Numerical method for continuous and discontinuous mechanical behavior of coarse aggregates

Abstract

The application provides a coarse-grained aggregate mechanical behavior continuous-discontinuous numerical calculation method, including: establishing a numerical model of coarse-grained aggregate, the numerical model including a constant strain elastic triangular element and an initial thicknessless cohesive force element distributed along the boundary of the triangular element; determining the constitutive relation of the cohesive force element in the numerical model under a continuous deformation analysis framework; determining the contact relation between discrete triangular elements in the numerical model under a discontinuous deformation analysis framework; obtaining a continuous-discontinuous coupling model of the coarse-grained aggregate based on the determined constitutive relation and contact relation, inputting boundary constraint conditions and external loads into the continuous-discontinuous coupling model according to actual working conditions, and performing simulation calculation to obtain the mechanical properties and deformation failure forms of the coarse-grained aggregate under external loads. The application establishes a corresponding numerical model through digital image analysis and recognition technology, completes continuous-discontinuous coupling calculation of the mechanical behavior of coarse-grained aggregate, and takes into account solving accuracy and calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of civil engineering construction, specifically a continuous-discontinuous coupled numerical calculation method for the mechanical behavior of coarse aggregates. Background Technology

[0002] In civil engineering design and construction, coarse aggregates are widely used as important building materials in infrastructure construction such as roads, bridges, and dams. However, due to the complex particle shape, size distribution, and contact interface characteristics of coarse aggregates, their mechanical behavior significantly affects the safety and reliability of engineering projects, necessitating accurate prediction of their mechanical behavior. Existing numerical calculation methods often fail to adequately capture the complex mechanical behavior of coarse aggregates in practical engineering applications, particularly when dealing with large deformations, interparticle interactions, and particle breakage.

[0003] Traditional numerical calculation methods are mainly divided into two categories: one is based on the continuum assumption, such as the finite element method (FEM). This type of method treats the material as a continuum and is suitable for handling problems such as large deformation and plastic flow. However, it cannot accurately reflect the behavior of discontinuous materials composed of discrete particles, such as coarse-grained aggregates, at the particle scale. The other category is discontinuous methods, such as the discrete element method (DEM). This type of method simulates the material behavior by simulating the interactions between particles. It is suitable for handling particle motion and crushing processes. However, DEM is less efficient when dealing with large-scale structures and is not accurate enough in simulating continuum effects (such as overall deformation and stress redistribution). Therefore, there is an urgent need to develop a new numerical calculation method that can comprehensively consider both continuity and discontinuity. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a continuous-discontinuous coupled numerical calculation method for the mechanical behavior of coarse aggregates, thereby improving solution accuracy and computational efficiency.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A continuous-discontinuous coupled numerical calculation method for the mechanical behavior of coarse aggregates includes the following steps:

[0007] Step 1: Establish a numerical model of coarse aggregate. The numerical model includes constant strain elastic triangular elements and cohesive elements with no initial thickness distributed along the boundaries of the triangular elements.

[0008] Step 2: Determine the constitutive relations of the cohesive elements in the numerical model within the framework of continuous deformation analysis;

[0009] Step 3: Determine the contact relationships between discrete triangular elements in the numerical model within the framework of discontinuous deformation analysis;

[0010] Step 4: Based on the constitutive relation determined in Step 2 and the contact relation determined in Step 3, obtain the continuous-discontinuous coupled model of coarse aggregate. Input the boundary constraints and external loads into the continuous-discontinuous coupled model according to the actual working conditions, and perform simulation calculations to obtain the mechanical properties and deformation failure modes of coarse aggregate under external loads.

