Improved Hoek-Brown criterion-based slate softening constitutive model strength prediction method and system

Abstract

The invention discloses an improved Hoek-Brown criterion-based slate softening constitutive model strength prediction method, which comprises the following steps of: respectively introducing water saturation and bedding dip angle parameters on the basis of the traditional Hoek-Brown criterion, correcting by taking the water saturation and bedding dip angle parameters as independent variables influencing rock strength parameters, and constructing an improved constitutive model considering the combined action of environmental conditions and bedding geometry. The model is combined with anisotropic elastic parameters of the layered slate, the change rule of the triaxial compression strength of the slate under the conditions of different water saturations and bedding dip angles can be reflected, and high-precision strength prediction is achieved. Meanwhile, the invention provides a corresponding numerical simulation process which comprises the steps of improved criterion parameter calibration, anisotropic elastic parameter determination, yield criterion construction, software implementation and the like, and a reliable safety evaluation and prediction means is provided for geotechnical engineering.

Description

Technical Field

[0001] The invention relates to the technical field of slate strength prediction, and in particular to a strength prediction method based on an improved Hoek-Brown criterion slate softening constitutive model. Background Art

[0002] The Hoek-Brown strength criterion, an empirical rock mass strength criterion first proposed in 1980, is based on Griffith's theory. By summarizing a large amount of triaxial compression experimental data from various rock types, the Hoek-Brown strength criterion establishes a nonlinear relationship between rock failure strength and confining pressure. Compared with the traditional Mohr-Coulomb strength criterion, the Hoek-Brown criterion more accurately describes the nonlinear failure behavior of rock materials under varying confining pressures. In particular, it effectively avoids the deviations introduced by the Mohr-Coulomb criterion's linear assumptions under high confining pressures.

[0003] With the deepening of rock mass engineering research, the classic Hoek-Brown criterion was revised in the 1990s, introducing a new parameter a to adjust the tensile strength of rock masses under low normal stress conditions, bringing it close to zero. This allows for a more accurate description of the mechanical response of loose, broken, or disturbed rock masses. This generalized Hoek-Brown strength criterion not only improves the accuracy of fitting the nonlinear strength envelope of rock masses but also better adapts to the prediction of the mechanical characteristics of rock masses subjected to strong disturbances such as explosions, vibrations, and tunneling. It also considers the influence of the characteristics of rock mass structural planes and their spatial distribution on the overall strength, expanding its application from intact rock to jointed rock masses and rock masses with complex structures.

[0004] However, for some water-softening layered rocks, such as slate, phyllite, and argillaceous schist, their mechanical properties are significantly affected by water saturation, causing them to soften upon contact with water, leading to a sharp decrease in strength and stiffness. While the existing Hoek-Brown criterion can account for the influence of structural surfaces on rock mass strength, it has yet to effectively incorporate a quantitative description of the softening effect of water saturation on rock. Consequently, existing models struggle to predict the multiaxial strength variations of water-softening layered rocks under varying water saturations and bedding inclinations.

[0005] Therefore, there is an urgent need for a multiaxial strength prediction method that can simultaneously consider the effects of bedding dip and water saturation and is suitable for water-softened rock masses such as layered slate. Summary of the Invention

[0006] Purpose of the invention: In order to overcome the above shortcomings, the purpose of the present invention is to provide a strength prediction method and system based on the improved Hoek-Brown criterion slate softening constitutive model.

[0007] To solve the above technical problems, the present invention provides a strength prediction method based on an improved Hoek-Brown criterion slate softening constitutive model, comprising: S1: Constructing the improved Hoek-Brown strength criterion by combining water saturation parameters and bedding dip parameters; S2: Based on the anisotropic elastic theory, a constitutive model is established to describe the anisotropic elastic behavior of layered slate; S3: Combine the improved Hoek-Brown strength criterion with the constitutive model describing the anisotropic elastic behavior of layered slate and introduce the theory of plasticity to construct a constitutive model for strength prediction of layered slate; S4: Using the constructed softening constitutive model, predict the multiaxial compressive strength of a preset layered slate sample at different water saturations and bedding inclinations.

[0008] In one aspect, in S1, the method comprises: S11: Based on the quadratic polynomial relationship between water saturation and compressive strength, the relationship between the peak strength and water saturation of slate under the same confining pressure and inclination angle is generated: ,in 、 、 is the fitting parameter, is the water saturation, The water saturation is The peak strength of the lower rock, is the peak strength of the rock in the dry state; S12: The relationship between the compressive strength and water saturation of slate is combined with the generalized Hoek-Brown criterion and the water saturation influencing parameter is added: ,in, represents the maximum principal stress, represents the minimum principal stress, The bedding dip is The uniaxial compressive strength of rock in dry state, s, represents the rock block characteristic parameters, The bedding dip angle in dry state is The rock m parameter value, is the parameter that affects the rate at which the peak strength of rock increases with confining pressure.

