Parameterization construction method of recycled concrete three-dimensional mesoscopic numerical model

Abstract

The invention provides a parameterization construction method of a recycled concrete three-dimensional mesoscopic numerical model. The parameterization construction method comprises the following steps: 1) calculating the particle number and the particle size of recycled concrete aggregate and the thickness of an old mortar layer; 2) constructing a geometric model of the recycled concrete three-dimensional random spherical aggregate test piece; (3) constructing a geometric model of the recycled concrete three-dimensional random convex polyhedral aggregate test piece; (4) carrying out unstructured grid division; and 5) construction of a recycled concrete projection network model. According to the method, the problem that the geometric space structure of the recycled concrete is complex is solved, and the established geometric model can truly reflect the actual grading, content and shape of the aggregate in the recycled concrete; according to the unstructured mesh generation method aligned with the interface, the problems that mesh generation is difficult, and modeling is difficult due to the fact that an interface transition area is too thin are solved, and the generated mesh model has extremely high unit quality.

Description

Technical Field

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

[0002] As the global urbanization process accelerates, the resource consumption and environmental impact of the construction industry have gradually attracted widespread attention. In this context, recycled concrete, as a green building material, has the significant advantages of saving resources and reducing construction waste. Therefore, the research and application of recycled concrete has become the focus of the current construction field. However, how to introduce recycled aggregates into concrete so that it has good mechanical properties while maintaining environmental characteristics has always been a difficult problem in this field.

[0003] At present, the mesoscopic modeling of recycled concrete is one of the important means to analyze its mechanical properties. Mesoscopic modeling can deeply reveal the initiation and expansion of microcracks and their influence on macroscopic mechanical behavior by simulating the structure of recycled concrete. This method is of great significance for optimizing the mix design of recycled concrete and improving the performance of recycled concrete. In the prior art, three-dimensional random aggregate models based on parametric modeling and aggregate morphology reconstruction based on digital images are commonly used methods. The method based on parametric modeling can effectively simplify the calculation work and maintain a high modeling efficiency by generating aggregates of regular shapes such as spheres or ellipsoids. However, this method deviates from the actual situation in terms of aggregate morphology, thickness of interface transition zone, etc., and it is difficult to accurately describe the stress concentration phenomenon in recycled aggregates. Although the modeling method based on digital images can obtain more realistic aggregate morphology, its process is complicated and requires high computing resources, which makes it difficult to apply to large-scale engineering calculations.

[0004] The application technology of recycled concrete materials is a major engineering topic. The relationship between its microstructure and macroscopic mechanical properties and the research on its failure mechanism are very important frontier hot issues. Due to the limitations of test conditions, the failure mechanism and failure law of recycled concrete are often not fully reflected by the mechanical test results. With the development of mesomechanics theory and the emergence of high-speed and large-capacity electronic computers, a new approach has been provided for the numerical analysis of the failure mechanism and failure law of recycled concrete. However, there are relatively few studies and applications on the mesomechanical model of recycled concrete. The mesoscopic modeling of recycled concrete has problems such as complex geometric space structure, difficult meshing, and the interface transition zone is too thin to simulate.

[0005] Traditional mesoscopic modeling methods for recycled concrete are inadequate in simulating aggregate morphology and interface transition zone characteristics, making it difficult to accurately predict the mechanical properties of recycled concrete.

[0006] In order to solve the above technical problems, the present invention proposes a new mesoscopic modeling method based on three-dimensional convex polyhedron aggregate, in order to provide more scientific and reliable technical support for the design and application of recycled concrete. Summary of the invention

[0007] In view of the technical problems existing in the above-mentioned background technology, the present invention proposes a parametric construction method for a three-dimensional microscopic numerical model of recycled concrete, which solves the problem of complex geometric space structure of recycled concrete. The established geometric model can truly reflect the actual grading, content and shape of aggregates in recycled concrete; the interface-aligned unstructured grid division method proposed in the present invention solves the problem of difficult grid division and difficult modeling of interface transition zones that are too thin, and the generated grid model has extremely high unit quality.

[0008] In order to solve the above technical problems, the present invention provides a parameterized construction method of a three-dimensional mesoscopic numerical model of recycled concrete, which mainly includes the following steps:

[0009] 1) Calculate the number of particles, particle size and thickness of the old mortar layer of recycled concrete aggregate;

[0010] 2) Construction of geometric model of three-dimensional random spherical aggregate specimens of recycled concrete;

[0011] 3) Construction of geometric model of three-dimensional random convex polyhedron aggregate specimens of recycled concrete;

[0012] 4) Unstructured grid division

[0013] By using the mesh generation algorithm of the geometric shape specified by the implicit function, considering the boundary and mesh refinement of the interface transition zone, the algorithm is optimized and applied to the "3D random spherical aggregate geometric model of recycled concrete" and "3D random convex polyhedral aggregate geometric model of recycled concrete", and a high-quality recycled concrete mesh model is obtained.

