A method for calibrating parameters of a bond element constitutive model

Abstract

The application discloses a method for calibrating parameters of a bond element constitutive model, and relates to the technical field of rock mechanics numerical simulation. The method for calibrating parameters of the bond element constitutive model replaces a nonlinear bond element constitutive curve with a linear segmented curve in a pre-peak stage and a linear segmented curve in a post-peak stage, correlates post-peak displacement with pre-peak displacement by using a post-peak tensile strain ratio and a post-peak shear strain ratio, obtains cohesion, internal friction angle and tensile strength data of the bond element by means of a Brazilian disc test, a uniaxial compression test and a triaxial compression test, adjusts the values of the post-peak tensile strain ratio and the post-peak shear strain ratio so that the peak strength obtained by the bond element constitutive simulation is consistent with the data obtained by the Brazilian disc test, the uniaxial compression test and the triaxial compression test, and the above steps are repeated to obtain optimal values of the post-peak tensile strain ratio and the post-peak shear strain ratio. The method for calibrating parameters of the bond element constitutive model reduces the workload and difficulty of calibration and effectively improves the calculation efficiency.

Description

Technical Field

[0001] This application relates to the field of numerical simulation technology in rock mechanics, and more specifically, to a method for calibrating parameters of a constitutive model of a bonded element. Background Technology

[0002] In rock fracture simulation, bonded elements are often inserted into adjacent solid elements, and the fracture of these bonded elements is used to simulate crack initiation and propagation. However, existing constitutive models of bonded elements have the following problems: 1. Complex parameter calibration: The five parameters of the bonded element (cohesion, internal friction angle, tensile strength, Type I fracture energy, and Type II fracture energy) all require tedious calibration and cannot be directly obtained from experimental values, making the calibration of the constitutive model of the bonded element cumbersome; 2. Unclear physical meaning: The fracture energy parameters of the bonded element lack clear physical meaning and have a weak correlation with macroscopic mechanical behavior, resulting in low calibration efficiency; 3. Low computational efficiency: The constitutive model of the bonded element uses a nonlinear peak-end curve, resulting in high computational complexity and limiting its engineering applications.

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

[0004] The purpose of this application is to provide a method for calibrating the parameters of a constitutive model of a bonded element, which reduces the workload and difficulty of calibration, effectively improves computational efficiency, and facilitates users to adjust 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 parameters of a constitutive model of a bonded element, including the following steps:

[0007] The nonlinear constitutive curve of the bonding unit is replaced with a linear pre-peak segment curve and a post-peak segment curve.

[0008] The peak-post tensile strain ratio and peak-post shear strain ratio are used to correlate the peak-post displacement with the peak-preced displacement.

[0009] Data on cohesion, internal friction angle, and tensile strength of the bonded unit were obtained through Brazilian splitting test, uniaxial compression test, and triaxial compression test.

[0010] The values ​​of the post-peak tensile strain ratio and the post-peak shear strain ratio were adjusted so that the peak strength obtained by the constitutive simulation of the bonded element was consistent with the data from the Brazilian splitting test, uniaxial compression test and triaxial compression test.

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

[0012] In some alternative implementations, both the pre-peak segment and the post-peak segment are straight lines.

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

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

[0015] In some alternative implementations, replacing the nonlinear constitutive curve of the bonding unit with a linear pre-peak segment curve and post-peak segment curve includes the following steps:

[0016] The damage variable D of the bonded element is calculated using the following formula:

[0017]

[0018] In the formula, D is the damage variable of the bonded element; o is the normal displacement of the bonded element; s is the tangential displacement of the bonded element; ο p The critical normal opening of the bonding unit; s p This represents the critical tangential displacement of the bonding unit; t The difference between the normal opening displacement of the bonded element at the point of pure tensile failure and the critical normal opening amount; s t The difference between the tangential displacement of the bonded element at the point of pure shear failure and the critical tangential displacement is taken; when D>1, D=1 is taken;

[0019] The reduction factor f(D) of the tangential and normal stresses of the bonded element is calculated according to the following formula: f(D)=(1-D); where D is the damage variable of the bonded element;

[0020] The normal and tangential stresses of the bonded elements are calculated using the following formulas:

[0021]

[0022] In the formula, σ is the normal stress of the bonded element; τ coh σ represents the tangential stress of the bonded element; o represents the normal displacement of the bonded element; ο p s is the critical normal opening of the bonding element; s is the tangential displacement of the bonding element; s p f is the critical tangential displacement of the bonding unit. t φ 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.