[0009] On the one hand, in S12, the parameters of the rock in the dry state are , where x is , y is , n is the number of parameters used in the fitting.

[0010] In one aspect, in S2, the method includes: S21: Establish the stress-strain relationship of the elastic body in the local coordinate system: =[ ] ,in, and are the stress matrix and strain matrix in the local coordinate system, respectively. ] is the elastic matrix in the local coordinate system, and its expression is: =M ,in, , , , , The water saturation is w s Elastic modulus, shear modulus, and Poisson's ratio of the lower rock parallel to the bedding direction, The water content is w s Elastic modulus, shear modulus, and Poisson's ratio of the lower rock perpendicular to the bedding direction, The calculation formula is: , The calculation formula is: , is the elastic modulus parallel to the bedding direction in the dry state, is the elastic modulus perpendicular to the bedding direction, 、 、 、 is the fitting parameter; S22: Convert the stress-strain relationship in the local coordinate system to the global coordinate system to obtain: ,in, and are the stress matrix and strain matrix in the global coordinate system, respectively. [D] is the elastic matrix in the global coordinate system, and its expression is: , [L] is the transformation matrix, and its expression is: [L]= ,in , , (i=1, 2, 3) is the cosine of the angle between the global coordinate system and the local coordinate system.

[0011] In one aspect, in S3, the method includes: S31: The improved Hoek-Brown strength criterion is used as the criterion for shear failure: ,in is the shear yield function, is the tensile yield function; S32: Select the maximum tensile stress criterion as the criterion for determining tensile failure: ,in is the tensile strength, .

[0012] In one aspect, in S3, the method further includes: S33: The material is in the elastic stage at the early stage of loading, and its stress-strain increment relationship is: ,in 、 、 are the stress increments in the three principal directions, 、 、 is the strain increment in the three main directions; S34: When the stress state reaches the initial yield surface, the total strain increment includes plastic deformation, and the total strain increment is decomposed into elastic strain and plastic strain: ,in 、 、 is the elastic strain increment in the three main directions, 、 、 is the plastic strain increment in the three main directions; S35: According to the plastic flow law, the plastic strain increments in the three main directions are expressed as: ,in, is the plastic multiplier, is the plastic potential function; S36: Using the associated flow law, the plastic potential function according to the yield criterion is expressed as: ; S37: According to the plastic potential function, the plastic strain increments in the three main directions are: , , ; S38: If plastic strain occurs, the stress increment expression is: , and simplifies it to: ,in , , is the elastic test stress; S39: Substitute the elastic test stress into the yield criterion. If the yield surface is exceeded, the stress is corrected using the stress increment expression.

[0013] In one aspect, the plasticity multiplier is: .

[0014] On the one hand, in S3, when constructing the softening constitutive model for predicting the strength of layered slate, an empirical formula for predicting the compressive strength of layered rock specimens at various inclination angles was introduced: , , , ,in is the uniaxial compressive strength at an azimuth angle of 90°, c is the minimum value of the uniaxial compressive strength at all azimuth angles, and usually takes the smaller value of the uniaxial compressive strength at β = 30° and β = 45°. This value characterizes the uniaxial compressive strength of the rock sample when it fails by sliding along the weak plane.

[0015] In one aspect, in S4, the method includes: The goodness of fit R2 error index is used to evaluate the multiaxial compressive strength prediction results: ,in, is the number of triaxial compression test data, predop and test rp are the predicted and experimental values ​​of the peak stress of layered rock mass under different bedding plane inclinations and confining pressures, is the average value of the peak stress test values ​​of layered rock mass under different bedding plane inclinations and confining pressures.

[0016] The present application also provides a strength prediction system based on an improved Hoek-Brown criterion slate softening constitutive model using the method, comprising: Criterion improvement module, used to construct an improved Hoek-Brown strength criterion by combining water saturation parameters and bedding dip parameters; Elastic building block, used to build a constitutive model describing the anisotropic elastic behavior of slate based on anisotropic elastic theory; A softening construction module is used to combine the improved Hoek-Brown strength criterion with the constitutive model describing the anisotropic elastic behavior of layered slate and introduce it into the theory of plasticity to construct a softening constitutive model for strength prediction of layered slate; The strength prediction module is used to predict the multiaxial compressive strength of a preset layered slate sample under different water saturations and bedding inclinations using the constructed softening constitutive model.

