Continuous and discontinuous numerical calculation method for mechanical behavior of coarse-grained aggregate

Abstract

The invention provides a continuous and discontinuous numerical calculation method for mechanical behaviors of coarse-grained aggregates, which comprises the following steps: establishing a numerical model of the coarse-grained aggregates, the numerical model comprising a constant strain elastic triangular unit and an initial thickness-free cohesion unit distributed along the boundary of the triangular unit; determining a constitutive relation of a cohesive force unit in the numerical model under a continuous deformation analysis framework; determining a contact relation between discrete triangular units in the numerical model under a discontinuous deformation analysis framework; and obtaining a continuous-discontinuous coupling model of the coarse-grained aggregate based on the determined constitutive relationship and contact relationship, inputting boundary constraint conditions and an external load to the continuous-discontinuous coupling model according to actual working conditions, and carrying out simulation calculation to obtain mechanical properties and a deformation failure form of the coarse-grained aggregate when the coarse-grained aggregate bears the external load. According to the method, a corresponding numerical model is established through a digital image analysis and recognition technology, continuous-discontinuous coupling calculation of the mechanical behavior of the coarse-grained aggregate is completed, and the solution precision and the calculation efficiency are both considered.

Description

Technical Field

[0001] The invention relates to the field of civil engineering construction, and in particular to a continuous-discontinuous coupling numerical calculation method for mechanical behavior of coarse-grained aggregate. Background Art

[0002] In the process of civil engineering design and construction, coarse-grained aggregates are widely used as important building materials in the construction of infrastructure such as roads, bridges, and dams. However, due to the complex particle shape, size distribution, and contact interface characteristics of coarse-grained aggregates, the safety and reliability of the project are seriously affected, and its mechanical behavior needs to be accurately predicted. Existing numerical calculation methods often cannot capture the complex mechanical behavior of coarse-grained aggregates in actual engineering applications, especially when dealing with large deformations, particle interactions, and particle crushing.

[0003] Traditional numerical calculation methods are mainly divided into two categories: one is based on the continuous medium assumption, such as the finite element method (FEM). This method regards the material as a continuum and is suitable for dealing with large deformation and plastic flow problems. However, for discontinuous materials such as coarse aggregates composed of discrete particles, their behavior at the particle scale cannot be accurately reflected; the other is discontinuous methods, such as the discrete element method (DEM). This method simulates the behavior of the material by simulating the interaction between particles. It is suitable for dealing with particle movement and crushing processes, but DEM is less efficient in dealing with large-scale structures, and the simulation of continuous medium effects (such as overall deformation and stress redistribution) is not accurate enough. Therefore, it is urgent to develop a new numerical calculation method that can comprehensively consider continuity and discontinuity. Summary of the invention

[0004] In response to the above problems, the present invention provides a continuous-discontinuous coupling numerical calculation method for the mechanical behavior of coarse-grained aggregates to improve solution accuracy and calculation efficiency.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is:

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

[0007] Step 1, establishing a numerical model of coarse aggregate, wherein the numerical model includes constant strain elastic triangular units and initial thickness-free cohesion units distributed along the boundaries of the triangular units;

[0008] Step 2: Determine the constitutive relation of the cohesion unit in the numerical model under the framework of continuous deformation analysis;

[0009] Step 3, determining the contact relationship between discrete triangle elements in the numerical model under the framework of discontinuous deformation analysis;

[0010] Step 4: Based on the constitutive relationship determined in step 2 and the contact relationship determined in step 3, a continuous-discontinuous coupling model of coarse-grained aggregate is obtained. According to the actual working conditions, boundary constraints and external loads are input into the continuous-discontinuous coupling model, and simulation calculations are performed to obtain the mechanical properties and deformation and failure forms of the coarse-grained aggregate when subjected to external loads.

[0011] Furthermore, step 1 includes:

[0012] Step 1.1, digital image preprocessing: Use image software to perform denoising on the coarse aggregate photos taken on site to increase the brightness and contrast of the image to enhance the difference between coarse aggregate and other media;

[0013] Step 1.2, use grayscale analysis to perform binary transformation, set the threshold of binary medium, distinguish coarse aggregate from other media, and obtain grid information of different materials;

[0014] Step 1.3, establish a numerical model: according to the mesh information obtained in step 1.2, establish a numerical model including constant strain triangular elastic units and cohesion units, wherein cohesion units without thickness are inserted at the boundaries of adjacent triangular units.