[0011] Furthermore, step 1 includes:

[0012] Step 1.1, Digital Image Preprocessing: The coarse aggregate photos taken on site are processed with image software to remove noise, increase the brightness and contrast of the image, so as to improve the difference between coarse aggregate and other media;

[0013] Step 1.2: Use grayscale analysis to perform binary classification, set the threshold of the binary medium, distinguish coarse aggregates from other media, and obtain mesh information of different materials;

[0014] Step 1.3: Establish a numerical model: Based on the mesh information obtained in Step 1.2, establish a numerical model including constant strain triangular elastic elements and cohesive elements, wherein cohesive elements without thickness are inserted at the boundaries of adjacent triangular elements.

[0015] Furthermore, step 2 includes:

[0016] Step 2.1: Preliminary determination of the constitutive relations of the cohesive unit: To assess the mechanical properties of the reaction continuity model, the constitutive relations of the cohesive unit are preliminarily determined to be in the linear elastic stage, softening stage, and complete separation stage, specifically as follows:

[0017] (1)

[0018] In the formula Shear stress; This refers to the relative shear displacement. To disrupt the initial displacement; To disrupt displacement; Shear stiffness; For damage variables;

[0019] Step 2.2: Determine the damage variables of the cohesive elements during the softening stage: During the softening stage, the shear stress of the cohesive elements gradually decreases with relative slip displacement until complete failure. The damage variables are expressed as follows:

[0020] (2)

[0021] In the formula This represents the maximum relative displacement during the loading process;

[0022] Step 2.3, Improve the constitutive relation of the cohesive unit: Considering the influence of interfacial friction on the interfacial mechanical properties, the traction-separation relationship of the interfacial cohesive unit is improved to a constitutive relation considering normal pressure. Interfacial friction is introduced at the unit interface to reflect the influence of normal pressure on the interfacial mechanical properties. Assumptions:

[0023] (a) As shown in equation (3), the shear stress originates from the combined effects of bonding and friction at the interface;

[0024] (b) The adhesive stress and the frictional stress are independent of each other;

[0025] (c) Frictional stress is proportional to normal pressure, which can be expressed as equation (4).

[0026] (d) After the cohesive unit fails, the bonding stress becomes zero, as shown in equation (5);

[0027] (3)

[0028] (4)

[0029] (5)

[0030] In the formula, This refers to adhesive stress; for The maximum value; Frictional stress; For the cohesive unit normal pressure; The coefficient of friction;

[0031] Step 2.4: Introduce interfacial friction into the cohesive constitutive relation: Substitute equations (3)-(5) into equation (1) during the initial crushing process. In this equation, assuming that shear stress is proportional to shear displacement and stiffness is the same as bond strength, the improved constitutive relation can be expressed by equation (6). The shear stress is composed of interfacial bond stress and friction. When the cohesive unit fails, the bond stress becomes zero, and the shear stress becomes friction.

[0032] (6).

[0033] Furthermore, step 3 includes:

[0034] Step 3.1: Determine the contact relationship between discrete triangular elements based on the penalty function: In the discrete element method (DEM) calculation based on the penalty function, a linear contact model is used to calculate the relationship between contact force and contact displacement. The linear contact model is divided into two aspects: normal contact and tangential contact. The normal contact force is expressed as:

[0035] (7)

[0036] In the formula, Normal contact force; For the normal penalty factor; This is the normal contact displacement;

[0037] The tangential contact force is expressed as:

[0038] (8)

[0039] In the formula, It is a tangential contact force; The tangential penalty factor; This represents the tangential contact displacement; the tangential contact force must also consider the frictional effect, which is achieved through Coulomb's law of friction:

[0040] (9)

[0041] In the formula, The coefficient of friction;

[0042] The penalty factor is defined by the penalty function, and the normal and tangential penalty factors are calculated according to formula (10):

[0043] (10)

[0044] In the formula, For the rigidity of the penalty; For tangential penalty stiffness; The control area for vertex contact;

[0045] Set the contact relationship between discrete elements as a linear contact model and assign corresponding material parameters;

[0046] Step 3.2 Determine viscous damping: Add a viscous damping term to the numerical model to describe the energy dissipation when discrete elements are in contact:

[0047] (11)

[0048] In the formula, For damping force; The damping coefficient; The contact displacement velocity is set; the viscous damping of the discrete element is set, and the corresponding material parameters are assigned.

