A method for constructing a hard rock mechanical model considering three-dimensional stress-dependent brittleness and failure process

Abstract

This invention provides a method for constructing a hard rock mechanics model that considers three-dimensional stress-dependent brittleness and failure processes. It introduces a brittleness index coupled with three-dimensional stress state as a key internal variable, constructing an internal variable evolution criterion that quantitatively reflects the influence of three-dimensional stress level on the brittleness of the material. Based on this internal variable, it drives the phased differentiated evolution of strength parameters such as cohesion and internal friction angle, realistically simulating the complete failure sequence from elastic deformation, plastic yielding, brittle fracture to ductile flow and even residual slip through physical mechanisms. By establishing a damage tensor related to stress state and this internal variable, it describes the anisotropic degradation of the deformation modulus induced by three-dimensional stress, forming a constitutive model. This invention constructs a constitutive model that uses a three-dimensional stress-dependent brittleness index as a link to unify the driving force of strength parameter evolution and anisotropic damage development, providing a more advanced and reliable theoretical tool and numerical analysis foundation for safety assessment and disaster prevention in deep hard rock engineering.

Description

Technical Field

[0001] This invention relates to the fields of rock mechanics and geotechnical engineering, specifically to a method for constructing a hard rock mechanics model that considers three-dimensional stress-dependent brittleness and failure processes. This method is applicable to engineering fields such as deep underground engineering, tunnel and chamber excavation, mineral resource mining, high slopes in water conservancy and hydropower projects, and geological disposal sites for nuclear waste, for deformation prediction, failure process simulation, and stability analysis of hard rock media under true triaxial stress conditions. Technical Background

[0002] In deep rock engineering, the surrounding rock is often under complex true triaxial stress states. Traditional rock mechanics models are mostly based on conventional triaxial tests, failing to fully consider the significant influence of intermediate principal stress on rock strength, deformation, and failure modes. This leads to limitations in predicting the nonlinear mechanical behavior of deep hard rock, especially its failure process. In recent years, the development of true triaxial testing technology has revealed that the failure behavior of hard rock exhibits a distinct three-dimensional stress dependence. Specifically, the brittleness of the material increases with the increase of intermediate principal stress and the decrease of minimum principal stress; its failure process can present various types, ranging from instantaneous brittle fracture to progressive ductile failure; and the orientation of the failure surface and deformation response show obvious stress-induced anisotropy. However, most existing constitutive models are unable to simultaneously characterize the aforementioned three-dimensional stress-dependent brittle evolution, diverse failure processes, and associated anisotropic damage within a unified framework. This restricts the ability to accurately analyze and predict the fracture mechanism and stability of surrounding rock in deep engineering. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of the prior art by providing a method for constructing a hard rock mechanics model that considers three-dimensional stress-dependent brittleness and failure processes. This method aims to form a self-consistent constitutive model within a thermodynamic framework that can uniformly characterize the three-dimensional stress-dependent brittle behavior, complex failure processes, and anisotropic responses of hard rock under true triaxial compression. This will provide a more advanced and reliable theoretical tool and numerical analysis basis for the safety assessment and disaster prevention of deep hard rock engineering.

[0004] Therefore, the present invention adopts the following technical solution:

[0005] A method for constructing a hard rock mechanics model considering three-dimensional stress-dependent brittleness and failure processes is proposed. This method introduces a brittleness index coupled with the three-dimensional stress state as a key internal variable, constructing an internal variable evolution criterion that reflects the quantitative influence of the three-dimensional stress level on the brittleness of the material. Furthermore, based on this internal variable, the method drives the phased differential evolution of strength parameters such as cohesion and internal friction angle, realistically simulating the complete failure sequence from elastic deformation, plastic yielding, brittle fracture to ductile flow and even residual slip through physical mechanisms. Simultaneously, by establishing a damage tensor related to the stress state and this internal variable, the anisotropic degradation of the deformation modulus induced by three-dimensional stress is described, forming a self-consistent constitutive model within a thermodynamic framework that can uniformly characterize the three-dimensional stress-dependent brittle behavior, complex failure process, and anisotropic response of hard rock under true triaxial compression.