[0015] Furthermore, step 2 includes:

[0016] Step 2.1, preliminarily determine the constitutive relationship of the cohesion unit: To reflect the mechanical properties of the continuous model, the constitutive relationship of the cohesion unit is preliminarily determined as the linear elastic stage, the softening stage and the complete separation stage, specifically:

[0017]

[0018] Where τ is the shear stress; δ s is the relative shear displacement; δ i is the initial displacement of damage; δ f is the damage displacement; K s is the shear stiffness; D s is the damage variable;

[0019] Step 2.2, determine the damage variable of the cohesion unit in the softening stage: In the softening stage, the shear stress of the cohesion unit will gradually weaken with the relative slip displacement until it fails completely, where the damage variable is expressed as:

[0020]

[0021] Where δ s,max is the maximum value of relative displacement during loading;

[0022] Step 2.3, improve the constitutive relation of the cohesion unit: Consider the influence of the unit interface friction on the interface mechanical properties, improve the traction-separation relation of the interface cohesion unit to a constitutive relation considering the normal pressure, introduce the interface friction at the unit interface to reflect the influence of the normal pressure on the interface mechanical properties, and assume that:

[0023] (a) As shown in formula (3), the shear stress comes from the combined effect of adhesion and friction at the interface;

[0024] (b) Adhesive stress and friction stress are independent of each other;

[0025] (c) Friction stress is proportional to normal pressure and can be expressed as formula (4);

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

[0027] τ=τ coh +τ fri (3)

[0028] τ fri =μσ n (4)

[0029] τ coh ≤(τ coh ) max (5)

[0030] In the formula, τ coh is the bonding stress; (τ coh ) max is τ coh The maximum value of τ fri is the friction stress; σ n is the normal pressure of the cohesive unit; μ is the friction coefficient;

[0031] Step 2.4: Introduce interface friction into the cohesion constitutive relation: Substitute equations (3)-(5) into equation (1). s ≤δ0), assuming that the shear stress is proportional to the shear displacement and the stiffness is the same as the bond strength, the improved constitutive relation can be expressed by equation (6). The shear stress is composed of the interface bond stress and the friction force. When the cohesion unit fails, the bond stress becomes zero and the shear stress is the friction force:

[0032]

[0033] Furthermore, step 3 includes:

[0034] Step 3.1, determine the contact relationship between discrete triangular units based on penalty function: In the discrete element calculation based on penalty function, the 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] F n =k n ·δ n (7)

[0036] In the formula, F n is the normal contact force; k n is the normal penalty factor; δ n is the normal contact displacement;

[0037] The tangential contact force is expressed as:

[0038] F t =k t ·δ t (8)

[0039] In the formula, F t is the tangential contact force; k t is the tangential penalty factor; δ t is the tangential contact displacement; the tangential contact force also needs to consider the friction effect, which is realized by Coulomb's friction law:

[0040] |F t |≤μ·|F n |(9)

[0041] Where μ is the friction coefficient;

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

[0043]

[0044] In the formula, p n is the normal penalty stiffness; p t is the tangential penalty stiffness; A is the control area of ​​vertex contact;

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

[0046] Step 3.2 Determine viscous damping: Add viscous damping terms to the numerical model to describe the energy dissipation when discrete elements come into contact:

[0047]

[0048] In the formula, F d is the damping force; c is the damping coefficient; is the contact displacement velocity; set the viscous damping of the discrete unit and assign the corresponding material parameters.

[0049] Aiming at the problem that the existing numerical methods cannot calculate the complex mechanical behavior of coarse-grained aggregates in practical engineering applications, the present invention proposes a continuous-discontinuous coupling calculation method. The method establishes a corresponding numerical model through digital image analysis and recognition technology; proposes a new cohesion constitutive relationship to realize the mechanical performance calculation of the numerical model under the framework of continuous deformation analysis, and at the same time determines the transition conditions of some continuous models to discontinuous models; determines the contact relationship of triangular units under the framework of discontinuous deformation, completes the continuous-discontinuous coupling calculation of the mechanical behavior of coarse-grained aggregates, and takes into account both solution accuracy and calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It 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 It is a schematic diagram of the traction-separation law of the cohesion unit and its tangential failure mode;

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

[0054] Figure 5 It is a schematic diagram comparing the numerical calculation of triaxial shear test and the indoor test results. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments, and different "one embodiment" or "embodiment" does not necessarily refer to the same embodiment. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0056] like Figure 1As shown in the figure, the coarse aggregate is composed of constant strain elastic triangular units and cohesion units with initial thickness free distributed along the boundaries of the triangular units. The constant strain elastic triangular units only undergo elastic deformation under external loads, and the yield and rupture of the material are realized through the deformation and failure of the cohesion units. The model is regarded as a continuous material before the cohesion unit is destroyed, and the finite element method can be used for calculation. When the displacement of the cohesion unit reaches the destruction criterion, the cohesion unit is deleted from the model, and the adjacent triangular units are converted from a bonding relationship to a block contact relationship or discretized into independent blocks. The model is transformed into a discontinuous model, and the contact force of the solid unit is calculated by the penalty function as the discrete element method.

