Recycled aggregate close packing method established based on volume expansion and contraction putting principle

Abstract

The invention discloses a recycled aggregate close packing method established based on a volume expansion and contraction putting principle, belongs to the technical field of building material preparation, and is mainly applied to grading optimization and close packing treatment of recycled aggregate in production of building materials such as concrete. Comprising the following steps: S1, constructing a recycled aggregate three-dimensional particle model; S2, constructing a recycled aggregate accumulation model; and S3, performing grading optimization. The three-dimensional morphology characteristics of irregular shape, protruding edges and corners and the like of the recycled aggregate are fully considered, the volume expansion and shrinkage putting principle is combined, efficient collaborative accumulation of the coarse and fine aggregate is achieved, the accumulation density is improved by 8%-12% compared with that of a traditional method, and the accumulation structure is remarkably improved; the optimal feeding proportion and sequence of the aggregates of different particle sizes are accurately determined, the advantages of all the particle sizes are fully played, and the filling effect in the concrete is improved.

Description

Technical Field

[0001] This invention belongs to the field of building material preparation technology, specifically relating to a method for compact packing of recycled aggregates based on the principle of volume expansion and contraction. Background Technology

[0002] As an important product of the resource utilization of construction waste, recycled aggregates are receiving increasing attention for their application in building materials such as concrete. Due to their complex origins, recycled aggregates, compared with natural aggregates, have characteristics such as irregular shape, prominent angularity, and high porosity. These characteristics significantly affect their particle size distribution and compact packing state, thus playing a key role in the performance of recycled aggregate-based building materials.

[0003] In the application research of recycled aggregates, particle size distribution optimization and the establishment of a close packing model are core aspects. Traditional aggregate packing studies are mostly based on continuous medium analysis methods, focusing on the influence of particle size distribution on packing effect, but neglecting the true three-dimensional morphological characteristics of recycled aggregates (such as aspect ratio, convexity, etc.). Discrete element method, as a numerical calculation and analysis technique based on the discrete characteristics of particles, provides a new approach for accurately simulating the aggregate packing process. ITASCA's PFC3D software (Particle Flow Code in Three - Dimensions) is based on this method and can simulate the close packing process of three-dimensional particles according to the true particle shape of recycled aggregates. Compared with traditional methods, it can more accurately describe particle rotation, position changes, and interparticle interaction forces.

[0004] Currently, although some studies have attempted to optimize the packing of recycled aggregates, shortcomings remain. Existing packing methods often fail to fully consider the impact of the three-dimensional morphological characteristics (such as shape and angularity) of recycled aggregate particles of different sizes on compact packing, making it difficult to accurately construct a compact packing model that conforms to the actual characteristics of recycled aggregates. Regarding particle placement and packing optimization strategies, there is a lack of an effective method to utilize the principle of volume expansion and contraction to achieve efficient and coordinated packing of recycled coarse and fine aggregates, resulting in limited packing density of recycled aggregates and affecting the subsequent performance improvement of recycled building materials. Therefore, there is an urgent need for a compact packing method that considers the three-dimensional morphology of recycled aggregates and is based on a reasonable placement and packing strategy to optimize the gradation of recycled aggregates, improve their packing density, and promote the high-quality resource utilization of recycled aggregates in the construction field. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a method for compact packing of recycled aggregates based on the principle of volume expansion and contraction, which solves the problems of insufficient consideration of three-dimensional morphological characteristics and imperfect packing strategies in existing studies on recycled aggregate packing. By using the discrete element method and the principle of volume expansion and contraction, combined with the three-dimensional morphology of recycled aggregates (aspect ratio, convexity, etc.), the gradation of the whole particle size distribution is optimized to achieve efficient and coordinated packing of recycled aggregates and improve their density, thus providing support for their application in building materials.