[0023] In some alternative implementations, the critical normal opening of the bonding unit is calculated using the following formula. p :

[0024]

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

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

[0027]

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

[0029] In some alternative implementations, the post-peak tensile strain ratio is used to correlate the post-peak displacement with the pre-peak displacement according to the following formula:

[0030]

[0031] In the formula, ο t r is the difference between the normal opening displacement of the bonded element at the point of pure tensile failure and the critical normal opening amount. o The tensile strain ratio after the peak; p P represents the critical normal opening of the bonding unit. f is the normal parameter of the bonding element; E is the elastic modulus.

[0032] In some alternative implementations, the post-peak shear strain ratio is used to correlate the post-peak displacement with the pre-peak displacement according to the following formula:

[0033]

[0034] In the formula, s t The difference between the tangential displacement of the bonded element at the point of pure shear failure and the critical tangential displacement; r s The shear strain ratio after the peak; s p P represents the critical tangential displacement of the bonding unit. f G represents the normal parameter of the bonding element; G is the shear modulus.

[0035] The beneficial effects of this application are as follows: The method for calibrating the constitutive model parameters of the bonded element provided in this application replaces the nonlinear constitutive curve of the bonded element with linear pre-peak and post-peak segment curves. It uses the post-peak tensile strain ratio and post-peak shear strain ratio to correlate the post-peak displacement with the pre-peak displacement. Through Brazilian splitting tests, uniaxial compression tests, and triaxial compression tests, it obtains the cohesion, internal friction angle, and tensile strength data of the bonded element. It then adjusts the values ​​of the post-peak tensile strain ratio and post-peak shear strain ratio to ensure that the peak strength obtained from the constitutive model of the bonded element is consistent with the data from the Brazilian splitting test, uniaxial compression test, and triaxial compression test. Repeating the above steps yields the optimal values ​​of the post-peak tensile strain ratio and post-peak shear strain ratio. The method for calibrating the constitutive model parameters of the bonded element provided in this application only requires calibrating two parameters: the post-peak tensile strain ratio and the post-peak shear strain ratio. This greatly reduces the workload and difficulty of calibration, effectively improves computational efficiency, and facilitates users in adjusting parameter values ​​based on the macroscopic mechanical behavior of numerical samples. Attached Figure Description

[0036] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 A schematic flowchart illustrating the method for calibrating the constitutive model parameters of the bonding unit provided in this application embodiment;

[0038] Figure 2 The peak-front segment and peak-back segment are obtained by replacing the stretched constitutive model of the bonding unit provided in the embodiments of this application.

[0039] Figure 3 The segmented curves of the pre-peak and post-peak segments are obtained by replacing the constitutive model of the bonding unit provided in the embodiments of this application after shearing. Detailed Implementation

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

[0041] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0042] The features and performance of the constitutive model parameter calibration method for the bonding unit of this application are further described in detail below with reference to embodiments.

[0043] like Figure 1 As shown in the figure, this application provides a method for calibrating the parameters of a constitutive model of a bonding element, including the following steps:

[0044] S1. Linearization of the pre-peak and post-peak segments: The existing nonlinear constitutive curves of the bonding unit are replaced with linear pre-peak and post-peak segment piecewise curves; wherein, both the pre-peak and post-peak segment piecewise curves are straight lines.

[0045] Specifically, it includes the following steps:

[0046] S11. Based on the relationship between the normal displacement and tangential displacement of the bonded element and the critical normal opening and critical tangential displacement of the bonded element, the damage variable D of the bonded element is calculated using the following formula:

[0047]

[0048] In the formula, D is the damage variable of the bonded element; o is the normal displacement of the bonded element, m; s is the tangential displacement of the bonded element, m; ο p The critical normal opening of the bonding unit is m; s p The critical tangential displacement of the bonding unit is m; t The difference between the normal opening displacement of the bonded element at the point of pure tensile failure and the critical normal opening, m; s t The difference between the tangential displacement of the bonded unit when it undergoes pure shear failure and the critical tangential displacement is m; when D calculated according to the above formula (1) is greater than 1, D is taken as 1;