[0057] The embodiment of the present invention provides a continuous and discontinuous numerical calculation method for mechanical behavior of coarse aggregate, comprising the following steps:

[0058] Step 1: Establish a numerical model of coarse aggregate, which includes constant strain elastic triangular units and initial thickness-free cohesion units distributed along the triangular unit boundaries. Perform digital image recognition analysis on coarse aggregate photos, and convert the image digital information of the coarse aggregate photos into microstructure modeling information, such as Figure 2 Step 1 specifically includes:

[0059] Step 1.1: Digital image preprocessing. Figure 1 (a) shows that PS and other image software are used for denoising to increase the brightness and contrast of the image to enhance the difference between coarse aggregate and other media.

[0060] Step 1.2, using grayscale analysis (such as Figure 1 Set the threshold of the binary medium to distinguish the coarse aggregate from other media and obtain the grid information of different materials, such as Figure 1 As shown in (c).

[0061] Step 1.3: Establish a numerical model. According to the grid information obtained in step 1.2, establish a numerical model, that is, establish the corresponding constant strain triangular elastic unit and cohesion unit. Figure 1 As shown in (d), in order to describe the deformation and cracking behavior of the continuous unit body under tension or shear load, cohesion units without thickness are inserted at the boundaries of adjacent triangular units, and corresponding material parameters are assigned to transform the image digital information into micro-structure modeling information.

[0062] Step 2: Determine the constitutive relation of the cohesion unit in the numerical model under the framework of continuous deformation analysis. After completing the establishment of the numerical model in step 1, it is necessary to determine the constitutive relation of the cohesion unit to realize the calculation of the continuous model and the transformation of some continuous models to discontinuous models. The constant strain elastic triangular unit only undergoes elastic deformation under the action of external loads, and the yield and rupture of the material are realized through the deformation and failure of the cohesion unit. Therefore, determining the constitutive relation of the cohesion unit can realize the calculation of the mechanical properties of the coarse-grained aggregate numerical model under the framework of continuous deformation analysis. At the same time, when the displacement of the cohesion unit reaches the failure criterion, the cohesion unit is deleted from the model, and the adjacent triangular units are converted from the bonding form to the discrete form of block contact or independent blocks, and the model is transformed into a discontinuous model. Step 2 specifically includes:

[0063] Step 2.1: Preliminarily determine the constitutive relation of the cohesion unit. To reflect the mechanical properties of the continuous model, the constitutive relation of the cohesion unit is preliminarily determined as the linear elastic stage, the softening stage, and the complete separation stage, such as Figure 3 As shown, specifically:

[0064]

[0065] Where τ is the shear stress; δ s is the relative shear displacement; δ i is the initial displacement of damage; δ f is the damage displacement; K s is the shear stiffness; D s is the damage variable.

[0066] Step 2.2, determine the damage variable of the cohesion unit in the softening stage. In the softening stage, the shear stress of the cohesion unit will gradually weaken with the relative slip displacement until it fails completely. The damage variable is expressed as:

[0067]

[0068] Where δ s,max is the maximum relative displacement during the loading process.

[0069] Step 2.3, improve the constitutive relation of the cohesion unit: Consider the influence of the unit interface friction on the interface mechanical properties, and improve the traction-separation relation of the interface cohesion unit to a constitutive relation that considers the normal pressure. In the above steps, the constitutive relation of the cohesion unit does not consider the influence of the normal pressure on the interface mechanical properties. Therefore, the interface friction is introduced at the unit interface to reflect the influence of the normal pressure on the interface mechanical properties. Assume:

[0070] (a) As shown in formula (3), the shear stress comes from the combined effect of adhesion and friction at the interface;

[0071] (b) Adhesive stress and friction stress are independent of each other;

[0072] (c) Friction stress is proportional to normal pressure and can be expressed as formula (4);

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

[0074] τ=τ coh +τ fri (3)

[0075] τ fri =μσ n (4)

[0076] τ coh ≤(τ coh ) max (5)

[0077] In the formula, τ coh is the bonding stress; (τ coh ) max is τ coh The maximum value of τ fri is the friction stress; σ n is the normal pressure of the cohesive unit; μ is the friction coefficient.