[0006] The present invention may also employ the following further technical solutions, or a combination of these further technical solutions, based on the above-described technical solutions:

[0007] Step 1: Establish the overall framework of the model and the incremental stress-strain relationship

[0008] First, the incremental constitutive relation of the model is established within the framework of elastoplastic theory; the total strain increment ( It is decomposed into elastic components ( ) and plastic part ( ); Stress increment ( ) through a stress-induced anisotropic elastic stiffness tensor ( The relationship between elastic strain increment and elastic strain increment is as follows:

[0009] (1)

[0010] in, The method for determining the intrinsic variables that characterize loading history and damage level is the core innovation point, and it is defined in detail in step two; It is anisotropic;

[0011] Determined by the plastic potential function g, g is determined by cohesion c and internal friction angle. Sure; ≥0 is the plasticity increment factor, which is an index describing the magnitude of the plastic strain increment.

[0012] Step 2: Define the three-dimensional stress-dependent brittleness index and internal variables

[0013] This step aims to quantitatively characterize the three-dimensional stress state (maximum principal stress). Intermediate principal stress minimum principal stress The influence of rock brittleness on the degree of rock brittleness was investigated and coupled with internal variables.

[0014] (1). Define the three-dimensional stress brittleness index: Based on the results of true triaxial tests, a brittleness index Brit is defined, which is the plastic volumetric strain under residual stress ( res The function of the reciprocal of the normalized stress () is fitted to the normalized stress () / UCS, Empirical formula for / UCS:

[0015] (2)

[0016] Where UCS is the uniaxial compressive strength of rock, and D b The ductility coefficient is determined by uniaxial compression testing;

[0017] (2). Calculate the driving internal variable: the equivalent plastic shear strain (Or plastic work) multiplied by the brittleness index forms the core internal variable driving the evolution of the model. :

[0018] (3)

[0019] This equation shows that, under the same equivalent plastic strain, the highly brittle state will lead to a faster increase in internal variables, thereby accelerating the material degradation process.

[0020] Step 3: Constructing a plastic potential function based on internal variables and conceptual mechanisms

[0021] g is determined by cohesion and the angle of internal friction, which are influenced by internal variables. Control. This step utilizes internal variables. This allows for the control of the phased evolution of cohesion and internal friction angle, thereby simulating the rock failure process.

[0022] (1). Classification of failure process types and threshold of internal variables: Based on experimental observations, a brittleness index B was established. c =ln(Brit) and the threshold corresponding to the typical failure process. Simultaneously, define the threshold κ for the internal variable. p , κ b , κ d , κ u This is used to divide the deformation stages within a single stress-strain curve, including elastic, plastic, brittle, ductile, and residual deformation stages.

[0023] (2). Define the piecewise strength evolution function: For each deformation stage i (elastic, plastic, brittle, ductile, residual), assign it a specific cohesion weakening rate w. i and friction angle strengthening rate s i :

[0024] Elastic stage: Cohesion weakening rate is not considered and friction angle strengthening rate Changes;

[0025] Plastic stage: , (Microcrack initiation leads to decreased cohesion, and friction begins to intensify.)

[0026] Delayed phase: , (Crack interaction, strength relatively stable);

[0027] Brittle stage: , (Macroscopic crack penetration leads to a sharp drop in cohesion, and friction is not mobilized in time).

[0028] Residual stage: , (Sliding along the main sliding surface, with constant strength);

[0029] (3). Update the intensity parameters: Based on the current stage of the internal variable κ, update the intensity parameters using a piecewise linear or nonlinear function:

[0030] (4)

[0031] (5)

[0032] Where, Δκ i Let c0 and c be the cumulative increments of the internal variables within the current stage i. r , , These are the initial and residual intensity parameters, respectively.

[0033] This step can be found in [link / reference]. Figure 1 .

