Method for constructing three-dimensional seven-phase mesoscopic model of steel reinforced concrete based on vector tracking

Abstract

The invention provides a vector tracking-based steel reinforced concrete three-dimensional seven-phase mesoscopic model construction method, and a steel reinforced concrete three-dimensional seven-phase mesoscopic model comprises mortar, coarse aggregate, a coarse aggregate-mortar interface layer, reinforcing steel bars, a mortar-reinforcing steel bar bonding interface layer, profile steel and a profile steel-mortar bonding interface layer. Generating a cuboid matrix according to given height, length and width; generating section steel and a bonding layer between the section steel and mortar according to a given shape and size; reinforcing steel bars are generated according to the given position and size, and an interface layer between the reinforcing steel bars and mortar is generated; generating coarse aggregate according to a given shape and gradation, and generating an interface layer between the aggregate and mortar; aggregate is sequentially doped into a base body, and collision inspection is carried out on the aggregate and reinforcing steel bars, section steel and between the aggregate and the aggregate based on a vector tracking algorithm. Simulation precision is improved, interface layer description is perfected, rapid model generation is achieved, and the application capability of the model is enhanced.

Description

Technical Field

[0001] The invention provides a method for constructing a three-dimensional seven-phase mesoscopic model of steel-concrete based on vector tracking, and belongs to the technical field of civil engineering. Background Art

[0002] Steel concrete is a common and important structural form in the civil engineering industry, and is widely used in civil and military engineering. Researching and analyzing the mechanical properties of steel concrete under various working conditions such as earthquakes, fires, and continuous loads has important theoretical and practical significance for optimizing its internal structure and improving structural safety and durability. With the rapid development of computer technology, numerical simulation has gradually become a key tool for engineering research, especially in large-scale engineering structure projects, where numerical simulation analysis can significantly save manpower and financial resources in research.

[0003] At present, the research on numerical simulation of steel-concrete is gradually developing towards the mesoscopic scale. In the prior art, the invention patent application with publication number CN113010940A proposes a method for a mesoscopic two-dimensional model of steel-concrete, which includes three-phase mesoscopic structures such as steel, concrete, and mortar. However, this method does not take into account the transition layer between the steel and the mortar, the transition layer between the aggregate and the mortar, and the gradation distribution of the aggregate, which is quite different from the actual steel-concrete structure. The invention patent application with publication number CN110442922A proposes a method for establishing a mesoscopic numerical model of stainless steel reinforced concrete, which includes five-phase mesoscopic structures such as coarse aggregate, mortar, mortar-coarse aggregate interface, stainless steel bars, and steel-mortar bonding interface. Although this method takes into account the gradation distribution of coarse aggregate, the shape of the aggregate established is round or spherical, which fails to truly reflect the actual shape of the aggregate. In addition, the invention patent with publication number CN113962066A proposes a three-dimensional mesoscopic model method for reinforced concrete, which includes six phase structures such as convex polyhedral aggregate, mortar, aggregate-mortar interface layer, steel bar, mortar-steel bonding layer and pore defects, and takes into account the gradation distribution of coarse aggregate. However, this method fails to include the steel phase. In summary, the existing methods for generating mesoscopic models of reinforced concrete have been improved, but there are few methods for generating mesoscopic models of steel concrete. The prior art is insufficient in describing the complexity and accuracy of the mesoscopic structure of steel concrete, and cannot fully reflect the situation of steel concrete in actual engineering. Therefore, there is an urgent need for a new method to more accurately construct a three-dimensional mesoscopic model of steel concrete, to make up for the shortcomings of the prior art, and to improve the prediction accuracy and optimization effect of the performance of steel concrete structures. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention aims to solve the following main technical problems, which are ranked in order of importance as follows:

[0005] (1) Insufficient simulation of coarse aggregate gradation and shape: The existing three-dimensional mesoscopic model of steel concrete does not adequately describe the gradation distribution and true shape of coarse aggregate, resulting in a large difference between the simulation results and the actual situation.

[0006] (2) Lack of interface layer between steel section and mortar: The existing model fails to accurately describe the transition interface between steel section and mortar, which affects the prediction and analysis of the mechanical properties of the structure.

[0007] (3) Simplified treatment of the interaction between multiphase components: Traditional models do not deal with the interaction between multiphase components (such as coarse aggregate, mortar, steel bars and steel sections) in detail, which limits the accuracy and applicability of the model.

[0008] (4) Low model generation efficiency: The existing technology has low computational efficiency when generating complex microscopic models, making it difficult to quickly generate high-precision three-dimensional models.

[0009] The main purpose of the present invention is to solve the above technical problems by constructing a three-dimensional mesoscopic model of steel-concrete with seven phase components, which specifically includes the following objectives:

[0010] (1) Improve simulation accuracy: Fully consider the gradation and shape of coarse aggregate and the actual shape of steel sections to improve the authenticity and accuracy of the model.

