Bonding unit constitutive model parameter calibration method

Abstract

The invention discloses a cohesive unit constitutive model parameter calibration method, and relates to the technical field of rock mechanics numerical simulation. According to the bonding unit constitutive model parameter calibration method, a nonlinear bonding unit constitutive curve is replaced by a linear peak front segment segmentation curve and a peak rear segment segmentation curve, and a peak rear segment tension strain ratio and a peak rear segment shear strain ratio are used for associating peak rear segment displacement and peak front segment displacement. Through a Brazilian splitting test, a uniaxial compression test and a triaxial compression test, the cohesive force, the internal friction angle and the tensile strength data of the bonding unit are obtained, and the numerical values of the post-peak tensile strain ratio and the post-peak shear strain ratio are adjusted; enabling the peak intensity obtained by constitutive simulation of the bonding unit to be consistent with the data of the Brazilian splitting test, the uniaxial compression test and the triaxial compression test, and repeating the steps to obtain the optimal values of the post-peak tensile strain ratio and the post-peak shear strain ratio. According to the bonding unit constitutive model parameter calibration method, the calibration workload and difficulty are reduced, and the calculation efficiency is effectively improved.

Description

Technical Field

[0001] This application relates to the technical field of numerical simulation of rock mechanics, and more particularly, to a method for calibrating the constitutive model parameters of cohesive elements. Background Art

[0002] In rock fracture simulation, cohesive elements are often inserted into adjacent solid elements, and the initiation and propagation of cracks are simulated through the fracture of cohesive elements. However, the existing constitutive models of cohesive elements have the following problems: First, the parameter calibration is complex. All five parameters of the cohesive element (cohesion, internal friction angle, tensile strength, mode I fracture energy, mode II fracture energy) need to be obtained through cumbersome calibration and cannot directly use experimental values, resulting in cumbersome calibration of the constitutive model of cohesive elements. Second, the physical meaning is not clear. The fracture energy parameter of the cohesive element lacks a clear physical meaning and has a weak correlation with macroscopic mechanical behavior, resulting in low calibration efficiency. Third, the calculation efficiency is low. The constitutive model of the cohesive element adopts a non-linear post-peak curve, resulting in high computational complexity and limiting engineering applications.

[0003] Therefore, a method for calibrating the constitutive model parameters of cohesive elements with low calibration difficulty and high calculation efficiency is needed. Summary of the Invention

[0004] The purpose of this application is to provide a method for calibrating the constitutive model parameters of cohesive elements, which reduces the calibration workload and difficulty, effectively improves the calculation efficiency, and facilitates users to adjust the parameter values according to the macroscopic mechanical behavior of numerical specimens.

[0005] This application is implemented as follows:

[0006] This application provides a method for calibrating the constitutive model parameters of cohesive elements, including the following steps:

[0007] Replace the non-linear constitutive curve of the cohesive element with a linear pre-peak segmented curve and a post-peak segmented curve;

[0008] Use the post-peak tensile strain ratio and the post-peak shear strain ratio to correlate the post-peak displacement with the pre-peak displacement;

[0009] Obtain the cohesion, internal friction angle, and tensile strength data of the cohesive element through Brazilian split test, uniaxial compression test, and triaxial compression test;

[0010] Adjust the values of the post-peak tensile strain ratio and the post-peak shear strain ratio so that the peak strength obtained from the constitutive simulation of the cohesive element is consistent with the data of the Brazilian split test, uniaxial compression test, and triaxial compression test;

[0011] Repeat the above steps to obtain the optimal values of the post-peak tensile strain ratio and the post-peak shear strain ratio.

[0012] In some alternative embodiments, both the pre-peak segmented curve and the post-peak segmented curve are straight lines.

[0013] In some alternative embodiments, the post-peak tensile strain ratio is the ratio of the post-peak tensile strain to the total pre-peak strain.

[0014] In some alternative embodiments, the post-peak shear strain ratio is the ratio of the post-peak shear strain to the total pre-peak strain.

