A parameterized construction method of a three-dimensional fine numerical model of recycled concrete

Abstract

The application provides a parameterized construction method of a three-dimensional fine numerical model of recycled concrete, which comprises the following steps: 1) calculating the particle number, particle size and old mortar layer thickness of recycled concrete aggregate; 2) constructing a three-dimensional random spherical aggregate specimen geometric model of recycled concrete; 3) constructing a three-dimensional random convex polyhedral aggregate specimen geometric model of recycled concrete; 4) non-structured grid division; and 5) constructing a recycled concrete projection network model. The application solves the problem of complex geometric space construction of recycled concrete, and the established geometric model can truly reflect the actual gradation, content and shape of the aggregate in the recycled concrete; the non-structured grid division method proposed by the application solves the problems of difficult grid division and too thin interface transition zone to be modeled, and the generated grid model has extremely high unit quality.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of building materials, and particularly relates to a parameterized construction method of a three-dimensional fine numerical model of recycled concrete. BACKGROUND

[0002] With the acceleration of global urbanization, the consumption of resources 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 have become the focus of the current construction field. However, how to introduce recycled aggregates into concrete while maintaining its environmental characteristics and good mechanical properties has always been a problem in this field.

[0003] At present, the meso modeling of recycled concrete is one of the important means to analyze its mechanical properties. Meso modeling can reveal the initiation, propagation of micro cracks and their influence on macro 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 parameterized modeling and aggregate morphology reconstruction based on digital images are common methods. The method based on parameterized modeling can effectively simplify the calculation and maintain high modeling efficiency by generating spherical or ellipsoidal aggregates of regular shape. However, this method has deviations in aggregate morphology, interface transition zone thickness, etc. and is difficult to accurately describe the stress concentration phenomenon in recycled aggregates. While the modeling method based on digital image can obtain more realistic aggregate morphology, but its process is complex and requires high computing resources, making it difficult to apply to large-scale engineering calculations.

[0004] The application technology of recycled concrete material is a major engineering project, and the relationship between its mesostructure and macro mechanical properties and the failure mechanism are very important frontier hot issues. Due to the limitations of experimental conditions, the failure mechanism and failure law of recycled concrete cannot be fully reflected by the mechanical test results. With the development of micromechanics theory and the emergence of high-speed large-capacity electronic computers, a new way is provided for numerical analysis of the failure mechanism and failure law of recycled concrete. However, there are still few studies and applications of recycled concrete meso-mechanical models. The meso-modeling of recycled concrete has the problems of complex geometric space construction, difficult meshing and too thin interface transition zone to simulate.

[0005] The traditional meso-modeling method of recycled concrete has deficiencies in simulating the aggregate morphology and interface transition zone characteristics, and it is difficult to accurately predict the mechanical properties of recycled concrete.

[0006] In order to solve the above technical problems, the present application proposes a new method of meso-modeling based on three-dimensional convex polyhedral aggregates, so as to provide more scientific and reliable technical support for the design and application of recycled concrete. SUMMARY

[0007] In view of the technical problems in the above background art, the present application proposes a parameterized construction method of a three-dimensional meso-numerical model of recycled concrete, which solves the problem of complex geometric space construction of recycled concrete, and the established geometric model can truly reflect the actual gradation, content and shape of the aggregate in the recycled concrete; the non-structured grid division method proposed by the present application solves the problems of difficult grid division and too thin interface transition zone to be modeled, and the generated grid model has extremely high unit quality.

[0008] To solve the above technical problems, the present application provides a parameterized construction method of a three-dimensional meso-numerical model of recycled concrete, which mainly includes the following steps:

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

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

[0011] 3) Construction of a three-dimensional random convex polyhedral aggregate specimen geometric model of recycled concrete;

[0012] 4) Non-structured grid division

[0013] The grid generation algorithm of the geometric shape defined by the implicit function is considered, the boundary of the interface transition zone and the grid refinement are considered, and is optimized and applied to the three-dimensional random spherical aggregate specimen geometric model of recycled concrete and the three-dimensional random convex polyhedral aggregate specimen geometric model of recycled concrete, to obtain a high-quality recycled concrete grid model;