[0011] (2) Improve the description of interface layers: Add the description of the steel section-mortar bonding interface layer to fully reflect the physical properties and interactions of each interface layer.

[0012] (3) Rapid model generation: Based on the vector tracking algorithm, collision checks are performed on each phase component to quickly generate a three-dimensional microscopic model of steel concrete.

[0013] (4) Enhance the application capability of the model: By improving the description of multiphase components and the simulation of their interactions, the model can more effectively simulate the actual failure characteristics of steel-concrete reinforcement and provide a reliable theoretical basis for engineering applications.

[0014] The specific technical solution is:

[0015] A method for constructing a three-dimensional seven-phase mesoscopic model of steel-concrete based on vector tracking, wherein the three-dimensional seven-phase mesoscopic model of steel-concrete comprises: mortar, coarse aggregate, coarse aggregate-mortar interface layer, steel bars, mortar-steel bonding interface layer, steel, and steel-mortar bonding interface layer;

[0016] The construction method includes the following steps:

[0017] Step 1: Generate a rectangular block base according to the given height, length and width;

[0018] Step 2: Generate the steel section and the bonding layer between the steel section and the mortar according to the given shape and size;

[0019] Step 3: Generate steel bars according to given positions and sizes, and generate the interface layer between the steel bars and the mortar;

[0020] Step 4: Generate coarse aggregate according to the given shape and gradation, and generate the interface layer between aggregate and mortar; add aggregates into the matrix in sequence, and perform collision checks between aggregates and steel bars, steel sections, and between aggregates based on the vector tracking algorithm.

[0021] Furthermore, step 2 specifically includes the following sub-steps:

[0022] Sub-step 2.1, determine the shape of the steel, box steel and H-shaped steel, the center of the steel coincides with the center of the base; the size of the steel includes the height, width and thickness of the steel; H-shaped steel includes the thickness of the web and flange;

[0023] Sub-step 2.2, determining the position of the steel section through sub-step 2.1, calculating the position coordinates of each corner point of the steel section in the xy plane, and generating the steel section by stretching method;

[0024] The steel section is divided into a plurality of cuboids; for H-shaped steel section, it is divided into 3 cuboids, and for box-shaped steel section, it is divided into 4 cuboids.

[0025] Step 3 specifically includes the following sub-steps:

[0026] Sub-step 3.1, generate longitudinal reinforcement at the four corners of the base, the position of the longitudinal reinforcement is related to the thickness of the concrete cover; the shape of the reinforcement is cylindrical;

[0027] Sub-step 3.2, by determining the position of the steel bar in sub-step 3.1, generating a circle in the xy plane, and generating the steel bar by stretching.

[0028] Step 4 specifically includes the following sub-steps:

[0029] Sub-step 4.1, determine the shape of the aggregate;

[0030] Sub-step 4.2, determine aggregate gradation;

[0031] According to the Fuller curve theoretical formula and Monte Carlo random probability model, the gradation of aggregate in three-dimensional space is determined; the Fuller curve formula is as follows:

[0032]

[0033] Where P is the mass percentage of aggregate passing through the sieve hole diameter D0, D max is the maximum aggregate particle size;

[0034] Based on the Fuller curve formula, calculate the aggregate volume in each particle size range:

[0035]

[0036] In the formula, V(D i ,D j ) indicates the particle size in D i —D j The volume of coarse aggregate within the range, D min ,D max Respectively represent the minimum and maximum coarse aggregate particle size, p k Indicates the volume ratio of coarse aggregate to concrete, V con Indicates the volume of concrete;

[0037] The volume of concrete is expressed as:

[0038] V con =length*width*height-S v1 -S v2

[0039] Among them, length, width, and height represent the length, width, and height of the matrix respectively, and S v1 and S v2 Represent the volume of steel sections and reinforcing bars respectively;

[0040] According to the above formula, the Monte Carlo random method is used to generate aggregate distribution that conforms to the Fuller curve gradation, ensuring that the aggregate volume in each particle size range reaches the predetermined value;

[0041] Sub-step 4.3: Generate aggregate.