[0006] To achieve the above objectives, the present invention provides the following technical solution: Using computed tomography (CT) and 3D reconstruction, STL format files containing the true morphology of recycled fine and coarse aggregates are created. The STL files are then imported into Discrete Element Method (DEM) software, and the Bubble-Pack algorithm is used to build a mathematical model of the recycled coarse and fine aggregate particles to restore the true geometric shape information of the aggregates. At the same time, it is necessary to control key parameters such as the degree of overlap between adjacent spheres (overlap amount), determine the size ratio of the minimum and maximum filling spheres (particle size ratio), adjust the fit of the sphere attachment surface (radius coefficient), and control the number of mesh faces to improve the filling density (optimization coefficient).

[0007] In the model initialization phase of PFC3D software, the spatial dimensions of the calculation model and the sample size are determined. For concrete, the sample size is usually selected as a cube with an aggregate placement space of 100mm×100mm×100mm and a spatial dimension of 300mm×300mm×300mm. An aggregate random generation algorithm is written in the fish language. Particle templates are selected from the particle library and their positions are randomly set during placement to ensure that there is no overlap between particles. The program generates particles in sequence. If a new particle cannot be generated at a certain position, other aggregates in the particle library are selected to continue to try to generate particles until no particles can be placed in the spatial position. First, the particles with the largest particle size (10.00-20.00mm) are placed. The placement is determined by detecting whether there is overlap between particles. If there is no overlap, the placement is successful. The coordinate information of the small ball filled in the particle is recorded and marked. Otherwise, the current placement attempt is terminated and the placement is returned to continue. It is determined whether the container is full. If there is remaining space, the particles of the current particle size segment are placed. If it is full, the process of placing particles of the next smaller particle size segment is started. The process is repeated until all particle sizes are placed.

[0008] Contact detection first uses screening and bounding box algorithms to eliminate a large number of non-contact aggregate pairs. The axis-aligned bounding box is a hexahedral cubic box that surrounds the particles and corresponds to the global coordinate system. The overlap of bounding boxes is determined by comparing the projected lengths of the particles on the X, Y, and Z axes. For irregularly shaped aggregates, the contact between spherical particles in the discrete element method is used to determine whether there is overlap between irregular aggregates by checking the contact between the filling spheres. In PFC3D, a linear contact stiffness model is used as the micro-contact model when aggregates are added to eliminate the small overlap between particles caused by expansion. This model assumes that there is no slippage or adhesion between particles, and only a small contact pressure is generated when a collision occurs. It has a small amount of computation and high computational efficiency.

[0009] The principle of volume expansion and contraction in aggregate delivery involves first reducing the size of the aggregate before delivery, and then restoring it to its actual size after delivery. This reduces the porosity. To avoid problems such as large overlap between particles, increased computational complexity, reduced computational efficiency, and system numerical instability caused by directly expanding the particles to the target size all at once, a step-by-step expansion method is adopted to adjust the size of the particles in stages and gradually eliminate the overlap of the initially generated particles.

[0010] Key morphological parameters include aspect ratio (defined as the ratio of the maximum to the minimum Feretta diameter of the particle, reflecting the particle's extensibility) and convexity (described by the ratio of the actual volume of the particle to the volume of the convex hull, indicating the degree of concavity). Analysis shows that as the aspect ratio increases, the sieve residue in the coarse particle segment increases while the sieve residue in the fine particle segment decreases. This is because the long axis arrangement of the particles hinders the filling of fine particles, and the cross-packing of slender particles forms a stable arch structure, significantly hindering the migration of fine particles. When the convexity decreases, more voids are generated at the corners of the particles, making it impossible to perfectly fit and match the size of the fine aggregate, resulting in a reduction in the amount of fine aggregate particles fed. As the convexity increases, the curve shows that the sieve residue in the coarse particle segment decreases while the sieve residue in the fine particle segment increases. The gradation distribution obtained based on the volume shrinkage method shows a significant correlation with the Talbol theoretical curve. The aspect ratio and convexity are introduced as morphological factors to modify the Talbol model. MATLAB software is used to fit the gradation optimization calculation formula considering morphological parameters, and the final formula is obtained using the least squares method.

[0011] The beneficial effects of this invention are as follows: (1) Taking into full account the three-dimensional morphological characteristics of recycled aggregates, such as irregular shape and protruding edges, and combining the principle of volume expansion and contraction, the coarse and fine aggregates are efficiently and synergistically stacked, and the stacking density is increased by 8%-12% compared with the traditional method, which significantly improves the stacking structure.