[0049] This invention addresses the problem that existing numerical methods cannot adequately calculate the complex mechanical behavior of coarse aggregates in practical engineering applications, proposing a continuous-discontinuous coupled calculation method. This method establishes a corresponding numerical model through digital image analysis and recognition technology; proposes a novel cohesive constitutive relation to realize the calculation of mechanical properties of the numerical model within a continuous deformation analysis framework, while simultaneously determining the transformation conditions from a partially continuous model to a discontinuous model; and determines the contact relationships of triangular elements within the discontinuous deformation framework, completing the continuous-discontinuous coupled calculation of the mechanical behavior of coarse aggregates, balancing solution accuracy and computational efficiency. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the unit structure of coarse aggregate;

[0051] Figure 2 This is a schematic diagram of image digital analysis and recognition modeling.

[0052] Figure 3 This is a schematic diagram of the traction-separation law and tangential failure mode of cohesive units;

[0053] Figure 4 This is a schematic diagram of the new traction separation law of the interfacial cohesion unit;

[0054] Figure 5 This is a schematic diagram comparing the numerical calculations of the triaxial shear test with the results of the indoor test. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments, and different "embodiments" or "embodiments" do not necessarily refer to the same embodiment. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] like Figure 1 As shown, the coarse aggregate consists of constant-strain elastic triangular elements and initially thin cohesive elements distributed along the boundaries of the triangular elements. Under external loads, the constant-strain elastic triangular elements only undergo elastic deformation; the yielding and fracture of the material are achieved through the deformation and failure of the cohesive elements. The model is considered a continuous material before the cohesive elements fail, and calculations can be performed using the finite element method. When the displacement of a cohesive element reaches the failure criterion, the cohesive element is removed from the model. Adjacent triangular elements are converted from a bonded relationship to a block contact relationship or discretized into independent blocks, transforming the model into a discontinuous model. The contact forces of the solid elements are calculated using the penalty function as a discrete element method.

[0057] This invention provides a method for continuous and discontinuous numerical calculation of the mechanical behavior of coarse aggregates, comprising the following steps:

[0058] Step 1: Establish a numerical model of the coarse aggregate. The numerical model includes constant-strain elastic triangular elements and initially thin cohesive elements distributed along the boundaries of the triangular elements. Perform digital image recognition analysis on the coarse aggregate photographs to convert the image digital information into mesoscopic structure modeling information, such as... Figure 2 As shown. Step 1 specifically includes:

[0059] Step 1.1: Digital Image Preprocessing. This involves preprocessing the images of coarse aggregates taken on-site (e.g., ...). Figure 2 As shown in (a), image processing software such as PS was used to remove noise and increase the brightness and contrast of the image to improve the difference between coarse aggregate and other media.

[0060] Step 1.2: Utilize grayscale analysis (e.g.) Figure 2 Binarization is performed as shown in (b). A threshold is set for the binary medium to distinguish coarse aggregates from other media, and mesh information for different materials is obtained, such as... Figure 2 As shown in (c).

[0061] Step 1.3: Establish the numerical model. Based on the mesh information obtained in Step 1.2, establish the numerical model, that is, establish the corresponding constant strain triangular elastic elements and cohesive elements. For example... Figure 2 As shown in (d), in order to describe the deformation and cracking behavior of a continuous unit under tensile or shear load, cohesive elements without thickness are inserted at the boundaries of adjacent triangular elements and assigned corresponding material parameters, thus transforming the digital information of the image into information for microstructural modeling.

