A method for establishing a constitutive model of fractured rock considering the closure effect of microcracks

Abstract

The present invention discloses a method for establishing a constitutive model of fractured rock considering the closure effect of microcracks, comprising the following steps: decomposing the total strain into elastic strain, plastic strain and microcrack closure strain; deriving the constitutive relationship based on the irreversible thermodynamic principle of continuous media; establishing the evolution equation of microcrack closure strain; establishing the yield criterion containing hardening / softening internal variables and the unified evolution equation of hardening / softening internal variables; calculating the plastic strain increment using the orthogonal rule; deriving the incremental form and consistent tangent tensor of the constitutive model; calibrating the parameters required for the model, etc. The present invention considers the microcrack closure strain generated by the closure of naturally existing microcracks in rocks under the action of compressive stress, and establishes a constitutive model that can describe the entire process of rock deformation and destruction, and can more accurately simulate the nonlinear mechanical properties of rocks. The established model has fewer parameters and clear physical meanings, and can all be obtained through conventional triaxial tests, which is convenient for application in numerical simulations.

Description

Technical Field

[0001] The invention belongs to the technical field of rock constitutive models, and in particular relates to a method for establishing a fractured rock constitutive model taking into account microcrack closure effects. Background Art

[0002] Rock is a non-uniform medium produced by long-term geological tectonic action. It is a composite material composed of various mineral crystals, amorphous cementing materials and micro-defects (micropores, microcracks). Micropores (cracks) are the main carriers of the nonlinear mechanical properties of rock materials, which lead to complex mechanical properties of rocks under compression, such as the nonlinear closure effect of microcracks under compressive stress and plastic dissipation caused by friction and slip of closed cracks. Accurately evaluating the stress and deformation characteristics of rocks is the key to the design and operation of rock engineering. At present, numerical analysis is a commonly used analysis method for solving rock engineering problems, and constitutive models are the core technology of numerical analysis. Accurate evaluation of the safety status of actual rock engineering requires a constitutive model that can accurately reflect the entire process of rock deformation and destruction, which has important theoretical significance and application value for the safe construction and operation and maintenance of rock engineering.

[0003] At present, many scholars have conducted extensive research on the constitutive model of rock materials. Zhu Qizhi constructed a quasi-brittle rock friction damage constitutive model based on mesomechanics in his paper "Research on the Constitutive Model of Beishan Granite Microscopic Damage Mechanics", and Yuan Xiaoping proposed an elastoplastic damage constitutive model based on the Drucker-Prager criterion in his paper "Research on the Elastic-Plastic Damage Constitutive Model of Rock Based on the Drucker-Prager Criterion". Fang Jingnian constructed an elastoplastic damage coupling constitutive model in his paper "Research on the Elastic-Plastic Damage Coupling Model of Rock Salt". However, the above models only consider the mechanical properties of the rock in the elastic and plastic stages, ignoring the nonlinear closure process of microcracks under compressive stress. For rocks with obvious microcrack closure effects, the establishment method of this type of constitutive model will lead to a smaller strain field predicted by the model, resulting in a large deviation in actual engineering. In response to this deficiency, the nonlinear process caused by the closure of microcracks in rocks has gradually received attention. Li Xiulei established a damage statistical constitutive model that takes into account the closure effect of rock microcracks in his paper "Statistical damage constitutive model of rock deformation during the entire process considering initial void compression characteristics". Xiao Haibin disclosed a rock statistical damage constitutive model in his patent "A new method for constructing a statistical damage constitutive model of rock". Although the above models can simulate the closure effect of microcracks, they both ignore the plastic dissipation characteristics of rock deformation.

[0004] In summary, the existing methods for constructing rock constitutive models have certain defects, which are manifested in not considering the microcrack closure effect, or only considering the microcrack closure effect, ignoring the plastic dissipation characteristics, the established model lacks reliable physical meaning, and the calculation results are inaccurate. Therefore, it is urgent to establish an elastoplastic constitutive model based on the irreversible thermodynamic framework, considering the microcrack closure effect, with a wide range of applicability and high accuracy to describe the entire process of rock deformation and destruction, so as to provide reasonable guidance for the safe construction and normal operation of rock engineering. Summary of the invention

[0005] In order to solve the above problems, the purpose of the present invention is to provide a method for establishing a constitutive model of fractured rock taking into account the closure effect of microcracks.