[0012] (2) By using discrete element method simulation and parameter optimization, the optimal proportion and order of different particle size aggregates are accurately determined, giving full play to the advantages of each particle size and improving the filling effect in concrete.

[0013] (3) Improve the quality of recycled aggregates, expand their application in construction projects, reduce dependence on natural aggregates, promote large-scale resource utilization of construction waste, and help alleviate resource shortages and environmental pollution problems.

[0014] (4) This method is not only applicable to recycled aggregates, but can also be applied to the optimization of other types of aggregate packing after adjustment. It can also be combined with advanced material preparation technology to further expand the scope of application and effect.

[0015] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0016] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 This is a schematic diagram of the three-dimensional modeling process and spherical cluster model of recycled aggregates in this invention; Figure 2 This is a model diagram of recycled aggregate clusters of different particle sizes according to the present invention; (a) Model diagram for particle sizes of 0.60~1.18 mm; (b) Model diagram for particle sizes of 1.18~2.36 mm; (c) Model diagram for particle sizes of 2.36~4.75 mm; (d) Model diagram for particle sizes of 4.75~10.00 mm; (e) Model diagram for particle sizes of 10.00~20.00 mm; Figure 3 This refers to the model domain and sample size of the present invention; Figure 4 This is the process of randomly adding aggregates according to the present invention; (a) Particle size of 10.00~20.00 mm; (b) Particle size of 4.75~20.00 mm; (c) Particle size of 2.36~20.00 mm; (d) Particle size distribution of 1.18~20.00 mm; (e) Particle size of 0.60~20.00 mm; Figure 5 This is a two-dimensional schematic diagram of the contact detection of the particles of the present invention: (a) is a schematic diagram of spherical particles, and (b) is a schematic diagram of clustered particles; Figure 6 This invention relates to the process for eliminating aggregate overlap. (a) is a schematic diagram of the position of the aggregates before the overlap is eliminated; (b) is a schematic diagram of the positional state of the aggregates after the overlap is eliminated; Figure 7 This is a flowchart of the aggregate expansion process of the present invention; Figure 8 This is a comparison of the actual morphology of the recycled aggregate before and after its accumulation and expansion, as presented in this invention. Figure 9 The results of random particle placement with different aspect ratios according to the present invention; Figure 10 These are polyhedral structural units with different convexity ratios in this invention; Figure 11 The results of random particle placement with different convexity ratios according to the present invention; Figure 12 The cumulative sieve residue curves for different aspect ratios of the present invention are shown. Figure 13 The cumulative sieve residue curves for different convexity ratios in this invention; Figure 14 The cumulative sieve residue curves for different gradation models of this invention; Figure 15 This is a distribution chart of the predicted values ​​and residual values ​​of this invention; (a) shows the actual and predicted values ​​when the aspect ratio is 1.0; (b) shows the actual and predicted values ​​when the aspect ratio is 1.5; (c) shows the actual and predicted values ​​when the aspect ratio is 2.0; (d) shows the actual and predicted values ​​when the aspect ratio is 2.5; (e) shows the actual and predicted values ​​when the convexity is 0.815; (f) represents the actual and predicted values ​​when the convexity is 0.874; (g) represents the actual and predicted values ​​when the convexity is 0.959; (h) represents the actual and predicted values ​​when the morphology is true. Detailed Implementation

[0017] like Figures 1-15As shown, this invention first constructs a three-dimensional particle model of recycled aggregate. Using computed tomography (CT) and 3D reconstruction, it establishes an STL file containing the true morphology of 255 recycled fine aggregate particles and 100 recycled coarse aggregate particles. The STL file is then imported into discrete element method (DEM) software. Finally, this invention uses the Bubble-Pack algorithm to establish a mathematical model of the recycled coarse and fine aggregate particles, restoring the true geometric shape information of the aggregate. The modeling process is as follows: Figure 1 As shown.

