A parametric construction method for a two-dimensional microscopic numerical model of recycled concrete

Abstract

The present invention provides a parametric method for constructing a two-dimensional mesoscopic numerical model of recycled concrete, comprising the following steps: 1) calculating the particle count and particle size of recycled concrete aggregate and the thickness of the old mortar layer; 2) constructing a geometric model of a two-dimensional random circular aggregate specimen of recycled concrete; 3) constructing a geometric model of a two-dimensional random convex polygonal aggregate specimen of recycled concrete; 4) performing unstructured meshing; and 5) constructing a projected mesh model of recycled concrete. This method effectively addresses the complex geometric spatial structure of recycled concrete. The resulting geometric model can truly reflect the actual gradation, content, and shape of the aggregate in the recycled concrete. It also effectively addresses the difficulty of meshing, resulting in a mesh model with extremely high unit quality.

Description

Technical Field

[0001] The present invention relates to the technical field of building materials, and in particular to a parameterized construction method of a two-dimensional mesoscopic numerical model of recycled concrete. Background Art

[0002] With the rapid development of the global economy, the construction industry has experienced significant growth worldwide, and the demand for building materials has continued to increase, especially in countries such as China, India, and Brazil. However, this growth has been accompanied by significant resource consumption and environmental issues, such as the increase in construction waste and increased carbon dioxide emissions. Therefore, research on how to better utilize construction waste has become a key issue in the current construction industry.

[0003] As a sustainable building material, recycled concrete has great application potential. The basic principle of recycled concrete is to clean, crush, and grade the aggregates in waste concrete, and then add them to a new cement matrix in a certain proportion to partially or completely replace the natural aggregates to prepare new concrete. Although recycled concrete helps to save natural resources and reduce environmental pollution, due to the complexity of its internal structure, the mechanical properties of recycled concrete at the macro and micro levels show great differences. Its performance is affected by the replacement rate of recycled aggregate, the presence of old mortar, and the characteristics of the interface transition zone. Therefore, a deep understanding of the microstructural characteristics of recycled concrete is crucial for optimizing its macro mechanical properties.

[0004] Currently, studies have used numerical simulation methods to analyze the mechanical behavior of recycled concrete. Micromechanical models provide an effective means of understanding the damage evolution within recycled concrete. These models typically consider recycled concrete as a five-phase composite material consisting of natural aggregate, old cement mortar, new cement mortar, the old interface transition zone between the natural aggregate and the old cement mortar, and the new interface transition zone between the old cement mortar and the new cement mortar. Traditional mesoscopic models mostly use simplified circular aggregate shapes and employ uniform structured meshing methods. These models either ignore or simplify the interface transition zone, making them difficult to meet the model accuracy requirements of engineering practice. Summary of the Invention

[0005] In order to solve the problems of complex geometric space structure, difficult meshing and thin interface transition zone that are difficult to simulate in the mesoscopic modeling of recycled concrete, the present invention proposes a parametric construction method for a two-dimensional mesoscopic numerical model of recycled concrete to address the technical problems existing in the above-mentioned background technology.

[0006] To solve the above technical problems, the present invention provides a parameterized construction method for a two-dimensional mesoscopic numerical model of recycled concrete, which comprises the following steps:

[0007] 1) Calculate the particle number, particle size and thickness of the old mortar layer of recycled concrete aggregate;

[0008] 2) Construction of geometric model of two-dimensional random circular aggregate specimens of recycled concrete

[0009] After the aggregate particles were generated, the “pick-and-place method” was used to establish the geometric model of the two-dimensional random circular aggregate specimen of recycled concrete;

[0010] 3) Construction of geometric model of recycled concrete two-dimensional random convex polygonal aggregate specimen

[0011] The inscribed polygon of each outer circle of recycled concrete circular aggregate is first extended outward, and then the inscribed polygon of each inner circle of recycled concrete circular aggregate is extended outward until the areas of the outer circle and inner circle are reached respectively. Thus, a two-dimensional random convex polygon aggregate geometric model of recycled concrete is generated.

[0012] 4) Unstructured grid division

[0013] Considering the boundary of the interface transition zone between aggregate and matrix in recycled concrete and the mesh refinement of the interface transition zone, a high-quality recycled concrete mesh model is obtained by using a mesh generation algorithm with geometric shapes specified by implicit functions.

[0014] 5) Construction of recycled concrete projection grid model.

[0015] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein the step 1) specifically includes the following steps:

[0016] 1.1) Calculate the particle size and gradation of recycled concrete aggregate

[0017] The Walraven formula is used to calculate the number of aggregate particles with different particle sizes in a two-dimensional cross section. The cumulative distribution probability of aggregate with particle size D < D0 is as follows:

[0018]

[0019] Where, P k is the percentage of aggregate volume to total concrete volume; P c is the cumulative distribution probability of aggregate with particle size smaller than D0;

[0020] The formula for calculating the number n of aggregate particles with particle size D1<D<D2 in a recycled aggregate concrete specimen with a cross-sectional area of ​​A is as follows:

[0021] n=[P c (D<D2)-P c (D<D1)]×A / A i ;

[0022] Where A i is the area of ​​recycled aggregate with diameter D;

[0023] 1.2) Calculate the thickness of the recycled aggregate old mortar layer

[0024] On the premise that the volume percentage of aggregate in concrete is equal to the area percentage of aggregate at a certain section, calculate the area ratio of old mortar to natural aggregate in the recycled aggregate at a certain section, and then calculate the thickness of the old mortar layer in the recycled aggregate:

[0025]

[0026] Where V s ,V g Respectively represent the area occupied by old mortar and aggregate in the recycled aggregate; ρ s ,ρ g Represent the density of old mortar and aggregate respectively; m s ,m 总 Respectively represent the mass of old mortar and recycled aggregate; ω represents the mass content of old mortar; It represents the ratio of old mortar area to aggregate area;

[0027] The mortar layer thickness h is obtained from the ratio of the old mortar area to the aggregate area:

[0028]

[0029] Where a represents the aggregate particle size.