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

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

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

[0017] The random generation formula of the recycled concrete aggregate particle size is derived by using the Fuller gradation curve; the specific process is:

[0018] Assuming that the Fuller gradation curve equation index n=0.5, the recycled concrete aggregate content gradation curve 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 particle size d;

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

[0025]

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

[0027] Assuming that the probability of each recycled concrete aggregate particle size appearing on the grading curve is the same:

[0028]

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

[0030] Then the random particle size of recycled concrete aggregate is:

[0031]

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

[0033] The volume content percentage of the old mortar layer of recycled concrete aggregate is calculated by the density of natural aggregate, the density of mortar and its 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 represent the volume occupied by the old mortar and natural aggregate in recycled concrete aggregate, respectively; s , ρ g represent the density of old mortar and natural aggregate, respectively; s , m 总 represent the mass of old mortar and recycled concrete aggregate, respectively; ω represents the mass content of old mortar; represents the ratio of old mortar area to natural aggregate volume;

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

[0037]

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

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

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

[0041] 2.2) According to the coordinates of the center of the recycled concrete aggregate sphere and the radius, the specific position of the recycled concrete aggregate is determined, and the x, y, and z coordinates of the center of the recycled concrete aggregate sphere are randomly given by the multiplication and addition congruence method, which can ensure the random distribution of the recycled concrete aggregate in the spatial range;

[0042] 2.3) When positioning the coordinates of the center of the recycled concrete aggregate sphere, the unplaced recycled concrete aggregate is compared with all the placed recycled concrete aggregate, and all the recycled concrete aggregate must satisfy that the distance between any two is greater than the sum of the radii of the two spheres, so as to ensure that the recycled concrete aggregate does not invade each other.

[0043] The parameterized construction method of the three-dimensional numerical model of recycled concrete, wherein the three-dimensional random convex polyhedral aggregate specimen geometric model of recycled concrete in step 3) is constructed by generating convex polyhedrons based on spheres, and each vertex of the convex polyhedron is located on the sphere surface, which is called the base sphere of the polyhedron; the specific process of constructing the three-dimensional random convex polyhedral aggregate specimen geometric model of recycled concrete is as follows:

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

[0045] 3.2) Generate an inner convex polyhedron on the inner base sphere by the same method as in step 3.1), 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 need to be ensured within the corresponding outer convex polyhedron.

[0046] The method for generating a convex polyhedron on a base sphere is as follows:

[0047] Randomly generate 10-18 points on the base sphere as polyhedral vertices, and the polyhedral vertices can be represented as:

[0048]

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

[0050] To prevent the vertices of the polyhedron from being too close to cause the deformation of the triangular surface, the distance between the vertices on the base spherical surface is ensured to be not less than ηr0, and then the MATLAB convhulln algorithm is used to establish the triangular surface based on the vertices of the polyhedron, and the triangular surface constitutes the convex polyhedron base aggregate; according to the ratio r s of the volume V c of the convex polyhedron base aggregate to the volume V i of the base sphere, the volume of the base sphere is expanded, and the relative positions of the vertices remain unchanged; if the aggregates overlap, the above formula (9) is used to regenerate the vertices;

[0051]

[0052] 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 another convex polyhedron aggregate is determined, and whether the boundary lines of the aggregates intersect is determined, and if the convex polyhedron aggregates do not overlap, the regenerated concrete three-dimensional random spherical aggregate specimen geometric model can be finally converted into a regenerated concrete three-dimensional random convex polyhedron aggregate specimen geometric model; the gradations of the two kinds of aggregate models and the corresponding aggregate content and old mortar content are the same, only the shapes of the aggregates are different.

[0053] The parameterized construction method of the regenerated concrete three-dimensional fine numerical model, wherein 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 another convex polyhedron aggregate is determined, and the specific process is as follows:

[0054] ①First, each convex polyhedron aggregate needs to be divided into multiple tetrahedrons, and the Delaunay triangulation function provided by the matrix laboratory can be directly used;

[0055] ②Whether the vertex P(x, y, z) is inside the tetrahedrons is determined, if the point is inside one of the tetrahedrons, then the point is inside the polyhedron; if the point is not inside any tetrahedron, then the point is not inside the polyhedron;

[0056] Suppose 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 in the tetrahedron.