[0034] Step 4: Establish a three-dimensional stress-induced anisotropic damage and stiffness evolution model

[0035] This step describes the anisotropic degradation of the deformation modulus caused by three-dimensional stress. For details, please refer to [link to relevant documentation]. Figure 2 and Figure 3

[0036] (1). Based on the concept of energy equivalence or effective stress, an anisotropic elastic stiffness tensor dependent on integrity is constructed in the principal coordinate system of damage. =f( ), yes The deformation modulus in the direction (j=1, 2, 3) can be expressed in general form as the initial isotropic stiffness E0 is calculated and transformed through the elastic stiffness matrix;

[0037] (6)

[0038] (2). Establish the law of deformation modulus degradation: Define the principal direction σ j The deformation modulus degradation ratio q j =E j / E0. Its evolution with respect to the internal variable κ is described using a negative exponential form:

[0039] (7)

[0040] Among them, R j This represents the residual proportion of the modulus in that direction;

[0041] (3). Determine R j The stress dependence of R2 (the residual proportion of the modulus in the intermediate principal stress direction) varies with the stress state. Experiments show that the residual proportion of the modulus in the maximum principal stress direction, R1 ≈ 1.0, while the residual proportion of the modulus in the minimum principal stress direction, R3, remains essentially constant. R2, however, correlates with the stress difference. A linear relationship exists:

[0042] (8)

[0043] Among them, R s R is the slope. When σ2 = σ3 (conventional triaxial), R2 = R3, indicating degenerate isotropy; when σ2 > σ3, R2 approaches 1.0, indicating almost no damage in the σ2 direction.

[0044] Step 5: Implementation and Application Process of the Model in the Numerical Computing Platform

[0045] The above constitutive model is integrated into the finite element / finite difference platform and executed in each computational iteration step according to the following procedure:

[0046] (1). Stress update and yield judgment: Calculate the stress value at this moment based on the given strain increment. Use the current strength parameter (c, updated in step three) to update the current strength parameter (c, Calculate the plastic potential function g (using a three-dimensional nonlinear criterion that reflects the effect of intermediate principal stress).

[0047] (2). Internal variable update and process identification: If under plastic loading, calculate the current equivalent plastic strain and stress level (σ2, σ3), calculate the current brittleness index Brit and internal variable increment Δκ through step two, and accumulate them to obtain the new κ. According to B cDetermine the type of failure process (elastic, plastic, brittle, ductile, residual) of the current unit.

[0048] (3). Parameter synchronous evolution:

[0049] (3-1) Based on the new κ and the identified destruction process type, update c and c by invoking the rule from step three. .

[0050] (3-2) Based on the new κ and the current stress state, update the deformation modulus degradation ratio d in the three principal directions by invoking the rule in step four. j This updates the integrity tensor β and the anisotropic stiffness matrix E. a .

[0051] (3-3) Plastic correction and state output: Using numerical integration schemes such as implicit backward Euler method, the final stress state, plastic strain and all updated internal variables that satisfy the yield condition and flow law (using non-associated flow, the plastic potential function g is determined by cohesion and dilatation angle) are solved.

[0052] (3-4) Global Iteration and Failure Analysis: Repeat the above steps on a global scale until the system reaches equilibrium. Post-processing indicators such as "Rock Fracture Degree (RFD)" can be used to visualize and analyze the entire process of fracture initiation, propagation, and eventual penetration based on the yield proximity and plastic strain of the elements.

[0053] By implementing the above five steps, the hard rock mechanics model can be constructed and applied to achieve accurate numerical simulation of the complex mechanical behavior of surrounding rock in deep engineering under true triaxial stress. Model parameters (E0, c0, c...) r , , D b w i s i R3, R s (etc.) can be determined by combining conventional triaxial, uniaxial and some biaxial tests with the formula, without the need for a large number of complex true triaxial cyclic loading and unloading tests, and has good engineering applicability.

[0054] In summary, this invention constructs a constitutive model that uses a three-dimensional stress-dependent brittleness index as a link to unify the driving force of strength parameter evolution and anisotropic damage development, providing a more advanced and reliable theoretical tool and numerical analysis basis for safety assessment and disaster prevention in deep hard rock engineering. Attached Figure Description

[0055] Figure 1 It is the evolution of strength parameters and the corresponding fracture process;

[0056] Figure 2 It is the evolution of deformation modulus;

[0057] Figure 3 This relates Rj to the stress level;

[0058] Figure 4 It is a comparison between simulation results and experimental results. Detailed Implementation

[0059] To illustrate the implementation methods and effects of the present invention, CJPL-II marble is used as an example to demonstrate the entire process of the model from parameter determination, numerical implementation to result verification.