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

[0015] The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete, wherein the specific process of step 1) is as follows:

[0016] 1.1) Random generation of particle size of recycled concrete aggregate

[0017] The Fuller gradation curve is used to derive the random generation formula of recycled concrete aggregate particle size; the specific process is as follows:

[0018] Assuming that the Fuller gradation curve equation index n = 0.5, the gradation curve of recycled concrete aggregate content is:

[0019]

[0020] In formula (1), d is the particle size of recycled concrete aggregate, D max is the maximum particle size of recycled concrete aggregate, V max is the content of recycled concrete aggregate;

[0021] The derivative of the above formula (1) with respect to d is:

[0022]

[0023] In the above formula (2), k is the number of particles of recycled concrete aggregate with a particle size of d;

[0024] The integral of both ends of the above formula (2) is:

[0025]

[0026] In formula (3), D min is the minimum particle size of recycled concrete aggregate; A is a constant coefficient,

[0027] Assume that the particle sizes of each recycled concrete aggregate have the same probability of appearing on the grading curve:

[0028]

[0029] In formula (4), P is uniformly distributed between [0 1];

[0030] The particle sizes of randomly generated recycled concrete aggregates are:

[0031]

[0032] 1.2) Calculate the thickness of the old mortar layer of recycled concrete aggregate

[0033] The volume percentage of the old mortar layer of recycled concrete aggregate is calculated by the density of natural aggregate, the density of mortar and their mass content percentage, and then the thickness of the old mortar layer of recycled concrete aggregate is calculated:

[0034]

[0035] In formulas (6)-(7), V s ,V g Respectively represent the volume of old mortar and natural aggregate in recycled concrete aggregate; ρ s ,ρ g Represent the density of old mortar and natural aggregate respectively; m s ,m 总 Respectively represent the mass of old mortar and recycled concrete aggregate; ω represents the mass content of old mortar; It represents the ratio of the old mortar area to the natural aggregate volume;

[0036] The mortar layer thickness h is obtained from the volume ratio:

[0037]

[0038] In formula (8), d represents the particle size of recycled concrete aggregate.

[0039] The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete, wherein the step 2) is to use the "pick-and-place method" to complete the placement of recycled concrete aggregates and establish a three-dimensional random distribution geometric model of recycled aggregates. The specific process is as follows:

[0040] 2.1) Determine the spatial scope of recycled concrete aggregate;

[0041] 2.2) Determine the specific location of the recycled concrete aggregate according to the coordinates and radius of the center of the recycled concrete aggregate. The x, y, and z coordinates of the center of the recycled concrete aggregate are randomly given by the multiplication and addition congruential method, which can ensure that the recycled concrete aggregate is randomly distributed within the spatial range;

[0042] 2.3) When locating the coordinates of the center of the recycled concrete aggregate, the unplaced recycled concrete aggregate is compared with all the placed recycled concrete aggregates in a cycle. All recycled concrete aggregates must satisfy the requirement that the distance between each other is greater than the sum of the radii of the two spheres to ensure that the recycled concrete aggregates do not invade each other.

[0043] The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete, wherein the construction of the three-dimensional random convex polyhedron aggregate specimen geometric model of recycled concrete in step 3) is to generate a convex polyhedron in a sphere-based manner, and each vertex of the convex polyhedron is located on the spherical surface, and the sphere is called the base sphere of the polyhedron; the specific process of constructing the three-dimensional random convex polyhedron aggregate specimen geometric model of recycled concrete is as follows:

[0044] 3.1) Randomly generate several points on the outer base sphere as the convex polyhedron aggregate base frame, keep the relative positions of the base points unchanged, expand the radius of the outer base sphere, and make the volume of the generated convex polyhedron equal to the volume of the outer sphere;

[0045] 3.2) Using the same method as that used in step 3.1) to generate the outer convex polyhedron, randomly generate an inner convex polyhedron on the inner base sphere, so that the volume of the generated inner convex polyhedron is equal to the volume of the inner sphere; at the same time, the vertices of the inner convex polyhedron must be guaranteed to be within the corresponding outer convex polyhedron.

[0046] The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete, wherein the method of generating a convex polyhedron on a base sphere is as follows:

[0047] Randomly generate 10 to 18 points on the base sphere as polyhedron vertices. The polyhedron vertices can be expressed as:

[0048]

[0049] In formula (9), (x0, y0) is the coordinate of the center of the sphere, r0 is the radius of the sphere; α i Randomly generated in the range [0,π], β i Randomly generated in the range [0,2π];

[0050] In order to prevent the polyhedron vertices from being too close and causing the triangular faces to be deformed, it is necessary to ensure that the vertex spacing on the base sphere is not less than ηr0. Then, the convhulln algorithm of MATLAB is used to establish triangular faces based on these polyhedron vertices. The triangular faces constitute the convex polyhedron base aggregate; according to the volume V of the base sphere s and the volume V of the convex polyhedron-based aggregate c Ratio i , the volume of the base ball is enlarged, while the relative position of the vertices remains unchanged; if there is cross-overlap between aggregates, repeat the above formula (9) to regenerate the vertices;

[0051]

[0052] Determine whether the convex polyhedral aggregates cross or overlap, that is, determine whether the vertex P(x, y, z) of one convex polyhedral aggregate is inside the other convex polyhedral aggregate, and determine whether the aggregate boundary lines intersect. If there is no cross or overlap between the convex polyhedral aggregates, the three-dimensional random spherical aggregate specimen geometric model of recycled concrete can be finally converted into a three-dimensional random convex polyhedral aggregate specimen geometric model of recycled concrete; the gradation and corresponding aggregate content and old mortar content of these two aggregate models are the same, but the aggregate shape is different.

