Construction method of rock seepage-stress coupling damage constitutive model

Abstract

The application discloses a construction method of a rock seepage-stress coupling damage constitutive model. The construction method is based on the basic theory of rock seepage-stress coupling, the concept of seepage-stress coupling variables is proposed by analyzing the porosity variation characteristics of the internal structure in rock seepage-stress coupling, the relationship between the coupling variables and damage and plastic deformation is established, the coupling variables are introduced into the elastoplastic damage constitutive framework to represent the characteristics of seepage-stress coupling, and the method has reference value for accurately evaluating the safety and 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 rock seepage-stress coupled damage constitutive model. Background Technology

[0002] The flow-stress coupling characteristics of rocks are a research hotspot in rock mechanics and engineering. In recent years, numerous studies have been conducted on the flow-stress coupling characteristics of rocks, proposing new coupling models and empirical formulas to describe these characteristics. Constitutive models under flow-stress coupling are one of the effective means to study the coupling characteristics of rocks in aquatic environments. Existing methods for studying flow-stress coupling mainly include empirical formula fitting and the permeability coefficient method. These methods are simple, intuitive, and agree well with experimental results, but their universality is limited. Therefore, by introducing flow-stress coupling variables to simulate the interaction between seepage and stress within rocks, the influence of seepage water on the internal stress field of rocks and the influence of deformation behavior under stress on the internal seepage evolution of rocks can be effectively realized, thus achieving the flow-stress coupling effect of rocks. Summary of the Invention

[0003] Purpose of the invention: The present invention aims to provide a method for constructing a rock seepage-stress coupled damage constitutive model. This method introduces seepage-stress coupling variables and establishes the relationship between the coupling variables and damage and plastic deformation to obtain a rock seepage-stress coupled damage constitutive model.

[0004] Technical solution: The method for constructing the rock seepage-stress coupled damage constitutive model according to the present invention includes the following steps:

[0005] (1) Introduce a seepage-stress coupling variable to characterize the rock seepage-stress coupling characteristics under water pressure, and obtain the coupling variable ξ;

[0006] (2) Introduce the damage evolution criterion of the loading stage to characterize the damage evolution during the rock loading process and obtain the damage variable d;

[0007] (3) By introducing the coupling variable and 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 seepage-stress coupling constitutive model are obtained.

[0008] (4) Based on the consistency principle, and according to the plastic yield surface and plastic potential energy function, the consistency conditions of plasticity and damage are listed. Based on the plastic flow law, the damage multiplier dd, the seepage-stress coupling multiplier dξ, and the plastic multiplier λ under coupling are calculated. s ;

[0009] (5) Based on the principle of modulus degradation under rock seepage-stress coupling, the coupling variables, damage variables, damage multipliers dd, seepage-stress coupling multipliers dξ, and plasticity multipliers λ under coupling are introduced. s The stiffness tensor under seepage-stress coupling is calculated to obtain the seepage-stress coupling damage constitutive model.

[0010] (6) Based on the results of the triaxial compression test of rock and the test results of rock physical properties, determine the parameters of the rock seepage-stress coupling constitutive model.

[0011] Furthermore, in step (1), the seepage-stress coupling variable ξ is

[0012]

[0013] In the formula, A s The cross-sectional area of ​​the rock sample is expressed in m². 2 L s The height of the rock sample is in meters (m); φ is the porosity; ΔV l The volume of water that seeps into the rock sample at any given moment, expressed in cubic meters (m³). 3 ;

[0014] The volume ΔV of water infiltrating the rock sample at any given moment l for

[0015]

[0016] In the formula, p l The osmotic pressure difference applied between the upper and lower ends of the rock sample is expressed in Pa; Δt is the time interval expressed in seconds; μ l Let be the dynamic viscosity coefficient of water, expressed in Pa·s. Preferably, the dynamic viscosity coefficient of water at 20°C is 1 × 10⁻⁶. -3 Pa·s; K is the permeability of the rock, in meters. 2 ;

[0017] The permeability K of the rock is

[0018]

[0019] In the formula, K0 is the initial permeability, φ0 is the initial porosity, and φ is the porosity;

[0020] Porosity φ is

[0021]

[0022]

[0023] In the formula, d is the damage variable, m dThe parameters characterizing the rock dilatation rate are p and q, which represent the mean stress and deviatoric stress of the rock, respectively. φ is the maximum threshold for expanded porosity. dil To increase the porosity, dε p This represents the plastic strain increment.