[0059] The parameterized construction method of the three-dimensional fine numerical model of recycled concrete, wherein the process of checking whether the aggregate boundary lines intersect specifically comprises: ① judging whether the expanded base sphere overlaps with other base spheres, if not, the convex polyhedral aggregate boundary lines do not intersect; ② judging whether any boundary line of the convex polyhedral aggregate intersects with any convex surface of another convex polyhedral aggregate, then the problem is converted into the relationship between a straight line and a spatial plane, and the determinant of the coefficient matrix of the straight line and the plane can be used for judgment.

[0060] The parameterized construction method of the three-dimensional fine 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 polyhedral aggregate particle cannot exceed the size range of the test piece; ② it is necessary to ensure that the convex polyhedral aggregates do not overlap, that is, to check whether any vertex of the convex polyhedral aggregate particle is inside or outside other convex polyhedral aggregates, and to check whether the convex polyhedral aggregate boundary lines intersect.

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

[0062] 4.1) Grid optimization

[0063] Based on the physical analogy between the edges of the tetrahedral unit and the truss structure, the linear force-displacement relationship is used to solve the balance problem in the truss structure to improve the initial grid, and the specific solving process is:

[0064] The difference between the ideal length and the current length of each edge is set as the spring force, the grid is adjusted by updating the node position and recalculating the Delaunay triangulation until the system reaches the equilibrium state, and the solving formula is:

[0065]

[0066] In the above formula (12), k is the coefficient of the simulated linear spring rod, which can be set to 1; when F>0, the grid boundary is lengthened; for all internal nodes, there is a balance: For most rods, the repulsive force (F>0) helps the nodes to expand within the entire geometric boundary;

[0067] The ideal length l0 of the tetrahedron unit edge is described by the mesh size function h(x, y), which is noted that h(x, y) does not have to be equal to the actual size; the mesh size function gives the relative distribution on the domain; in order to avoid large changes in the size of the unit, the gradient in h(x, y) is limited;

[0068]

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

[0070] Wherein, d(x i ,y i ) in the above formula (14) is a distance function, and {|d(x i ,y i )|} is a set of absolute values of distances from the point (x i ,y i ) to each aggregate interface; a, b, c are the relative sizes of the mesh at the interface;

[0071] 4.2) Formation of the internal boundary layer of the mesh

[0072] Given a unit node P and the node P to the interface distance function F(P), the corrected ΔP needs to be found, and by using an infinitesimal quantity ψ, the gradient at the node P can be obtained:

[0073]

[0074] Thus, the following can be obtained:

[0075]

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

[0077] After the non-structured mesh is divided for the geometric model of recycled concrete, the element type is determined by judging the relative position of the element nodes; when all the nodes of the element fall in the natural aggregate area, the element is defined as a natural aggregate element; when all the nodes fall in the old mortar area, the element is defined as an old mortar element; when all the nodes fall in the new mortar area, the element is defined as a new mortar element; when part of the nodes fall in the natural aggregate area and part of the nodes fall in the old mortar area, the element is defined as an old interface transition zone element; when part of the nodes fall in the old mortar area and part of the nodes fall in the new mortar area, the element is a new interface transition zone element; finally, the generated element is assigned with material parameters.

[0078] By adopting the technical scheme, the present application has the following beneficial effects:

[0079] The present application solves the problem of complex geometric space construction of recycled concrete, and the established geometric model can truly reflect the actual gradation, content and shape of the aggregate in the recycled concrete. Meanwhile, the non-structured mesh division method proposed in the present application solves the problems of difficult mesh division and too thin interface transition zone, and the generated mesh model has extremely high element quality, thereby providing a theoretical basis and technical reserve for the design and development of recycled concrete buildings. BRIEF DESCRIPTION OF DRAWINGS

[0080] In order to more clearly illustrate the specific embodiments of the present application or the technical solutions in the prior art, the drawings needed in the following specific embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0081] Figure 1 The present application relates to a parameterized construction method of a three-dimensional meso-scale numerical model of recycled concrete.

[0082] Figure 2 The present application relates to a parameterized construction method of a three-dimensional meso-scale numerical model of recycled concrete.

[0083] Figure 3 The present application relates to a parameterized construction method of a three-dimensional meso-scale numerical model of recycled concrete.