[0030] The parameterized construction method of the two-dimensional microscopic numerical model of recycled concrete, wherein: the step 1) is to regard the recycled concrete as a five-phase composite material consisting of natural aggregate, old cement mortar, new cement mortar, old interface transition zone between natural aggregate and old cement mortar, and new interface transition zone between old cement mortar and new cement mortar at the microscopic level.

[0031] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein the process of establishing the two-dimensional recycled aggregate random distribution geometric model using the "pick-and-place method" in step 2) is as follows: using coordinates generated by a random number generator to place aggregate particles, and checking whether the placed particles meet the requirements, the aggregates are placed in a certain space in order from the largest particle to the smallest particle until a specified volume fraction is reached; and each aggregate is randomly placed at a position in the certain space, and an aggregate particle is placed at this position. If this position overlaps with an existing aggregate particle, a new position is selected until a suitable non-overlapping space is found; the aggregate placement process is described by the following mathematical model:

[0032] P new =(xnew ,y new );

[0033] Where, P new is the new particle position, x new ,y new is the coordinate of the new position and should satisfy:

[0034] ‖P new -P i ‖>r i +r new ;

[0035] Where, P i is the position of the existing particle, r i and r new are the radii of the existing particles and the new particles respectively.

[0036] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein the specific process of step 3) is as follows:

[0037] 3.1) Randomly generate several points on the circumference of each circular aggregate as the polygonal aggregate base frame; note that the number of base points of large aggregates is greater than that of small aggregates, and control the distance between the base points of large aggregates and small aggregates so that the centers of large and small aggregates are inside the generated polygonal aggregate base frame;

[0038] 3.2) The polygonal aggregate frame generated on the circumference of each circular aggregate is extended outwards in sequence until the area of ​​the circular aggregate in the inner cross section of the two-dimensional random circular aggregate specimen of recycled concrete is reached; the polygonal aggregate frame with a much smaller area than the corresponding circular aggregate is preferably selected, and the longer side is selected to extend outwards; for each vertex A1, A2, ..., A i , A i+1 ,…,A n ;Polygonal aggregate base frame vertex A i The coordinates of (x i ,y i ), A i+1 The coordinates of (x i+1 ,y i+1 );

[0039] The coordinates of the new insertion point convex outward are:

[0040]

[0041] Where R1, R2 are random numbers in the interval (0,1);

[0042] When the area of ​​the convex polygonal aggregate after extension is greater than or equal to the area of ​​the corresponding circular aggregate, the extension ends.

[0043] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete comprises: compiling automatic generation software of a convex polygonal aggregate geometric model through the steps (1) to (3), utilizing the automatic generation software to transform the two-dimensional random circular aggregate geometric model of recycled concrete into a two-dimensional random convex polygonal aggregate geometric model of recycled concrete, wherein the two-dimensional random circular aggregate geometric model of recycled concrete and the two-dimensional random convex polygonal aggregate geometric model of recycled concrete have the same aggregate gradation, corresponding aggregate content and old mortar content, but different aggregate shapes;

[0044] The main program flow of converting the recycled concrete two-dimensional random circular aggregate geometric model into the recycled concrete two-dimensional random convex polygonal aggregate geometric model using the automatic generation software of the convex polygonal aggregate geometric model is as follows:

[0045] (1) Input round aggregate information

[0046] Input information about recycled concrete circular aggregates. This information includes physical parameters such as location, gradation, and old mortar content of circular aggregates;

[0047] (2) Generate a polygonal base frame on the old mortar boundary

[0048] According to the recycled concrete circular aggregate information, a polygonal old mortar base frame is created on the old mortar boundary;

[0049] (3) Extended convex polygonal old mortar base frame;

[0050] (4) Generate a polygonal natural aggregate base frame on the natural aggregate boundary

[0051] (5) Extended polygonal natural aggregate base frame;

[0052] (6) Output convex polygon aggregate information

[0053] After completing the generation and extension of all frames, the final convex polygon aggregate information is output.

[0054] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete is described, wherein the newly inserted points must meet the following requirements: ① the newly inserted points cannot exceed the specimen size range; ② the newly formed side length must be greater than the set minimum value; ③ the convexity condition must be met; ④ for the extension and convexity of the old mortar boundary, it must be ensured that there is no cross-overlap between the aggregates, and the extension and convexity of the natural aggregate boundary must ensure that the extension and convexity points are within the corresponding old mortar boundary.

[0055] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein the specific process of step 4) is as follows:

[0056] 4.1) Meshing of the 2D microscopic model of recycled concrete

[0057] Based on the physical analogy between the edges of triangular elements and truss structures, a linear force-displacement relationship is used to solve the equilibrium problem in the truss structure to improve the initial mesh. The specific solution process is as follows:

[0058] The difference between the ideal length and the current length of each side of the triangular element is set as the spring force. The mesh is adjusted by updating the node position and recalculating the Delaunay triangulation until the node system reaches equilibrium. The node update formula is:

[0059]

[0060] In the above formula, k is the coefficient of the simulated linear spring rod, which can be set to 1. When F>0, the mesh boundary is stretched. For all internal nodes, there is a balance: For most rods, the force is repulsive, i.e., F>0, to help the nodes expand within the entire geometric boundary;

[0061] The ideal length l0 of the side of the triangular element is described by the mesh size function h(x,y). h(x,y) does not have to be equal to the actual size. The mesh size function h(x,y) gives the relative distribution on the domain.