[0006] The present invention is achieved by at least one of the following technical solutions.

[0007] A method for establishing a constitutive model of fractured rock considering microcrack closure effect, characterized in that it comprises the following steps:

[0008] 1) According to the stress-strain curve, the total strain is decomposed into three parts: elastic strain, plastic strain and microcrack closure strain;

[0009] 2) Based on the strain decomposition made in step 1), the variables describing the hardening / softening phenomenon are used as internal variables, and according to the Helmholtz free energy, the constitutive relationship of the rock based on the irreversible thermodynamic framework considering the microcrack closure effect is established;

[0010] 3) Construct a model to describe the evolution of microcrack closure strain under compressive stress;

[0011] 4) Establish a yield function including hardening / softening internal variables, and establish a unified evolution equation of hardening / softening internal variables based on generalized plastic shear strain;

[0012] 5) Calculate the plastic strain increment using the orthogonal rule;

[0013] 6) According to the closure strain evolution equation and yield function established in step 3) and step 4), on the basis of the rock constitutive relation considering the crack closure effect obtained in step 2), construct the incremental form of the constitutive relation and the consistent tangent tensor;

[0014] 7) Calibrate the plastic potential function and the model parameters in the closed strain evolution equation and yield function established in step 3) and step 4) to obtain the final constitutive model.

[0015] Furthermore, according to the stress-strain curve of rock in triaxial compression test, the total strain is decomposed into three parts: elastic strain, plastic strain and microcrack closure strain.

[0016] The total strain ε of rock in triaxial compression test is decomposed into:

[0017] ε=ε e +ε c +ε p (1)

[0018] Among them, ε e is the elastic strain, ε c is the microcrack closure strain, ε p is the plastic strain.

[0019] Furthermore, in step 2), the constitutive relation of rock considering the microcrack closure effect based on the irreversible thermodynamic framework is expressed as:

[0020]

[0021] in,

[0022]

[0023] Where σ is the current stress state, ε is the total strain, and ε c is the microcrack closure strain, ε p is the plastic strain, is the elastic stiffness matrix; μ and k are the shear modulus and bulk modulus, respectively; is the fourth-order isotropic unit ball tensor; is the fourth-order isotropic unit deviator.

[0024] Furthermore, the model used to describe the evolution law of microcrack closure strain under compressive stress includes:

[0025] Microcrack closure strain ε caused by microcrack closure at the initial loading stage c It is described by the following tensor equation Q:

[0026]

[0027] Where σ is the current stress state; p is the average principal stress; P m is the maximum microcrack closure strain obtained under uniaxial compression; is the parameter that controls the evolution rate of microcracks; It is a parameter related to the loading path.

[0028] Furthermore, the yield function adopts different yield criteria, including Mohr-Coulomb, Drucker-Prager or Hoek-Brown yield criteria.

[0029] Furthermore, the internal variable κ of the hardening / softening phenomenon is:

[0030]

[0031] In the formula,

[0032]

[0033] Among them, κ 0 is the value of κ at the initial yield; A∈(1,+∞] is the model parameter that controls the evolution rate of κ; ξ represents the degree of plastic evolution; is the generalized plastic shear strain, is the fourth-order isotropic unit partial tensor; is the generalized plastic shear strain at the peak stress, called the critical generalized plastic shear strain, that is, when κ = 1, γ p The value of ε p is the plastic strain.

[0034] Further, in step 5), the plastic strain increment is calculated using the orthogonal rule as follows:

[0035]

[0036] Among them, λ p is the plasticity scalar factor; is the plastic potential function, ε p is the plastic strain and σ is the current stress state.

[0037] Furthermore, the incremental form of the constitutive relation in step 6) is expressed as:

[0038]

[0039] Where dσ is the stress increment, dε is the strain increment, is the consistent tangent tensor.