[0084] Figure 4 The present application relates to a parameterized construction method of a three-dimensional meso-scale numerical model of recycled concrete.

[0085] Figure 5This is a diagram showing the location of the boundary line involved in the parameterized construction method of the three-dimensional microscopic numerical model of recycled concrete in this invention.

[0086] Figure 6 This is a diagram illustrating the process of convex aggregate generation in the parametric construction method of the three-dimensional microscopic numerical model of recycled concrete in this invention.

[0087] Figure 7 The parametric construction method for the three-dimensional microscopic numerical model of recycled concrete in this invention involves ellipsoidal aggregates and the resulting convex aggregate diagrams.

[0088] Figure 8 The parametric construction method of the three-dimensional microscopic numerical model of recycled concrete in this invention involves a three-dimensional random convex polyhedral aggregate model of recycled concrete.

[0089] Figure 9 A diagram illustrating the interface layer generation process involved in the parameterized construction method of the three-dimensional microscopic numerical model of recycled concrete in this invention.

[0090] Figure 10 A diagram illustrating the mesh generation process involved in the parametric construction method of the three-dimensional microscopic numerical model of recycled concrete in this invention;

[0091] Figure 11 Side cross-sectional view of the projected mesh model involved in the parameterized construction method of the three-dimensional microscopic numerical model of recycled concrete in this invention;

[0092] Figure 12 The background mesh diagram (average quality of unit mesh 0.818) involved in the parameterized construction method of the three-dimensional microscopic numerical model of recycled concrete in this invention;

[0093] Figure 13 The side profile of the projected mesh model involved in the parameterized construction method of the three-dimensional microscopic numerical model of recycled concrete in this invention. Detailed Implementation

[0094] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0095] The present invention will be further explained below with reference to specific embodiments.

[0096] like Figure 1 As shown in this embodiment, a parameterized construction method for a three-dimensional microscopic numerical model of recycled concrete includes the following steps:

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

[0098] S101, random generation of recycled concrete aggregate particle size

[0099] The random generation formula of recycled concrete aggregate particle size is derived by using the Fuller grading curve. The specific process is as follows:

[0100] Assuming that the Fuller grading curve equation index n = 0.5, the recycled concrete aggregate content grading curve 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 particle number of recycled concrete aggregate with particle size d;

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

[0107]

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

[0109] Assuming that each recycled concrete aggregate particle size appears with the same probability on the grading curve:

[0110]

[0111] In formula (4), P is uniformly distributed in [0 1]; wherein, [0 1] uniformly distributed means that P obeys the uniform distribution in the interval [0 1], that is, each value appears with equal probability.

[0112] Then the particle size of the randomly generated recycled concrete aggregate is:

[0113]

[0114] S102, calculate the old mortar layer thickness of recycled concrete aggregate

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

[0116]

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

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

[0119]

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

[0121] S200, construction of a recycled concrete three-dimensional random spherical aggregate specimen geometric model

[0122] The generation of aggregate particles is the first step of generating a mesoscopic model by parameterized modeling, and the recycled aggregate is simplified as two concentric spheres, as shown in Figure 2 .

[0123] The present application adopts the "pick-and-place method" to complete the placement of aggregate, establishes a three-dimensional random distribution geometric model of recycled aggregate, and the specific process is as follows:

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

[0125] S202, determining the specific position of the recycled concrete aggregate according to the recycled concrete aggregate sphere center coordinates and radius, the x, y and z of the recycled concrete aggregate sphere center coordinates are randomly given by the multiplication and addition congruence method, which can ensure that the recycled concrete aggregate is randomly distributed in the space range;

[0126] S203, when the position of the recycled concrete aggregate sphere center coordinates is determined, the unplaced recycled concrete aggregate is compared with all the placed recycled concrete aggregate, and all the recycled concrete aggregate must satisfy that the distance between each other is greater than the sum of the radii of the two spheres, so as to ensure that the recycled concrete aggregate does not invade each other.

[0127] According to the order of the size of the aggregate particle size, the cubic specimen and the cylindrical specimen are taken as examples, Figure 3 The model diagram of random aggregate placement, wherein the blue particles represent natural aggregate particles, and the cyan particles represent recycled aggregate.