[0017] The above technical solution of the present application has the following advantages over the prior art: 1. This application introduces water saturation and bedding dip parameters based on the Hoek-Brown strength criterion, achieving a quantitative prediction of the strength changes of layered slate under different environmental conditions. Experimental results show that the goodness of fit (R²) between the predicted values ​​of this application and the results of indoor triaxial compression tests is generally higher than 0.98, significantly outperforming traditional models and meeting the needs of engineering design for high-precision rock strength assessment.

[0018] 2. This application couples the anisotropic characteristics of rocks with the softening effect upon contact with water. By introducing the strength anisotropy coefficient and the water saturation correction function, it comprehensively reflects the sensitivity of the strength of layered slate to the bedding structure and environmental humidity, overcoming the defect that the traditional Hoek-Brown strength criterion cannot take both into account at the same time.

[0019] 3. The softening constitutive model of layered slate was written into the FLAC3D software for secondary development, and numerical simulations of layered slate specimens under different confining pressures and bedding plane inclinations were carried out. The simulation results show that the developed softening constitutive model of layered slate can effectively reflect the anisotropic characteristics of layered slate. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0021] Figure 1 Schematic diagram of the relationship between the global coordinate system and the local coordinate system provided by an embodiment of the present invention.

[0022] Figure 2 It is a numerical simulation schematic diagram of a layered rock specimen provided by an embodiment of the present invention.

[0023] Figure 3 It is a schematic diagram of the results of the finite element numerical simulation test provided by the embodiment of the present invention.

[0024] Figure 4 It is a schematic diagram of the results of the discrete element numerical simulation test provided by the embodiment of the present invention.

[0025] Figure 5 It is a schematic diagram of fitting the formula to the triaxial test results of different water saturations at 0° provided by an embodiment of the present invention.

[0026] Figure 630° is a schematic diagram of fitting the triaxial test results of different water saturations to the formula provided by an embodiment of the present invention.

[0027] Figure 7 It is a schematic diagram of fitting the formula to the triaxial test results of different water saturations at 45° provided by an embodiment of the present invention.

[0028] Figure 8 1 is a schematic diagram of fitting the formula to the triaxial test results of different water saturations at 60° provided by an embodiment of the present invention.

[0029] Figure 9 1 is a schematic diagram of fitting the formula to the triaxial test results of different water saturations at 90° provided by an embodiment of the present invention.

[0030] Figure 10 It is a schematic diagram of a fitting image for predicting the compressive strength values ​​of other angles using the simplified formula provided in an embodiment of the present invention.

[0031] Figure 11 It is a flow chart of a strength prediction method based on an improved Hoek-Brown criterion slate softening constitutive model provided by an embodiment of the present invention.

[0032] Figure 12 Schematic diagram of module connections of a strength prediction system based on an improved Hoek-Brown criterion slate softening constitutive model provided by an embodiment of the present invention.

[0033] Description of the accompanying drawings: 101. Criterion improvement module, 102. Elasticity construction module, 103. Softening construction module, 104. Strength prediction module. DETAILED DESCRIPTION

[0034] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0035] The Hoek-Brown strength criterion, an empirical rock mass strength criterion, was first proposed in 1980. It is based on Griffith's theory and a wealth of rock experimental data. The classic Hoek-Brown strength criterion is primarily used to describe the failure behavior of rock under varying confining pressures. It effectively reflects the nonlinear failure characteristics of rock and compensates for the shortcomings of the Mohr-Coulomb strength criterion under its linear assumption.

[0036] The expression of the narrow Hoek-Brown intensity criterion is: ,in represents the maximum principal stress, represents the minimum principal stress, It represents the uniaxial compressive strength of the rock mass and can be measured through experiments; m is a rock parameter, and its value range is generally 3~44; s is a parameter that reflects the rock mass fragmentation. The more intact the rock mass, the larger the value, and its value range is 0~1, s=1 (m and s are both empirical parameters).

[0037] With the advancement of rock mass engineering research, the classic criterion was revised in the 1990s with the introduction of a new parameter, a, which allows the tensile strength of rock masses under low normal stress conditions to be zero, thereby more accurately describing the mechanical behavior of loose or broken rock masses. The generalized Hoek-Brown strength criterion demonstrates greater adaptability in dealing with rock masses damaged by explosions or subjected to significant disturbances. It also considers the influence of rock mass structural planes and their distribution, broadening the criterion's scope of application.

[0038] The generalized Hoek-Brown strength criterion expression is: ,in It represents the uniaxial compressive strength of the rock block, which can be measured through experiments; m is the rock parameter, and s and a represent the characteristic parameters of the rock block.

[0039] For the relationship between the strength of various anisotropic rocks, the constant and s, and established the relationship between the constant and the inclination angle: , , , , where N1, P, N2, N3, P2, and P3 are constants.