[0042] Sub-step 4.3 includes the following steps:

[0043] Step 4.3.1, randomly generate aggregates;

[0044] Generate the initial coordinates of a single aggregate using the method described in sub-step 4.2 and place the aggregate into the matrix;

[0045] Calculate the coordinates of the aggregate and determine whether the aggregate is inside the matrix; if the coordinates of the aggregate are outside the matrix, abandon the aggregate and recalculate the coordinates; if the aggregate is inside the matrix, it is considered that the aggregate is generated successfully and proceed to the next step;

[0046] Step 4.3.2, check the collision between the newly placed aggregate and the steel and reinforcement;

[0047] Conduct collision checks on newly placed aggregates, steel sections and reinforcements;

[0048] Split the steel into multiple cuboids; if it is an H-shaped steel, split it into 3 cuboids according to the position of the flange and web; if it is a box-shaped steel, split it into 2 horizontal and 2 vertical cuboids; a single steel bar is a cylinder, simplify it into a cuboid, the four faces of the cuboid are tangent to the side of the cylinder, and the two faces coincide with the upper and lower bottom surfaces of the cylinder; perform collision detection on the aggregate and each cuboid in turn. If there is a collision, that is, the new aggregate overlaps with the steel bar or the steel, then abandon the addition of the aggregate and return to step 4.3.1, then abandon the aggregate and recalculate the coordinates; if the collision check passes, it is considered that the aggregate is generated successfully and proceed to the next step;

[0049] Step 4.3.3, check the collision of the newly placed aggregates with the already placed aggregates in turn;

[0050] If the aggregate is the first aggregate to be placed, skip this step and go directly to step 4.3.4;

[0051] If there is a collision, abandon the aggregate and return to step 4.3.1 to recalculate the coordinates;

[0052] If the collision check passes, the aggregate is considered to be generated successfully and proceed to the next step;

[0053] Step 4.3.4, record and collection update;

[0054] The successfully generated aggregates are retained and added to the collection of aggregates used for collision checking;

[0055] Record the aggregate particle size and volume information;

[0056] When each particle size range (D i —D j ) The volume of aggregate put in reaches V (Di—Dj) Aggregate generation and placement are completed;

[0057] Rotate the aggregates In step 4.3.1, if convex aggregates are selected for placement, randomly rotate each aggregate to ensure that the spatial orientation of the aggregates is different; the specific steps are as follows

[0058] Rotate the aggregate around the x-axis and z-axis and calculate the coordinates of the aggregate after rotation;

[0059] Define the rotation matrix R of the aggregate around the x-axis and z-axis x and R z :

[0060]

[0061] Where θ is the angle of rotation around the x-axis, and α is the angle of rotation around the z-axis;

[0062] Step 4.3.5, aggregate volume calculation;

[0063] In step 4.3.4, the volume of the aggregate is calculated by adding up the volumes of each tetrahedron that makes up the aggregate; the volume of a single tetrahedron is calculated as follows:

[0064]

[0065] Where V i Represents the volume of a single tetrahedron, V represents the volume of the aggregate, A, B, C, O are the vertex coordinates of the tetrahedron, and || represents the modulus of the vector.

[0066] The present invention proposes a method for constructing a three-dimensional seven-phase mesoscopic model of steel-concrete based on vector tracking, which solves the deficiencies in the prior art and has the following significant advantages:

[0067] (1) Improve simulation accuracy

[0068] The present invention subdivides the steel concrete microscopic model into seven components, namely, coarse aggregate, mortar, coarse aggregate-mortar interface layer, steel bars, mortar-steel bonding interface, steel sections, and steel section-mortar bonding interface; a detailed component division enables the model to more accurately reflect the complexity of actual materials and significantly improves the accuracy of numerical simulation.

[0069] (2) Actual aggregate form

[0070] The aggregate of the present invention is described by a convex polyhedron rather than a simplified sphere. The convex polyhedron aggregate is closer to the actual aggregate shape and can more accurately simulate the distribution and behavior of aggregate in concrete materials, thereby more accurately analyzing the performance of concrete in different engineering scenarios.

[0071] (3) Improve structural durability and reliability:

[0072] The present invention optimizes the design and material selection of concrete structures through the detailed simulation of the mesoscopic model. This more realistic simulation can more accurately analyze and optimize the performance of concrete structures, improve the durability and reliability of the structure, and provide more reliable analysis results, especially in complex working conditions such as earthquakes and fires.

[0073] (4) Easy to operate

[0074] The present invention uses a vector tracking algorithm to perform physical collision checks, and quickly detects and adjusts the collisions of each phase component. The operation steps are simplified, allowing researchers and engineers to efficiently build and analyze models, greatly reducing the threshold for learning and operation.

[0075] (5) Reduce costs

[0076] The present invention reduces computing time and resource consumption through efficient algorithms and simplified processes.