[0078] Step 2.4: Introduce interface friction into the cohesion constitutive relation. Substitute equations (3)-(5) into equation (1). In the initial crushing process (δ s ≤δ0), it is assumed that the shear stress is proportional to the shear displacement, and the stiffness is the same as the bond strength. Therefore, the improved constitutive relation can be expressed by equation (6). The new cohesion unit constitutive model is as follows: Figure 4 As shown in the figure, the shear stress is composed of the interfacial bonding stress and the friction force. When the cohesion unit fails, the bonding stress becomes zero and the shear stress is the friction force.

[0079]

[0080] The independent parameters of the new model are still 3 (δ f , K s , μ), and the friction coefficient μ is a new parameter. The constitutive relation of the cohesion unit is set as equation (6), and the corresponding material parameters are assigned.

[0081] Step 3: Determine the contact relationship between discrete triangular units in the numerical model under the framework of discontinuous deformation analysis. When the displacement of the cohesion unit reaches the failure criterion, the cohesion unit is deleted from the model, and the adjacent triangular units are converted from the bonding form to the block contact or independent block form. Therefore, determining the contact relationship between discrete triangular units can realize the mechanical property calculation of the coarse-grained aggregate numerical model under the framework of discontinuous deformation. Step 3 specifically includes:

[0082] Step 3.1, determine the contact relationship between discrete triangular units based on penalty function. In the discrete element calculation based on penalty function, the linear contact model is used to calculate the relationship between contact force and contact displacement. The linear contact model is mainly divided into two aspects: normal contact and tangential contact. The normal contact force can be expressed as:

[0083] F n =k n ·δ n (7)

[0084] In the formula, F n is the normal contact force; k n is the normal penalty factor; δ n is the normal contact displacement.

[0085] The tangential contact force can be expressed as:

[0086] F t =k t ·δ t (8)

[0087] In the formula, F t is the tangential contact force; k t is the tangential penalty factor; δ t is the tangential contact displacement. The tangential contact force usually also needs to consider the friction effect, which can be achieved through Coulomb's friction law:

[0088] |F t |≤μ·|F n |(9)

[0089] Where μ is the friction coefficient.

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

[0091]

[0092] In the formula, p n is the normal penalty stiffness; p t is the tangential penalty stiffness; A is the control area of ​​vertex contact.

[0093] Set the contact relationship between discrete units to a linear contact model and assign corresponding material parameters.

[0094] Step 3.2 Determine the viscous damping. In order to better understand the dynamic behavior of the discrete elements, add a viscous damping term to the model to describe the energy dissipation when the discrete elements are in contact:

[0095]

[0096] In the formula, F d is the damping force; c is the damping coefficient; is 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 coupling model of coarse aggregate is established. According to the actual working conditions, the boundary constraints and external loads are input into the continuous-discontinuous coupling model to start the simulation calculation. This method can be used to calculate the mechanical properties and deformation failure forms of coarse aggregate when subjected to external loads. The specific calculation results are shown in the following example.

[0099] This method is used to simulate the unconfined uniaxial compression and triaxial compression tests of standard cylindrical specimens, and the deformation, failure form and mechanical properties of the specimens are obtained, which are then compared with the indoor test results. The specific results are as follows: Figure 5 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 consistent with that in the indoor test, both of which are simple shear failures, and the size of the main shear failure angle is also relatively close. Figure 5 The comparison of the envelope curves of the numerical calculation and the indoor test stress and the constraint stress in (b) shows that under different constraint stresses, the variation trend and numerical value of the deviation stress are basically consistent, reflecting the feasibility and accuracy of the present invention. The present invention can not only obtain a numerical model that is more in line with the actual working conditions, but also simulate the elastic-plastic continuous deformation and internal cracking failure of the material, and can also simulate the contact between blocks after the material cracks and fails.

[0101] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A continuous and discontinuous numerical calculation method for mechanical behavior of coarse aggregate, characterized in that: The steps include: Step 1, establishing a numerical model of coarse aggregate, wherein the numerical model includes constant strain elastic triangular units and initial thickness-free cohesion units distributed along the boundaries of the triangular units; Step 2: Determine the constitutive relation of the cohesion unit in the numerical model under the framework of continuous deformation analysis; Step 3, determining the contact relationship between discrete triangle elements in the numerical model under the framework of discontinuous deformation analysis; Step 4: Based on the constitutive relationship determined in step 2 and the contact relationship determined in step 3, a continuous-discontinuous coupling model of coarse-grained aggregate is obtained. According to the actual working conditions, boundary constraints and external loads are input into the continuous-discontinuous coupling model, and simulation calculations are performed to obtain the mechanical properties and deformation and failure forms of the coarse-grained aggregate when subjected to external loads.