[0053] The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete, wherein the relative position of the convex polyhedron aggregates is determined, that is, whether the vertex P (x, y, z) of one convex polyhedron aggregate is inside another convex polyhedron aggregate, and the specific process is as follows:

[0054] ① First, each convex polyhedron aggregate needs to be divided into multiple tetrahedrons. The Delaunay triangulation function provided by the Matrix Laboratory can be used directly to achieve this;

[0055] ② Determine whether the vertex P(x, y, z) is inside these tetrahedrons. If this point is inside one of the tetrahedrons, then this point is inside the polyhedron; if this point is not inside any tetrahedron, then this point is not inside the polyhedron;

[0056] Assuming that the four vertices of the tetrahedron are P1(x1,y1,z1), P2(x2,y2,z2), P3(x3,y3,z3), and P4(x4,y4,z4), then:

[0057]

[0058] If F0·F1>0, F0·F2>0, F0·F3>0, F0·F4>0, then the point P(x,y,z) is inside the tetrahedron.

[0059] The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete, wherein the process of checking whether the aggregate boundary lines intersect specifically includes: ① judging whether the enlarged base sphere overlaps with other base spheres, if not, the convex polyhedron aggregate boundary lines will not intersect; ② judging whether any boundary line of the convex polyhedron aggregate intersects with any convex surface of another convex polyhedron aggregate, then the problem is converted into the relationship between a straight line and a spatial plane, which can be judged by the determinant of the coefficient matrix of the straight line and the plane.

[0060] The parameterized construction method of the three-dimensional microscopic numerical model of recycled concrete, wherein the vertices of the convex polyhedron in step 3.1) need to meet the following requirements: ① any vertex of the convex polyhedron aggregate particles cannot exceed the specimen size range; ② it is necessary to ensure that there is no intersection and overlap between the convex polyhedron aggregates, that is, to check whether any vertex of the convex polyhedron aggregate particles is inside or outside other convex polyhedron aggregates, and to check whether the boundary lines of the convex polyhedron aggregates intersect.

[0061] The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete, wherein the specific process of step 4) is as follows:

[0062] 4.1) Grid Optimization

[0063] Based on the physical analogy between the edge of the tetrahedron element and the truss structure, the 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:

[0064] The difference between the ideal length and the current length of each edge is set as the spring force. The mesh is adjusted by updating the node positions and recalculating the Delaunay triangulation until the system reaches a balanced state. The solution formula is:

[0065]

[0066] Wherein, k in the above formula (12) is the coefficient of the simulated linear spring rod, which can be set to 1; when F>0, the mesh boundary is elongated; for all internal nodes, there is a balance: For most rods, it is a repulsive force (F>0) to help the nodes spread out within the entire geometric boundary;

[0067] The ideal length l0 of the tetrahedral element edge 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 changes in element size, this is achieved by limiting the gradient in h(x,y).

[0068]

[0069] h(xi,y i )=min(min(a+b*{|d(x i ,y i )|}),c) (14);

[0070] 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 from the interface to each aggregate; a, b, c are the relative sizes of the mesh at the interface;

[0071] 4.2) Grid internal boundary layer formation

[0072] Given a unit node P and the distance function F(P) from node P to the interface, we need to find the corrected ΔP. Using the infinitesimal ψ, we can get the gradient at node P:

[0073]

[0074] Thus we can get:

[0075]

[0076] The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete, wherein the step 5) is to apply the projection grid method to assign material properties to the generated grid units; for the convex aggregate model, a high-quality background grid can also be generated, and the projection grid model is finally generated; and the specific construction process of the projection grid model is as follows:

[0077] After unstructured meshing of the recycled concrete geometric model, the unit type is determined by judging the relative position of the unit nodes; when all the unit nodes 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 generated units are assigned material parameters.

[0078] By adopting the above technical solution, the present invention has the following beneficial effects:

[0079] The present invention solves the problem of complex geometric space structure of recycled concrete, and the established geometric model can truly reflect the actual gradation, content and shape of aggregates in recycled concrete. At the same time, the interface-aligned unstructured grid division method proposed by the present invention solves the problem of difficult grid division and difficult modeling of the interface transition zone being too thin. The generated grid model has extremely high unit quality, thus providing a theoretical basis and technical reserve for the design and development of recycled concrete buildings. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0081] Figure 1 The three-dimensional mesoscopic numerical model construction process of recycled concrete involved in the parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete of the present invention;

[0082] Figure 2 A three-dimensional mesoscopic structure diagram of recycled concrete involved in the parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete of the present invention;