[0077] While ensuring high-precision simulation, the calculation and operation costs are reduced, so that high-quality mesoscopic numerical simulation can be performed within a limited budget. In summary, the present invention is superior to the prior art in terms of simulation accuracy, model authenticity, ease of operation and cost control. Combined with the key technical solutions, the present invention can produce good technical effects in various engineering applications and provide strong technical support for the mesoscopic numerical simulation of steel-concrete. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 These are the main steps of the three-dimensional vector tracking algorithm involved in the present invention;

[0079] Figure 2 A flowchart for constructing a three-dimensional seven-phase mesoscopic model of steel-concrete based on vector tracking involved in the present invention;

[0080] Figure 3 Schematic diagram of the collision between aggregates

[0081] Figure 4 This is a schematic diagram showing that there is no collision between aggregates;

[0082] Figure 5 It is a schematic diagram of the collision between aggregate and steel;

[0083] Figure 6 This is a schematic diagram showing that there is no collision between aggregate and steel;

[0084] Figure 7 This is a schematic diagram of the box-shaped steel section involved in the present invention;

[0085] Figure 8 A schematic diagram of the H-shaped steel involved in the present invention;

[0086] Fig. 9 A schematic diagram for generating the geometry of coarse aggregates involved in the present invention;

[0087] Fig.10 This is the H-beam microscopic model in the first embodiment of the present invention, and the aggregate is a polyhedron;

[0088] Fig.11 This is the box-shaped steel microscopic model in the second embodiment of the present invention, and the aggregate is a polyhedron.

[0089] Fig.12 This is the H-beam microscopic model in the first embodiment of the present invention, and the aggregate is spherical;

[0090] Fig.13This is the box-shaped steel microscopic model in the second embodiment of the present invention, and the aggregate is spherical. DETAILED DESCRIPTION

[0091] The specific technical solution of the present invention is explained in conjunction with embodiments.

[0092] The present invention proposes a three-dimensional seven-phase mesoscopic model of steel-concrete containing seven-phase components, which specifically includes:

[0093] (1) Coarse aggregate: consider its gradation and actual shape.

[0094] (2) Mortar: as base material.

[0095] (3) Coarse aggregate-mortar interface: describes the transition zone between coarse aggregate and mortar.

[0096] (4) Steel bars: including their location and size.

[0097] (5) Mortar-rebar bonding interface: describes the bonding behavior between the steel bars and the mortar.

[0098] (6) Steel sections: consider their actual shape and distribution.

[0099] (7) Steel-mortar bonding interface: describes the bonding layer between the steel and the mortar. By using a vector tracking algorithm, collision checks are performed on the above phase components to ensure that the geometric characteristics and interactions of the model are accurate. This method can quickly generate a three-dimensional mesoscopic model of steel-concrete and can be effectively used to simulate the mechanical properties and failure characteristics of steel-concrete under actual working conditions.

[0100] The present invention proposes a three-dimensional seven-phase mesoscopic model of steel-concrete containing seven phase components, specifically including: mortar, coarse aggregate, coarse aggregate-mortar interface layer, steel bar, mortar-steel bonding interface layer, steel, steel-mortar bonding interface layer. The model comprehensively considers different phase components and their interactions to ensure that the simulation results are consistent with the steel-concrete structure in actual engineering, and significantly improves the simulation accuracy and modeling efficiency. The input parameters include:

[0101] Rectangular base dimensions: height (h), length (l) and width (b).

[0102] Corner reinforcement information: Concrete cover thickness (c r ), steel bar embedding (d r ), the thickness of the steel bar interface layer h r .

[0103] Aggregate shape: any octahedron, regular octahedron and spherical aggregate.

[0104] Other aggregate parameters: volume fraction s, aggregate interface thickness ha .

[0105] Aggregate particle size parameters: small particle size, D1~D2, small particle size ratio (ρ1); medium particle size, D2~D3, medium particle size ratio (ρ2); large particle size, D3~D4, large particle size ratio (ρ3).

[0106] Steel parameters: width (W), height (H), length (L), web thickness (t w ), flange thickness (t b ), thickness of the steel interface layer (h s ).

[0107] The three-dimensional vector tracking algorithm used in the present invention is specifically:

[0108] The three-dimensional vector tracking algorithm is an efficient algorithm for determining whether two convex polyhedrons collide. The core idea is to use the support function and Minkowski difference to gradually obtain the convex polyhedron that surrounds the origin. If the convex polyhedron surrounds the origin, the two convex polyhedrons involved in the calculation collide. The following explains the basic process and principle of the three-dimensional vector algorithm. Figure 1 shown.

[0109] (1) Select the initial direction

[0110] The initial direction may be a vector formed by the center points of the two convex polyhedrons A and B, a vector formed by selecting a vertex from each of the two convex polyhedrons, or an arbitrarily given vector.

[0111] (2) Calculate the first Minkowski difference support point (hereinafter referred to as support point) S1.

[0112] According to the initial direction Use the Support function to calculate the first support point;

[0113]

[0114] In the formula, To support the function, it means that the geometry X is in a given vector The farthest point in a direction (coordinates).

[0115] (3) Calculate the second support point S2.