[0128] S300, recycled concrete three-dimensional random convex polyhedral aggregate specimen geometric model

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

[0130] S301, a plurality of points are randomly generated on the outer base sphere as the convex polyhedral aggregate base framework, the relative positions of the base points are kept unchanged, the radius of the outer base sphere is expanded, and the volume of the generated outer convex polyhedron is equal to the volume of the outer sphere, as shown in 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 polyhedral aggregate particle cannot exceed the size range of the specimen; ② to ensure that the convex polyhedral aggregates do not overlap, that is, to check whether any vertex of the convex polyhedral aggregate particle is inside or outside other convex polyhedral aggregates, and to check whether the boundary lines of the convex polyhedral aggregates intersect.

[0131] S302, the same method as generating the outer convex polyhedron in step 3.1) is used to randomly generate the 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 need to be ensured to be inside the corresponding outer convex polyhedron, as shown in Figure 6 (c).

[0132] The method of generating a convex polyhedron on a base sphere is as follows:

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

[0134]

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

[0136] To prevent the polyhedron vertex distance too close and cause the triangular face abnormal (not conducive to subsequent meshing), the vertex distance on the base sphere should be ensured not less than ηr0, and η = 0.55 is taken. Then the MATLAB convhulln algorithm is used to establish triangular faces based on these polyhedron vertices, and the triangular faces constitute the convex polyhedron base aggregate. According to the ratio r s of the volume V c of the base sphere and the volume V i of the convex polyhedron base aggregate, the base sphere volume is expanded, and the relative position of the vertex remains unchanged. If the aggregates overlap, repeat the above formula (9) to regenerate the vertex;

[0137]

[0138] Whether the convex polyhedron aggregates overlap is judged, that is, whether the vertex P(x, y, z) of one convex polyhedron aggregate is inside another convex polyhedron aggregate, and whether the aggregate boundary line intersects. If the convex polyhedron aggregates do not overlap, the recycled concrete three-dimensional random spherical aggregate specimen geometric model can be finally converted into a recycled concrete three-dimensional random convex polyhedron aggregate specimen geometric model. The gradation of the two kinds of aggregate models and the corresponding aggregate content and old mortar content are the same, only the shape of the aggregate is different;

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

[0140] ①First, each convex polyhedron aggregate needs to be divided into multiple tetrahedrons. The Delaunay triangulation function provided by the matrix laboratory can be directly used.

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

[0142] For example Figure 4 , assume 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), and

[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] As shown in FIG. 2, the method includes two steps: ① judging whether the expanded base sphere overlaps with other base spheres, if not, the convex polyhedral aggregate boundary line will not intersect; ② judging whether the convex polyhedral aggregate arbitrary boundary line intersects with the arbitrary convex surface of another convex polyhedral 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. Figure 5

[0146] Generally, the ellipsoid is used, and the regenerated convex aggregate with different axis length ratios can be generated according to the algorithm, as shown in FIG. 3. Figure 7 It is a regenerated aggregate with an axis length ratio of 2 (here, the aggregate axis length ratio is defined as the ratio of the longest axis and the shortest axis of the circumscribed ellipsoid of the aggregate).

[0147] According to the algorithm, the three-dimensional spherical aggregate model in FIG. 1 can be converted into a convex polyhedral aggregate model, as shown in FIG. 2. Figure 3 The gradation of the two aggregate models and the corresponding aggregate content and old mortar content are the same, only the shape of the aggregate is different. Figure 8

[0148] S400, unstructured meshing

[0149] After the geometric model is generated, it needs to be meshed; in order to generate high-quality meshes, the mesh generation algorithm of the geometric shape defined by the implicit function (the function used to describe the geometric shape) is used, considering the boundary of the interface transition zone and the mesh refinement, and 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, to obtain a high-quality recycled concrete mesh model.

[0150] S401, mesh optimization

[0151] Based on the physical analogy between the edges of tetrahedral elements and the truss structure, the linear force-displacement relationship is used to solve the balance problem in the truss structure to improve the initial mesh. Any set of points in the plane can be triangulated by the Delaunay algorithm, and when the nodes move, the mesh is optimized by recalculating the Delaunay triangulation or by local updating to improve the quality of the tetrahedral elements. In the equilibrium state, the tetrahedral elements often have high quality, and this method can be extended to higher dimensions.