[0062] Step 2: Determine the constitutive relations of cohesive elements in the numerical model within the framework of continuous deformation analysis. After establishing the numerical model in Step 1, it is necessary to determine the constitutive relations of the cohesive elements to realize the calculation of the continuous model and the transformation of the partially continuous model into a discontinuous model. Constant strain elastic triangular elements only undergo elastic deformation under external loads; the yielding and fracture of the material are achieved through the deformation and failure of the cohesive elements. Therefore, determining the constitutive relations of the cohesive elements enables the calculation of the mechanical properties of the coarse aggregate numerical model within the framework of continuous deformation analysis. Simultaneously, when the displacement of a cohesive element reaches the failure criterion, that cohesive element is deleted from the model, and adjacent triangular elements are transformed from a bonded form to a discrete form of block contact or independent blocks, thus transforming the model into a discontinuous model. Step 2 specifically includes:

[0063] Step 2.1: Preliminary determination of the constitutive relations of the cohesive elements. To reflect the mechanical properties of the continuous model, the constitutive relations of the cohesive elements are preliminarily determined to be a linear elastic stage, a softening stage, and a complete separation stage, such as... Figure 3 As shown, specifically:

[0064] (1)

[0065] In the formula Shear stress; This refers to the relative shear displacement. To disrupt the initial displacement; To disrupt displacement; Shear stiffness; For damage variables.

[0066] Step 2.2: Determine the damage variables of the cohesive elements during the softening stage. During the softening stage, the shear stress of the cohesive elements gradually decreases with relative slip displacement until complete failure. The damage variables are expressed as follows:

[0067] (2)

[0068] In the formula This represents the maximum relative displacement during the loading process.

[0069] Step 2.3, Improve the constitutive relation of the cohesive unit: Considering the influence of interfacial friction on the interfacial mechanical properties, the traction-separation relationship of the interfacial cohesive unit is improved to a constitutive relation that considers normal pressure. In the above steps, the constitutive relation of the cohesive unit did not consider the influence of normal pressure on the interfacial mechanical properties. Therefore, interfacial friction is introduced at the unit interface to reflect the influence of normal pressure on the interfacial mechanical properties. Assume:

[0070] (a) As shown in equation (3), the shear stress originates from the combined effects of bonding and friction at the interface;

[0071] (b) The adhesive stress and the frictional stress are independent of each other;

[0072] (c) Frictional stress is proportional to normal pressure, which can be expressed as equation (4).

[0073] (d) After the cohesive unit fails, the bonding stress becomes zero, as shown in equation (5).

[0074] (3)

[0075] (4)

[0076] (5)

[0077] In the formula, This refers to adhesive stress; for The maximum value; Frictional stress; For the cohesive unit normal pressure; is the coefficient of friction.

[0078] Step 2.4: Introduce interfacial friction into the cohesive constitutive relation. Substitute equations (3)-(5) into equation (1) during the initial crushing process. In this model, it is assumed that the shear stress is proportional to the shear displacement, and that the stiffness is the same as the bond strength. Therefore, the improved constitutive relation can be expressed by equation (6). The new cohesive element constitutive model is as follows: Figure 4 As shown, the shear stress is composed of the interfacial adhesive stress and the frictional force. When the cohesive unit fails, the adhesive stress becomes zero, and the shear stress becomes the frictional force.

[0079] (6)

[0080] The new model still has 3 independent parameters. , , coefficient of friction The new parameters are set as follows: The constitutive relation of the cohesive element is set as Equation (6), and the corresponding material parameters are assigned.

[0081] Step 3: Determine the contact relationships between discrete triangular elements in the numerical model within the discontinuous deformation analysis framework. When the displacement of a cohesive element reaches the failure criterion, that cohesive element is deleted from the model, and adjacent triangular elements are transformed from bonded to block contact or independent block forms. Therefore, determining the contact relationships between discrete triangular elements enables the calculation of the mechanical properties of coarse aggregate numerical models within the discontinuous deformation framework. Step 3 specifically includes:

[0082] Step 3.1: Determine the contact relationship between discrete triangular element units based on the penalty function. In discrete element method (DEM) calculations based on the penalty function, a linear contact model is used to calculate the relationship between contact force and contact displacement. The linear contact model mainly consists of two aspects: normal contact and tangential contact. The normal contact force can be expressed as:

[0083] (7)

[0084] In the formula, Normal contact force; For the normal penalty factor; This represents the normal contact displacement.