[0040] However, because the above formula has many parameters, it requires a lot of experiments to solve, and ignores the change of uniaxial compressive strength with anisotropy, resulting in inaccurate calculation results. In order to improve this, Saroglou and Tsiambaos (2008) proposed a new parameter - strength anisotropy coefficient, which can accurately reflect the effect of strength anisotropy on rock strength. The new strength criterion describes the effect of anisotropy on strength through two parameters: one is the change of uniaxial compressive strength with loading angle, and the other represents the variation between the maximum and minimum values ​​of rock strength. Introducing a new parameter that can reflect the anisotropy of rock strength ,in for Bedding dip parameters value, For bedding with a 90° dip value.

[0041] The revised strength criterion formula is as follows: in, represents the maximum principal stress, represents the minimum principal stress, It represents the uniaxial compressive strength of the rock block, which can be measured by experiment; m is the rock parameter, s and a represent the characteristic parameters of the rock block, is a parameter describing the anisotropy of rocks. ,in for The m parameter of the sample under the bedding dip, is the m parameter of the sample at an inclination angle of 90°.

[0042] This modified form can better express the changes in uniaxial compressive strength caused by anisotropy. By fitting triaxial test data at different angles, it can accurately reflect the strength behavior of anisotropic rocks under different conditions. However, for some layered rocks that are easily softened by water, such as slate, they are anisotropic and soften when exposed to water. If you want to predict the properties of such rocks, you must consider the influence of water. From the above content, it can be seen that water saturation and compressive strength are in a quadratic polynomial relationship. That is, under the same confining pressure and inclination angle, the relationship between the peak strength of slate and water saturation can be expressed as: ,in , , is the fitting parameter, is the water saturation, The water saturation is The peak strength of the lower rock, is the peak strength of the rock in dry state.

[0043] Combining it with the generalized Hoek-Brown criterion and adding the water saturation influencing parameter h, the following formula can be obtained: ,in, represents the maximum principal stress; Represents the minimum principal stress: The bedding dip is The uniaxial compressive strength of rock in dry state; s, Represents the characteristic parameters of rock blocks. The bedding dip angle in dry state is The rock m parameter value; is the parameter that affects the rate at which the peak strength of rock increases with confining pressure due to water saturation; , , is the fitting parameter. The Hoek-Brown intensity criterion considering water saturation can be found in Peak intensity of samples with different water saturation at different angles. Can be obtained from uniaxial test; s, are empirical parameters, and for intact rocks, the values ​​are s=1 and a=0.5; , , , Derived from the test data fitting. It can be calculated by the following formula: , where = , = , n The number of parameters used for the fit.

[0044] Therefore, the above completion combines the water saturation parameter and the bedding dip parameter to construct the improved Hoek-Brown strength criterion.

[0045] Furthermore, based on the above-mentioned improved Hoek-Brown strength criterion, a softening constitutive model of layered slate is established. The specific process is as follows: First, for the elastic stage, the anisotropy of geomaterials is generally studied using the generalized Hooke's law, in which the strain increment is a linear function of the stress increment, and the global coordinate system ( x , y , z ) and the local coordinate system ( x' , y' , z' )like Figure 1 As shown, z Axis as the axis of symmetry, along x Axis rotation Angle, the global coordinate system can be converted into the local coordinate system.

[0046] In the local coordinate system, the stress-strain relationship of the elastic body is: =[ ] ,in, and are the stress matrix and strain matrix in the local coordinate system, respectively. ] is the elastic matrix in the local coordinate system, and its expression is: =M ,in, , , , , where The water saturation is w s Elastic modulus, shear modulus, and Poisson's ratio of the lower rock parallel to the bedding direction, The water content isw s The elastic modulus, shear modulus and Poisson's ratio of the lower rock perpendicular to the bedding direction have small differences in the Poisson's ratio values ​​of the samples at the same inclination angle. In order to simplify the calculation, the Poisson's ratio is taken as the value in the dry state.

[0047] From the above content, we can know that the elastic modulus and water content are in a linear function relationship, so , ,in is the elastic modulus parallel to the bedding direction in the dry state, is the elastic modulus perpendicular to the bedding direction , , , is the fitting parameter.

[0048] Convert the stress-strain relationship in the local coordinate system to the global coordinate system to obtain: ,in, and are the stress matrix and strain matrix in the global coordinate system, respectively. [D] is the elastic matrix in the global coordinate system, and its expression is: , [L] is the transformation matrix, and its expression is: [L]= ,in , , (i=1, 2, 3) is the cosine of the angle between the global coordinate system and the local coordinate system.

[0049] Secondly, in elastic-plastic mechanics analysis, the yield criterion is used to define the critical stress condition for the material to transition from elastic deformation to plastic deformation. For rock materials, their failure mechanisms are generally manifested in two basic forms: shear failure and tensile failure. When constructing the elastic-plastic constitutive model of slate under water-rock coupling, the Hoek-Brown strength criterion considering water saturation is used as the basis for judging shear failure, while the maximum tensile stress criterion is used as the basis for tensile failure. The expression is: ,in is the shear yield function, is the tensile yield function; ,in is the tensile strength, .