[0062]

[0063] h(x i ,y i )=min(min(a+b*{|d(x i ,y i )|}),c);

[0064] In the above formula, d(x i ,y i ) is the distance function, {|d(x i ,y i )|} is the point (x i ,y i ) is the set of absolute values ​​of the distances to each aggregate interface; a, b, c are the relative size parameters of the mesh at the interface;

[0065] 4.2) Formation of boundary layer inside the mesh in the interface transition zone

[0066] During the mesh generation process, when nodes are within a certain range hp from the geometric boundary of the aggregate, these nodes will be "pulled back" to the nearest position on the boundary of the interface transition zone; the thickness of the interface transition zone is h, and it is assumed that the distance from the aggregate geometric boundary to the aggregate is ±h / 2 as the interface transition zone, and the points within the range hp from the interface transition zone boundary need to be moved and corrected to the nearest point on its boundary; the node correction distance hp can be taken as 20% to 50% of the thickness of the interface transition zone h, that is, hp = 0.2h to 0.5h, to ensure a reasonable correction range;

[0067] The first-order Taylor approximation is used to calculate the node correction distance vector to form the internal boundary layer. The correction distance refers to the correction amount from the current position of the node to the nearest interface transition zone boundary. Assuming a node P and an interface function F(P), the corrected node position P′ can be obtained by the formula:

[0068] P'=P+ΔP;

[0069] And the node correction distance vector ΔP is approximately calculated by the first-order Taylor expansion:

[0070]

[0071] 4.3) Meshing of the 2D microscopic model of recycled concrete

[0072] 4.3.1) Create uniformly distributed nodes within the geometric boundary, corresponding to equilateral triangle elements;

[0073] 4.3.2) Calculate the size function h(x,y) of each node and use the rejection sampling method to calculate the size function h(x,y) of each node. i ,y i ) 2 The nodes are selected with probability; the mesh refinement gradients inside and outside the natural aggregate are set separately, and the maximum mesh size is specified;

[0074] 4.3.3) Enter the main loop of mesh optimization, and continuously iterate and optimize the node positions until a certain convergence criterion is met

[0075] 4.3.4) Terminate the loop. The termination condition is determined by the maximum motion displacement of the node in the current iteration. The maximum motion displacement of the node is obtained by the following formula:

[0076]

[0077] Where ΔP max is the maximum motion displacement of all nodes in the current iteration; Δx i and Δy i are the displacements of the i-th node in the x and y directions, respectively.

[0078] The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete, wherein the specific steps of entering the main loop of the grid optimization in step 4.3.3) are as follows:

[0079] 4.3.3.1) Remove triangular meshes whose centroids are outside the geometric boundary;

[0080] 4.3.3.2) Calculate the ideal triangle side length using the mesh size function h(x,y), and adjust the side length and move nodes based on the difference between the ideal and actual side lengths.

[0081] 4.3.3.3) If a node moves outside the geometric boundary of the two-dimensional random circular aggregate recycled concrete specimen geometric model and the two-dimensional random convex polygonal aggregate recycled concrete specimen geometric model after the update, move it back to the nearest point on its boundary to avoid node loss;

[0082] 4.3.3.4) Set the node correction distance hp and pull the points within the interface transition zone hp back to the boundary of the interface transition zone to form an internal boundary layer.

[0083] The parameterized construction method of the two-dimensional microscopic numerical model of recycled concrete, wherein: the specific process of step (5) is: firstly, a geometric model of the recycled concrete specimen is established and meshed, and then the recycled concrete aggregate is projected into the mesh unit area; the unit type is determined by judging the relative position of each mesh unit node; finally, the material parameters are assigned to the generated units.

[0084] The parameterized construction method of the two-dimensional microscopic numerical model of recycled concrete, wherein the process of determining its unit type is as follows: when all nodes of the unit fall in the natural aggregate area, this unit will be defined as a natural aggregate unit; when all nodes fall in the old mortar area, this unit will be defined as an old mortar unit; when all nodes fall in the new mortar area, this unit will be defined as a new mortar unit; and when some nodes are in the natural aggregate area and some fall in the old mortar area, they will be defined as old interface transition zone units; when some nodes are in the old mortar area and some fall in the new mortar area, this unit is a new interface transition zone unit.

[0085] By adopting the above technical solution, the present invention has the following beneficial effects:

[0086] The parametric construction method for the two-dimensional mesoscopic numerical model of recycled concrete proposed in the present invention is well-conceived and can effectively solve the problem of complex geometric spatial structure of recycled concrete. Through parametric construction, the geometric model of recycled concrete can truly reflect the actual gradation, content and shape of aggregates, ensuring the authenticity and accuracy of the model and providing a reliable basis for mechanical analysis at the mesoscopic level.

[0087] This paper proposes a new interface-aligned unstructured mesh optimization method that successfully addresses the difficulties of traditional mesh generation. Taking into account the interface transition zone between aggregate and matrix in recycled concrete, the present invention refines the mesh in this transition zone. Using a mesh generation algorithm based on geometric shapes specified by implicit functions, a mesh model with extremely high element quality is generated. The resulting mesh model not only improves the accuracy of finite element analysis but also effectively reduces the computational effort and improves computational efficiency.

[0088] The present invention has significant advantages in the parametric construction and high-quality meshing of recycled concrete micro-numerical models, solving key problems in the existing technology. It is suitable for recycled concrete specimen models of different shapes and sizes, and provides strong technical support for the numerical simulation and engineering application of recycled concrete. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0090] Figure 1 Construct a flow chart for a two-dimensional mesoscopic numerical model of recycled concrete;

[0091] Figure 2 Schematic diagram of the mesostructure of recycled concrete;

[0092] Figure 3 Schematic diagram of the microstructure of recycled convex aggregate concrete;

[0093] Figure 4 Generate a schematic diagram for the new vertex;

[0094] Figure 5 Generate process diagrams for polygonal aggregates;

[0095] Figure 6 Flowchart of the main program for building polygonal aggregate model;

[0096] Figure 7 Schematic diagram of the process of generating geometric model of random convex polygon aggregate of recycled concrete ( Figure 6 Middle: (a) Random circular aggregate model of recycled concrete, (b) Generate an inscribed polygon on the outer circle (blue line) and extend it outward as the outer boundary of the convex recycled aggregate (black line), (c) Generate an inscribed polygon on the inner circle (blue line) and extend it outward as the outer boundary of the convex natural aggregate (black line), (d) Random convex polygonal aggregate model of recycled concrete);

[0097] Figure 8 This is a diagram of the interface layer formation process;

[0098] Figure 9 This is the mesh generation process diagram;

[0099] Figure 10 is a schematic diagram of mesh quality;

[0100] Figure 11 Schematic diagram of the projection grid model;

[0101] Figure 12 This is the projection grid model and unit mass diagram of the circular aggregate recycled concrete square slab;

[0102] Figure 13 The projection mesh model and unit mass diagram of the convex aggregate recycled concrete square slab. DETAILED DESCRIPTION

[0103] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0104] The present invention will be further explained below with reference to specific embodiments.