[0015] In some alternative embodiments, replacing the non-linear constitutive curve of the cohesive element with the linear pre-peak segmented curve and post-peak segmented curve includes the following steps:

[0016] Calculate the damage variable D of the cohesive element according to the following formula:

[0017]

[0018] In the formula, D is the damage variable of the cohesive element; o is the normal displacement of the cohesive element; s is the tangential displacement of the cohesive element; ο p is the critical normal opening amount of the cohesive element; s p is the critical tangential displacement amount of the cohesive element; ο t is the difference between the normal opening displacement at pure tensile failure of the cohesive element and the critical normal opening amount; s t is the difference between the tangential displacement at pure shear failure of the cohesive element and the critical tangential displacement amount; when D > 1, take D = 1;

[0019] Calculate the reduction coefficient f(D) of the tangential stress and normal stress of the cohesive element according to the following formula: f(D) = (1 - D); in the formula, D is the damage variable of the cohesive element;

[0020] Calculate the normal stress and tangential stress of the cohesive element according to the following formula:

[0021]

[0022] In the formula, σ is the normal stress of the cohesive element; τ coh is the tangential stress of the cohesive element; o is the normal displacement of the cohesive element; ο p is the critical normal opening amount of the cohesive element; s is the tangential displacement of the cohesive element; s p is the critical tangential displacement amount of the cohesive element; f t is the tensile strength of the cohesive element; φ is the internal friction angle of the cohesive element; c is the cohesion of the cohesive element.

[0023] In some alternative embodiments, the critical normal opening amount ο of the cohesive element is calculated using the following formula p :

[0024]

[0025] In the formula, f t is the tensile strength of the bonding unit; P f is the normal parameter of the bonding unit; h is the length of the bonding unit.

[0026] In some alternative embodiments, the critical tangential displacement s of the bonding unit is calculated using the following formula p :

[0027]

[0028] In the formula, f S is the shear strength of the bonding unit; P f is the normal parameter of the bonding unit; h is the length of the bonding unit.

[0029] In some alternative embodiments, when correlating the post-peak displacement with the pre-peak displacement using the post-peak tensile strain ratio, the following formula is used:

[0030]

[0031] In the formula, ο t is the difference between the normal opening displacement of the bonding unit at the time of pure tensile failure minus the critical normal opening amount, r o is the post-peak tensile strain ratio; ο p is the critical normal opening amount of the bonding unit; P f is the normal parameter of the bonding unit; E is the elastic modulus.

[0032] In some alternative embodiments, when correlating the post-peak displacement with the pre-peak displacement using the post-peak shear strain ratio, the following formula is used:

[0033]

[0034] In the formula, s t is the difference between the tangential displacement of the bonding unit at the time of pure shear failure minus the critical tangential displacement amount; r s is the post-peak shear strain ratio; s p is the critical tangential displacement amount of the bonding unit; P f is the normal parameter of the bonding unit; G is the shear modulus.

[0035] The beneficial effects of the present application are as follows: The method for calibrating the constitutive model parameters of the bonding unit provided by the present application replaces the non-linear constitutive curve of the bonding unit with a linear segmented curve in the pre-peak section and a linear segmented curve in the post-peak section. The post-peak tensile strain ratio and the post-peak shear strain ratio are used to relate the post-peak displacement to the pre-peak displacement. The cohesion, internal friction angle, and tensile strength data of the bonding unit are obtained through the Brazilian splitting test, uniaxial compression test, and triaxial compression test. The values of the post-peak tensile strain ratio and the post-peak shear strain ratio are adjusted so that the peak strength obtained from the constitutive simulation of the bonding unit is consistent with the data from the Brazilian splitting test, uniaxial compression test, and triaxial compression test. By repeating the above steps, the optimal values of the post-peak tensile strain ratio and the post-peak shear strain ratio are obtained. The method for calibrating the constitutive model parameters of the bonding unit provided by the present application only needs to calibrate two parameters, namely the post-peak tensile strain ratio and the post-peak shear strain ratio, thus greatly reducing the calibration workload and difficulty, effectively improving the calculation efficiency, and facilitating users to adjust the parameter values according to the macroscopic mechanical behavior of the numerical specimen. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present application and should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0037] Figure 1 It is a schematic flow chart of the method for calibrating the constitutive model parameters of the bonding unit provided by the embodiment of the present application;

[0038] Figure 2 It is the segmented curve in the pre-peak section and the segmented curve in the post-peak section obtained after the tensile replacement of the constitutive model of the bonding unit provided by the embodiment of the present application;

[0039] Figure 3 It is the segmented curve in the pre-peak section and the segmented curve in the post-peak section obtained after the shear replacement of the constitutive model of the bonding unit provided by the embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some, but not all, of the embodiments of the present application.