2. The continuous and discontinuous numerical calculation method for mechanical behavior of coarse aggregate according to claim 1, characterized in that: Step 1 includes: Step 1.1, digital image preprocessing: Use image software to perform denoising on the coarse aggregate photos taken on site to increase the brightness and contrast of the image to enhance the difference between coarse aggregate and other media; Step 1.2, use grayscale analysis to perform binary transformation, set the threshold of binary medium, distinguish coarse aggregate from other media, and obtain grid information of different materials; Step 1.3, establish a numerical model: according to the mesh information obtained in step 1.2, establish a numerical model including constant strain triangular elastic units and cohesion units, wherein cohesion units without thickness are inserted at the boundaries of adjacent triangular units.

3. The continuous and discontinuous numerical calculation method for mechanical behavior of coarse aggregate according to claim 1, characterized in that: Step 2 includes: Step 2.1, preliminarily determine the constitutive relationship of the cohesion unit: To reflect the mechanical properties of the continuous model, the constitutive relationship of the cohesion unit is preliminarily determined as the linear elastic stage, the softening stage and the complete separation stage, specifically: Where τ is the shear stress; δ s is the relative shear displacement; δ i is the initial displacement of damage; δ f is the damage displacement; K s is the shear stiffness; D s is the damage variable; Step 2.2, determine the damage variable of the cohesion unit in the softening stage: In the softening stage, the shear stress of the cohesion unit will gradually weaken with the relative slip displacement until it fails completely, where the damage variable is expressed as: Where δ s,max is the maximum value of relative displacement during loading; Step 2.3, improve the constitutive relation of the cohesion unit: Consider the influence of the unit interface friction on the interface mechanical properties, improve the traction-separation relation of the interface cohesion unit to a constitutive relation considering the normal pressure, introduce the interface friction at the unit interface to reflect the influence of the normal pressure on the interface mechanical properties, and assume that: (a) As shown in formula (3), the shear stress comes from the combined effect of adhesion and friction at the interface; (b) Adhesive stress and friction stress are independent of each other; (c) Friction stress is proportional to normal pressure and can be expressed as formula (4); (d) After the cohesion unit fails, the bonding stress becomes zero, as shown in formula (5); τ=τ coh +t fri (3) t fri =ms n (4) t coh ≤(τ coh ) max (5) In the formula, τ coh is the bonding stress; (τ coh ) max is τ coh The maximum value of τ fri is the friction stress; σ n is the normal pressure of the cohesive unit; μ is the friction coefficient; Step 2.4: Introduce interface friction into the cohesion constitutive relation: Substitute equations (3)-(5) into equation (1). s ≤δ0), assuming that the shear stress is proportional to the shear displacement and the stiffness is the same as the bond strength, the improved constitutive relation can be expressed by equation (6). The shear stress is composed of the interface bond stress and the friction force. When the cohesion unit fails, the bond stress becomes zero and the shear stress is the friction force:

4. The continuous and discontinuous numerical calculation method for mechanical behavior of coarse aggregate according to claim 1, characterized in that: Step 3 includes: Step 3.1, determine the contact relationship between discrete triangular units based on penalty function: In the discrete element calculation based on penalty function, the 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: F n =k n ·d n (7) In the formula, F n is the normal contact force; k n is the normal penalty factor; δ n is the normal contact displacement; The tangential contact force is expressed as: F t =k t ·d t (8) In the formula, F t is the tangential contact force; k t is the tangential penalty factor; δ t is the tangential contact displacement; the tangential contact force also needs to consider the friction effect, which is realized by Coulomb's friction law: |F t |≤μ·|F n |(9) Where μ is the friction coefficient; The penalty factor is defined by the penalty function, and the normal and tangential penalty factors are calculated according to formula (10): In the formula, p n is the normal penalty stiffness; p t is the tangential penalty stiffness; A is the control area of ​​vertex contact; Set the contact relationship between discrete units to a linear contact model and assign corresponding material parameters; Step 3.2 Determine viscous damping: Add viscous damping terms to the numerical model to describe the energy dissipation when discrete elements come into contact: In the formula, F d is the damping force; c is the damping coefficient; is the contact displacement velocity; set the viscous damping of the discrete unit and assign the corresponding material parameters.

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