[0083] Figure 3 A diagram of a three-dimensional random aggregate placement model of recycled concrete involved in the parameterized construction method of a three-dimensional mesoscopic numerical model of recycled concrete of the present invention;

[0084] Figure 4 It is a vertex position determination diagram involved in the parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete of the present invention;

[0085] Figure 5It is a judgment boundary line position map involved in the parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete of the present invention;

[0086] Figure 6 A diagram of the convex aggregate production process involved in the parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete of the present invention;

[0087] Figure 7 The ellipsoidal aggregate and the resulting convex aggregate map involved in the parametric construction method of the three-dimensional mesoscopic numerical model of recycled concrete of the present invention;

[0088] Figure 8 A diagram of a three-dimensional random convex polyhedron aggregate model of recycled concrete involved in the parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete of the present invention;

[0089] Fig. 9 A diagram of the interface layer generation process involved in the parametric construction method of the three-dimensional mesoscopic numerical model of recycled concrete of the present invention;

[0090] Fig.10 A diagram of the mesh generation process involved in the parametric construction method of the three-dimensional mesoscopic numerical model of recycled concrete according to the present invention;

[0091] Fig.11 A side profile of a projection grid model involved in the parametric construction method of a three-dimensional mesoscopic numerical model of recycled concrete according to the present invention;

[0092] Fig.12 Background grid diagram (average quality of unit grid is 0.818) involved in the parametric construction method of the three-dimensional mesoscopic numerical model of recycled concrete of the present invention;

[0093] Fig.13 A side profile view of a projection grid model involved in the parametric construction method of a three-dimensional mesoscopic numerical model of recycled concrete according to the present invention. DETAILED DESCRIPTION

[0094] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0095] The present invention is further explained below in conjunction with specific implementation modes.

[0096] like Figure 1 As shown, the present embodiment provides a parameterized construction method of a three-dimensional mesoscopic numerical model of recycled concrete, comprising the following steps:

[0097] S100, Calculate the number and size of recycled concrete aggregate and the thickness of old mortar layer

[0098] S101. Random generation of particle size of recycled concrete aggregate

[0099] The Fuller gradation curve is used to derive the random generation formula of recycled concrete aggregate particle size; the specific process is as follows:

[0100] Assuming that the Fuller gradation curve equation index n = 0.5, the gradation curve of recycled concrete aggregate content is:

[0101]

[0102] In formula (1), d is the particle size of recycled concrete aggregate; D max is the maximum particle size of recycled concrete aggregate; V max is the recycled concrete aggregate content.

[0103] The derivative of the above formula (1) with respect to d is:

[0104]

[0105] In the above formula (2), k is the number of particles of recycled concrete aggregate with a particle size of d;

[0106] The integral of both ends of the above formula (2) is:

[0107]

[0108] In formula (3), D min is the minimum particle size of recycled concrete aggregate; A is a constant coefficient,

[0109] Assume that the probability of each recycled concrete aggregate particle size appearing on the grading curve is the same:

[0110]

[0111] In formula (4), P is a uniform distribution between [0 and 1]; the uniform distribution between [0 and 1] means that P obeys a uniform distribution on the interval [0 and 1], that is, the probability of each value appearing is equal.

[0112] The particle sizes of randomly generated recycled concrete aggregates are:

[0113]

[0114] S102. Calculate the thickness of the old mortar layer of recycled concrete aggregate

[0115] The volume percentage of the old mortar layer of recycled concrete aggregate is calculated by the density of natural aggregate, the density of mortar and their mass content percentage, and then the thickness of the old mortar layer of recycled concrete aggregate is calculated:

[0116]

[0117] In formulas (6)-(7), V s ,V g Respectively represent the volume of old mortar and natural aggregate in recycled concrete aggregate; ρ s ,ρ g Represent the density of old mortar and natural aggregate respectively; m s ,m 总 Respectively represent the mass of old mortar and recycled concrete aggregate; ω represents the mass content of old mortar; It represents the ratio of old mortar area to natural aggregate volume.

[0118] The mortar layer thickness h is obtained from the volume ratio.

[0119]

[0120] In formula (8), d Indicates the particle size of recycled concrete aggregate.

[0121] Construction of geometric model of S200 and recycled concrete three-dimensional random spherical aggregate specimens

[0122] The generation of aggregate particles is the first step in generating the mesoscopic model using parametric modeling. The recycled aggregate is simplified into two concentric spheres, e.g. Figure 2 shown.

[0123] The present invention adopts the "pick-and-place method" to complete the placement of aggregates and establish a three-dimensional random distribution geometric model of recycled aggregates. The specific process is as follows:

[0124] S201, determining the spatial range where the recycled concrete aggregate is located;

[0125] S202, determining the specific position of the recycled concrete aggregate according to the coordinates and radius of the center of the recycled concrete aggregate, wherein the x, y, and z coordinates of the center of the recycled concrete aggregate are randomly given by the multiplication-addition congruential method, so as to ensure that the recycled concrete aggregate is randomly distributed within the spatial range;

[0126] S203. When locating the coordinates of the center of the sphere of recycled concrete aggregate, the recycled concrete aggregate that has not been placed is compared cyclically with all the recycled concrete aggregates that have been placed. All recycled concrete aggregates must satisfy that the distance between any two of them is greater than the sum of the radii of the two spheres to ensure that the recycled concrete aggregates do not invade each other.