[0041] Accordingly, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the claimed present application, but merely represents selected embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts fall within the scope of protection of the present application.

[0042] The following further describes in detail the characteristics and performance of the method for calibrating the constitutive model parameters of the bonding unit of the present application in combination with embodiments.

[0043] As Figure 1 shown, an embodiment of the present application provides a method for calibrating the constitutive model parameters of a bonding unit, including the following steps:

[0044] S1. Linearize the pre-peak and post-peak segments; replace the existing non-linear constitutive curve of the bonding unit with a linear pre-peak segmented curve and a linear post-peak segmented curve; wherein, both the pre-peak segmented curve and the post-peak segmented curve are straight lines.

[0045] Specifically, it includes the following steps:

[0046] S11. According to the relationship between the normal displacement of the bonding unit and the tangential displacement of the bonding unit and the critical normal opening amount of the bonding unit and the critical tangential displacement amount of the bonding unit, calculate the damage variable D of the bonding unit by using the following formula:

[0047]

[0048] In the formula, D is the damage variable of the bonding unit; o is the normal displacement of the bonding unit, m; s is the tangential displacement of the bonding unit, m; ο p is the critical normal opening amount of the bonding unit, m; s p is the critical tangential displacement amount of the bonding unit, m; ο t is the difference between the normal opening displacement when the bonding unit undergoes pure tensile failure and the critical normal opening amount, m; s t is the difference between the tangential displacement when the bonding unit undergoes pure shear failure and the critical tangential displacement amount, m; when D>1 calculated according to the above formula (1), take D = 1;

[0049] S12. According to the damage variable D of the bonding unit, define the reduction coefficient f(D) of the tangential stress and normal stress of the bonding unit by using the following formula:

[0050] f(D)=(1 - D) (2);

[0051] In the formula, D is the damage variable of the bonding unit;

[0052] S13. Calculate the normal stress and tangential stress of the bonding unit according to the following formula:

[0053]

[0054] Wherein, σ is the normal stress of the bonding element, in Pa; τ is the shear stress of the bonding element, in Pa; o is the normal displacement of the bonding element, in m; ο p is the critical normal opening amount of the bonding element, in m; s is the shear displacement of the bonding element, in m; s p is the critical shear displacement amount of the bonding element, in m; f t is the tensile strength of the bonding element, in Pa; φ is the internal friction angle of the bonding element; c is the cohesion of the bonding element, in Pa.

[0055] Among them, the critical normal opening amount ο of the bonding element is calculated using the following formula p :

[0056]

[0057] Wherein, f t is the tensile strength of the bonding element, in Pa; P f is the normal parameter of the bonding element, in Pa; h is the length of the bonding element, in m.

[0058] The critical shear displacement amount s of the bonding element is calculated using the following formula p :

[0059]

[0060] Wherein, f S is the shear strength of the bonding element, in Pa; P f is the normal parameter of the bonding element, in Pa; h is the length of the bonding element, in m.