[0040] Furthermore, the consistent tangent tensor It is expressed as:

[0041]

[0042] In the formula, is the elastic stiffness matrix; is the fourth-order isotropic unit tensor; is the partial derivative of the microcrack closure strain evolution function Q with respect to stress σ; is the yield function The partial derivative of stress σ; is the yield function The partial derivative with respect to the internal variable κ; is the internal variable κ for the generalized plastic shear strain γ p The partial derivative of is the plastic potential function The partial derivative of stress σ is the direction of plastic flow.

[0043] Furthermore, in step 7), the calibrated model parameters include elastic modulus E, Poisson's ratio v, strength parameter, critical generalized plastic shear strain The expansion coefficient ζ and the initial value κ of the internal variable κ 0 , model parameter A controlling the κ evolution rate, maximum microcrack closure strain P m , microcrack closure rate parameters

[0044] In step 8), the specific method of writing the numerical calculation program of the model and comparing and verifying it with the test data is as follows:

[0045] A unit-scale numerical calculation model of the model was written and compared with the experimental data to verify and improve the model.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] 1) The constitutive model establishment method provided by the present invention is based on the irreversible thermodynamics of continuous media, with a rigorous derivation process and clear physical mechanism. It makes up for the defect that the traditional elastic-plastic constitutive model cannot consider the microcrack closure effect, and can be used to describe the entire process of rock deformation and destruction, making the analysis of actual rock engineering problems more reasonable, and has high scalability and wide applicability.

[0048] 2) The constitutive model establishment method provided by the present invention includes a microcrack closure strain evolution formula, which has a clear physical mechanism and can uniformly and continuously describe the nonlinear closure process of microcracks under compressive stress under different loading paths with high accuracy.

[0049] 3) The constitutive model establishment method provided by the present invention has fewer parameters and clear physical meanings, and can be obtained through conventional triaxial tests, which is convenient for application in the optimization design and operation and maintenance of rock engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a schematic flow chart of a method for establishing a constitutive model of fractured rock taking into account the microcrack closure effect in this embodiment;

[0051] Figure 2 The typical stress-strain curve of the embodiment and the corresponding deformation and failure schematic diagram;

[0052] Figure 3 It is a curve diagram of the unified evolution function of the hardening / softening internal variables of the embodiment under different parameter values;

[0053] Figure 4This is a comparison chart of the coarse-grained granite model prediction and the test results of Example 1;

[0054] Figure 5 is a comparison chart of the sandstone model prediction and the test results of Example 2;

[0055] Figure 6 A comparison diagram of the fractured rock model prediction and the test results of Example 3;

[0056] Figure 7 is a unified evolution function curve of sandstone microcrack closure strain in Example 3;

[0057] Figure 8 This is a comparison chart of the prediction results of fractured rock with and without considering the microcrack closure effect in Example 3;

[0058] Fig. 9 This is a sensitivity analysis result diagram of the model parameters in Example 3. DETAILED DESCRIPTION

[0059] In order to further understand the characteristics, technical means and advantages of the present invention, the method for establishing a constitutive model of fractured rock taking into account the microcrack closure effect provided by the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0060] Example 1

[0061] like Figure 1 As shown, the method for establishing a constitutive model of fractured rock considering the microcrack closure effect provided by the present invention comprises the following steps performed in sequence:

[0062] 1) According to the typical stress-strain curve of rock in triaxial compression test, the total strain is decomposed into three parts: elastic strain, plastic strain and microcrack closure strain;

[0063] Figure 2 This is a typical stress-strain curve of the whole deformation and failure process of rock in triaxial compression test and a schematic diagram of the corresponding crack evolution process, such as Figure 2 As shown in Figure 2, the total strain ε of rock in the triaxial compression test can be decomposed as follows:

[0064] ε=ε e +ε c +ε p (1) Where ε e is the elastic strain, ε p is the plastic strain, ε c is the microcrack closure strain. In the microcrack closure stage at the initial stage of loading, the elastic strain and microcrack closure strain determine the deformation characteristics of the rock; Figure 2 a is the typical stress-strain curve of the whole process of rock deformation and failure in triaxial compression test; Figure 2 b is a schematic diagram of the crack evolution process of rock under compressive stress;

[0065] 2) Based on the basic principle of irreversible thermodynamics of continuous media and the strain decomposition made in step 1), the variables describing the hardening / softening phenomenon are taken as internal variables, and according to the Helmholtz free energy, the constitutive relationship of rock considering the microcrack closure effect based on the irreversible thermodynamic framework is derived;

[0066] Under the assumption of isothermal small deformation, the Helmholtz free energy Π can be decomposed into the elastic free energy ∏ e and plastic free energy ∏ p :

[0067] Π(ε e ,κ)=∏ e (ε e )+∏ p (κ) (2)

[0068] Where κ is an internal variable describing hardening / softening, and elastic free energy ∏ e It can be expressed as:

[0069]

[0070] in,

[0071]

[0072] Where ε is the total strain, ε c is the microcrack closure strain, ε p is the plastic strain, is the elastic stiffness matrix; μ and k are the shear modulus and bulk modulus, respectively; is the fourth-order isotropic unit ball tensor; is the fourth-order isotropic unit deviator.

[0073] According to the Clausius-Planck inequality:

[0074]

[0075] The time derivative of the Helmholtz free energy Π Substituting into formula (5), we can get:

[0076]

[0077] Where: Ξ represents the dissipation inequality; σ is the stress tensor; is the strain tensor increment; is the elastic strain increment; is the plastic strain increment; is the microcrack closure strain increment; Increment the internal variable. represents the plastic dissipation process, represents the dissipation process caused by the closure of microcracks. and The arbitrariness of , the following constitutive equation can be obtained from equations (3) and (6):

[0078]

[0079] 3) Establish a formula to describe the evolution of microcrack closure strain under compressive stress;

[0080] Microcrack closure strain ε c The evolution law under compressive stress can be described by the following tensor equation Q:

[0081]

[0082] Where σ is the current stress state; p is the average principal stress; P m is the maximum microcrack closure strain obtained under uniaxial compression; is the parameter that controls the evolution rate of microcracks, and its unit is MPa; It is a parameter related to the loading path.

[0083] 4) Establish a yield criterion including hardening / softening internal variables, and establish a unified evolution equation of hardening / softening internal variables based on generalized plastic shear strain;

[0084] The yield criterion of the method of the present invention is not limited to a specific form, and different yield criteria can be used, such as the Mohr-Coulomb, Drucker-Prager or Hoek-Brown yield criteria widely used in the field of geotechnical engineering, and the model is constructed by introducing hardening / softening internal variables. Experimental studies have shown that the yield surface of rock under a wide range of loads usually has nonlinear characteristics. Without loss of generality, the yield function of the Hoek-Brown form is used in this embodiment, and the expression is:

[0085]

[0086] Among them, σ 1 is the first principal stress, σ 3 is the third principal stress; m b , s and a are material parameters; σ c is the uniaxial compressive strength of rock;

[0087] κ is an internal variable that uniformly describes the hardening / softening phenomenon, and its evolution equation can be expressed as:

[0088]

[0089] In the formula,

[0090]

[0091] Among them, κ 0 is the value of κ at the initial yield; A∈(1,+∞] is the model parameter that controls the evolution rate of κ; is the generalized plastic shear strain, is the fourth-order isotropic unit partial tensor; is the generalized plastic shear strain at the peak stress, called the critical generalized plastic shear strain, that is, when κ = 1, γ p The value of .

[0092] 5) Calculate the plastic strain increment using the orthogonal rule;

[0093] is the plastic potential function. When , it is the associated flow law, otherwise it is the non-associated flow law. In this embodiment, the non-associated flow law is adopted, and the Drucker-Prager plastic potential function is selected:

[0094]

[0095] The plastic strain increment can be calculated using the orthogonal rule:

[0096]

[0097] Among them, λ p is the plasticity scalar factor, and σ is the current stress state.