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

[0153] ​​

[0154] In equation (12) above, k is the coefficient of the simulated linear spring bar, 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 (F > 0) to help the node unfold within the entire geometric boundary. This means that when the current length is near the ideal length, F should be greater than zero. This can be achieved by appropriately scaling up the desired ideal length, typically by 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 necessarily equal 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):

[0156]

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

[0158] In equation (14) above, d(x) i ,y i Let ) be the distance function, {|d(x)} i ,y i )|} is the point (x i ,y i The set of absolute distances to each aggregate interface. a, b, c are the relative dimensions of the grid at the interface.

[0159] S402, Formation of boundary layer inside the grid

[0160] like Figure 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 an infinitesimal ψ, we can obtain the gradient at node P:

[0161]

[0162] Therefore, we can obtain:

[0163]

[0164] In this study, to improve accuracy, the above steps were repeated, and the iteration was terminated and corrected when the result of two iterations was less than a preset value.

[0165] A three-dimensional specimen with a size of 50mmx50mmx50mm was taken as an example, and a recycled round aggregate with a particle size of 20mm and an old mortar layer thickness of 2.5mm was placed at the center of the specimen, and the interface transition zone was 0.5mm. As shown in Figure 10 (a), Figure 10 (b) and Figure 10 (c), which are the Delaunay subdivision diagrams after the first, fifth and 100th iterations, respectively, and it can be seen from the diagrams that the grid uniformity is getting better and better as the iteration proceeds.

[0166] S500, recycled concrete projection network model construction

[0167] The projection grid method is applied to assign material properties to the generated grid elements; for the convex aggregate model, high-quality background grids can also be generated, such as Figure 11 The final generated projection grid model; and the specific construction process of the projection grid model is as follows:

[0168] After the unstructured grid division of the recycled concrete geometric model, the relative position of the element nodes is judged to determine the element type; when all the nodes of the element fall in the natural aggregate area, the element will be defined as a natural aggregate element; when all the nodes fall in the old mortar area, the element will be defined as an old mortar element; when all the nodes fall in the new mortar area, the element will be defined as a new mortar element; and when some nodes are in the natural aggregate area and some nodes are in the old mortar area, the element will be defined as an old interface transition zone element; when some nodes are in the old mortar area and some nodes are in the new mortar area, the element is a new interface transition zone element; finally, the generated elements are assigned material parameters.

[0169] Example application

[0170] In the following examples, a disc-shaped specimen for a splitting test is taken as an example, as shown in Figure 12 Its characteristic is that the damage position in the specimen is relatively fixed, in order to reduce the degrees of freedom, the specimen is divided into a macroscopic region and a mesoscopic region, the material in the macroscopic region is almost not damaged in the stress process, and therefore is regarded as homogeneous, the mesoscopic region under the action of external force has internal microcracks initiation, expansion and penetration until the formation of macroscopic cracks, leading to the instability and fracture of the specimen, therefore, in order to reflect the localization and stress redistribution characteristics in the fracture process, the mesoscopic region needs to be modeled according to the mesoscopic scale.

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

[0172] The application 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 the aggregate in the recycled concrete.

[0173] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the application, but not to limit them; although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the application.