[0049] S12. Based on the damage variable D of the bond element, the reduction factor f(D) of the tangential stress and normal stress of the bond element is defined 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 and tangential stresses of the bonded elements according to the following formulas:

[0053]

[0054] In the formula, σ is the normal stress of the bonded element, Pa; τ is the tangential stress of the bonded element, Pa; o is the normal displacement of the bonded element, m; ο p denoted as σc, where m is the critical normal opening of the bonded element; and s is the tangential displacement of the bonded element, also in m and sc. p m; f represents the critical tangential displacement of the bonding unit. t φ is the tensile strength of the bonding unit, Pa; φ is the internal friction angle of the bonding unit; c is the cohesion of the bonding unit, Pa.

[0055] The critical normal opening of the bonding unit is calculated using the following formula. p :

[0056]

[0057] In the formula, f t P represents the tensile strength of the bonded unit, in Pa; f Pa is the normal parameter of the bonding element; h is the length of the bonding element, m.

[0058] The critical tangential displacement s of the bonded unit is calculated using the following formula. p :

[0059]

[0060] In the formula, f S P represents the shear strength of the bonded unit, in Pa; f Pa is the normal parameter of the bonding element; h is the length of the bonding element, m.

[0061] S2. Parameters are redefined; two dimensionless parameters are introduced: the post-peak tensile strain ratio r. o and the shear strain ratio r of the peak segment s These represent the ratios of the tensile strain and shear strain in the post-peak segment to the total strain in the pre-peak segment, respectively; that is, the tensile strain ratio r in the post-peak segment is used. o and the shear strain ratio r of the peak segment s Correlate the post-peak displacement with the pre-peak displacement to respond to macroscopic mechanics, facilitating control of softening behavior through parameter adjustment. Among these parameters is the post-peak tensile strain ratio r. o and the shear strain ratio r of the peak segment s The opening (or tangential slip) of the bonded element after the peak is a multiple of the sum of the normal opening (tangential slip) of the bonded element when it is at its peak and the tensile deformation (or shear deformation) of the triangular element. These two parameters replace the Type I fracture energy Gf in the original bonded element constitutive model. Ⅰand 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 applies:

[0063]

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

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

[0066]

[0067] In the formula, s t m; r is the difference between the tangential displacement of the bonded element at the point of pure shear failure and the critical tangential displacement. s The shear strain ratio after the peak; s p P represents the critical tangential displacement of the bonding unit, in meters (m). f is the normal parameter of the bonding element, Pa; G is the shear modulus, Pa.

[0068] S3. Obtain experimental data; acquire data on cohesion, internal friction angle, tensile strength, and post-peak tensile strain ratio r of the bonded unit through Brazilian splitting test, uniaxial compression test, and triaxial compression test. o and the shear strain ratio r of the peak segment s 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 by the constitutive simulation of the bonded element is consistent with the data from the Brazilian splitting test, uniaxial compression test and triaxial compression test.

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

[0071] The constitutive model parameter calibration method for the bonding element provided in this application introduces the post-peak tensile strain ratio r. o and the shear strain ratio r of the peak segment s The type I fracture energy Gf in the original bonded unit constitutive model is replaced Ⅰ and Type II fracture energy Gf ⅡThe 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 The values ​​obtained directly from experiments can be used, which simplifies the parameter calibration in the constitutive model of the bonded element. This means the new constitutive model only requires calibration of two parameters, significantly reducing the workload and difficulty of calibration and effectively improving computational efficiency. Simultaneously, the tensile strain ratio r in the post-peak segment... o and the shear strain ratio r of the peak segment s The relationship between the value of r and the peak intensity is very clear, making it easy for users to adjust the peak intensity based on the macroscopic mechanical behavior of the numerical specimen. o and r s The parameters were selected and their validity verified. Numerical simulations and experimental results from Brazilian splitting, uniaxial compression, and triaxial compression tests were compared, and the calibrated r was used. o and r s The peak strength results obtained from triaxial compression numerical tests are in good agreement with the peak strength of real rock samples measured in laboratory tests, proving the effectiveness of the new method for calibrating the parameters of the constitutive model of the bonded unit. This method can greatly reduce the workload and difficulty of parameter calibration.