[0116] Reverse the initial direction (i.e. ), use the Support function to calculate the second support point;

[0117]

[0118] (4) Calculate the third support point S3.

[0119] The third supporting point must satisfy the following requirement: the projection of the origin (0,0,0) on the plane where triangle S1S2S3 is located must be inside triangle S1S2S3. The calculation steps are as follows:

[0120] ① Calculate the direction vector of the third support point.

[0121] According to S1 and S2, the direction vector of the third support point is obtained by vector triple cross product

[0122]

[0123] ② According to the direction vector of the third support point Calculate the third support point.

[0124]

[0125] ③ Determine whether the projection of the origin on the plane where triangle S1S2S3 is located is inside triangle S1S2S3.

[0126] Then the projection of the origin on the plane where triangle S1S2S3 is located is inside triangle S1S2S3, and we can go directly to step (5).

[0127] If not satisfied and Then execute the following steps and return to step ②:

[0128]

[0129] if but

[0130]

[0131] if but

[0132]

[0133] (5) Calculate the fourth support point S4.

[0134] ① Calculate the direction vector of the 4th support point

[0135] if but

[0136]

[0137] otherwise

[0138]

[0139] ②According to the direction vector Calculate the fourth support point S4.

[0140]

[0141] ③ Determine whether the origin (0,0,0) is inside the simplex (tetrahedron) formed by S1, S2, S3, and S4.

[0142] The details are as follows:

[0143]

[0144] when hour,

[0145]

[0146] if Update the simplex vertex coordinates,

[0147] S3=S2 S2=S1 (21)

[0148] if

[0149]

[0150] when When , update the simplex vertex coordinates,

[0151] S2=S3 S3=S1 (23)

[0152] when When , it means that the origin is inside the simplex, which means that the two convex polyhedrons collided, and the collision detection ends. If the origin is not inside the simplex, it is also necessary to update the direction vector of the fourth support point, recalculate the fourth support point, and enter step ④.

[0153] ④ When When , update the simplex vertex coordinates and the direction vector of the fourth support point, and calculate the fourth support point.

[0154]

[0155] when hour,

[0156]

[0157] After updating the fourth support point, it is still necessary to determine whether the origin is inside the simplicity through step ③. Each time the fourth support point is updated, record the convex polyhedron A and B in the direction vector If, when updating the fourth support point, we repeatedly search for the convex polyhedron A and B in the direction vector If the fourth support point is repeated, it means that the origin cannot be inside the simplex, and the two convex polyhedrons do not collide. There is no need to enter step ③, and the collision detection ends. If the fourth support point does not appear repeatedly when updating the fourth support point, and the points of convex polyhedrons A and B have appeared, it also means that the origin cannot be inside the simplex, and the two convex polyhedrons do not collide. There is no need to enter step ③, and the collision detection ends.

[0158] The present invention provides a method for constructing a three-dimensional seven-phase mesoscopic model of steel-concrete based on vector tracking, such as Figure 2 As shown, the specific steps are as follows:

[0159] Step 1: Generate a rectangular base according to the given height (h), length (l) and width (b).

[0160] Step 2: Generate the steel section and the bonding layer between the steel section and the mortar according to the given shape and size;

[0161] It includes the following sub-steps:

[0162] Sub-step 2.1, determine the shape of the steel. Figure 7 and Figure 8 The present invention considers box-shaped steel and H-shaped steel, and the center of the steel coincides with the center of the base. The size of the steel includes the height, width and thickness of the steel (H-shaped steel includes the thickness of the web and flange).

[0163] Sub-step 2.2, determine the position of the steel section through sub-step 2.1, calculate the position coordinates of each corner point of the steel section in the xy plane, and generate the steel section by stretching method.

[0164] Divide the steel into multiple cuboids. For H-shaped steel, divide it into 3 cuboids, and for box-shaped steel, divide it into 4 cuboids.

[0165] Step 3: Generate steel bars according to given positions and sizes, and generate the interface layer between the steel bars and the mortar;

[0166] It includes the following sub-steps:

[0167] Sub-step 3.1, generate longitudinal reinforcement at the four corners of the base. The position of the longitudinal reinforcement is related to the thickness of the concrete cover. The shape of the reinforcement is cylindrical.

[0168] Sub-step 3.2, by determining the position of the steel bar in sub-step 3.1, generating a circle in the xy plane, and generating the steel bar by stretching.

[0169] Step 4: Generate coarse aggregate according to the given shape (sphere or polyhedron) and gradation, and generate the interface layer between aggregate and mortar. Add aggregates into the matrix one by one, and perform collision checks between aggregates and steel bars, steel sections, and between aggregates based on the vector tracking algorithm.