[0085] Tangential contact force can be expressed as:

[0086] (8)

[0087] In the formula, It is a tangential contact force; The tangential penalty factor; This represents the tangential contact displacement. Tangential contact force usually also needs to consider frictional effects, which can be achieved using Coulomb's law of friction:

[0088] (9)

[0089] In the formula, is the coefficient of friction.

[0090] The penalty factor is defined by the penalty function, and the normal and tangential penalty factors are calculated according to formula (10):

[0091] (10)

[0092] In the formula, For the rigidity of the penalty; For tangential penalty stiffness; The control area for vertex contact.

[0093] The contact relationship between discrete elements is set as a linear contact model, and corresponding material parameters are assigned.

[0094] Step 3.2 Determine viscous damping. To better understand the dynamic behavior of the discrete elements, a viscous damping term is added to the model to describe the energy dissipation during contact between the discrete elements:

[0095] (11)

[0096] In the formula, For damping force; The damping coefficient; This represents the contact displacement velocity.

[0097] Set the viscous damping of the discrete element and assign the corresponding material parameters.

[0098] Step 4: The continuous-discontinuous coupled model of coarse aggregate is established. Boundary constraints and external loads are input into the continuous-discontinuous coupled model according to the actual working conditions, and simulation calculations begin. This method can calculate the mechanical properties and deformation / failure modes of coarse aggregate under external loads. Specific calculation results are shown in the following example.

[0099] This method was used to simulate and calculate unconfined uniaxial and triaxial compression tests on standard cylindrical specimens, obtaining the deformation and failure modes and mechanical properties of the specimens. The results were then compared with those from laboratory tests. Specific results are as follows: Figure 5 As shown.

[0100] Figure 5 (a) shows the failure model of the specimen under different loads. It can be seen that the failure mode of the specimen in the numerical calculation is almost the same as that in the laboratory test. Both are single shear failures, and the magnitudes of the principal shear failure angles are also quite similar. Figure 5 The comparison between the numerical calculations and the envelope curves of the stress and constraint stress shown in Figure (b) demonstrates that the variation trend and magnitude of the deviation stress are basically consistent under different constraint stresses, reflecting the feasibility and accuracy of the present invention. This invention not only provides numerical models that better reflect real-world working conditions, but also simulates the continuous elastic-plastic deformation and internal cracking failure of materials, as well as the contact interaction between blocks after material cracking failure.