[0105] like Figure 1 As shown, this embodiment provides a parameterized construction method of a two-dimensional mesoscopic numerical model of recycled concrete, which includes the following steps:

[0106] S100, calculating the particle number and particle size of recycled concrete aggregate and the thickness of the old mortar layer;

[0107] At the microscopic level, recycled aggregate concrete is considered as a five-phase composite material consisting of natural aggregate, old cement mortar, new cement mortar, old interface transition zone between natural aggregate and old cement mortar, and new interface transition zone between old cement mortar and new cement mortar, such as Figure 2 shown.

[0108] S101. Calculate the particle size and gradation of recycled concrete aggregate

[0109] The Walraven formula is used to calculate the number of aggregate particles with different particle sizes in a two-dimensional cross section. The cumulative distribution probability of aggregate with particle size D < D0 is as follows:

[0110]

[0111] Where, P kIt is the percentage of aggregate volume to total concrete volume, generally taken as 0.75; P c is the cumulative distribution probability of aggregate with particle size smaller than D0.

[0112] The formula for calculating the number n of aggregate particles with particle size D1<D<D2 in a recycled aggregate concrete specimen with a cross-sectional area of ​​A is as follows:

[0113] n=[P c (D<D2)-P c (D<D1)]×A / A i ;

[0114] Where A i is the area of ​​recycled aggregate with diameter D.

[0115] S102, thickness of recycled aggregate old mortar layer

[0116] The volume percentage of aggregate in concrete is basically equal to the area percentage of aggregate at a certain section. From this, the area ratio of old mortar and natural aggregate in the recycled aggregate at a certain section can be calculated, and then the thickness of the old mortar layer in the recycled aggregate can be calculated.

[0117]

[0118] Where V s ,V g Respectively represent the area occupied by old mortar and aggregate in the recycled aggregate, ρ s ,ρ g Represent the density of old mortar and aggregate, m s ,m 总 Represent the mass of old mortar and recycled aggregate respectively, ω represents the mass content of old mortar, It represents the ratio of old mortar area to aggregate area.

[0119] The mortar layer thickness h is obtained from the area ratio.

[0120]

[0121] Where a represents the aggregate particle size.

[0122] S200, Construction of geometric model of two-dimensional random circular aggregate specimens of recycled concrete

[0123] After the aggregate particles are generated, they need to be placed in a certain space. The present invention adopts the "pick-and-place method" to establish a two-dimensional recycled aggregate random distribution geometric model. Specifically, the "pick-and-place method" is used to place the aggregates in the order from the largest to the smallest particles in a certain space until a specified volume fraction is reached. Starting from the largest particles rather than the smallest particles, the aggregates are placed in the specified space, which can greatly improve the efficiency of the aggregate placement algorithm. The aggregate particles are placed using coordinates generated by a random number generator, and the placed particles are checked to see if they meet the requirements. Each aggregate particle is randomly placed at a position in a certain space. If this position overlaps with an existing aggregate particle, a new position is selected until a suitable non-overlapping space is found. The aggregate placement process is described by the following mathematical model:

[0124] P new =(x new ,y new );

[0125] Where, P new is the new particle position, x new ,y new is the coordinate of the new position and should satisfy:

[0126] ‖P new -P i ‖>r i +r new ;

[0127] Where, P i is the position of the existing particle, r i and r new are the radii of the existing particles and the new particles respectively.

[0128] S300, Geometric model of two-dimensional random convex polygonal aggregate specimens of recycled concrete

[0129] Based on the geometric model of the two-dimensional random circular aggregate specimen of recycled concrete, a random polygonal aggregate specimen model is generated. Specifically, the inscribed polygon of each outer circle of the recycled concrete circular aggregate is first extended outward, and then the inscribed polygon of each inner circle of the recycled concrete circular aggregate is extended outward until the areas of the outer circle and inner circle are reached respectively. In this way, a two-dimensional random convex polygonal aggregate specimen geometric model of recycled concrete with the same area as the circular aggregate is generated, as shown in the figure. Figure 3 shown.

[0130] S301. Randomly generate several points on the circumference of each circular aggregate as a polygonal aggregate base frame. Note that the number of base points for large aggregates is greater than the number of base points for small aggregates. The distance between the base points of large aggregates and small aggregates is controlled so that the centers of the large and small aggregates are within the generated polygonal aggregate base frame.

[0131] S302, sequentially extending the polygonal aggregate base frame generated on the circumference of each circular aggregate outward until the area of ​​the inner cross-section of the two-dimensional random circular aggregate specimen of recycled concrete is reached; preferentially selecting a polygonal aggregate base frame that is much smaller than the area of ​​the corresponding circular aggregate, and selecting the longer side to extend outward;

[0132] like Figure 4 As shown, for each vertex A1, A2, ..., A of any polygonal aggregate base frame i , A i+1 ,…,A n ;Polygonal aggregate base frame vertex A i The coordinates of (x i ,y i ), A i+1 The coordinates of (x i+1 ,y i+1 );

[0133] The coordinates of the new insertion point convex outward are:

[0134]

[0135] Where R1 and R2 are random numbers in the interval (0,1).

[0136] At the same time, the newly inserted points must meet the following requirements: ① The newly inserted points cannot exceed the specimen size range; ② The newly formed side length must be greater than the set minimum value; ③ The convex condition must be met; ④ For the extension and convexity of the old mortar boundary, it must be ensured that there is no cross-overlap between the aggregates, and the extension and convexity of the natural aggregate boundary must ensure that the extension and convexity points are within the corresponding old mortar boundary.