[0127] The aggregates are placed in order of their particle size, taking cubic specimens and cylindrical specimens as examples. Figure 3 This is a model diagram of random placement of aggregates, where blue particles represent natural aggregate particles and cyan particles represent recycled aggregate.

[0128] S300, Geometric model of three-dimensional random convex polyhedron aggregate specimen of recycled concrete

[0129] Furthermore, the three-dimensional spherical aggregate model is transformed into a three-dimensional convex polyhedral aggregate model, that is, a convex polyhedron is generated based on a sphere, and each vertex of the convex polyhedron is located on the sphere. The sphere is called the base sphere of the polyhedron. The specific process of constructing the geometric model of the three-dimensional random convex polyhedral aggregate specimen of recycled concrete is as follows:

[0130] S301, randomly generate several points on the outer base sphere as the convex polyhedron aggregate base frame, keep the relative position of the base points unchanged, expand the radius of the outer base sphere, and make the volume of the generated convex polyhedron equal to the volume of the outer sphere, such as Figure 6 (a) and Figure 6 (b). At the same time, the vertices of the convex polyhedron need to meet the following requirements: ① Any vertex of the convex polyhedron aggregate particle cannot exceed the size range of the specimen; ② It is necessary to ensure that there is no intersection or overlap between the convex polyhedron aggregates, that is, check whether any vertex of the convex polyhedron aggregate particle is inside or outside other convex polyhedron aggregates, and check whether the boundary lines of the convex polyhedron aggregates intersect.

[0131] S302, using the same method as step 3.1) to generate the outer convex polyhedron, randomly generate an inner convex polyhedron on the inner base sphere, so that the volume of the generated inner convex polyhedron is equal to the volume of the inner sphere. At the same time, the vertices of the inner convex polyhedron must be guaranteed to be within the corresponding outer convex polyhedron, such as Figure 6 (c).

[0132] The method to generate a convex polyhedron on the base sphere is as follows:

[0133] Randomly generate 10 to 18 points on the base sphere as the vertices of the polyhedron. The vertices of the polyhedron can be expressed as:

[0134]

[0135] In formula (9), (x0, y0) is the coordinate of the center of the sphere, r0 is the radius of the sphere; α i Randomly generated in the range [0,π], β i Randomly generated in the range [0,2π].

[0136] In order to prevent the polyhedron vertices from being too close and causing the triangular faces to be deformed (which is not conducive to subsequent meshing), it is necessary to ensure that the vertex spacing on the base sphere surface is not less than ηr0, and η = 0.55; then the convhulln algorithm of MATLAB is used to establish triangular faces based on these polyhedron vertices, and the triangular faces constitute the convex polyhedron base aggregate. According to the volume V of the base sphere s and the volume V of the convex polyhedron-based aggregate c Ratio i , the volume of the base ball is enlarged, while the relative position of the vertices remains unchanged. If there is cross-overlap between aggregates, repeat the above formula (9) to regenerate the vertices;

[0137]

[0138] Determine whether the convex polyhedral aggregates are crossed or overlapped, that is, determine whether the vertex P(x, y, z) of one convex polyhedral aggregate is inside the other convex polyhedral aggregate, and determine whether the aggregate boundary lines intersect. If there is no crossing or overlap between the convex polyhedral aggregates, the geometric model of the three-dimensional random spherical aggregate specimen of recycled concrete can be finally converted into the geometric model of the three-dimensional random convex polyhedral aggregate specimen of recycled concrete; the gradation and corresponding aggregate content and old mortar content of these two aggregate models are the same, but the aggregate shapes are different;

[0139] Regarding checking whether any vertex of an aggregate particle is inside or outside other aggregates, it is easier to judge the relative position of the aggregate vertex and the spherical aggregate. For the relative position judgment of the aggregate and any convex polyhedral aggregate, that is, judging whether the vertex P(x, y, z) of one convex polyhedral aggregate is inside another convex polyhedral aggregate, the specific process is as follows:

[0140] ①First, each convex polyhedron aggregate needs to be divided into multiple tetrahedrons. The Matrix Laboratory provides a direct function Delaunay triangulation to achieve this.

[0141] ② Determine whether the vertex P(x, y, z) is inside these tetrahedrons. If this point is inside one of the tetrahedrons, then this point is inside the polyhedron; if this point is not inside any tetrahedron, then this point is not inside the polyhedron;

[0142] like Figure 4 , assuming that the four vertices of the tetrahedron are P1(x1,y1,z1), P2(x2,y2,z2), P3(x3,y3,z3), P4(x4,y4,z4), we have:

[0143]

[0144] If F0·F1>0, F0·F2>0, F0·F3>0, F0·F4>0, then the point P(x,y,z) is inside the tetrahedron.

