Construction method of rock triaxial rheological damage constitutive model

Abstract

The application discloses a construction method of a rock triaxial rheological damage constitutive model, which is based on the basic principle of thermodynamics and starts from the energy dissipation in the rheological process of rock, and an elastoplastic rheological constitutive model is established by defining the plastic yield surface and plastic potential energy equation in the rheological process of rock, so that the mechanical and deformation behaviors in the rheological process of rock are described, and the rheological mechanical behavior of rock can be better characterized. The coupling between plastic flow and damage is realized by introducing the form of damage variable, which is the basis for in-depth research on the real structure change behavior of rock, and has reference value for accurately evaluating the safety and long-term stability of rock in major projects.

Description

Technical Field

[0001] This invention relates to the field of rock mechanics and engineering, and in particular to a method for constructing a triaxial rheological damage constitutive model of rock. Background Technology

[0002] Rock rheological constitutive models can describe the rheological behavior of rocks under long-term loads. The main research methods include: directly applying empirical formulas to rheological test results; establishing component models through series and parallel combinations of various elements and the addition of nonlinear terms; and establishing rock constitutive models using elastoplastic theory, damage mechanics, and internal time theory. Empirical rock rheological models are simple, intuitive, and highly applicable, showing good agreement with experimental results, but their universality is limited. Furthermore, the rheological properties exhibited by rocks under complex stress states and geological environments are highly complex, and in practical engineering, component combinations cannot fully characterize the constitutive relationships during rock rheological processes. Therefore, adopting an elastoplastic theory framework, focusing on energy dissipation during rock rheological processes, can better characterize the rheological behavior of rocks and provides valuable reference for accurately evaluating the safety and long-term stability of rocks in major engineering projects. Summary of the Invention

[0003] Purpose of the invention: The present invention aims to provide a method for constructing a triaxial rheological damage constitutive model of rock. This method achieves the coupling between plastic flow and damage by introducing damage variables, thereby describing the triaxial rheological process of rock.

[0004] Technical solution: The method for constructing a triaxial rheological damage constitutive model of rock according to the present invention includes the following steps:

[0005] (1) Introduce the damage evolution criterion of the instantaneous loading stage to characterize the instantaneous loading damage evolution of the rock and obtain the instantaneous damage d;

[0006] (2) Determine the criteria for the evolution of time-related damage, introduce the internal variables of time-related damage to describe the characteristics of time-related damage, and obtain the time-related damage ζ;

[0007] (3) By introducing the damage variable into the plastic yield surface equation and the plastic potential energy equation, the yield surface equation and the plastic potential energy equation of the elastoplastic rheological damage constitutive model are obtained.

[0008] (4) Divide the rheological constitutive model into an instantaneous loading stage and a rheological stage to obtain the total rheological strain decomposition formula;

[0009] (5) Based on the consistency principle, and according to the plastic yield surface, plastic potential energy function, and instantaneous and time-dependent damage evolution criteria, the consistency conditions of plasticity and damage are obtained, and the instantaneous plastic multiplier λ is calculated. cp , Aging plasticity multiplier λ ctThe instantaneous damage multiplier dd and the time-dependent damage multiplier dζ;

[0010] (6) Based on the plastic flow law, λ cp , λ ct Substituting , dd, and dζ into the total strain decomposition formula yields the rock rheological damage constitutive model;

[0011] (7) Determine the parameters of the rheological constitutive model based on the results of the triaxial compression test of the rock.

[0012] Furthermore, in step (1), the instantaneous damage f d for

[0013]

[0014] In the formula, As the driving force for rock damage evolution, d c B is the maximum critical value of the damage variable. d Parameters used to control the rate of damage evolution.

[0015] Furthermore, in step (2), the time-related damage ζ is

[0016]

[0017] In the formula, For the time-dependent damage variable under equilibrium conditions, γ is the experimental constant neglecting the influence of external factors such as temperature changes and chemical corrosion, t is the duration, and ω is the total damage expressed as the sum of instantaneous damage d and time-dependent damage ζ; α p It is a plastic hardening function, related to the internal friction angle of the material, and is a function of plastic deformation used to describe the plastic hardening phenomenon during the plastic deformation process.