Claims

1. A parameterized construction method of a three-dimensional fine numerical model of recycled concrete, characterized in that, The method comprises the following steps: 1) calculating the particle number, particle size and old mortar layer thickness of the recycled concrete aggregate; 2) constructing a three-dimensional random spherical aggregate specimen geometric model of recycled concrete; 3) constructing a three-dimensional random convex polyhedral aggregate specimen geometric model of recycled concrete; 4) unstructured meshing The mesh generation algorithm of the geometric shape defined by the implicit function is considered to optimize and apply the boundary of the interface transition zone and the mesh refinement to the three-dimensional random spherical aggregate specimen geometric model of recycled concrete and the three-dimensional random convex polyhedral aggregate specimen geometric model of recycled concrete, so that a high-quality recycled concrete mesh model is obtained; the specific process is as follows: 4.1) mesh optimization Based on the physical analogy between the edges of the tetrahedral unit and the truss structure, the linear force-displacement relationship is used to solve the balance problem in the truss structure to improve the initial mesh, and the specific solving process is as follows: The difference between the ideal length and the current length of each edge is set as the spring force, the node position is updated, and the Delaunay triangulation is recalculated to adjust the mesh, until the system reaches the equilibrium state, and the solving formula is as follows: （12）； where k in equation (12) is a coefficient for the simulated linear spring bar, set to 1; when F > 0, the grid boundary is stretched; for all interior nodes, there is equilibrium: ; for most bars, the repulsive force (F > 0) to help the nodes spread out within the entire geometric boundary; Ideal length of tetrahedron edge Described by a mesh size function h(x,y,z), note that h(x, y,z) 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 cell size, this is achieved by limiting the gradient in h(x,y,z); （13）； （14）； wherein the above formula (14) is is a distance function, is a point is a set of absolute values of distances to each aggregate interface; a, b, c are relative sizes of the grid at the interface; 4.2) formation of the internal boundary layer of the mesh Given a cell node and nodes to interface distance function , one needs to find the corrected , using an infinitesimal , one can get the gradient at node : （15）； Thus, the following can be obtained: （16）； 5) construction of a recycled concrete projection network model.

2. The method of claim 1, wherein, The specific process of step 1) is as follows: 1.1) random generation of recycled concrete aggregate particle size The random generation formula of the recycled concrete aggregate particle size is derived by adopting the Fuller grading curve; the specific process is as follows: Assuming that the Fuller grading curve equation index n = 0.5, the recycled concrete aggregate content grading curve is as follows: （1）； In formula (1), is the particle size of the recycled concrete aggregate, is the maximum particle size of the recycled concrete aggregate, is the recycled concrete aggregate content; With respect to the above equation (1) The derivative is: （2）； In the above formula (2), N is the particle number of the recycled concrete aggregate with a particle size of d; Integrating both ends of the above formula (2) has: （3）； In formula (3), Dmin is the minimum particle size of the recycled concrete aggregate; A is a constant coefficient, ; Assuming that the probability of each recycled concrete aggregate particle size appearing on the grading curve is the same: （4）； In formula (4), P is Uniform distribution; Then the random generation of the recycled concrete aggregate particle size is as follows: （5）； 1.2) calculation of the old mortar layer thickness of the recycled concrete aggregate The volume content percentage of the old mortar layer of the recycled concrete aggregate is calculated by the density of the natural aggregate, the density of the mortar and the mass content percentage, and then the old mortar layer thickness of the recycled concrete aggregate is calculated: （6）； （7）； In formulas (6)-(7), , respectively represent the volume of old mortar in recycled concrete aggregate and natural aggregate; , respectively represent the density of old mortar and natural aggregate; , respectively represent the mass of old mortar and recycled concrete aggregate; represents the mass content of old mortar; represents the area of old mortar to volume of natural aggregate ratio; The mortar layer thickness h is obtained from the volume ratio: （8）； In formula (8), denotes the particle size of the recycled concrete aggregate.

3. The method of claim 1, wherein, The step 2) is to complete the placement of the recycled concrete aggregate by using the "pick-and-place method" to establish a three-dimensional random distribution geometric model of the recycled aggregate, and the specific process is as follows: 2.1) determining the space range where the recycled concrete aggregate is located; 2.2) According to the specific position of the recycled concrete aggregate determined by the recycled concrete aggregate sphere center coordinates and radius, the sphere center coordinates of the recycled concrete aggregate are Randomly given by the multiplication and addition congruence method, it can be ensured that the recycled concrete aggregate is randomly distributed in the space range; 2.3) when positioning the center coordinates of the recycled concrete aggregate spheres, the unplaced recycled concrete aggregate is compared with all the placed recycled concrete aggregate in a cycle, and all the recycled concrete aggregates must satisfy the condition that the distance between any two recycled concrete aggregates is greater than the sum of the radii of the two spheres, so as to ensure that the recycled concrete aggregates do not invade each other.