[0170] Figures 3 to 6 The present invention relates to collision inspection operations between aggregates and aggregates, and between aggregates and steel sections. Figure 3 and Figure 4 For the collision check between aggregates, if the origin is in the constructed simplex (tetrahedron), there is a collision between the aggregates, otherwise there is no collision. Figure 5 and Figure 6 For collision check between aggregate and steel section, if the origin is in the constructed simplex (tetrahedron), the aggregate and steel section have collided, otherwise there is no collision.

[0171] It includes the following sub-steps:

[0172] Sub-step 4.1, determine the shape of the aggregate. You can choose spherical aggregates and polyhedral aggregates. For polyhedral aggregates, the method mentioned by Wang Ben in "Research on the Microscopic Modeling Method of Three-Dimensional Random Concave-convex Concrete Aggregates" is adopted, which is: determine 26 points as the vertices of the aggregate; connect these points to form an envelope; use these lines to form a surface to generate the shell structure of the aggregate; finally fill the shell to form an aggregate entity. Fig. 9 This is a schematic diagram of the geometric generation of coarse aggregate involved in the present invention.

[0173] Sub-step 4.2, determine the aggregate gradation. According to the Fuller curve theory formula and the Monte Carlo random probability model, determine the aggregate gradation in three-dimensional space. The Fuller curve formula is as follows:

[0174]

[0175] Where P is the mass percentage of aggregate passing through the sieve hole diameter D0, D max is the maximum aggregate particle size.

[0176] Based on the Fuller curve formula, the aggregate volume within each particle size range can be calculated:

[0177]

[0178] In the formula, V(D i ,D j ) indicates the particle size in D i —D j The volume of coarse aggregate within the range, D min ,D max Respectively represent the minimum and maximum coarse aggregate particle size, p kIndicates the volume ratio of coarse aggregate to concrete, V con Indicates the volume of concrete.

[0179] Among them, the volume of concrete can be expressed as:

[0180] V con =length*width*height-S v1 -S v2

[0181] Among them, length, width, and height represent the length, width, and height of the matrix respectively, and S v1 and S v2 Represent the volume of steel sections and steel bars respectively.

[0182] According to the above formula, the Monte Carlo random method is used to generate aggregate distribution that conforms to the Fuller curve gradation to ensure that the aggregate volume in each particle size range reaches the predetermined value.

[0183] Sub-step 4.3: Generate aggregate. Specifically includes the following steps:

[0184] Step 4.3.1, randomly generate aggregates.

[0185] Generate the initial coordinates of a single aggregate using the method described in sub-step 4.2 and place the aggregate into the matrix.

[0186] Calculate the coordinates of the aggregate and determine whether the aggregate is inside the matrix. If the coordinates of the aggregate are outside the matrix, the aggregate is abandoned and the coordinates are recalculated; if the aggregate is inside the matrix, it is considered that the aggregate is generated successfully and proceed to the next step.

[0187] Step 4.3.2: Check the collision between the newly placed aggregate and the steel sections and reinforcements.

[0188] The newly placed aggregate is checked for collision with the steel and steel bars. The shape of the steel is complex, so it is split into multiple cuboids. If it is an H-shaped steel, it is split into 3 cuboids according to the position of the flange and web. If it is a box-shaped steel, it is split into 2 horizontal and 2 vertical cuboids. A single steel bar is a cylinder, which is also simplified into a cuboid. The four faces of the cuboid are tangent to the side of the cylinder, and the two faces coincide with the upper and lower bottom surfaces of the cylinder. The shape simplification of steel and steel bars is to facilitate collision detection. The method described above is used to perform collision detection on the aggregate and each cuboid in turn. If there is a collision (the new aggregate overlaps with the steel bar or steel), the aggregate is abandoned and the step 4.3.1 is returned to abandon the aggregate and the coordinates are recalculated; if the collision check passes, it is considered that the aggregate is generated successfully and the next step is entered.

[0189] Step 4.3.3, use the method described above to check the collision between the newly placed aggregates and the already placed aggregates in turn.

[0190] If this aggregate is the first aggregate to be placed, skip this step and go directly to step 4.3.4.

[0191] If there is a collision (the new aggregate overlaps with the existing aggregate), abandon the aggregate and return to step 4.3.1 to recalculate the coordinates.

[0192] If the collision check passes, the aggregate is considered to be generated successfully and proceed to the next step.

[0193] Step 4.3.4, record and collection update.

[0194] The successfully generated aggregates are retained and added to the collection of aggregates used for collision checking;

[0195] Record the aggregate particle size and volume information;

[0196] When each particle size range (D i —D j ) The volume of aggregate put in reaches V (Di—Dj) Aggregate generation and placement are completed.