[0018] Plastic hardening function α p for

[0019]

[0020] In the formula, γ is a parameter describing the location of the initial yield surface of the rock. p is the plastic shear deformation value, and B is the parameter of the plastic hardening function.

[0021] Furthermore, in step (3), the yield surface equation f and the plastic potential energy equation g of the rheological damage constitutive model are:

[0022] f = q 2 +A0(1-ω)α p (p-C0)p0=0 (4)

[0023]

[0024] In the formula, p is the average stress, q is the deviatoric stress, A0 and C0 are model parameters obtained from the trajectories of the average stress p and the deviatoric stress q on the plane, p0 is the normalized parameter, p0 is preferably 1 MPa, η is the slope of the boundary line of the rock compression and expansion region, and I0 is the intersection value of the plastic potential surface and the average stress.

[0025] Furthermore, in step (4), the total rheological strain decomposition ε is:

[0026]

[0027] In the formula, It is the fourth-order damage compliance matrix of the total damage, where σ is the stress tensor and ε is the total damage. cp and ε ct These represent plastic strain and time-dependent strain during the rock rheological process, respectively.

[0028] Furthermore, in step (5), the instantaneous damage multiplier dd and the instantaneous plasticity multiplier λ cp for

[0029]

[0030] Among them, f s The equation for the rheological yield surface is ε. p For plastic strain, H σ It is the instantaneous plastic hardening modulus;

[0031] Instantaneous plastic hardening modulus H σ for

[0032]

[0033] Where, dε p This represents the increment of plastic strain.

[0034] Age-dependent plastic multipliers λ ct and the time-dependent damage multiplier dζ is

[0035]

[0036] Among them, the age-hardening plastic modulus H t for

[0037]

[0038] Furthermore, the rock rheological damage constitutive model in step (6) is:

[0039]

[0040]

[0041]

[0042]

[0043] In the formula,

[0044]

[0045] in, Ψ is the constitutive compliance matrix of rheological damage under stress. σ This is the constitutive compliance matrix of rheological damage under aging.

[0046] Beneficial effects: Compared with the prior art, the significant advantages of this invention are: Based on the basic theory of thermodynamics, this invention introduces instantaneous damage and time-dependent damage criteria, and incorporates damage variables into the plastic yield surface equation and plastic potential energy equation. Based on the plastic flow law, a triaxial rheological damage constitutive model of rock is obtained, which can better describe the rheological deformation characteristics and mechanical behavior caused by instantaneous loading damage and time-dependent damage of rock. Moreover, the numerical simulation results under different stress levels are basically consistent with the experimental results. It overcomes the problems of weak universality of traditional empirical models and incomplete characterization of component models. It has important scientific significance and reference value for accurately evaluating the long-term safety and stability of rock engineering under complex environments. Attached Figure Description

[0047] Figure 1 This diagram illustrates the comparison between the triaxial rheological constitutive model of rock determined by this invention and the experimental results. Detailed Implementation

[0048] The invention will now be further described with reference to the accompanying drawings.

[0049] This invention introduces instantaneous damage criteria and time-dependent damage criteria, incorporates damage variables into the plastic yield surface equation and plastic potential energy equation, describes the rheological constitutive model in stages, lists the consistency conditions of plasticity and damage, obtains the rock rheological damage constitutive model based on the plastic flow law, and determines the rheological constitutive model parameters for model verification.

[0050] The method for constructing the triaxial rheological damage constitutive model of rock includes the following steps:

[0051] (1) A damage evolution criterion for the instantaneous loading stage is introduced to characterize the instantaneous loading damage evolution of the rock, and the instantaneous damage d is obtained. The instantaneous damage is expressed by formula (1):

[0052]

[0053] In the formula: d c B is the maximum critical value of the damage variable. d Parameters used to control the rate of damage evolution. Yd p It is the driving force for the evolution of rock damage.