[0145] Regarding checking whether aggregate boundary lines intersect, such as Figure 5 As shown, this includes two steps: 1. Determine whether the enlarged base sphere overlaps with other base spheres. If not, the boundary lines of the convex polyhedron aggregates will not intersect; 2. Determine whether any boundary line of the convex polyhedron aggregate intersects with any convex surface of another convex polyhedron aggregate. The problem is transformed into the relationship between a straight line and a spatial plane, which can be determined by the determinant of the coefficient matrix of the straight line and the plane.

[0146] Generally, an ellipsoid is used and the algorithm can generate recycled convex aggregates with different axis length ratios, such as Figure 7 It is a recycled aggregate with an axis length ratio equal to 2 (herein, the axis length ratio of the aggregate is defined as the ratio of the longest axis to the shortest axis of the circumscribed ellipsoid of the aggregate).

[0147] According to this algorithm, Figure 3 The three-dimensional spherical aggregate model in is converted into a convex polyhedral aggregate model, such as Figure 8 As shown in Figure 2, the grading of these two aggregate models and the corresponding aggregate content and old mortar content are the same, but the aggregate shapes are different.

[0148] S400, unstructured meshing

[0149] After the geometric model is generated, it needs to be meshed. In order to generate high-quality meshes, a mesh generation algorithm of the geometric shape specified by an implicit function (a function used to describe the geometric shape) is used, and the boundary and mesh refinement of the interface transition zone are considered. The algorithm is optimized and applied to the geometric models of three-dimensional random spherical aggregate specimens of recycled concrete and three-dimensional random convex polyhedral aggregate specimens of recycled concrete to obtain a high-quality recycled concrete mesh model.

[0150] S401, Grid Optimization

[0151] Based on the physical analogy between the edges of tetrahedral elements and truss structures, the initial mesh is improved by solving equilibrium problems in truss structures using linear force-displacement relationships. Any set of points in the plane can be triangulated by the Delaunay algorithm, and when nodes are moved, the mesh is optimized to improve the tetrahedral element quality by recalculating the Delaunay triangulation or by local updates. In equilibrium, tetrahedral elements tend to have high quality, and the method can be generalized to higher dimensions.

[0152] The force F on each edge of the element depends on the difference between its current length l and its ideal length l0:

[0153]

[0154] Wherein, k in the above formula (12) is the coefficient of the simulated linear spring rod, which can be set to 1; when F>0, the mesh boundary is elongated; 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, usually 20% (Fscale=1.2).

[0155] The ideal length l0 of the tetrahedral element edge 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 changes in element size, this is achieved by limiting the gradient in h(x,y):

[0156]

[0157] h(x i ,y i )=min(min(a+b*{|d(x i ,y i )|}),c) (14);

[0158] 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 from the interface to each aggregate. a, b, c are the relative sizes of the mesh at the interface.

[0159] S402, grid internal boundary layer formation

[0160] like Fig. 9 Given a unit node P and the distance function F(P) from node P to the interface, we need to find the corrected ΔP. Using the infinitesimal ψ, we can get the gradient at node P:

[0161]

[0162] Thus we can get:

[0163]

[0164] In this study, in order to improve the accuracy, the above steps are repeated, and the iterative correction is terminated when the results of two iterations are less than the preset value.

[0165] Taking a 50mm×50mm×50mm three-dimensional specimen as an example, a recycled round aggregate with a particle size of 20mm and an old mortar layer thickness of 2.5mm is placed in the center of the specimen, and the interface transition zone is 0.5mm. Fig.10 (a) Fig.10 (b) and Fig.10 (c) shows the Delaunay mesh diagrams after the 1st, 5th and 100th iterations. It can be seen from the figure that the grid uniformity becomes better and better as the iteration proceeds.

[0166] S500, Recycled Concrete Projection Network Model Construction

[0167] The projected mesh method is used to assign material properties to the generated mesh units; for the convex aggregate model, high-quality background meshes can also be generated, such as Fig.11 is the final generated projection mesh model; and the specific construction process of the projection mesh model is as follows:

[0168] After unstructured meshing of the recycled concrete geometric model, the unit type is determined by judging the relative position of the unit nodes; when all the unit nodes 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 generated units are assigned material parameters.

[0169] Example Application

[0170] In the following examples, a disk-shaped specimen for splitting tensile test is taken as an example. Fig.12 Its characteristic is that the damage position in the specimen is relatively fixed. In order to reduce the degree of freedom, the specimen is divided into a macro region and a micro region. The material in the macro region is almost not damaged during the stress process, so it is considered to be homogeneous. Under the action of external force, the microcracks in the meso region initiate, expand and penetrate until the macro cracks are formed, causing the specimen to become unstable and rupture. Therefore, in order to reflect the characteristics of localization and stress redistribution in the fracture process, the meso region needs to be modeled at the meso scale.

[0171] Aggregates are randomly generated according to the Fuller grading curve, with a maximum particle size of 20 mm, a minimum particle size of 5 mm, an aggregate content of 40%, an old mortar content of 42%, and an interface transition zone thickness of 0.5 mm. In terms of meshing, it is assumed that the initial mesh size is 0.5 mm and the interface transition zone node correction range is 0.25 mm. Fig.13As shown in the figure, the average quality of each model unit of the established projection mesh model is above 0.75, indicating that the units in each model are almost equilateral and the model has a high mesh quality.