[0098] 6) According to the closure strain evolution equation and yield function established in step 3) and step 4), based on the rock constitutive relation considering the crack closure effect obtained in step 2), the incremental form of the constitutive relation and the consistent tangent tensor are derived;

[0099] According to formula (7), the incremental form of the constitutive relation is as follows:

[0100]

[0101] The consistency condition of the simultaneous yield criterion and microcrack closure strain evolution criterion is:

[0102]

[0103] In the formula, is the partial derivative of the microcrack closure strain evolution function with respect to the stress; is a fourth-order unit tensor; is the partial derivative of the yield function with respect to stress; is the partial derivative of the yield function with respect to the internal variable κ; is the partial derivative of the evolution function of the internal variable κ with respect to the generalized plastic shear strain.

[0104] when The nonlinear characteristics of the constitutive model are caused by the microcrack closure strain, and the microcrack closure strain increment is calculated by the following formula:

[0105]

[0106] when The nonlinear characteristics of the constitutive model are caused by plastic strain and microcrack closure strain. The expressions of plastic multiplier and microcrack closure strain increment are:

[0107]

[0108] The constitutive relation in incremental form is expressed as follows:

[0109]

[0110] Among them, the consistent tangent tensor The expression is:

[0111]

[0112] 7) Based on conventional triaxial compression test data, calibrate the plastic potential function used and the model parameters in the microcrack closure strain evolution equation (8) and the yield criterion (9) established in steps 3) and 4).

[0113] The model contains 12 parameters in total, which can be calibrated by conventional triaxial compression tests. The calibration methods of the main parameters are as follows:

[0114] Elastic parameters (E, v): The elastic modulus E and Poisson's ratio v of the rock can be obtained from the linear segment of the stress-strain curve of the triaxial compression test; the strength parameter (σ c 、m b , s, a): σ c is the uniaxial compressive strength of rock, which can be obtained through uniaxial compression test. According to the peak strength of triaxial compression test of rock under different confining pressures, 1 -σ 3 The failure envelope is drawn on the plane, and the strength criterion is used to fit the failure envelope to obtain the model strength parameter m b , s and a; plasticity parameters and ζ can be obtained from the strain data corresponding to the peak strength of the triaxial compression test. According to the yield strength of the triaxial compression test of rock under different confining pressures, σ 1 -σ3 The initial yield envelope is drawn on the plane, and the initial yield criterion is used to fit the envelope to obtain the parameter κ 0 , parameter A controls the residual strength; microcrack closure effect parameter P m represents the maximum closure strain of microcracks, which can be obtained through uniaxial compression test. It is a model parameter in MPa that controls the evolution rate of microcrack closure strain, which can be obtained by fitting the microcrack closure strain under different confining pressures.

[0115] In this embodiment, the triaxial compression test data of sandstone, fractured rock and coarse-grained granite in Dong Jinpeng's paper [Dong Jinpeng. Research on triaxial mechanical properties and particle flow simulation of granite with different particle sizes after high temperature [D]. China University of Mining and Technology, 2020.] are used to verify this model. Table 1 shows the parameters of the embodiment model obtained by the above parameter calibration method.

[0116] Table 1 Coarse-grained granite model parameters

[0117]

[0118]

[0119] 8) Write a unit-scale numerical calculation model for the model and compare it with the experimental data.

[0120] Based on the above model parameters, the stress-strain curves of coarse-grained granite under different confining pressures were simulated. Figure 4 As shown, the model prediction results are in good agreement with the triaxial test results, and can accurately predict the microcrack closure stage, linear elastic stage, strain hardening and strain softening stages, indicating that the model of the present invention can be used to simulate the entire process of rock deformation and failure.