[0050] Again, for the plastic stage, the material is considered to be in the elastic stage at the early stage of loading, and its stress-strain increment relationship is: ,in 、 、 are the stress increments in the three principal directions, 、 、 are the strain increments in the three principal directions.

[0051] When the stress state reaches the initial yield surface, the total strain increment will include plastic deformation, and the total strain increment can be decomposed into elastic strain and plastic strain: ,in 、 、 is the elastic strain increment in the three main directions, 、 、 is the plastic strain increment in the three main directions; According to the plastic flow law, the plastic strain increments in the three main directions can be expressed as: ,in, is the plastic multiplier, is the plastic potential function.

[0052] Using the associated flow law, the plastic potential function is expressed according to the yield criterion as follows: .

[0053] According to the plastic potential function, the plastic strain increments in the three main directions are: , , .

[0054] If plastic strain occurs, the stress increment can be expressed as: , and simplifies it to: ,in , , is the elastic test stress, which can be obtained using Hooke's law. Substitute the elastic test stress into the yield criterion. If it exceeds the yield surface, the stress needs to be corrected using the stress increment expression.

[0055] According to the above formula, the plasticity multiplier is: .

[0056] Thus, the construction of the softening constitutive model for the strength prediction of layered slate is completed.

[0057] Furthermore, after completing the construction of the softening constitutive model of layered slate, secondary development and verification were carried out, specifically: First, the constitutive model was developed within LAC3D. LAC3D is written in the standard object-oriented C++ language. All constitutive models are provided to users as dynamic link libraries (.dll files). During numerical simulations, the main program automatically calls the specified constitutive model dynamic link library file. The .dll file for the custom constitutive model in this paper was compiled in Visual Studio 2015 and then executed by the main program.

[0058] FLAC3D is implemented based on the C++ object-oriented programming architecture, and its built-in constitutive models are all encapsulated in the form of dynamic link libraries (DLL files). During the numerical calculation process, the computing core automatically calls the corresponding constitutive model library file through a dynamic loading mechanism. The custom constitutive model developed in this study was compiled and generated using the Visual Studio 2015 development environment. This study uses the laniso model and Hoek model built into FLAC3D as the development basis, and realizes the constitutive modeling suitable for slate characteristics by integrating the water-rock coupling equations obtained by derivation. The specific development process includes three key steps: (1) adjusting the parameter definitions in the model header file (.h); (2) rewriting the calculation logic in the source code (.cpp); and (3) finally compiling and generating an executable dynamic link library file. In addition, a dynamic parameter calculation program based on the improved layered slate softening constitutive model was written in Python. It can quickly calculate the dynamic parameters that change with the bedding inclination and output the FLAC3D parameter setting code to facilitate actual modeling work.

[0059] Secondly, in C++ programming, the header file (.h) plays a key role in defining the class architecture of the material constitutive model. Its contents include base class declarations, model naming rules, externally callable function interfaces, and private data members within the class. To modify the header file, you first need to rename the base class name. First, import the header files of the Anisotropic constitutive model and the Hoek constitutive model. Rename the base class name and change Modelhoek to Modelhoek-water. Then, use public ModelAnisotropic in the header file of the Modelhoek-water constitutive model to inherit the Anisotropic constitutive model, thereby calling its anisotropic elastic property calculation method. Then modify the private variables in the header file. Compared with the original model, the variables w_, h_, A0_, B0_, C0_, AE0_, BE0_, AE90_, and BE90_ have been added. These correspond to the parameters in the slate constitutive model under water-rock coupling. , , , , , , , .

[0060] In the C++ program implementation, the core functions of the source file (.cpp) include configuring the constitutive model input parameters, performing state evaluation of finite element elements, initializing computational variables, and implementing key computational processes during the iterative process of the nonlinear solution. Modifications were made in the following areas: First, adjustments were made to parameter assignment, return value, copy, and initialization functions, including those in GetProperty(), SetProperty(), Copy(), and Initialize(). Due to the addition of new parameters to the namespace and the introduction of parameters related to the anisotropic constitutive model, the corresponding new parameters needed to be added to these functions simultaneously. The order of parameters within each function also needed to be consistent to prevent parameter transfer errors. To accurately simulate the mechanical properties of slate under water-rock coupling, the constitutive calculation logic of the Run() function needed to be optimized. Based on the formulas derived in this paper, the yield surface function and plastic increment calculation components of the Hoek constitutive model were adjusted to accurately characterize the plastic deformation characteristics under water-rock coupling. At the same time, the ModelAnisotropic::AnisotropicElasticTrial(s) function is called in the elastic calculation stage to introduce the calculation method of the anisotropic constitutive model to reflect the anisotropy of the material.