[0197] Rotate the aggregates In step 4.3.1, if you choose convex aggregates for placement, you need to randomly rotate each aggregate to ensure that the spatial orientation of the aggregates is different. The specific steps are as follows

[0198] Rotate the aggregate around the x-axis and z-axis and calculate the coordinates of the aggregate after rotation;

[0199] Define the rotation matrix R of the aggregate around the x-axis and z-axis x and R z :

[0200]

[0201] Where θ is the angle of rotation around the x-axis, and α is the angle of rotation around the z-axis.

[0202] Step 4.3.5, aggregate volume calculation.

[0203] In step 4.3.4, the volume of the aggregate is calculated by adding up the volumes of each tetrahedron that makes up the aggregate. The volume of a single tetrahedron is calculated as follows:

[0204]

[0205] Where V iRepresents the volume of a single tetrahedron, V represents the volume of the aggregate, A, B, C, O are the vertex coordinates of the tetrahedron, and || represents the modulus of the vector.

[0206] In order to facilitate scholars in the field to understand and implement the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the implementation examples described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0207] (1) Embodiment 1

[0208] The purpose of this example is to generate a three-dimensional mesoscopic model of steel-concrete with different steel shapes. The size of the base is 380mm×380mm×400mm. The size of the box-shaped steel is 250mm×200mm, and the thickness of the steel is 10mm. Fig.10 This is the H-beam microscopic model in the first embodiment of the present invention, and the aggregate is a polyhedron; Fig.12 This is the H-steel microscopic model in the first embodiment of the present invention, the aggregate is spherical; the size of the H-steel is 200mm×200mm, and the thickness of the web and flange are 8mm and 10mm respectively. The length of the two types of steel is 600mm. The thickness of the concrete cover is 10mm, and the diameter of the steel bar is 14mm. The shape of the coarse aggregate is a convex polyhedron, the particle size range is 10-40mm, and the volume content is 0.2. In this embodiment, by adjusting the shape and size of different steel sections, a three-dimensional microscopic model of steel-concrete is generated to study the influence of different steel section shapes on the performance of concrete structures.

[0209] (2) Embodiment 2

[0210] The purpose of this example is to generate a three-dimensional mesoscopic model of steel-concrete with different aggregate shapes. The size of the matrix is ​​380mm×380mm×400mm. The size of the H-shaped steel is 200mm×200mm, and the thickness of the web and flange are 8mm and 10mm respectively. Fig.11 This is the box-shaped steel microscopic model in the second embodiment of the present invention, and the aggregate is a polyhedron. Fig.13 This is the box-shaped steel micro-model in Example 2 of the present invention, and the aggregate is spherical. The length of both steel sections is 600 mm. The thickness of the concrete cover is 10 mm, and the diameter of the steel bar is 14 mm. The coarse aggregate is in the shape of a sphere and a convex polyhedron, with a particle size range of 10 to 40 mm and a volume content of 0.2. In this embodiment, by adjusting the shape of the aggregate, a three-dimensional micro-model of steel-concrete is generated to study the influence of different aggregate shapes on the performance of the concrete structure.

Claims

1. A method for constructing a three-dimensional seven-phase mesoscopic model of steel-concrete based on vector tracking, characterized in that: The three-dimensional seven-phase mesoscopic model of steel-concrete comprises: mortar, coarse aggregate, coarse aggregate-mortar interface layer, steel bars, mortar-steel bonding interface layer, steel, steel-mortar bonding interface layer; The construction method includes the following steps: Step 1: Generate a rectangular block base according to the given height, length and width; Step 2: Generate the steel section and the bonding layer between the steel section and the mortar according to the given shape and size; Step 3: Generate steel bars according to given positions and sizes, and generate the interface layer between the steel bars and the mortar; Step 4: Generate coarse aggregate according to the given shape and gradation, and generate the interface layer between aggregate and mortar; add aggregates into the matrix in sequence, and perform collision checks between aggregates and steel bars, steel sections, and between aggregates based on the vector tracking algorithm.

2. The method for constructing a three-dimensional seven-phase mesoscopic model of steel-concrete based on vector tracking according to claim 1 is characterized in that: Step 2 specifically includes the following sub-steps: Sub-step 2.1, determine the shape of the steel, box steel and H-shaped steel, the center of the steel coincides with the center of the base; the size of the steel includes the height, width and thickness of the steel; H-shaped steel includes the thickness of the web and flange; Sub-step 2.2, determining the position of the steel section through sub-step 2.1, calculating the position coordinates of each corner point of the steel section in the xy plane, and generating the steel section by stretching method; The steel section is divided into a plurality of cuboids; for H-shaped steel section, it is divided into 3 cuboids, and for box-shaped steel section, it is divided into 4 cuboids.