[0121] Example 2

[0122] In step 4) of this embodiment, the yield criterion of the Mohr-Coulomb form is adopted, and the expression is:

[0123]

[0124] Among them, σ 1 is the first principal stress; σ 3 is the third principal stress; is the internal friction angle of the material; c is the cohesion of the material; κ is the internal variable that uniformly describes the hardening and softening phenomenon. The model using this yield function contains a total of 10 parameters, which can all be calibrated by conventional triaxial compression tests. The calibration method of the main parameters is as follows:

[0125] Elastic parameters (E, v): The elastic modulus E and Poisson's ratio v of the rock can be obtained from the linear segment of the stress-strain curve of the triaxial compression test; strength parameters c is the cohesion parameter of rock, is the friction angle parameter of rock, according to the peak strength of triaxial compression test of rock under different confining pressures, in σ 1 -σ 3 The failure envelope is drawn on the plane and the strength criterion is used to fit the failure envelope to obtain the model strength parameters c and Plasticity parameters and ζ can be obtained from the strain data corresponding to the peak strength of the triaxial compression test. According to the yield strength of the triaxial compression test of rock under different confining pressures, σ 1 -σ 3 The initial yield envelope is drawn on the plane, and the initial yield criterion is used to fit the envelope to obtain the parameter κ 0 , parameter A controls the residual strength; microcrack closure effect parameter P m represents the maximum closure strain of microcracks, which can be obtained through uniaxial compression test. It is a model parameter in MPa that controls the evolution rate of microcrack closure strain, which can be obtained by fitting the microcrack closure strain under different confining pressures.

[0126] The model was verified using the triaxial compression test data of sandstone in the paper by Liu, Si-Li, et al. [Liu, Si-Li, et al. "Experimental investigation and micromechanical modeling of the brittle-ductile transition behaviors in low-porosity sandstone." International Journal of Mechanical Sciences 179 (2020): 105654.] Table 2 shows the model parameters of the embodiment obtained using the above parameter calibration method.

[0127] Table 2 Sandstone model parameters

[0128]

[0129]

[0130] A numerical calculation model of the model unit scale was compiled and compared with the test data. Based on the above model parameters, the stress-strain curves of sandstone under different confining pressures were simulated. Figure 5As shown, the model prediction results are in good agreement with the triaxial test results, and can accurately predict the microcrack closure stage, linear elastic stage, strain hardening and strain softening stages, indicating that the model of the present invention can be used to simulate the entire process of rock deformation and failure.

[0131] Example 3

[0132] In step 4) of this embodiment, a yield function in the form of Drucker-Prager is used, and the expression is:

[0133]

[0134] Among them, J 2 is the second invariant of deviatoric stress; I 1 is the first stress invariant; C s yes The yield surface in the plane and The intersection of the axes; η is related to the internal friction angle of the material; κ is an internal variable that uniformly describes the hardening and softening phenomenon. After adopting this yield function, the model contains a total of 10 parameters, which can all be calibrated by conventional triaxial compression tests. The calibration method of the main parameters is as follows:

[0135] Elastic parameters (E, v): The elastic modulus E and Poisson's ratio v of the rock can be obtained from the linear segment of the stress-strain curve of the triaxial compression test; the strength parameter (η p , C s ): According to the triaxial test results of rock under different confining pressures, Draw the failure envelope on the plane and determine the parameter η in the yield function p and C s . ; Plastic parameters and ζ can be obtained from the strain data corresponding to the peak strength of the triaxial compression test. According to the yield strength of the triaxial compression test of rock under different confining pressures, σ 1 -σ 3 The initial yield envelope is drawn on the plane, and the initial yield criterion is used to fit the envelope to obtain the parameter κ 0 , parameter A controls the residual strength; microcrack closure effect parameter P m represents the maximum closure strain of microcracks, which can be obtained through uniaxial compression test. It is a model parameter in MPa that controls the evolution rate of microcrack closure strain, which can be obtained by fitting the microcrack closure strain under different confining pressures.

[0136] The model is verified by using the triaxial compression test data of fractured rock in the paper by Yang Chao [Yang Chao. Research on triaxial loading and unloading creep characteristics of hard fractured rock mass [D]. Chongqing University, 2015.]. Table 3 shows the model parameters of the embodiment obtained by using the above parameter calibration method.