[0061] After programming is complete, the code needs to be compiled and debugged to ensure that all functions execute correctly and meet the FLAC3D constitutive model interface requirements. Successful compilation will generate a dynamic link library (.dll) file. This file must be copied to the Itasca\exe64\plugins\cmodel directory within the FLAC3D installation directory. This directory is where FLAC3D's default custom constitutive model is stored. Then, execute the `model configureplugin` command in the FLAC3D command window. The software will automatically search for all dynamic link libraries in the `cmodel` directory and call the custom constitutive model for analysis.

[0062] The triaxial compression test was carried out to verify the softening constitutive model of layered slate developed by the secondary development. In order to verify whether the developed anisotropic damage constitutive model of layered rock mass is written successfully and its anisotropic characteristics, a triaxial compression finite element numerical simulation of layered rock mass was carried out. The size of the layered rock mass specimen in the numerical simulation is the same as that of the indoor test specimen, that is, the reference Figure 2The numerical model shown here was built based on standard laboratory specimen dimensions, employing a cylindrical geometry with a diameter of 50 mm and a height of 100 mm, divided into 7500 computational cells. The constitutive relationship for the specimen in the numerical model utilizes an elastic-plastic constitutive model for slate that accounts for water-bedding coupling. By adjusting the model parameters, the mechanical properties of slate specimens under varying bedding angles and water saturations were simulated. Loading was applied using a strain-controlled method, with the loading rate consistent with both discrete element simulations and laboratory tests.

[0063] The calculation parameters of the constitutive model are shown in the following table: Fixed parameter table Dynamic parameter table The fixed parameter table is the fixed parameters of the rock sample that do not change with the inclination angle, and the dynamic parameter table is the dynamic parameters that change with the bedding inclination angle.

[0064] The samples with bedding plane dip angles of 0° and 60° were selected, and the results of finite element numerical simulation and discrete element numerical simulation tests were compared under water saturations of 0, 0.3, 0.6, and 0.9 and confining pressures of 0, 5, 10, and 20 MP, as shown in Figure 2. Figure 3 and Figure 4 shown.

[0065] It can be found that the softening constitutive model of layered slate is very close to the results of discrete element numerical simulation. Its compressive strength gradually decreases with the increase of water saturation and gradually increases with the increase of confining pressure. Its growth rate gradually decreases with the increase of confining pressure. Its elastic modulus also gradually decreases with the increase of water saturation and increases slightly with the increase of confining pressure. The change trend is similar to the results of discrete element numerical simulation. This shows that the secondary developed softening constitutive model of layered slate can better reflect the mechanical characteristics of layered slate under different water saturations.

[0066] Therefore, the softening constitutive model of layered slate can be actually deployed, so as to use the constructed softening constitutive model to predict the multiaxial compressive strength of the layered slate samples specified by the test personnel under different water saturations and bedding inclinations.

[0067] Specifically, after prediction, the goodness of fit R 2 Error index is used to evaluate the prediction results of triaxial compressive strength of layered slate specimens: ,in, is the number of triaxial compression test data, predop and test rp are the predicted and experimental values ​​of the peak stress of the layered slate specimens under different bedding plane inclinations and confining pressures, respectively. is the average value of the peak stress test values ​​of layered slate specimens under different bedding plane inclinations and confining pressures.

[0068] Origin 2022 was used to fit the formula using triaxial test results at different angles and different water saturations. The results are shown in the figure below. Figures 5 to 9 As shown. You can see its R 2 They are all above 0.98, indicating that the softening constitutive model of layered slate including the Hoke-Brown strength criterion with water saturation can well predict the peak strength of layered slate.

[0069] In order to further predict the strength changes of samples at different inclination angles, the empirical formula for predicting the compressive strength of layered rock samples at various inclination angles is used as a reference: , , , ,in is the uniaxial compressive strength at an azimuth angle of 90°, which is determined by uniaxial compression tests at different azimuth angles; c is the minimum value of the uniaxial compressive strength at all azimuth angles, usually the smaller value of the uniaxial compressive strength at β = 30° and β = 45°. This value characterizes the uniaxial compressive strength of the rock sample when it fails by sliding along the weak plane. The values ​​of m and n in the formula can be decimals, similar to the above m and n, which characterize the anisotropy type of the rock.

[0070] When the number of specimens with different inclination angles is insufficient, m=n can be set to simplify the calculation, and the compressive strength values ​​of the remaining angles can be predicted using the formula. The fitting image is as follows: Figure 10 As shown, the fitting parameter results and the goodness of fit R 2 As shown in the following table: You can see that the goodness of fit R for most data sets 2 All of them are above 0.98, and a few data are 0.96, which shows that the empirical formula can well predict the peak strength of slate at different inclination angles.