[0101] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for continuous-discontinuous numerical calculation of the mechanical behavior of coarse aggregate, characterized in that, The method comprises the following steps: Step 1, establishing a numerical model of coarse-grained aggregates, wherein the numerical model comprises constant-strain elastic triangular elements and initial-thickness-free cohesive elements distributed along the boundaries of the triangular elements; Step 2, determining the constitutive relation of the cohesive elements in the numerical model under a continuous deformation analysis framework; Step 3, determining the contact relation between the discrete triangular elements in the numerical model under a discontinuous deformation analysis framework; Step 4, obtaining a continuous-discontinuous coupling model of the coarse-grained aggregates based on the constitutive relation determined in step 2 and the contact relation determined in step 3, inputting boundary constraint conditions and external loads into the continuous-discontinuous coupling model according to actual working conditions, and performing simulation calculation to obtain the mechanical properties and deformation and failure forms of the coarse-grained aggregates under the external loads; Step 2 comprises: Step 2.1, initially determining the constitutive relation of the cohesive elements: in order to reflect the mechanical properties of the continuous model, the constitutive relation of the cohesive elements is initially determined as a linear elastic stage, a softening stage and a complete separation stage, and specifically: （1）； wherein is the shear stress; is the relative shear displacement; is the initial displacement to failure; is the displacement to failure; is the shear stiffness; is the damage variable; Step 2.2, determining the damage variable of the cohesive elements in the softening stage: in the softening stage, the shear stress of the cohesive elements will gradually weaken with the relative slip displacement until complete failure, wherein the damage variable is represented as: （2）； In the formula is the maximum value of the relative displacement during the loading process; Step 2.3, improving the constitutive relation of the cohesive elements: considering the influence of the interfacial friction on the interfacial mechanical properties, the traction-separation relation of the interfacial cohesive elements is improved to a constitutive relation considering the normal pressure, the interfacial friction is introduced at the interface of the elements to reflect the influence of the normal pressure on the interfacial mechanical properties, and it is assumed that: (a) as shown in formula (3), the shear stress is derived from the joint action of the adhesion and the friction of the interface; (b) the adhesion stress and the friction stress are independent of each other; (c) the friction stress is proportional to the normal pressure, and can be represented as formula (4); (d) after the failure of the cohesive elements, the adhesion stress becomes zero, as shown in formula (5); （3）； （4）； （5）； wherein is the cohesive stress; is is the maximum value of is the friction stress; is the cohesive unit normal pressure; is the friction coefficient; Step 2.4, introducing the interfacial friction into the constitutive relation of the cohesive elements: substituting formula (3)-(5) into formula (1), in the initial breaking process, it is assumed that the shear stress is proportional to the shear displacement, and the stiffness is the same as the adhesion strength, the improved constitutive relation is represented by formula (6), the shear stress is composed of the interfacial adhesion stress and the friction, and when the cohesive elements fail, the adhesion stress becomes zero, and the shear stress is the friction: （6）。 2. The method for continuous-discontinuous numerical calculation of the mechanical behavior of coarse granular materials according to claim 1, characterized in that: Step 1 comprises: Step 1.1, digital image preprocessing: the rough-grained aggregate photos taken on site are denoised by using image software, and the brightness and contrast of the images are increased to improve the difference between the rough-grained aggregates and other media; Step 1.2, binaryzation is performed by using gray scale analysis, the threshold of the binary medium is set, the rough-grained aggregates are distinguished from other media, and the grid information of different materials is obtained; Step 1.3, establishing a numerical model: according to the grid information obtained in step 1.2, a numerical model comprising constant-strain triangular elastic elements and cohesive elements is established, wherein the initial-thickness-free cohesive elements are inserted at the boundaries of adjacent triangular elements.

3. The method for continuous-discontinuous numerical calculation of the mechanical behavior of coarse granular materials according to claim 1, characterized in that: Step 3 comprises: Step 3.1, determine the contact relationship between the discrete triangular elements based on the penalty function: in the calculation of the discrete element based on the penalty function, the linear contact model is used to calculate the relationship between the contact force and the contact displacement, which is divided into normal contact and tangential contact two aspects, wherein the normal contact force is expressed as: （7）； wherein is the normal contact force; is the normal penalty factor; is the normal contact displacement; The tangential contact force is expressed as: （8）； wherein is the tangential contact force; is the tangential penalty factor; is the tangential contact displacement; the tangential contact force also takes into account the friction effect, which is achieved through the Coulomb friction law: （9）； In the formula, is the coefficient of friction; The penalty factor is defined by the penalty function, and the normal and tangential penalty factors are calculated according to formula (10): （10）； wherein is the normal penalty stiffness; is the tangential penalty stiffness; is the control area of the vertex contact; Set the contact relationship between the discrete elements as the linear contact model, and give the corresponding material parameters; Step 3.2 determine the viscous damping: add the viscous damping term in the numerical model to describe the energy dissipation when the discrete elements contact: （11）； In the formula, is the damping force; is the damping coefficient; is the contact displacement velocity; the viscous damping of the discrete element is set, and the corresponding material parameters are given.

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