[0137] Table 3 Parameters of fractured rock model

[0138]

[0139] A numerical calculation model of the unit scale of the model was compiled and compared with the experimental data. Based on the above model parameters, the stress-strain curves of fractured rocks under different confining pressures were simulated. Figure 6 As shown, the model prediction results are in good agreement with the triaxial test results, and can accurately predict the microcrack closure stage, linear elastic stage, strain hardening and strain softening stages, indicating that the model of the present invention can be used to simulate the entire process of rock deformation and failure.

[0140] like Figure 7 As shown, taking the test data of fractured rock as an example, the maximum microcrack closure strain is 0.3%. The microcracks in the sample are partially closed in the hydrostatic pressure loading stage and completely closed in the bias loading stage, indicating that the microcrack closure strain evolution equation included in the present invention can uniformly and continuously describe the evolution law of microcrack closure strain under different loading paths. Figure 7 a is the microcrack closure strain evolution curve during the hydrostatic pressure loading stage; Figure 7 b is the microcrack closure strain evolution curve during the bias loading stage;

[0141] like Figure 8 As shown in the figure, taking the test data of fractured rock as an example, there is a large error between the simulation results of the model without considering the closure effect of microcracks and the test data, and the model considering the closure effect of microcracks is more consistent with the test data, indicating that the strain prediction accuracy of this model is significantly improved compared with the existing constitutive model without considering the closure effect of microcracks, which verifies the advantages of this model.

[0142] Fig. 9 The sensitivity analysis results of the constitutive model parameters of the present invention (a is the parameter P m Sensitivity analysis; b is parameter Sensitivity analysis; c is a parameter Sensitivity analysis; d is parameter A sensitivity analysis A). Fig. 9 As shown in a, parameter P m represents the maximum microcrack closure strain, parameter P m The larger the value, the more obvious the microcrack closure effect; Fig. 9 As shown in b, the parameters Control the evolution rate of microcrack closure strain, that is, the closing rate of microcracks under compressive stress. The larger the value, the faster the closure rate of the microcracks. The microcracks close quickly during the hydrostatic pressure loading stage, resulting in an insignificant microcrack closure effect during the bias pressure loading stage. Fig. 9 As shown in c, with the parameter From 0.001 to 0.005, the strain corresponding to the peak intensity increases. In addition, the parameter It also affects the damage mode. increases, the failure mode changes from brittle to ductile; Fig. 9 As shown in d, parameter A affects the residual strength and failure mode. As parameter A increases, the residual strength decreases, and the failure mode changes from ductile failure to brittle failure, which is similar to parameter Different, parameter A will not affect the strain corresponding to the peak strength. From the above analysis, it can be seen that by using different parameter combinations, this model can simulate rocks with various mechanical properties, including rocks with obvious crack closure effect or not obvious microcrack closure effect, rocks with obvious brittle characteristics or obvious ductile characteristics, etc., which once again verifies the high scalability and wide applicability of the model of the present invention.

[0143] In summary, the constitutive model considering the microcrack closure effect proposed in the present invention can accurately describe the entire process of rock deformation and failure.

[0144] The above description is only a verification embodiment of the present invention and is not intended to limit the present invention.

Claims

1. A method for establishing a constitutive model of fractured rock considering the closure effect of microcracks. Features: The following steps are involved: 1) According to the stress-strain curve, the total strain is decomposed into three parts: elastic strain, plastic strain and microcrack closure strain; 2) Based on the strain decomposition made in step 1), the variables describing the hardening / softening phenomenon are used as internal variables, and according to the Helmholtz free energy, the constitutive relationship of the rock based on the irreversible thermodynamic framework considering the microcrack closure effect is established; 3) Construct a model to describe the evolution of microcrack closure strain under compressive stress; 4) Establish a yield function including hardening / softening internal variables, and establish a unified evolution equation of hardening / softening internal variables based on generalized plastic shear strain; 5) Calculate the plastic strain increment using the orthogonal rule; 6) According to the closure strain evolution equation and yield function established in step 3) and step 4), on the basis of the rock constitutive relation considering the crack closure effect obtained in step 2), construct the incremental form of the constitutive relation and the consistent tangent tensor; 7) Calibrate the plastic potential function and the model parameters in the closed strain evolution equation and yield function established in step 3) and step 4) to obtain the final constitutive model.