[0024] Furthermore, in step (2), the instantaneous damage f d for

[0025]

[0026] In the formula, Y d p 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.

[0027] Furthermore, in step (3), the yield surface equation f and the plastic potential energy equation g of the seepage-stress coupled damage constitutive model are:

[0028] f = q 2 +A0(1-ξ)α p (p-C0)p0=0 (7)

[0029]

[0030] 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, 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.

[0031] Furthermore, in step (4), the damage multiplier dd is

[0032]

[0033] In the formula, ε p For plastic strain, γ p σ is the plastic shear deformation value, and σ is the stress tensor;

[0034] The seepage-stress coupling multiplier dξ is

[0035]

[0036] Plastic multiplier λ under coupling s for

[0037]

[0038] Plastic hardening modulus H of seepage-stress coupling ξdfor

[0039]

[0040] Furthermore, in step (5), the rock seepage-stress coupled damage constitutive model is expressed as follows:

[0041]

[0042] In the formula, Let ε be the initial fourth-order elastic tensor of the rock. e For strain tensor, The elastic stiffness matrix is ​​the result of seepage-stress coupling. Based on the principle of modulus degradation under rock seepage-stress coupling, the incremental constitutive equation for rock seepage-stress coupling damage is:

[0043]

[0044] In the formula, It is a fourth-order seepage-stress coupling compliance matrix. It is a fourth-order damage compliance matrix.

[0045] Beneficial effects: Compared with the prior art, the significant advantages of this invention are: by introducing the seepage-stress coupling variable ξ and the damage variable d into the constitutive model, this invention can not only better describe the plastic deformation, damage evolution, pressure dependence, compression-to-expansion transition, and pre-peak plastic hardening and post-peak strain softening of rocks, but also accurately describe the changes in rock sample deformation and strength characteristics caused by seepage-stress coupling. It can better interpret the seepage-stress coupling characteristics of rocks under seepage water pressure, and the numerical simulation results under different seepage water pressures are basically consistent with the experimental results. This overcomes the problem that traditional models cannot accurately simulate seepage-stress coupling characteristics, and has important scientific significance and reference value for accurately evaluating the safety and stability of rock engineering under seepage water pressure. Attached Figure Description

[0046] Figure 1 This is a schematic diagram comparing the results of the constitutive model of rock seepage-stress coupling under confining pressure of 4 MPa and seepage pressure of 1 MPa with the experimental results of the present invention;

[0047] Figure 2 This is a schematic diagram comparing the results of the constitutive model of rock seepage-stress coupling under confining pressure of 4 MPa and seepage pressure of 3 MPa with the experimental results of the present invention. Detailed Implementation

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

[0049] This invention introduces seepage-stress coupling variables and damage evolution criteria, incorporating these coupling and damage variables into the plastic yield surface equation and plastic potential energy equation. Based on the plastic flow law, it obtains the damage multiplier dd, the seepage-stress coupling multiplier dξ, and the plastic multiplier λ under coupling. s We obtained a constitutive model of rock seepage-stress occasion and damage, and determined the parameters of the coupled constitutive model for model verification.

[0050] The method for constructing a rock seepage-stress coupled damage constitutive model according to the present invention includes the following steps:

[0051] (1) Introduce a seepage-stress coupling variable to characterize the seepage-stress coupling characteristics of rock under water pressure, and obtain the coupling variable ξ:

[0052]

[0053] In the formula, A s The cross-sectional area of ​​the rock sample (m²) 2 );L s The height of the rock sample (m); ΔV l The volume of water that infiltrates into the rock sample at any given moment (m³) 3 );

[0054] The volume ΔV of water infiltrating the rock sample at any given moment l for

[0055]

[0056] In the formula, p l The osmotic pressure difference (Pa) applied between the upper and lower ends of the rock sample; Δt is the time interval (s); μ l The dynamic viscosity coefficient of water at 20℃ (Pa·s), μ l =1×10 -3 Pa·s; K is the permeability of the rock (m²) 2 );

[0057]

[0058] In the formula, φ0 is the initial porosity, K0 is the initial permeability, and φ is the porosity;

[0059]

[0060]

[0061] In the formula, d is the damage variable. m is the maximum threshold for expanded porosity. d The parameters characterizing the rock dilatation rate are p and q, respectively, the mean stress and deviatoric stress of the rock; φdil To increase the porosity, dε p This represents the plastic strain increment.