[0137] When the area of ​​the polygon after convexification is greater than or equal to the area of ​​the corresponding circle, the convexification ends. The polygon aggregate generation process is as follows: Figure 5 shown.

[0138] The method of steps S100-S300 above is used to compile automatic generation software for a convex polygonal aggregate geometric model. The automatic generation software is used to transform the two-dimensional random circular aggregate geometric model of recycled concrete into a two-dimensional random convex polygonal aggregate geometric model of recycled concrete. The two-dimensional random circular aggregate geometric model of recycled concrete and the two-dimensional random convex polygonal aggregate geometric model of recycled concrete have the same aggregate gradation, corresponding aggregate content and old mortar content, but different aggregate shapes.

[0139] The main program flow of using this automatic generation software to transform the recycled concrete two-dimensional random circular aggregate geometric model into the recycled concrete two-dimensional random convex polygonal aggregate geometric model is as follows (e.g. Figure 6 ):

[0140] (1) Input round aggregate information

[0141] Input information about recycled concrete circular aggregates. This information includes physical parameters such as location, gradation, and old mortar content of circular aggregates;

[0142] (2) Generate a polygonal base frame on the old mortar boundary

[0143] According to the recycled concrete circular aggregate information, a polygonal old mortar base frame is created on the old mortar boundary;

[0144] (3) Extended convex polygonal old mortar base frame;

[0145] (4) Generate a polygonal natural aggregate base frame on the natural aggregate boundary

[0146] (5) Extended polygonal natural aggregate base frame;

[0147] (6) Output convex polygon aggregate information

[0148] After completing the generation and extension of all frames, the final convex polygon aggregate information is output.

[0149] like Figure 7 Figure 3 shows the generation process of the two-dimensional random convex polygonal aggregate geometric model of recycled concrete: (a) Two-dimensional random circular aggregate model of recycled concrete; (b) Generate an inscribed polygon on the outer circle (blue line); and extend it outward to form the outer boundary of the convex recycled aggregate (black line); (c) Generate an inscribed polygon on the inner circle (blue line), and extend it outward to form the outer boundary of the convex natural aggregate (black line); (d) Two-dimensional random convex polygonal aggregate geometric model of recycled concrete.

[0150] S400, unstructured meshing

[0151] After generating the geometric models of the two-dimensional random circular aggregate and convex polygonal aggregate specimens of recycled concrete, they need to be meshed. To generate high-quality meshes, a mesh generation algorithm based on the geometry specified by implicit functions is used. This algorithm considers the boundaries of the interface transition zone and mesh refinement, optimizes the mesh, and applies it to the recycled concrete model, resulting in a high-quality recycled concrete mesh model.

[0152] S401. Meshing of a 2D microscopic model of recycled concrete

[0153] Based on the physical analogy between the edges of triangular elements and truss structures, a linear force-displacement relationship is used to solve the equilibrium problem in the truss structure to improve the initial mesh. The specific solution process is as follows:

[0154] The difference between the ideal length and the current length of each side of the triangular element is set as the spring force. The mesh is adjusted by updating the node positions and recalculating the Delaunay triangulation (any set of points can be triangulated by the Delaunay algorithm, that is, generating triangular elements that meet the Delaunay conditions, ensuring that no point is located within the circumcircle of any triangle) until the node system reaches equilibrium. When the node moves, the mesh is optimized by recalculating the Delaunay triangulation or by local updates to improve the element quality. In the equilibrium state, the elements tend to have high quality, and the method can be extended to higher dimensions.

[0155] The force F on each edge of a triangle element depends on the difference between its current length l and its ideal length l0:

[0156]

[0157] Where k is the coefficient for simulating a linear spring rod and can be set to 1. When F>0, the mesh boundary is stretched. For all internal nodes, there is a balance: For most rods, the force is repulsive (F>0) to help the node expand within the entire geometric boundary. This means that when the current length is close to the ideal length, F should be greater than zero. This can be achieved by appropriately scaling the desired ideal length, typically by 20% (Fscale=1.2).

[0158] The ideal length l0 of the side of a triangular element is described by the mesh size function h(x,y). Note that h(x,y) does not have to be equal to the actual size; the mesh size function gives the relative distribution over the domain; to avoid large variations in element size, this is achieved by limiting the gradient in h(x,y).

[0159]

[0160] h(x i ,y i )=min(min(a+b*{|d(x i ,y i )|}),c);

[0161] Among them, d(x i ,y i ) is the distance function, {|d(x i ,y i )|} is the point (x i ,y i ) is the set of absolute values ​​of the distances to each aggregate interface; a, b, and c are the relative size parameters of the mesh at the interface.

[0162] S402, formation of boundary layer inside the grid in the interface transition zone

[0163] During the mesh generation process, when nodes are within a certain range hp from the geometric boundary of the aggregate (the "certain range" here means that the distance between the node and the geometric boundary of the aggregate is less than a certain threshold. The nodes within this range will be corrected to the position closest to the boundary of the interface transition zone. Usually, this threshold is several millimeters), these nodes will be "pulled back" to the position closest to the boundary of the interface transition zone. Figure 8 , the thickness of the interface transition zone is h, and the node correction distance is hp. We can simply assume that the distance from the aggregate to the geometric boundary ±h / 2 is the interface transition zone, and the points within the range hp from the boundary of the interface transition zone need to be moved and corrected to the nearest point on its boundary; the node correction distance hp can be taken as 20% to 50% of the thickness of the interface transition zone h, that is, hp = 0.2h to 0.5h, to ensure that the correction range is reasonable;

[0164] The first-order Taylor approximation is used to calculate the node correction distance vector to form the internal boundary layer. The correction distance refers to the correction amount from the current node position to the nearest interface transition zone boundary. Assuming a point P and an interface function F(P), the corrected node position P′ can be obtained by the following formula:

[0165] P'=P+ΔP;

[0166] And the node correction distance vector ΔP is approximately calculated by the first-order Taylor expansion:

[0167]

[0168] S403. Meshing of a 2D microscopic model of recycled concrete

[0169] Taking a 100×100mm two-dimensional specimen as an example, a recycled round aggregate with a radius of 25mm is placed at the center of the specimen. The thickness of the old mortar is 5mm, and the interface transition zone is 1mm. The specimen mesh is divided as follows:

[0170] S4031. Create evenly distributed nodes within the geometric boundary, corresponding to equilateral triangle units, such as Figure 9 (a) shows an equilateral triangle grid with a side length of 1 mm;

[0171] S4032, calculate the size function h(x,y) of each node, and use the rejection sampling method to calculate the size function h(x,y) of each node. i ,y i ) 2Nodes are selected with probability (in order to adjust the mesh size more accurately, nodes need to be selected by rejection sampling, which is a way of selecting nodes with a specific probability within the model area); the mesh refinement gradients inside and outside the natural aggregate are set separately, and the maximum mesh size is specified; e.g. Figure 9 As shown in (b), the mesh refinement gradient is 1 inside the natural aggregate and 0.2 outside the natural aggregate, and the maximum mesh size is set to 3 mm.

[0172] S4033, enter the main loop, and continuously iteratively optimize the node position until a certain convergence standard is met; the main loop steps are as follows:

[0173] ① Remove the triangular mesh whose centroid is outside the geometric boundary;

[0174] ② Calculate the ideal triangle side length through the grid size function h(x,y), adjust the side length and move nodes based on the difference with the actual side length; Figure 9 (c) shows the Delaunay triangulation diagram after the first node movement;

[0175] ③ If a node moves outside the geometric boundaries of the two-dimensional random circular aggregate recycled concrete specimen geometric model and the two-dimensional random convex polygonal aggregate recycled concrete specimen geometric model after updating, it will be moved back to the nearest point on its boundary to avoid node loss;

[0176] ④ Set the node correction distance hp, and pull the points at a certain distance from the interface transition zone hp back to the boundary of the interface transition zone to form an internal boundary layer.

[0177] S4034. Terminate the loop. The termination condition is determined by the maximum motion displacement of the node in the current iteration. The maximum motion displacement of the node is obtained by the following formula:

[0178]

[0179] Where ΔP max is the maximum motion displacement of all nodes in the current iteration; Δx i and Δy i are the displacements of the i-th node in the x and y directions, respectively.

[0180] like Figure 9 (d) Figure 9 (e) and Figure 9As shown in Figure (f), assuming the interface transition zone is 1mm, these are the Delaunay meshes after the 1st, 5th, and 100th iterations. It can be seen from the figure that as the iterations progress, the mesh quality improves, and the resulting triangular elements are almost equilateral. A commonly used mesh quality evaluation metric is the ratio of the radius of the largest inscribed circle (multiplied by 2) to the radius of the smallest circumscribed circle:

[0181]

[0182] Where a, b, and c are the side lengths. As a rule of thumb, if q > 0.5 for all triangles, the result is good.

[0183] Figure 10 Respectively Figure 9 (d) Figure 9 (e) and Figure 9 (f) Histogram after calculating the grid quality, Figure 10 It can be seen that as the mesh quality is optimized through iteration, the quality and uniformity of the mesh units generated by the algorithm become better and better. At the 100th iteration, q of all units is greater than 0.6, and the average quality is 0.9359, which means that the quality of the generated mesh is extremely high.

[0184] It should be noted that since the natural aggregate units are often strong and rarely damaged under load, in order to reduce the calculation scale, different mesh refinement parameters are adopted inside and outside the natural aggregate to reduce the overall degrees of freedom of the specimen.

[0185] S500, Recycled Concrete Projection Mesh Model

[0186] First, the overall model of the recycled concrete specimen is established and meshed. Then, the recycled concrete aggregate (including circular aggregate and convex polygonal aggregate) is projected into the mesh unit area. The unit type is determined by judging the relative position of the unit nodes, and the material parameters of the generated units are assigned. When all the nodes of the unit fall in the natural aggregate area, this unit will be defined as a natural aggregate unit; when all the nodes fall in the old mortar area, this unit is defined as an old mortar unit; when all the nodes fall in the new mortar area, this unit is defined as a new mortar unit; and when some nodes are in the natural aggregate area and some fall in the old mortar area, they will be defined as old interface transition zone units; when some nodes are in the old mortar area and some fall in the new mortar area, this unit is a new interface transition zone unit. Finally, the material parameters of the generated units are assigned. As Figure 11(a), the light blue area represents the new mortar matrix, the blue area represents the old mortar matrix, the red area represents the natural aggregate, and the white thin layer area around the recycled aggregate particles is the interface transition zone. In addition, using the same method, a high-quality projection mesh model can also be generated for the convex aggregate concrete model, such as Figure 11 (b) shown.

[0187] Example Application

[0188] In the following example, a 100mm×100mm square specimen is used as a representative. It is assumed that the aggregate consists of three types of particle sizes: coarse aggregate, medium aggregate, and fine aggregate. Their diameters are 17.5, 12.5, and 7.5mm, respectively. The aggregate content is 40%, the content of old mortar attached to the aggregate is 42%, and the thickness of the interface transition zone is 0.25mm. The Walraven formula is used to calculate the number of particles of each size of aggregate. In the meshing, it is assumed that the initial mesh size is 0.25mm and the node correction range of the interface transition zone is 0.2mm. The random circular aggregate and convex polygonal aggregate specimen models of concrete and recycled concrete are established respectively, as shown in the following example. Figure 12-13 As shown in the figure, it can be seen that the average unit quality of each model is above 0.94, indicating that the units in each model are almost equilateral and the model has a higher mesh quality. In addition, compared with the traditional mesh division, the mesh division method in the patent method can generate a background mesh model with adjustable thickness in the interface transition zone. In addition, by controlling the mesh encryption gradient, the number of degrees of freedom can be significantly reduced, and the mesh quality and uniformity are better.