2. The method for establishing a constitutive model of fractured rock considering the closure effect of microcracks according to claim 1, Features: According to the stress-strain curve of rock in triaxial compression test, the total strain is decomposed into three parts: elastic strain, plastic strain and microcrack closure strain. The specific details include: The total strain ε of rock in triaxial compression test is decomposed into: e=e e +e c +e p (1) Among them, ε e is the elastic strain, ε c is the microcrack closure strain, ε p is the plastic strain.

3. According to the method for establishing a constitutive model of fractured rock taking into account the closure effect of microcracks as described in claim 1, Features: In step 2), the constitutive relation of rock considering the microcrack closure effect based on the irreversible thermodynamic framework is expressed as: in, Where σ is the current stress state, ε is the total strain, and ε c is the microcrack closure strain, ε p is the plastic strain, is the elastic stiffness matrix; μ and k are the shear modulus and bulk modulus, respectively; is the fourth-order isotropic unit ball tensor; is the fourth-order isotropic unit deviator.

4. According to the method for establishing a constitutive model of fractured rock taking into account the closure effect of microcracks as described in claim 1, Features: The model constructed to describe the evolution law of microcrack closure strain under compressive stress includes: Microcrack closure strain ε caused by microcrack closure at the initial loading stage c It is described by the following tensor equation Q: Where σ is the current stress state; p is the average principal stress; P m is the maximum microcrack closure strain obtained under uniaxial compression; is the parameter that controls the evolution rate of microcracks; It is a parameter related to the loading path.

5. According to the method for establishing a constitutive model of fractured rock taking into account the closure effect of microcracks as described in claim 1, Features: The yield function uses different yield criteria, including Mohr–Coulomb, Drucker–Prager, or Hoek–Brown.

6. The method for establishing a constitutive model of fractured rock considering the closure effect of microcracks according to claim 1, Features: The internal variable κ of the hardening / softening phenomenon is: In the formula, Among them, κ 0 is the value of k at the initial yield; A∈(1,+∞] is the model parameter that controls the evolution rate of k; ξ represents the degree of plastic evolution; is the generalized plastic shear strain, is the fourth-order isotropic unit partial tensor; is the generalized plastic shear strain at the peak stress, called the critical generalized plastic shear strain, that is, when κ = 1, γ p The value of ε p is the plastic strain.

7. The method for establishing a constitutive model of fractured rock considering the closure effect of microcracks according to claim 1, Features: In step 5), the plastic strain increment is calculated using the orthogonal rule as follows: Among them, λ p is the plasticity scalar factor; is the plastic potential function, ε p is the plastic strain and σ is the current stress state.

8. The method for establishing a constitutive model of fractured rock considering the closure effect of microcracks according to claim 1, Features: The incremental form of the constitutive relation in step 6) is expressed as: Where dσ is the stress increment, dε is the strain increment, is the consistent tangent tensor.

9. The method for establishing a constitutive model of fractured rock considering the closure effect of microcracks according to claim 8, Features: The consistent tangent tensor It is expressed as: In the formula, is the elastic stiffness matrix; is the fourth-order isotropic unit tensor; is the partial derivative of the microcrack closure strain evolution function Q with respect to stress σ; is the yield function The partial derivative of stress σ; is the yield function The partial derivative with respect to the internal variable κ; is the internal variable κ for the generalized plastic shear strain γ p The partial derivative of is the plastic potential function The partial derivative of stress σ is the direction of plastic flow.

10. The method for establishing a constitutive model of fractured rock considering microcrack closure effect according to any one of claims 1 to 9, Features: In step 7), the calibrated model parameters include elastic modulus E, Poisson's ratio ν, strength parameter, critical generalized plastic shear strain Expansion coefficient ζ, initial value κ of internal variable k 0 , model parameter A controlling the k evolution rate, maximum microcrack closure strain P m , microcrack closure rate parameters

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