[0071] Observing the relationship between the fitting parameter m, water saturation, and confining pressure, it is inversely proportional to water saturation and has little to do with confining pressure. Therefore, the calculations were further simplified by replacing the m values ​​at different confining pressures with the m values ​​obtained for the uniaxial state at the respective water saturations. The confining pressure values ​​at different water saturations were linearly interpolated using the values ​​obtained for the dry and saturated states. The results of this refitting are shown in the following table: It can be seen that after the simplified m value, the goodness of fit R of most data groups is 2All of them are above 0.97, and a small amount of data is 0.93, which shows that the simplified empirical formula can well predict the peak strength of slate at different inclination angles.

[0072] Therefore, reference Figure 11 In accordance with the above content, the present application relates to a strength prediction method for slate softening constitutive model based on an improved Hoek-Brown criterion, comprising the following steps: S1: Constructing the improved Hoek-Brown strength criterion by combining water saturation parameters and bedding dip parameters; S2: Based on the anisotropic elastic theory, a constitutive model is established to describe the anisotropic elastic behavior of layered slate; S3: Combine the improved Hoek-Brown strength criterion with the constitutive model describing the anisotropic elastic behavior of layered slate and introduce the theory of plasticity to construct a constitutive model for strength prediction of layered slate; S4: Using the constructed softening constitutive model, predict the multiaxial compressive strength of a preset layered slate sample at different water saturations and bedding inclinations.

[0073] Therefore, reference Figure 12 As shown and described above, the present application also relates to a strength prediction system based on an improved Hoek-Brown criterion slate softening constitutive model using the above method, comprising: Criterion improvement module 101, used to construct an improved Hoek-Brown strength criterion by combining water saturation parameters and bedding dip parameters; The elastic construction module 102 is used to establish a constitutive model describing the anisotropic elastic behavior of slate based on anisotropic elastic theory; A softening construction module 103 is used to combine the improved Hoek-Brown strength criterion with the constitutive model describing the anisotropic elastic behavior of layered slate and introduce the plasticity mechanics theory to construct a softening constitutive model for predicting the strength of layered slate; The strength prediction module 104 is used to predict the multiaxial compressive strength of a preset layered slate sample at different water saturations and bedding inclinations using the constructed softening constitutive model.

[0074] In some embodiments of the present application, the present application also relates to a computer medium having a computer program stored thereon, and the computer program is executed by a processor to implement the above-mentioned strength prediction method based on the improved Hoek-Brown criterion slate softening constitutive model.

[0075] In some embodiments of the present application, the present application also relates to a computer, including the computer medium described above.

[0076] In the description of this specification, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and features of different embodiments or examples without contradiction.

[0077] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A strength prediction method based on the improved Hoek-Brown criterion slate softening constitutive model, characterized in that: The following steps are involved: S1: Constructing an improved Hoek-Brown strength criterion by combining water saturation and bedding dip parameters; S2: Based on the anisotropic elastic theory, a constitutive model is established to describe the anisotropic elastic behavior of layered slate; S3: The improved Hoek-Brown strength criterion is combined with the constitutive model describing the anisotropic elastic behavior of layered slate and introduced into the theory of plasticity to construct a softening constitutive model for strength prediction of layered slate. S4: Using the constructed softening constitutive model, predict the multiaxial compressive strength of a preset layered slate sample at different water saturations and bedding inclinations.

2. The strength prediction method based on the improved Hoek-Brown criterion slate softening constitutive model according to claim 1, characterized in that: In S1, the method comprises: S11: Based on the quadratic polynomial relationship between water saturation and compressive strength, the relationship between the peak strength and water saturation of slate under the same confining pressure and inclination angle is generated: ,in 、 、 is the fitting parameter, is the water saturation, The water saturation is The peak strength of the lower rock, is the peak strength of the rock in the dry state; S12: The relationship between the compressive strength and water saturation of slate is combined with the generalized Hoek-Brown criterion and the water saturation influencing parameter is added: , where water saturation represents the maximum principal stress, represents the minimum principal stress, The bedding dip is The uniaxial compressive strength of rock in dry state, s, represents the rock block characteristic parameters, The bedding dip angle in dry state is The rock m parameter value, is the parameter that affects the rate at which the peak strength of rock increases with confining pressure.

3. The strength prediction method based on the improved Hoek-Brown criterion slate softening constitutive model according to claim 2, characterized in that: In S12, the parameters of the rock in the dry state are , where x is , y is , n is the number of parameters used in the fitting.

