Y0 is the damage threshold, and ω represents the damage during rock creep; Considering the potential mechanism of mutual reinforcement between damage and viscoplasticity, assuming that both occur simultaneously, the nonlinear deformation-induced damage increment It is expressed as: Where: pd represents the damage multiplier, represents the damage multiplier increment; S4. Construct a true triaxial time-dependent damage model for rock, use an explicit nonlinear numerical integration algorithm to achieve numerical solution of the mechanical model, and accurately calculate the evolution of time-dependent damage factors during creep; S4.

1. Incremental expression of true three-dimensional time-dependent damage mechanics model for rock; For any rock, the general constitutive relation for the entire creep process is expressed as follows: Where: represents the total strain increment, Stress increment, Time-dependent damage factor increment, represents the fourth-order elastic-plastic damage stiffness tensor, ψ represents the creep deformation tensor affected by the time-dependent damage factor; The entire creep deformation and failure process of rock is divided into two stages: instantaneous loading and creep deformation. The strain calculations at different stages meet the following conditions: (1) The known conditions in the transient loading stage are: dζ=0, and The strain in the instantaneous stage can be expressed as: Where: represents the total strain increment, σ represents the stress, Stress increment, represents the fourth-order elastoplastic damage stiffness tensor, represents the instantaneous plastic deformation increment, represents the damage increment caused by instantaneous nonlinear deformation, and ω represents the damage during rock creep; (2) The known conditions in the creep stage are: The strain in the creep stage is expressed as: Where: represents the total strain increment, σ represents the stress, represents the fourth-order elastoplastic damage stiffness tensor, represents the viscoplastic strain increment, Indicates the damage increment caused by aging deformation and aging damage factor; S4.

2. Use explicit nonlinear numerical integration algorithm to solve the numerical evolution of time-dependent damage factor.

2. The method for constructing a true triaxial time-dependent damage mechanics model of rock according to claim 1 is characterized by: The method of constructing the true three-dimensional yield function of rock by taking the crack azimuth into consideration and using damage variables to control the expansion and contraction of the driven yield surface in step S2 is: S2.

1. Considering the crack azimuth of the rock, a true three-dimensional Hoek-Brown strength criterion is constructed to describe the strength characteristics of the rock under true three-dimensional stress conditions; According to the theory of elasticity and fracture mechanics, the true three-dimensional Hoek-Brown strength criterion considering the crack orientation can be obtained. The formula is as follows: Where: σ1, σ2 and σ3 represent the major principal stress, the intermediate principal stress and the 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, using damage variables to control the expansion and contraction of the driven yield surface and construct the true three-dimensional yield function of rock; The damage ω in 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 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 nonlinear mechanical behavior of rock failure. The hardening / softening function α(ω) is expressed as: Among them, η(ω) max represents the maximum value of the function η(ω), and ω c Indicates the constant that needs to be obtained; Based on the method of finding the extreme value of the function derivative, the function η(ω) is differentiated to determine the critical damage variable ω cri represents the critical damage variable, and ω c Indicates a constant that needs to be obtained.

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