[0060] 1. Methods for determining model parameters

[0061] Based on the model construction framework proposed in this invention (steps one to five above), the required model parameters can be calibrated using conventional indoor rock mechanics tests, strictly following the formulas and evolution rules defined in this invention. The determination of all parameters does not depend on complex true triaxial cyclic tests; the specific methods and typical values ​​obtained are shown in the table below.

[0062]

[0063]

[0064]

[0065] 2. Model Implementation and Validation

[0066] Input the parameters determined in the table above into a numerical computing platform that integrates the model of this invention. Simulate under specific true triaxial stress conditions ( =10MPa, The compression failure process of hard rock (75 MPa) was studied to reproduce the "elastic-plastic-brittle" failure behavior.

[0067] 3. Results Comparison and Analysis

[0068] Reference Figure 4 The numerical simulation results validated the correctness and predictive ability of the method of this invention from multiple dimensions:

[0069] Stress-strain response: The complete axial stress-strain curve obtained from the simulation is in high agreement with the curve of the physical test under the same conditions, accurately reproducing key characteristics such as linear elasticity, nonlinear plastic hardening, peak value, and instantaneous brittle drop.

[0070] Failure Mode and Anisotropy: At the end of the simulation, the macroscopic fracture surface formed by the numerical specimen was strictly parallel to the direction of the intermediate principal stress σ2, which was completely consistent with the anisotropy phenomenon of failure induced by three-dimensional stress observed in the real test.

[0071] The above are merely embodiments of the present invention and are not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for constructing a hard rock mechanics model considering three-dimensional stress-dependent brittleness and failure processes, characterized in that, By introducing a brittleness index coupled with a three-dimensional stress state as a key intrinsic variable, an intrinsic variable evolution criterion that can quantitatively reflect the influence of three-dimensional stress level on the brittleness of materials is constructed. Furthermore, based on this intrinsic variable, the phased differential evolution of strength parameters such as cohesion and internal friction angle is driven, and the complete failure sequence from elastic deformation, plastic yielding, brittle fracture to ductile flow and even residual slip is realistically simulated through physical mechanisms. At the same time, by establishing a damage tensor related to stress state and this intrinsic variable, the anisotropic degradation of deformation modulus induced by three-dimensional stress is described, forming a self-consistent constitutive model within a thermodynamic framework that can uniformly characterize the three-dimensional stress-dependent brittle behavior, complex failure process and anisotropic response of hard rock under true triaxial compression.

2. The method for constructing a hard rock mechanics model considering three-dimensional stress-dependent brittleness and failure processes as described in claim 1, characterized in that, Includes the following steps: Step 1: Establish the overall framework of the model and the incremental stress-strain relationship; Step 2: Define the three-dimensional stress-dependent brittleness index and internal variables; Step 3: Construct a plastic potential function based on internal variables and conceptual mechanisms; Step 4: Establish a three-dimensional stress-induced anisotropic damage and stiffness evolution model.

3. The method for constructing a hard rock mechanics model considering three-dimensional stress-dependent brittleness and failure processes as described in claim 2, characterized in that, In step one: First, the incremental constitutive relation of the model is established within the framework of elastoplastic theory; the total strain increment... Decomposed into elastic components With plastic part Stress increment Through a stress-induced anisotropic elastic stiffness tensor The basic relationship with the elastic strain increment is as follows: （1） in, As intrinsic variables characterizing loading history and damage extent, It is anisotropic; Determined by the plastic potential function g, g is determined by cohesion c and internal friction angle. Sure; ≥0 is an index describing the magnitude of the plastic strain increment.