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

[0073] The embodiments described above are some, but not all, of the embodiments of this application. The detailed description of the embodiments of this application is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

Claims

1. A method for calibrating parameters of a constitutive model of a bonded element, characterized in that, Includes the following steps: The nonlinear constitutive curve of the bonding unit is replaced with a linear pre-peak segment curve and a post-peak segment curve. The post-peak tensile strain ratio and post-peak shear strain ratio are used to correlate the post-peak displacement with the pre-peak displacement; when using the post-peak tensile strain ratio to correlate the post-peak displacement with the pre-peak displacement, the following formula applies: ； In the formula, The difference between the normal opening displacement of the bonded element at the point of pure tensile failure and the critical normal opening amount is given. r o The tensile strain ratio after the peak; This represents the critical normal opening of the bonding unit; P f For the normal parameters of the bonding element; E It is the elastic modulus; When using the post-peak shear strain ratio to correlate the post-peak displacement with the pre-peak displacement, the following formula applies: ； In the formula, The difference between the tangential displacement of the bonded unit at the point of pure shear failure and the critical tangential displacement. r s The shear strain ratio after the peak; This represents the critical tangential displacement of the bonding unit. P f For the normal parameters of the bonding element; G Shear modulus; Data on cohesion, internal friction angle, and tensile strength 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 were adjusted so that the peak strength obtained by the constitutive simulation of the bonded element was consistent with the data from the Brazilian splitting test, uniaxial compression test, and triaxial compression test. The post-peak tensile strain ratio and the post-peak shear strain ratio represent the ratios of the post-peak tensile strain and the post-peak shear strain to the total strain before the peak, respectively. Repeat the above steps to obtain the optimal values ​​of the tensile strain ratio and the shear strain ratio after the peak.

2. The method for calibrating the constitutive model parameters of the bonding element according to claim 1, characterized in that, Both the segmented curves before and after the peak are straight lines.

3. The method for calibrating the constitutive model parameters of the bonding element according to claim 1, characterized in that, The post-peak tensile strain ratio is the ratio of the post-peak tensile strain to the total strain in the pre-peak section.

4. The method for calibrating the constitutive model parameters of the bonding element according to claim 1, characterized in that, The post-peak shear strain ratio is the ratio of the post-peak shear strain to the total strain in the pre-peak segment.

5. The method for calibrating the constitutive model parameters of the bonding element according to claim 1, characterized in that, Replacing the nonlinear constitutive curve of the bonding unit with a linear pre-peak segment piecewise curve and a post-peak segment piecewise curve includes the following steps: The damage variable of the bonded unit is calculated using the following formula. D : ； In the formula, D For the damage variable of the bonding unit; This represents the normal displacement of the bonding unit; This represents the tangential displacement of the bonding unit; This represents the critical normal opening of the bonding unit; This represents the critical tangential displacement of the bonding unit. The difference between the normal opening displacement of the bonded unit at the point of pure tensile failure and the critical normal opening amount; The difference between the tangential displacement of the bonded unit at the point of pure shear failure and the critical tangential displacement; when D When >1, take D =1; The reduction factors for the tangential and normal stresses of the bonded elements are calculated using the following formulas. : In the formula, D For the damage variable of the bonding unit; The normal and tangential stresses of the bonded elements are calculated using the following formulas: ； ； In the formula, For the normal stress of the bonding unit; The tangential stress of the bonding unit; This represents the normal displacement of the bonding unit; This represents the critical normal opening of the bonding unit; This represents the tangential displacement of the bonding unit; This represents the critical tangential displacement of the bonding unit. f t This refers to the tensile strength of the bonding unit; The internal friction angle of the bonding unit; c This represents the cohesive force of the bonding unit.

6. The method for calibrating constitutive model parameters of the bonding element according to claim 5, characterized in that, The critical normal opening of the bonded element is calculated using the following formula. : ； In the formula, f t This refers to the tensile strength of the bonding unit; P f For the normal parameters of the bonding element; h This represents the length of the bonding unit.

7. The method for calibrating constitutive model parameters of the bonding element according to claim 5, characterized in that, The critical tangential displacement of the bonded unit is calculated using the following formula. : ； In the formula, f S The shear strength of the bonded unit; P f For the normal parameters of the bonding element; h This represents the length of the bonding unit.

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