[0062] (2) A damage evolution criterion for the loading stage is introduced to characterize the damage evolution during the rock loading process, and the instantaneous damage f is obtained. d :

[0063]

[0064] In the formula, d c B represents the maximum critical value of the damage variable. d Parameters used to control the rate of damage evolution. Y d p It is the driving force for the evolution of rock damage.

[0065] (3) By introducing the coupling variable and 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 seepage-stress coupled constitutive model are expressed by formulas (7) and (8):

[0066] f = q 2 +A0(1-ξ)α p (p-C0)p0=0 (7)

[0067]

[0068] 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, 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.

[0069] (4) Based on the consistency principle, and according to the plastic yield surface and plastic potential energy function, the consistency conditions for plasticity and damage are listed. Based on the plastic flow law, the damage multiplier dd is obtained:

[0070]

[0071] ε p For plastic strain, γ p σ is the plastic shear deformation value, and σ is the stress tensor;

[0072] seepage-stress coupling multiplier dξ:

[0073]

[0074] Plastic multiplier λ under coupling s :

[0075]

[0076] Where H ξd The plastic hardening modulus of seepage-stress coupling is expressed as:

[0077]

[0078] (5) Based on the principle of modulus degradation under rock seepage-stress coupling, the coupling variables of seepage-stress coupling, damage variables, damage multipliers dd, seepage-stress coupling multipliers dξ, and plasticity multipliers λ under coupling are introduced. s We can obtain the stiffness tensor under seepage-stress coupling, and thus obtain the seepage-stress coupling damage constitutive model as follows:

[0079]

[0080] In the formula, Let ε be the initial fourth-order elastic tensor of the rock. e Let C(ξ,d) be the strain tensor, and C(ξ,d) be the seepage-stress coupled elastic stiffness matrix. 0 The initial fourth-order elastic tensor of the rock. Based on the principle of modulus degradation under rock seepage-stress coupling, the incremental constitutive equation for rock seepage-stress coupling damage can be expressed as:

[0081]

[0082] In the formula, It is a fourth-order seepage-stress coupling compliance matrix. It is a fourth-order damage compliance matrix.

[0083] (6) Based on the triaxial compression test results of granite and the rock physical property test, the parameters of the rock seepage-stress coupled constitutive model were determined. The model has a total of... φ0, A s L s A0, C0 B, η, d c B d The parameters need to be determined, and the maximum threshold of dilatational porosity of granite is obtained through rock physical property testing. The initial porosity φ0 of the granite was set to 0.018, and A was 0.05. s =6.25*10^ 4 m 2 L s =0.1m; obtained by conducting triaxial compression tests on granite, based on the trajectory 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, C0 = 18 MPa; parameters in the plastic hardening function. These are parameters describing the initial yield surface location of granite; parameter B = 0.0005 in the plastic hardening function; η = -0.0025 in the plastic potential energy function; and two parameters d in the 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.

[0084] like Figure 1 and 2 The figure shows a comparison between the simulation curves and experimental results of the constitutive model of seepage-stress coupling damage in granite under a confining pressure of 4 MPa and seepage pressures of 1 MPa and 3 MPa, respectively. It can be seen that the simulation curves and experimental results of the constitutive model of seepage-stress coupling damage in granite agree well. This model can not only describe well the plastic deformation, damage evolution, pressure dependence, transition from compression to expansion, and phenomena such as pre-peak plastic hardening and post-peak strain softening of the rock, but also accurately describe the changes in rock sample deformation and strength characteristics caused by seepage-stress coupling. It can effectively interpret the seepage-stress coupling characteristics of rock under seepage water pressure.