[0054] (2) Determine a criterion for the evolution of time-related damage, introduce an internal variable of time-related damage to describe its characteristics, and obtain the time-related damage ζ, which is expressed by formula (2):

[0055]

[0056] In the formula: t is the duration. Let ω be the time-dependent damage variable under equilibrium conditions, where ω represents the total damage expressed as the sum of instantaneous damage d and time-dependent damage ζ, γ represents the experimental constant neglecting the influence of external factors such as temperature changes and chemical corrosion, and α represents the time-dependent damage variable under equilibrium conditions. p It is a plastic hardening function, related to the internal friction angle of the material, and is a function of plastic deformation. It is used to describe the plastic hardening phenomenon during the plastic deformation process and can be expressed as:

[0057]

[0058] In the formula: γ p This represents the plastic shear deformation value. B is a parameter describing the location of the initial yield surface of the rock; B is a parameter of the plastic hardening function.

[0059] (3) By incorporating the damage variable into the plastic yield surface equation and the plastic potential energy equation, the yield surface equation and the plastic potential energy equation of the elastoplastic rheological damage constitutive model are obtained, which are expressed by formulas (4) and (5):

[0060] f = q 2 +A0(1-ω)α p (p-C0)p0=0 (4)

[0061]

[0062] In the formula: p is the average stress, q is the deviatoric stress; p0 is the normalized parameter with a value of 1 MPa; I0 is the intersection value of the plastic potential surface and the average stress; A0 and C0 are model parameters obtained from the trajectories of the average stress p and the deviatoric stress q on the plane; and η is the slope of the boundary line of the rock compression and expansion region.

[0063] (4) The rheological constitutive model is divided into two stages: the instantaneous loading stage and the rheological stage, to obtain the total rheological strain decomposition formula. The total rheological strain decomposition formula is expressed as elastic strain, plastic strain (related to instantaneous damage), and time-dependent strain (related to time-dependent damage), as shown in formula (6):

[0064]

[0065] In the formula, σ is the stress tensor. It is the fourth-order damage compliance matrix of the total damage, ε cp and ε ct These represent plastic strain and time-dependent strain during the rock rheological process, respectively.

[0066] (5) Based on the consistency principle, and according to the plastic yield surface, plastic potential energy function, instantaneous and aging damage criteria, the plasticity and damage consistency conditions are listed, and the instantaneous plastic multiplier λ is obtained. cp The instantaneous damage multiplier dd is shown in formula (7):

[0067]

[0068] Among them, f s The equation for the rheological yield surface is ε. p For plastic strain, the instantaneous plastic hardening modulus H σ It can be represented as

[0069]

[0070] Where, dε p This represents the plastic strain increment.

[0071] We obtain the time-dependent plastic multiplier λ ct And the time-dependent damage multiplier dζ, as shown in formula (9):

[0072]

[0073] Among them, the age-hardening plastic modulus H t It can be represented as

[0074]

[0075] (6) Based on the plastic flow law, λ cp , λ ct Substituting , dd, and dζ into the total strain decomposition formula yields the rock rheological damage constitutive model, which can be expressed as:

[0076]

[0077]

[0078]

[0079]

[0080] In the formula:

[0081]

[0082] in, Ψ is the constitutive compliance matrix of rheological damage under stress. σ This is the constitutive compliance matrix of rheological damage under aging.

[0083] (7) Based on the results of the triaxial compression test of the rock, the parameters of the rheological constitutive model were determined. The model has a total of A0, C0, ... B, η, d c B d Parameters such as γ need to be determined. These are obtained by conducting triaxial compression tests on granite, based on the trajectories of the peak strength of each rock sample on the plane of mean stress p and deviatoric stress q obtained from triaxial tests under different confining pressure conditions, where A0 = 950 and C0 = 18 MPa; parameters in the plastic hardening function. This is a parameter describing the location of the initial yield surface of the granite; the parameter B = 0.0005 of the plastic hardening function is obtained by plotting the function α. p and plastic shear strain γ p The curve represents the parameter characterizing the rate of plastic hardening of rock; η = -0.0025 in the plastic potential energy function represents the slope of the boundary line between the compression and expansion regions of the rock sample; the two parameters d in the instantaneous damage evolution criterion c and B d d represents the maximum critical value of the damage variable and the rate of change of damage, respectively. c =0.9, B d =125; the aging damage test constant γ is taken as 5.0×10. -7 / s .

[0084] See Figure 1 The comparison shows the results of the triaxial rheological constitutive model simulation and the experimental results of granite under a confining pressure of 4 MPa. It can be seen that the triaxial rheological simulation curve and the experimental results of granite are in good agreement, and can well describe the rheological deformation characteristics caused by aging damage in granite. With the increase of stress level and the continuous accumulation of damage (including instantaneous damage and aging damage), the rheological deformation characteristics are obvious.