4. The method for constructing a hard rock mechanics model considering three-dimensional stress-dependent brittleness and failure processes as described in claim 3, characterized in that, In step two: (1). Define the three-dimensional stress brittleness index: Based on the results of true triaxial tests, a brittleness index Brit is defined, which is the plastic volumetric strain under residual stress. res The reciprocal function, fitted to the normalized stress , Empirical formula: （2） Where UCS is the uniaxial compressive strength of rock, and D b The ductility coefficient is determined by uniaxial compression testing; (2). Calculate the driving internal variable: the equivalent plastic shear strain Alternatively, the plastic work can be multiplied by the brittleness index to form the internal variable driving the evolution of the model. : （3）。 5. The method for constructing a hard rock mechanics model considering three-dimensional stress-dependent brittleness and failure processes as described in claim 3, characterized in that, In step three: (1). Classification of damage process types and threshold of internal variables Establish the brittleness index B c =ln(Brit) and the threshold of the correspondence between typical failure processes; Define internal variable threshold , κ b , κ d , κ u To divide the elastic, plastic, brittle, ductile, and residual deformation stages within a single stress-strain curve; (2). Define the piecewise intensity evolution function For each deformation stage i, a specific cohesive weakening rate w is assigned. i and friction angle strengthening rate s i : Elastic stage: Cohesion weakening rate is not considered and friction angle strengthening rate Changes; Plastic stage: , ; Delayed phase: , ; Brittle stage: , ; Residual stage: , ; (3) Realize the updating of strength parameters Based on the current internal variables Depending on the current stage, the intensity parameters are updated using piecewise linear or nonlinear functions: （4） （5） Where, Δκ i Let c0 and c be the cumulative increments of the internal variables within the current stage i. r , , These are the initial and residual intensity parameters, respectively.

6. The method for constructing a hard rock mechanics model considering three-dimensional stress-dependent brittleness and failure processes as described in claim 3, characterized in that, In step four: (1). Based on the concept of energy equivalence or effective stress, an anisotropic elastic stiffness tensor dependent on integrity is constructed in the principal coordinate system of damage. =f( ), This is expressed as the initial isotropic stiffness E0 calculated and transformed using the elastic stiffness matrix: (6) (2). Establish the law of deformation modulus degradation Define the principal direction σ j The deformation modulus degradation ratio q j =E j / E0, whose evolution with respect to the internal variable κ is described by a negative exponential form: （7） Among them, R j The residual proportion of the modulus in this direction is affected by the stress level, and its fitting parameters A and B are influenced by the stress level. (3). Determine R j Stress dependence, where: （8） Where R2 is the direction of the intermediate principal stress; R s The slope; This is due to the stress difference.

7. The method for constructing a hard rock mechanics model considering three-dimensional stress-dependent brittleness and failure processes as described in claim 6, characterized in that, The obtained constitutive model is integrated into the finite element / finite difference platform, and the following procedure is followed in each computational iteration step: (1). Stress update and yield judgment: Calculate the stress value at this moment based on the given strain increment; Using the current intensity parameter c updated in step three, Calculate the plastic potential function g; (2). Internal variable update and process identification: If in a plastic loading state, calculate the current equivalent plastic strain σ2 and stress level σ3, calculate the current brittleness index Brit and internal variable increment Δκ through step two, and accumulate them to obtain the new κ; according to B c Determine the type of failure process to which the current unit belongs; (3). Parameter synchronous evolution: (3-1) Based on the new κ and the identified destruction process type, update c and c by invoking the rule from step three. ; (3-2) Based on the new κ and the current stress state, update the deformation modulus degradation ratio d in the three principal directions by invoking the rule in step four. j This updates the integrity tensor β and the anisotropic stiffness matrix E. a ; (3-3) Plasticity correction and state output: The final stress state, plastic strain and all updated internal variables satisfying the yield condition and flow law are solved by adopting numerical integration schemes such as the implicit backward Euler method. (3-4) Global Iteration and Failure Analysis: On a global scale, repeat the above steps until the system reaches equilibrium; post-processing indicators such as "Rock Fracture Degree RFD" can be used to visualize and analyze the entire process of fracture initiation, propagation and penetration based on the yield proximity and plastic strain of the elements.

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