Claims

1. A method for constructing a rock seepage-stress coupled damage constitutive model, characterized in that, Includes the following steps: (1) Introduce a seepage-stress coupling variable to characterize the seepage-stress coupling characteristics of rock under water pressure, and obtain the coupling variable ξ; (2) Introduce the damage evolution criterion of the loading stage to characterize the damage evolution during the rock loading process and obtain the damage variable d; (3) By introducing the coupling variables and damage variables into the plastic yield surface equation and the plastic potential energy equation, the yield surface equation and the plastic potential energy equation of the seepage-stress coupling constitutive model are obtained. (4) Based on the consistency principle, according to the plastic yield surface and plastic potential energy function, the consistency conditions of plasticity and damage are listed. Based on the plastic flow law, the damage multiplier dd, the seepage-stress coupling multiplier dξ, and the plastic multiplier λ under coupling are calculated. s ; (5) Based on the principle of modulus degradation under rock seepage-stress coupling, the coupling variables, damage variables, damage multipliers dd, seepage-stress coupling multipliers dξ, and plasticity multipliers λ under coupling are introduced. s The stiffness tensor under seepage-stress coupling is calculated to obtain the seepage-stress coupling damage constitutive model. (6) Based on the results of the triaxial compression test of rock and the test results of rock physical properties, determine the parameters of the rock seepage-stress coupling constitutive model; In step (1), the seepage-stress coupling variables for （1） In the formula, A s The cross-sectional area of ​​the rock sample is expressed in m². 2 ; L s The height of the rock sample is in meters (m); φ represents the porosity. The volume of water that seeps into the rock sample at any given moment, expressed in cubic meters (m³). 3 ; The volume of water that seeps into the rock sample at any given moment. for （2） In the formula, p l The osmotic pressure difference applied between the upper and lower ends of the rock sample is expressed in Pa; Δt is the time interval expressed in seconds; μ l ρ is the dynamic viscosity of water, in Pa·s; K is the permeability of rock, in m³. 2 ; The permeability K of the rock is （3） In the formula, K0 is the initial permeability, φ0 is the initial porosity, and φ is the porosity; The porosity φ is （4） （5） In the formula, d is the damage variable, m d The parameters characterizing the rock dilatation rate are p and q, which represent the mean stress and deviatoric stress of the rock, respectively. The maximum threshold for expanded porosity. To increase porosity, This represents the plastic strain increment.

2. The method for constructing the rock seepage-stress coupled damage constitutive model according to claim 1, characterized in that, In step (2), the instantaneous damage satisfies: （6） In the formula, Y d p As the driving force for rock damage evolution, d c B represents the maximum critical value of the damage variable. d Parameters used to control the rate of damage evolution.

3. The method for constructing the rock seepage-stress coupled damage constitutive model according to claim 2, characterized in that, In step (3), the yield surface equation of the seepage-stress coupled damage constitutive model and plastic potential energy equation for （7） （8） 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 average stress.

4. The method for constructing the rock seepage-stress coupled damage constitutive model according to claim 3, characterized in that, In step (4), the damage multiplier dd is （9） In the formula, For plastic strain, This represents the plastic shear deformation value. For stress tensor; The seepage-stress coupling multiplier dξ is （10） Plastic multiplier λ under coupling s for （11） In the formula, H ξd It represents the plastic hardening modulus of percolation-stress coupling.

5. The method for constructing the rock seepage-stress coupled damage constitutive model according to claim 4, characterized in that, The plastic hardening modulus H of the percolation-stress coupling ξd for （12）。 6. The method for constructing the rock seepage-stress coupled damage constitutive model according to claim 5, characterized in that, In step (5), the rock seepage-stress coupled damage constitutive model is expressed as follows: （13） In the formula, Let ε be the initial fourth-order elastic tensor of the rock. e For strain tensor, The elastic stiffness matrix is ​​the result of seepage-stress coupling. Based on the principle of modulus degradation under rock seepage-stress coupling, the incremental constitutive equation for rock seepage-stress coupling damage is: （14） In the formula, It is a fourth-order seepage-stress coupling compliance matrix. It is a fourth-order damage compliance matrix.

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