Claims

1. A method for constructing a triaxial rheological damage constitutive model for rock, characterized in that, Includes the following steps: (1) Introduce a damage evolution criterion for the instantaneous loading stage to characterize the instantaneous loading damage evolution of rocks and obtain the instantaneous damage. ; (2) Determine the criteria for the evolution of time-related damage, introduce the internal variables of time-related damage to describe the characteristics of time-related damage, and obtain the time-related damage ζ; (3) By introducing the damage variable into the plastic yield surface equation and the plastic potential energy equation, the yield surface equation and the plastic potential energy equation of the elastoplastic rheological damage constitutive model are obtained. (4) Divide the rheological constitutive model into an instantaneous loading stage and a rheological stage to obtain the total rheological strain decomposition formula; (5) Based on the consistency principle, and according to the plastic yield surface, plastic potential energy function, and instantaneous and aged damage evolution criteria, the consistency conditions of plasticity and damage are obtained, and the instantaneous plastic multiplier λ is calculated. cp , Aging plasticity multiplier λ ct The instantaneous damage multiplier dd and the time-dependent damage multiplier dζ; (6) Based on the plastic flow law, λ cp , λ ct Substituting , dd, and dζ into the total strain decomposition formula yields the rock rheological damage constitutive model; (7) Determine the parameters of the rheological constitutive model based on the results of the triaxial compression test of the rock; In step (1), instantaneous damage satisfy: ； In the formula, As the driving force for rock damage evolution, d c B is the maximum critical value of the damage variable. d Parameters used to control the rate of damage evolution; The yield surface equation of the rheological damage constitutive model in step (3) and plastic potential energy equation for ； ； In the formula, p is the mean stress, q is the deviatoric stress, and A0 and C0 are model parameters obtained from the plane trajectories of the mean stress p and the deviatoric stress q. Here, η is a normalized parameter, representing the slope of the boundary line between the rock compression and expansion regions. This represents the value at the intersection of the plastic potential surface and the mean stress. ω represents the total damage, expressed as the sum of instantaneous damage d and time-dependent damage ζ, α p This is the plastic hardening function.

2. The method for constructing the triaxial rheological damage constitutive model of rock according to claim 1, characterized in that, In step (2), the time-related damage ζ is ； In the formula, Let γ be the time-dependent damage variable under equilibrium conditions, t be the duration, ω be the total damage expressed as the sum of instantaneous damage d and time-dependent damage ζ, and α be the total damage variable. p This is the plastic hardening function.

3. The method for constructing the triaxial rheological damage constitutive model of rock according to claim 2, characterized in that, The plastic hardening function α p for ； In the formula, Parameters describing the location of the initial yield surface of the rock, is the plastic shear deformation value, and B is the parameter of the plastic hardening function.

4. The method for constructing the triaxial rheological damage constitutive model of rock according to claim 3, characterized in that, The total rheological strain decomposition in step (4) for ； In the formula, It is the fourth-order damage compliance matrix of the total damage. For stress tensor, and These represent plastic strain and time-dependent strain during the rock rheological process, respectively.

5. The method for constructing the triaxial rheological damage constitutive model of rock according to claim 4, characterized in that, In step (5), the instantaneous damage multiplier dd and the instantaneous plasticity multiplier λ cp for ； in, The equation for the rheological yield surface is... For plastic strain, It is the instantaneous plastic hardening modulus.

6. The method for constructing the triaxial rheological damage constitutive model of rock according to claim 5, characterized in that, The instantaneous plastic hardening modulus for ； in, This represents the plastic strain increment.

7. The method for constructing the triaxial rheological damage constitutive model of rock according to claim 6, characterized in that, In step (5), the aging plastic multiplier λ ct and the time-dependent damage multiplier dζ is ； Among them, age-hardening plastic modulus for ；。 8. The method for constructing the triaxial rheological damage constitutive model of rock according to claim 7, characterized in that, The constitutive model for rock rheological damage in step (6) is as follows: ； In the formula, ； in, The constitutive compliance matrix of rheological damage under stress application. This is the constitutive compliance matrix of rheological damage under aging.

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