4. The strength prediction method based on the improved Hoek-Brown criterion slate softening constitutive model according to claim 3 is characterized in that: In S2, the method comprises: S21: Establish the stress-strain relationship of the elastic body in the local coordinate system: =[ ] ,in, and are the stress matrix and strain matrix in the local coordinate system, respectively. ] is the elastic matrix in the local coordinate system, and its expression is: =M ,in, , , , , The water saturation is w s Elastic modulus, shear modulus, and Poisson's ratio of the lower rock parallel to the bedding direction, The water content is w s Elastic modulus, shear modulus, and Poisson's ratio of the lower rock perpendicular to the bedding direction, The calculation formula is: , The calculation formula is: , is the elastic modulus parallel to the bedding direction in the dry state, is the elastic modulus perpendicular to the bedding direction, 、 、 、 is the fitting parameter; S22: Convert the stress-strain relationship in the local coordinate system to the global coordinate system to obtain: ,in, and are the stress matrix and strain matrix in the global coordinate system, respectively. [D] is the elastic matrix in the global coordinate system, and its expression is: , [L] is the transformation matrix, and its expression is: [L]= ,in , , (i=1, 2, 3) is the cosine of the angle between the global coordinate system and the local coordinate system.

5. The strength prediction method based on the improved Hoek-Brown criterion slate softening constitutive model according to claim 4, characterized in that: In S3, the method includes: S31: The improved Hoek-Brown strength criterion is used as the criterion for shear failure: ,in is the shear yield function, is the tensile yield function; S32: Select the maximum tensile stress criterion as the criterion for determining tensile failure: ,in is the tensile strength, .

6. The strength prediction method based on the improved Hoek-Brown criterion slate softening constitutive model according to claim 5, characterized in that: In S3, the method further includes: S33: The material is in the elastic stage at the early stage of loading, and its stress-strain increment relationship is: ,in 、 、 are the stress increments in the three principal directions, 、 、 is the strain increment in the three main directions; S34: When the stress state reaches the initial yield surface, the total strain increment includes plastic deformation, and the total strain increment is decomposed into elastic strain and plastic strain: ,in 、 、 is the elastic strain increment in the three main directions, 、 、 is the plastic strain increment in the three main directions; S35: According to the plastic flow law, the plastic strain increments in the three main directions are expressed as: ,in, is the plastic multiplier, is the plastic potential function; S36: Using the associated flow law, the plastic potential function according to the yield criterion is expressed as: ； S37: According to the plastic potential function, the plastic strain increments in the three main directions are: ， ， ； S38: If plastic strain occurs, the stress increment expression is: , and simplifies it to: ,in , , is the elastic test stress; S39: Substitute the elastic test stress into the yield criterion. If the yield surface is exceeded, the stress is corrected using the stress increment expression.

7. The strength prediction method based on the improved Hoek-Brown criterion slate softening constitutive model according to claim 6, characterized in that: The plastic multiplier is: 。 8. The strength prediction method based on the improved Hoek-Brown criterion slate softening constitutive model according to claim 1 or 7, characterized in that: In S3, when constructing the softening constitutive model for predicting the strength of layered slate, the empirical formula for predicting the compressive strength of layered rock samples at various inclination angles was introduced: ， ， , ,in is the uniaxial compressive strength at an azimuth angle of 90°, c is the minimum value of the uniaxial compressive strength at all azimuth angles, and usually takes the smaller value of the uniaxial compressive strength at β = 30° and β = 45°. This value characterizes the uniaxial compressive strength of the rock sample when it fails by sliding along the weak plane.

9. The strength prediction method based on the improved Hoek-Brown criterion slate softening constitutive model according to claim 1 or 7, characterized in that: In S4, the method includes: The goodness of fit R2 error index is used to evaluate the multiaxial compressive strength prediction results: ,in, is the number of triaxial compression test data, predop and test rp are the predicted and experimental values ​​of the peak stress of layered rock mass under different bedding plane inclinations and confining pressures, is the average value of the peak stress test values ​​of layered rock mass under different bedding plane inclinations and confining pressures.

10. A strength prediction system based on an improved Hoek-Brown criterion slate softening constitutive model using the method according to any one of claims 1 to 9, characterized in that: include: Criterion improvement module, used to construct an improved Hoek-Brown strength criterion by combining water saturation parameters and bedding dip parameters; Elastic building block, used to build a constitutive model describing the anisotropic elastic behavior of slate based on anisotropic elastic theory; A softening construction module is used to combine the improved Hoek-Brown strength criterion with the constitutive model describing the anisotropic elastic behavior of layered slate and introduce it into the theory of plasticity to construct a softening constitutive model for strength prediction of layered slate; The strength prediction module is used to predict the multiaxial compressive strength of a preset layered slate sample under different water saturations and bedding inclinations using the constructed softening constitutive model.

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