4. The method of claim 1, wherein, In the step 3), the three-dimensional random convex polyhedral aggregate specimen geometric model of recycled concrete is constructed by generating convex polyhedrons based on spheres, and each vertex of the convex polyhedron is located on the sphere surface, which is called the base sphere of the polyhedron; the specific process of constructing the three-dimensional random convex polyhedral aggregate specimen geometric model of recycled concrete is as follows: 3.1) Randomly generate several points on the outer base sphere as the base frame of convex polyhedron aggregate, keep the relative position of the base points unchanged, expand the radius of the outer base sphere, and make the volume of the generated outer convex polyhedron equal to the volume of the outer sphere; 3.2) Randomly generate an inner convex polyhedron on the inner base sphere in the same way as generating the outer convex polyhedron in step 3.1), 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 need to be ensured within the corresponding outer convex polyhedron.

5. The method of claim 4, wherein, The method for generating convex polyhedrons on the base sphere is as follows: Randomly generate 10-18 points on the base sphere as polyhedron vertices, which can be represented as: （9）； In formula (9), is the coordinate of the sphere center, is the radius of the sphere; is randomly generated in the range [0, π], is randomly generated in the range [0, 2π]. To prevent triangular face distortion caused by the vertices of the polyhedron being too close together, the distance between vertices on the base sphere must be no less than [missing information]. Then, using MATLAB's convhull algorithm, triangular faces are constructed based on these polyhedron vertices. These triangular faces constitute the convex polyhedron aggregate; based on the volume of the base sphere... Volume of convex polyhedral aggregate ratio The volume of the base sphere is increased while the relative position of the vertices remains unchanged; if there is an overlap between aggregates, the above formula (9) is repeated to regenerate the vertices; （10）； Determining whether convex polyhedral aggregates intersect or overlap involves identifying the vertices of one of the convex polyhedral aggregates. Whether it is inside another convex polyhedral aggregate, and whether the aggregate boundary lines intersect. If there is no intersection or overlap between the convex polyhedral aggregates, the geometric model of the three-dimensional random spherical aggregate specimen of recycled concrete can be 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 the two aggregate models are the same, only the aggregate shape is different.

6. The method of claim 5, wherein, judging the relative position of the convex polyhedral aggregates, i.e. judging whether the vertex of one of the convex polyhedral aggregates is inside another convex polyhedral aggregate judging the relative position of the convex polyhedral aggregates, i.e. judging whether the vertex of one of the convex polyhedral aggregates is inside another convex polyhedral aggregate First, each convex polyhedral aggregate must be divided into tetrahedrons, which can be achieved by using the function DelaunayTriangulation provided by the Matrix Laboratory directly. determining whether a vertex is inside the tetrahedrons, if the point is inside one of the tetrahedrons, then the point is inside the polyhedron; if the point is not inside any of the tetrahedrons, then the point is not inside the polyhedron; Assume that the four vertices of the tetrahedron are , , , , then there are: （11）； If , , , , then the point is inside the tetrahedron.

7. The method of claim 5, wherein, The process of judging whether the aggregate boundary lines intersect specifically includes: ① judging whether the expanded 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.

8. The method of claim 4, wherein, The vertices of the convex polyhedron in the step 3.1) need to satisfy the following requirements: Any vertex of the convex polyhedron aggregate particle cannot exceed the specimen size range; To ensure that there is no intersection between the convex polyhedron aggregates, that is, to check whether any vertex of the convex polyhedron aggregate particle is inside or outside other convex polyhedron aggregates, and to check whether the boundary lines of the convex polyhedron aggregates intersect.

9. The method of claim 1, wherein, The step 5) is to apply the projection grid method to assign material properties to the generated grid cells; for convex aggregate models, high-quality background grids can also be generated, and the final projection grid model is generated; and the specific construction process of the projection grid model is as follows: After the non-structured grid division of the recycled concrete geometric model, the relative position of the cell nodes is determined to determine the cell type; when all nodes of the cell fall in the natural aggregate area, the cell will be defined as a natural aggregate cell; when all nodes fall in the old mortar area, the cell is defined as an old mortar cell; when all nodes fall in the new mortar area, the cell is defined as a new mortar cell; when some nodes are in the natural aggregate area and some are in the old mortar area, the cell is defined as an old interface transition zone cell; when some nodes are in the old mortar area and some are in the new mortar area, the cell is a new interface transition zone cell; finally, the generated cells are assigned material parameters.

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