[0189] (a) 100mm×100mm round aggregate recycled concrete square slab

[0190] Number of nodes: 50923; number of elements: 101285; average element quality: 0.9440.

[0191] (b) 100mm×100mm convex aggregate recycled concrete square slab

[0192] Number of nodes: 52066; number of elements: 103563; average element quality: 0.9429.

[0193] The present invention can effectively solve the problem of complex geometric space structure of recycled concrete. The established geometric model can truly reflect the actual gradation, content and shape of aggregate in recycled concrete. It can also effectively solve the problem of difficult grid division. The established grid model has extremely high unit quality.

[0194] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A parameterized construction method for a two-dimensional mesoscopic numerical model of recycled concrete, characterized in that: The following steps are involved: 1) Calculate the particle number, particle size and thickness of the old mortar layer of recycled concrete aggregate; 2) Construction of geometric model of two-dimensional random circular aggregate specimens of recycled concrete After the aggregate particles are generated, the "pick-and-place method" is used to establish the geometric model of the two-dimensional random circular aggregate specimen of recycled concrete; 3) Construction of geometric model of recycled concrete 2D random convex polygon aggregate specimen The inscribed polygon of each outer circle of recycled concrete circular aggregate is first extended outward, and then the inscribed polygon of each inner circle of recycled concrete circular aggregate is extended outward until the areas of the outer circle and inner circle are reached respectively. Thus, a two-dimensional random convex polygon aggregate geometric model of recycled concrete is generated. 4) Unstructured grid division Considering the boundary of the interface transition zone between aggregate and matrix in recycled concrete and the mesh refinement of the interface transition zone, a high-quality recycled concrete mesh model is obtained by using a mesh generation algorithm with geometric shapes specified by implicit functions. The specific process is as follows: 4.1) Meshing of the 2D microscopic model of recycled concrete Based on the physical analogy between the edges of triangular elements and truss structures, a linear force-displacement relationship is used to solve the equilibrium problem in the truss structure to improve the initial mesh. The specific solution process is as follows: The difference between the ideal length and the current length of each side of the triangular element is set as the spring force. The mesh is adjusted by updating the node position and recalculating the Delaunay triangulation until the node system reaches equilibrium. The node update formula is: ； In the above formula k To simulate the coefficient of the linear spring rod, it can be set to 1; when F > 0, the mesh boundary is stretched; for all internal nodes, there is a balance: ; For most rods, the force is repulsive. F > 0 to help nodes spread out within the entire geometry boundary; Ideal length of the sides of a triangular element As a function of the grid size h ( x , y )describe, h ( x , y ) does not have to be equal to the actual size, the grid size function h ( x , y ) gives the relative distribution over the domain; ； ； In the above formula is the distance function, Then it is a point The set of absolute values ​​of the distance to each aggregate interface; a, b, c are the relative size parameters of the mesh at the interface; 4.2) Formation of boundary layer inside the mesh in the interface transition zone During the mesh generation process, when the node is within a certain range from the aggregate geometry boundary hp When the interface transition zone is within , these nodes will be "pulled back" to the position closest to the boundary of the interface transition zone; the thickness of the interface transition zone is h , then it is assumed that the distance from the aggregate to the geometric boundary of the aggregate The interface transition zone is the interface transition zone. hp Points within the range need to be moved and corrected to the nearest point on its boundary; node correction distance hp Can be taken as the thickness of the interface transition zone h 20% to 50% of hp = 0.2h to 0.5h to ensure that the correction range is reasonable; The first-order Taylor approximation is used to calculate the node correction distance vector to form the internal boundary layer; the correction distance refers to the correction amount of the node from the current position to the nearest interface transition zone boundary; assuming that a node is given P and interface functions , then the corrected node position It can be obtained by the formula: ; And the node corrected distance vector Approximate calculation by first-order Taylor expansion: ； 4.3) Meshing of the 2D microscopic model of recycled concrete 4.3.1) Create uniformly distributed nodes within the geometric boundary, corresponding to equilateral triangle elements; 4.3.2) Calculate the size function of each node h ( x , y ), using the rejection sampling method to The nodes are selected with probability; the mesh refinement gradients inside and outside the natural aggregate are set separately, and the maximum mesh size is specified; 4.3.3) Entering the main loop of mesh optimization, the node positions are continuously optimized iteratively until a certain convergence criterion is met. The specific steps for entering the main loop of mesh optimization are as follows: 4.3.3.1) Remove triangular meshes whose centroids are outside the geometric boundary; 4.3.3.2) Through the grid size function h ( x , y ) Calculate the ideal triangle side length, adjust the side length based on the difference with the actual side length, and move nodes; 4.3.3.3) If a node moves outside the geometric boundary of the two-dimensional random circular aggregate recycled concrete specimen geometric model and the two-dimensional random convex polygonal aggregate recycled concrete specimen geometric model after the update, move it back to the nearest point on its boundary to avoid node loss; 4.3.3.4) Set node correction distance hp , the distance from the interface transition zone hp The points inside are pulled back to the boundary of the interface transition zone to form an internal boundary layer; 4.3.4) Terminate the loop. The termination condition is determined by the maximum motion displacement of the node in the current iteration. The maximum motion displacement of the node is obtained by the following formula: ； Where, is the maximum motion displacement of all nodes in the current iteration; and They are i Nodes in x and y Directional displacement; 5) Construction of recycled concrete projection grid model.