[0172] The present invention solves the problem of complex geometric space structure of recycled concrete, and the established geometric model can truly reflect the actual gradation, content and shape of aggregates in recycled concrete. The interface-aligned unstructured grid division method proposed by the present invention solves the problem of difficult grid division and difficult modeling of interface transition zone because the interface transition zone is too thin, and the generated grid model has extremely high unit quality.

[0173] 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 aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned 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 three-dimensional mesoscopic numerical model of recycled concrete, characterized in that: The main steps are as follows: 1) Calculate the number of particles, particle size and thickness of the old mortar layer of recycled concrete aggregate; 2) Construction of geometric model of three-dimensional random spherical aggregate specimens of recycled concrete; 3) Construction of geometric model of three-dimensional random convex polyhedron aggregate specimens of recycled concrete; 4) Unstructured grid division By using the mesh generation algorithm of the geometric shape specified by the implicit function, considering the boundary and mesh refinement of the interface transition zone, the algorithm is optimized and applied to the geometric model of the three-dimensional random spherical aggregate specimen of recycled concrete and the geometric model of the three-dimensional random convex polyhedral aggregate specimen of recycled concrete, and a high-quality recycled concrete mesh model is obtained. 5) Construction of recycled concrete projection network model.

2. The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: The specific process of step 1) is as follows: 1.1) Random generation of particle size of recycled concrete aggregate The Fuller gradation curve is used to derive the random generation formula of recycled concrete aggregate particle size; the specific process is as follows: Assuming that the Fuller gradation curve equation index n = 0.5, the gradation curve of recycled concrete aggregate content is: In formula (1), d is the particle size of recycled concrete aggregate, D max is the maximum particle size of recycled concrete aggregate, V max is the content of recycled concrete aggregate; The derivative of the above formula (1) with respect to d is: In the above formula (2), k is the number of particles of recycled concrete aggregate with a particle size of d; The integral of both ends of the above formula (2) is: In formula (3), D min is the minimum particle size of recycled concrete aggregate; A is a constant coefficient, Assume that the particle sizes of each recycled concrete aggregate have the same probability of appearing on the grading curve: In formula (4), P is uniformly distributed between [0 1]; The particle sizes of randomly generated recycled concrete aggregates are: 1.2) Calculate the thickness of the old mortar layer of recycled concrete aggregate The volume percentage of the old mortar layer of recycled concrete aggregate is calculated by the density of natural aggregate, the density of mortar and their mass content percentage, and then the thickness of the old mortar layer of recycled concrete aggregate is calculated: In formulas (6)-(7), V s ,V g Respectively represent the volume of old mortar and natural aggregate in recycled concrete aggregate; ρ s ,ρ g Represent the density of old mortar and natural aggregate respectively; m s ,m 总 Respectively represent the mass of old mortar and recycled concrete aggregate; ω represents the mass content of old mortar; It represents the ratio of the old mortar area to the natural aggregate volume; The mortar layer thickness h is obtained from the volume ratio: In formula (8), d represents the particle size of recycled concrete aggregate.

3. The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: The step 2) is to use the "pick-and-place method" to complete the placement of recycled concrete aggregates and establish a three-dimensional random distribution geometric model of recycled aggregates. The specific process is as follows: 2.1) Determine the spatial scope of recycled concrete aggregate; 2.2) Determine the specific location of the recycled concrete aggregate according to the coordinates and radius of the center of the recycled concrete aggregate. The x, y, and z coordinates of the center of the recycled concrete aggregate are randomly given by the multiplication and addition congruential method, which can ensure that the recycled concrete aggregate is randomly distributed within the spatial range; 2.3) When locating the coordinates of the center of the recycled concrete aggregate, the unplaced recycled concrete aggregate is compared with all the placed recycled concrete aggregates in a cycle. All recycled concrete aggregates must satisfy the requirement that the distance between each other is greater than the sum of the radii of the two spheres to ensure that the recycled concrete aggregates do not invade each other.

4. The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: In the step 3), the geometric model of the recycled concrete three-dimensional random convex polyhedron aggregate specimen is constructed by generating a convex polyhedron based on a sphere, and each vertex of the convex polyhedron is located on the sphere, and the sphere is called the base sphere of the polyhedron; the specific process of constructing the geometric model of the recycled concrete three-dimensional random convex polyhedron aggregate specimen is as follows: 3.1) Randomly generate several points on the outer base sphere as the convex polyhedron aggregate base frame, keep the relative positions of the base points unchanged, expand the radius of the outer base sphere, and make the volume of the generated convex polyhedron equal to the volume of the outer sphere; 3.2) Using the same method as that used in step 3.1) to generate the outer convex polyhedron, randomly generate an inner convex polyhedron on the inner base sphere, so that the volume of the generated inner convex polyhedron is equal to the volume of the inner sphere; at the same time, the vertices of the inner convex polyhedron must be guaranteed to be within the corresponding outer convex polyhedron.