3. The method for constructing a three-dimensional seven-phase mesoscopic model of steel-concrete based on vector tracking according to claim 2 is characterized in that: Step 3 specifically includes the following sub-steps: Sub-step 3.1, generate longitudinal reinforcement at the four corners of the base, the position of the longitudinal reinforcement is related to the thickness of the concrete cover; the shape of the reinforcement is cylindrical; Sub-step 3.2, by determining the position of the steel bar in sub-step 3.1, generating a circle in the xy plane, and generating the steel bar by stretching.

4. The method for constructing a three-dimensional seven-phase mesoscopic model of steel-concrete based on vector tracking according to claim 3 is characterized in that: Step 4 specifically includes the following sub-steps: Sub-step 4.1, determine the shape of the aggregate; Sub-step 4.2, determine aggregate gradation; According to the Fuller curve theoretical formula and Monte Carlo random probability model, the gradation of aggregate in three-dimensional space is determined; the Fuller curve formula is as follows: Where P is the mass percentage of aggregate passing through the sieve hole diameter D0, D max is the maximum aggregate particle size; Based on the Fuller curve formula, calculate the aggregate volume in each particle size range: In the formula, V(D i ,D j ) indicates the particle size in D i —D j The volume of coarse aggregate within the range, D min ,D max Respectively represent the minimum and maximum coarse aggregate particle size, p k Indicates the volume ratio of coarse aggregate to concrete, V con Indicates the volume of concrete; The volume of concrete is expressed as: V con =length*width*height-S v1 -S v2 Among them, length, width, and height represent the length, width, and height of the matrix respectively, and S v1 and S v2 Represent the volume of steel sections and reinforcing bars respectively; According to the above formula, the Monte Carlo random method is used to generate aggregate distribution that conforms to the Fuller curve gradation, ensuring that the aggregate volume in each particle size range reaches the predetermined value; Sub-step 4.3: Generate aggregate.

5. The method for constructing a three-dimensional seven-phase mesoscopic model of steel-concrete based on vector tracking according to claim 4 is characterized in that: Sub-step 4.3 includes the following steps: Step 4.3.1, randomly generate aggregates; Generate the initial coordinates of a single aggregate using the method described in sub-step 4.2 and place the aggregate into the matrix; Calculate the coordinates of the aggregate and determine whether the aggregate is inside the matrix; if the coordinates of the aggregate are outside the matrix, abandon the aggregate and recalculate the coordinates; if the aggregate is inside the matrix, it is considered that the aggregate is generated successfully and proceed to the next step; Step 4.3.2, check the collision between the newly placed aggregate and the steel and reinforcement; Conduct collision checks on newly placed aggregates, steel sections and reinforcements; Split the steel into multiple cuboids; if it is an H-shaped steel, split it into 3 cuboids according to the position of the flange and web; if it is a box-shaped steel, split it into 2 horizontal and 2 vertical cuboids; a single steel bar is a cylinder, simplify it into a cuboid, the four faces of the cuboid are tangent to the side of the cylinder, and the two faces coincide with the upper and lower bottom surfaces of the cylinder; perform collision detection on the aggregate and each cuboid in turn. If there is a collision, that is, the new aggregate overlaps with the steel bar or the steel, then abandon the addition of the aggregate and return to step 4.3.1, then abandon the aggregate and recalculate the coordinates; if the collision check passes, it is considered that the aggregate is generated successfully and proceed to the next step; Step 4.3.3, check the collision of the newly placed aggregates with the already placed aggregates in turn; If the aggregate is the first aggregate to be placed, skip this step and go directly to step 4.3.4; If there is a collision, abandon the aggregate and return to step 4.3.1 to recalculate the coordinates; If the collision check passes, the aggregate is considered to be generated successfully and proceed to the next step; Step 4.3.4, record and collection update; The successfully generated aggregates are retained and added to the collection of aggregates used for collision checking; Record the aggregate particle size and volume information; When each particle size range (D i —D j ) The volume of aggregate put in reaches V (Di—Dj) Aggregate generation and placement are completed; Rotate the aggregates In step 4.3.1, if convex aggregates are selected for placement, randomly rotate each aggregate to ensure that the spatial orientation of the aggregates is different; the specific steps are as follows Rotate the aggregate around the x-axis and z-axis and calculate the coordinates of the aggregate after rotation; Define the rotation matrix R of the aggregate around the x-axis and z-axis x and R z : Where θ is the angle of rotation around the x-axis, and α is the angle of rotation around the z-axis; Step 4.3.5, aggregate volume calculation; In step 4.3.4, the volume of the aggregate is calculated by adding up the volumes of each tetrahedron that makes up the aggregate; the volume of a single tetrahedron is calculated as follows: Where V i Represents the volume of a single tetrahedron, V represents the volume of the aggregate, A, B, C, O are the vertex coordinates of the tetrahedron, and || represents the modulus of the vector.

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