[0061] S2. Parameter redefinition; Two dimensionless parameters are introduced: the post-peak tensile strain ratio r o and the post-peak shear strain ratio r s respectively represent the ratios of the post-peak tensile strain and the post-peak shear strain to the total pre-peak strain, that is, the post-peak tensile strain ratio r o and the post-peak shear strain ratio r s are used to relate the post-peak displacement to the pre-peak displacement to respond to macroscopic mechanics, facilitating the control of the softening behavior by adjusting parameters. Among them, the post-peak tensile strain ratio r o and the post-peak shear strain ratio r s represent that the opening amount (or shear slip amount) of the bonding element in the post-peak section is a multiple of the sum of the normal opening amount (shear slip amount) of the bonding element at the peak and the tensile deformation amount (or shear deformation amount) of the triangular element. These two parameters replace the type-I fracture energy Gf in the original constitutive model of the bonding element Ⅰand the type-II fracture energy Gf Ⅱ ;

[0062] When using the post-peak tensile strain ratio to correlate the post-peak displacement with the pre-peak displacement, the following formula is used:

[0063]

[0064] In the formula, ο t is the difference between the normal opening displacement of the bonding unit during pure tensile failure and the critical normal opening amount, in m; r o is the post-peak tensile strain ratio; ο p is the critical normal opening amount of the bonding unit, in m; P f is the normal parameter of the bonding unit, in Pa; E is the elastic modulus, in Pa.

[0065] When using the post-peak shear strain ratio to correlate the post-peak displacement with the pre-peak displacement, the following formula is used:

[0066]

[0067] In the formula, s t is the difference between the tangential displacement of the bonding unit during pure shear failure and the critical tangential displacement amount, in m; r s is the post-peak shear strain ratio; s p is the critical tangential displacement amount of the bonding unit, in m; P f is the normal parameter of the bonding unit, in Pa; G is the shear modulus, in Pa.

[0068] S3. Obtain test data; obtain the cohesion, internal friction angle, and tensile strength data of the bonding unit through Brazilian splitting tests, uniaxial compression tests, and triaxial compression tests. The post-peak tensile strain ratio r o and the post-peak shear strain ratio r s are obtained through calibration;

[0069] S4. Sensitivity analysis; adjust the values of the post-peak tensile strain ratio and the post-peak shear strain ratio so that the peak strength obtained from the constitutive simulation of the bonding unit is consistent with the data from Brazilian splitting tests, uniaxial compression tests, and triaxial compression tests;

[0070] S5. Repeat the above steps S1 - S4 to obtain the optimal values of the post-peak tensile strain ratio and the post-peak shear strain ratio.

[0071] The method for calibrating the parameters of the constitutive model of the bonding unit provided in the embodiments of the present application replaces the type-I fracture energy Gf o and the type-II fracture energy Gf s in the original constitutive model of the bonding unit by introducing the post-peak tensile strain ratio r Ⅰ and the post-peak shear strain ratio r Ⅱ, and the remaining input parameters (density ρ, elastic modulus E, Poisson's ratio ν, cohesion c, internal friction angle and the tensile strength f of the joint element t ) can directly adopt the values measured by experiments, which can simplify the parameter calibration in the constitutive model of the bonding element, making the new constitutive model of the bonding element only need to calibrate two parameters, greatly reducing the calibration workload and difficulty, effectively improving the calculation efficiency. At the same time, the ratio r o of the post-peak tensile strain and the ratio r s of the post-peak shear strain have a very clear relationship with the peak strength, which is convenient for users to adjust r o and r s according to the peak strength of the macroscopic mechanical behavior of the numerical specimen, verify the parameter values and effectiveness. Through the comparison between the numerical simulation and the experimental results of the Brazilian splitting, uniaxial compression and triaxial compression tests, using the calibrated r o and r s to conduct triaxial compression numerical tests, the obtained peak strength results are in good agreement with the peak strength of the real rock specimens measured in the laboratory tests, proving the effectiveness of the new parameter calibration method for the constitutive model of the bonding element, which can greatly reduce the calibration workload and difficulty.

[0072] In this embodiment, the pre-peak section and the post-peak section refer to the curve section before the peak of the constitutive curve of the bonding element and the curve section after the peak of the constitutive curve of the bonding element.

[0073] The embodiments described above are some, but not all, of the embodiments of the present application. The detailed description of the embodiments of the present application is not intended to limit the scope of the present application claimed, but merely represents selected embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the scope of protection of the present application.