5. The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete according to claim 4, characterized in that: The method to generate a convex polyhedron on the base sphere is as follows: Randomly generate 10 to 18 points on the base sphere as polyhedron vertices. The polyhedron vertices can be expressed as: In formula (9), (x0, y0) is the coordinate of the center of the sphere, r0 is the radius of the sphere; α i Randomly generated in the range [0,π], β i Randomly generated in the range [0,2π]; In order to prevent the polyhedron vertices from being too close and causing the triangular faces to be deformed, it is necessary to ensure that the vertex spacing on the base sphere is not less than ηr0. Then, the convhulln algorithm of MATLAB is used to establish triangular faces based on these polyhedron vertices. The triangular faces constitute the convex polyhedron base aggregate; according to the volume V of the base sphere s and the volume V of the convex polyhedron-based aggregate c Ratio i , the volume of the base ball is enlarged, while the relative position of the vertices remains unchanged; if there is cross-overlap between aggregates, repeat the above formula (9) to regenerate the vertices; Determine whether the convex polyhedral aggregates cross or overlap, that is, determine whether the vertex P(x, y, z) of one convex polyhedral aggregate is inside the other convex polyhedral aggregate, and determine whether the aggregate boundary lines intersect. If there is no cross or overlap between the convex polyhedral aggregates, the three-dimensional random spherical aggregate specimen geometric model of recycled concrete can be finally converted into a three-dimensional random convex polyhedral aggregate specimen geometric model of recycled concrete; the gradation and corresponding aggregate content and old mortar content of these two aggregate models are the same, but the aggregate shape is different.

6. The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete according to claim 5, characterized in that: The relative positions of the convex polyhedron aggregates are determined, that is, whether the vertex P (x, y, z) of one convex polyhedron aggregate is inside the other convex polyhedron aggregate. The specific process is as follows: ① First, each convex polyhedron aggregate needs to be divided into multiple tetrahedrons. The Delaunay triangulation function provided by the Matrix Laboratory can be used directly to achieve this. ② Determine whether the vertex P(x, y, z) is inside these tetrahedrons. If this point is inside one of the tetrahedrons, then this point is inside the polyhedron; if this point is not inside any tetrahedron, then this point is not inside the polyhedron; Assuming that the four vertices of the tetrahedron are P1(x1,y1,z1), P2(x2,y2,z2), P3(x3,y3,z3), and P4(x4,y4,z4), then: If F0·F1>0, F0·F2>0, F0·F3>0, F0·F4>0, then the point P(x,y,z) is inside the tetrahedron.

7. The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete according to claim 5, characterized in that: The process of checking whether the aggregate boundary lines intersect specifically includes: ① determining whether the enlarged base sphere overlaps with other base spheres. If not, the convex polyhedron aggregate boundary lines will not intersect; ② determining whether any boundary line of the convex polyhedron aggregate intersects with any convex surface of another convex polyhedron aggregate. The problem is then transformed into the relationship between a straight line and a spatial plane, which can be determined by the determinant of the coefficient matrix of the straight line and the plane.

8. The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: The vertices of the convex polyhedron in step 3.1) need to meet the following requirements: ① any vertex of the convex polyhedron aggregate particles cannot exceed the specimen size range; ② it is necessary to ensure that there is no intersection or overlap between the convex polyhedron aggregates, that is, check whether any vertex of the convex polyhedron aggregate particles is inside or outside other convex polyhedron aggregates, and check whether the boundary lines of the convex polyhedron aggregates intersect.

9. The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: The specific process of step 4) is as follows: 4.1) Grid Optimization Based on the physical analogy between the edge of the tetrahedral element and the truss structure, the 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: The difference between the ideal length and the current length of each edge is set as the spring force. The mesh is adjusted by updating the node positions and recalculating the Delaunay triangulation until the system reaches a balanced state. The solution formula is: Wherein, k in the above formula (12) is the coefficient of the simulated linear spring rod, which can be set to 1; when F>0, the mesh boundary is elongated; for all internal nodes, there is a balance: For most rods, it is a repulsive force (F>0) to help the nodes spread out within the entire geometric boundary; The ideal length l0 of the tetrahedral element edge 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 changes in element size, this is achieved by limiting the gradient in h(x,y). h(x i ,y i )=min(min(a+b*{d(x i ,y i )}),c) (14); 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 from the interface to each aggregate; a, b, c are the relative sizes of the mesh at the interface; 4.2) Grid internal boundary layer formation Given a unit node P and the distance function F(P) from node P to the interface, we need to find the corrected ΔP using infinitesimal quantities ψ , we can get the gradient at node P: Thus we can get: ΔP≈▽F(P)F(P)(16).

10. The parameterized construction method of the three-dimensional mesoscopic numerical model of recycled concrete according to claim 1, characterized in that: The step 5) is to apply the projection grid method to assign material properties to the generated grid units; for the convex aggregate model, a high-quality background grid can also be generated, and the projected grid model is finally generated; and the specific construction process of the projected grid model is as follows: After unstructured meshing of the recycled concrete geometric model, the unit type is determined by judging the relative position of the unit nodes; when all the unit nodes 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 generated units are assigned material parameters.

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