2. The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: The step 1) specifically includes the following steps: 1.1) Calculation of particle size and gradation of recycled concrete aggregate Walraven formula is used to calculate the number of aggregate particles with different particle sizes in the two-dimensional cross section. The cumulative distribution probability of aggregate is as follows: ； Where, is the percentage of aggregate volume to total concrete volume; For particles smaller than The cumulative distribution probability of aggregate; Calculate the cross-sectional area as A In the recycled aggregate concrete specimens, the particle size The number of aggregate particles n is as follows: ； Where, The diameter is D area of ​​recycled aggregate; 1.2) Calculate the thickness of the recycled aggregate old mortar layer On the premise that the volume percentage of aggregate in concrete is equal to the area percentage of aggregate at a certain section, calculate the area ratio of old mortar to natural aggregate in the recycled aggregate at a certain section, and then calculate the thickness of the old mortar layer in the recycled aggregate: ； ； Where, , Respectively represent the area occupied by old mortar and aggregate in recycled aggregate; , represent the density of old mortar and aggregate respectively; , represent the mass of old mortar and recycled aggregate respectively; Indicates the mass content of old mortar; It represents the ratio of old mortar area to aggregate area; The thickness of the mortar layer is obtained from the ratio of the old mortar area to the aggregate area h : ； Where, Indicates aggregate particle size.

3. The method for parameterizing a two-dimensional mesoscopic numerical model of recycled concrete according to claim 1, wherein: The step 1) is to regard the recycled concrete as a five-phase composite material consisting of natural aggregate, old cement mortar, new cement mortar, old interface transition zone between natural aggregate and old cement mortar, and new interface transition zone between old cement mortar and new cement mortar at a microscopic level.

4. The parameterized construction method of the two-dimensional microscopic numerical model of recycled concrete according to claim 1, characterized in that The process of establishing a two-dimensional recycled aggregate random distribution geometric model using the "pick-and-place method" in step 2) is as follows: using the coordinates generated by the random number generator to place aggregate particles, and checking whether the placed particles meet the requirements, the aggregates are placed in a certain space in order from the largest particle to the smallest particle until the specified volume fraction is reached; and each aggregate particle is randomly placed at a position in a certain space, and an aggregate particle is placed at this position. If this position overlaps with an existing aggregate particle, a new position is selected until a suitable non-overlapping space is found; the aggregate placement process is described by the following mathematical model: ； Where, is the new particle position, is the coordinate of the new position and should satisfy: ； Where, is the position of the existing particles, and are the radii of the existing particles and the new particles respectively.

5. The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: The specific process of step 3) is as follows: 3.1) Randomly generate several points on the circumference of each circular aggregate as the polygonal aggregate base frame. Note that the number of base points of large aggregates is greater than that of small aggregates. Control the distance between the base points of large aggregates and small aggregates so that the centers of the large and small aggregates are inside the generated polygonal aggregate base frame. 3.2) The polygonal aggregate frame generated on the circumference of each circular aggregate is extended outwards in sequence until the area of ​​the circular aggregate in the inner cross section of the two-dimensional random circular aggregate specimen of recycled concrete is reached; the polygonal aggregate frame with a much smaller area than the corresponding circular aggregate is preferably selected, and the longer side is selected for extension and convexity; for each vertex of the arbitrary polygonal aggregate frame ;Polygonal aggregate base frame vertices The coordinates are , The coordinates are ; The coordinates of the new insertion point convex outward are: ； Where, is a random number in the interval (0, 1); When the area of ​​the convex polygonal aggregate after extension is greater than or equal to the area of ​​the corresponding circular aggregate, the extension ends.

6. The parameterized construction method of the two-dimensional microscopic numerical model of recycled concrete according to claim 1, characterized in that , through the steps 1)-3) of compiling the automatic generation software of the convex polygonal aggregate geometric model, using the automatic generation software to transform the recycled concrete two-dimensional random circular aggregate geometric model into a recycled concrete two-dimensional random convex polygonal aggregate geometric model, and the recycled concrete two-dimensional random circular aggregate geometric model and the recycled concrete two-dimensional random convex polygonal aggregate geometric model have the same aggregate gradation, corresponding aggregate content and old mortar content, but different aggregate shapes; The main program flow of converting the recycled concrete two-dimensional random circular aggregate geometric model into the recycled concrete two-dimensional random convex polygonal aggregate geometric model using the automatic generation software of the convex polygonal aggregate geometric model is as follows: (1) Input round aggregate information Input information about recycled concrete circular aggregates, including location, gradation and old mortar content; (2) Generate a polygonal base frame on the old mortar boundary According to the recycled concrete circular aggregate information, a polygonal old mortar base frame is created on the old mortar boundary; (3) Extended convex polygonal old mortar base frame; (4) Generate a polygonal natural aggregate base frame on the natural aggregate boundary; (5) Extended polygonal natural aggregate base frame; (6) Output convex polygon aggregate information After completing the generation and extension of all frames, the final convex polygon aggregate information is output.

7. The parameterized construction method of the two-dimensional mesoscopic numerical model of recycled concrete according to claim 5, characterized in that: The newly inserted points must meet the following requirements: ① The newly inserted points cannot exceed the specimen size range; ② The newly formed side length must be greater than the set minimum value; ③ The convex condition must be met; ④ For the extension and convexity of the old mortar boundary, it must be ensured that there is no cross-overlap between the aggregates, and the extension and convexity of the natural aggregate boundary must ensure that the extension and convexity points are within the corresponding old mortar boundary.

8. The parameterized construction method of the two-dimensional microscopic numerical model of recycled concrete according to claim 1, characterized in that The specific process of step 5) is as follows: first, a geometric model of the recycled concrete specimen is established and meshed, and then the recycled concrete aggregate is projected into the mesh unit area; the unit type is determined by judging the relative position of each mesh unit node; finally, the material parameters are assigned to the generated units.

9. The parameterized construction method of the two-dimensional microscopic numerical model of recycled concrete according to claim 8, characterized in that , the process of determining its unit type is: when all the nodes of the unit fall in the natural aggregate area, this unit will be defined as a natural aggregate unit; when all the nodes fall in the old mortar area, this unit will be defined as an old mortar unit; when all the nodes fall in the new mortar area, this unit will be defined as a new mortar unit; and when some nodes are in the natural aggregate area and some fall in the old mortar area, it will be defined as an old interface transition zone unit; when some nodes are in the old mortar area and some fall in the new mortar area, this unit is a new interface transition zone unit.

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