Claims

1. A method for calibrating parameters of a bonding unit constitutive model, characterized in that: The following steps are involved: The nonlinear bonding unit constitutive curve is replaced by a linear pre-peak segment curve and a post-peak segment curve; The post-peak displacement is related to the pre-peak displacement using the post-peak tensile strain ratio and the post-peak shear strain ratio; The cohesion, internal friction angle and tensile strength data of the bonded unit were obtained through Brazilian splitting test, uniaxial compression test and triaxial compression test; The values ​​of the post-peak tensile strain ratio and the post-peak shear strain ratio are adjusted so that the peak strength obtained by the constitutive simulation of the bonding unit is consistent with the data of the Brazilian splitting test, uniaxial compression test and triaxial compression test; Repeat the above steps to obtain the optimal values ​​of the post-peak tensile strain ratio and the post-peak shear strain ratio.

2. The bonding unit constitutive model parameter calibration method according to claim 1, characterized in that: The pre-peak segment curve and the post-peak segment curve are both straight lines.

3. The bonding unit constitutive model parameter calibration method according to claim 1, characterized in that: The post-peak tensile strain ratio is the ratio of the post-peak tensile strain to the pre-peak total strain.

4. The bonding unit constitutive model parameter calibration method according to claim 1, characterized in that: The post-peak shear strain ratio is the ratio of the post-peak shear strain to the pre-peak total strain.

5. The bonding unit constitutive model parameter calibration method according to claim 1, characterized in that: Replacing the nonlinear bonded unit constitutive curve with a linear pre-peak segment curve and a post-peak segment curve includes the following steps: The damage variable D of the bonded element is calculated according to the following formula: Where D is the damage variable of the bonding unit; o is the normal displacement of the bonding unit; s is the tangential displacement of the bonding unit; p is the critical normal opening of the bonding element; s p is the critical tangential displacement of the bonding unit; t It is the difference between the normal opening displacement of the bonding unit when pure tensile failure occurs and the critical normal opening; s t It is the difference between the tangential displacement of the bonding unit when pure shear failure occurs and the critical tangential displacement; when D>1, take D=1; The reduction factor f(D) of the tangential stress and normal stress of the bonding element is calculated according to the following formula: f(D) = (1-D); where D is the damage variable of the bonding element; The normal stress and tangential stress of the bonded element are calculated according to the following formula: Where σ is the normal stress of the bonded element; τ coh is the tangential stress of the bonding unit; o is the normal displacement of the bonding unit; p is the critical normal opening of the bonding unit; s is the tangential displacement of the bonding unit; s p is the critical tangential displacement of the bonding unit; f t is the tensile strength of the bonding unit; φ is the internal friction angle of the bonding unit; c is the cohesion of the bonding unit.

6. The bonding unit constitutive model parameter calibration method according to claim 5, characterized in that: The critical normal opening of the bonded element is calculated using the following formula: p : In the formula, f t is the tensile strength of the bonding unit; P f is the normal parameter of the bonding unit; h is the length of the bonding unit.

7. The bonding unit constitutive model parameter calibration method according to claim 5, characterized in that: The critical tangential displacement s of the bonded element is calculated using the following formula: p : In the formula, f S is the shear strength of the bonding unit; P f is the normal parameter of the bonding unit; h is the length of the bonding unit.

8. The bonding unit constitutive model parameter calibration method according to claim 1, characterized in that: The following formula is used to relate the post-peak displacement to the pre-peak displacement using the post-peak tensile strain ratio: Wherein, t is the difference between the normal opening displacement of the bonded element when pure tensile failure occurs and the critical normal opening, r o is the post-peak tensile strain ratio; p is the critical normal opening of the bonding element; P f is the normal parameter of the bonding unit; E is the elastic modulus.

9. The bonding unit constitutive model parameter calibration method according to claim 1, characterized in that: The following formula is used to relate the post-peak displacement to the pre-peak displacement using the post-peak shear strain ratio: In the formula, s t is the difference between the tangential displacement of the bonded element when pure shear failure occurs and the critical tangential displacement; r s is the shear strain ratio of the post-peak section; s p is the critical tangential displacement of the bonding unit; P f is the normal parameter of the bonding element; G is the shear modulus.

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