[0018] The Bubble-Pack algorithm approximates the shape of irregular aggregates with spheres. The more spheres that make up the aggregate, the more accurately the target particle shape can be fitted by the sphere cluster, offering flexibility and adaptability for complex aggregate shapes. The approximation effect of the sphere combination on irregular aggregates is optimized by adjusting four key parameters: (1) Overlap Amount: Controls the degree of overlap between adjacent spheres. The larger the value, the smoother the particle surface. When the overlap amount is 0, the two spheres only touch at a certain point and do not overlap. When the overlap amount is 180, one sphere will be contained inside the other sphere, and the spheres will completely overlap.

[0019] (2) Particle size ratio: determines the size ratio of the smallest and largest filling spheres, and affects the uniformity of sphere filling within the particle.

[0020] (3) Radius coefficient: Adjusts the fit of the ball to the surface.

[0021] (4) Optimization coefficient: control the number of mesh faces to increase the filling density.

[0022] By coordinating these parameters, the generated sphere combinations can more realistically simulate the geometric characteristics of aggregates. This invention uses ratio (particle size ratio) = 0.3, distance (overlap) = 160, radfactor (radius coefficient) = 2.0, and refinenum (optimization coefficient) = 1 to characterize the shape of recycled coarse and fine aggregates. Based on the Bubble-Pack algorithm, models of recycled coarse and fine aggregates of different particle sizes are established as follows... Figure 2 As shown.

[0023] Then, a recycled aggregate packing model is constructed. During the model initialization phase of the PFC3D software, the spatial dimensions (domain) and sample dimensions (wall) of the calculation model are determined. Since the sample size for concrete is typically 100mm × 100mm × 100mm, to ensure calculation accuracy, this invention selects a 100mm × 100mm × 100mm cube for aggregate placement, with spatial dimensions of 300mm × 300mm × 300mm. For example... Figure 3The model boundary shown should be set within the spatial dimensions. Areas outside the model should not participate in any force and displacement calculations, and the generation of particle and wall boundaries is not allowed.

[0024] An aggregate randomization algorithm was written using the fish programming language. The randomization steps are as follows: Figure 4 As shown in the diagram. Select a particle template from the particle library and randomly set its position during the placement process, ensuring no overlap between particles. The program will generate particles sequentially. If a new particle cannot be generated at a certain position, the program will select other aggregates from the particle library and continue trying to generate particles until no particles can be placed in the available space. First, the largest particle size (10.00~20.00mm) particles are placed, and this is determined by detecting whether particles overlap. If there is no overlap, the placement is considered successful, and the coordinates of the filling spheres inside the particle are recorded and marked as successful placement. Otherwise, the current placement attempt is terminated and the process continues. Next, it checks if the container is full. If there is still space inside the container for the current aggregate placement, the current particle size segment is placed; if it is full, the process moves to placing particles of the next smaller particle size segment. This process is repeated until all particle sizes are placed, and the final output is a randomly placed particle stacking model, as shown in the diagram. Figure 4 As shown.

[0025] In both the initial sample formation and subsequent dynamic expansion processes, contact detection between particles is required in each calculation cycle to prevent interference. Compared to the entire packing system, each aggregate only contacts the surrounding aggregates; that is, there is no overlap between a particular aggregate and the vast majority of particles in the packing system. Therefore, a sieving algorithm is first used to eliminate these numerous non-contact aggregate pairs. In the Discrete Element Method (DEM), the bounding box algorithm is an effective and fast method for initially eliminating non-contact aggregates. For irregular aggregates, axis-aligned bounding boxes are generally used; this method is widely applied in DEM particle contact detection. An axis-aligned bounding box is a hexahedral cubic box corresponding to the global coordinate system that surrounds the particle, compactly enclosing the entire particle. Figure 5 The cubic box shown is an axis-aligned bounding box. The overlap between two axis-aligned bounding boxes is detected by comparing the projected lengths of the particles on the X, Y, and Z axes. If the projections of the bounding boxes do not overlap on a certain coordinate axis, then the two bounding boxes are determined not to overlap, meaning there is no overlap between the two aggregates (e.g., ...). Figure 5 (a) The projections of the bounding boxes of particles A and B on the x-axis do not overlap. If the two bounding boxes overlap in the projection direction (e.g.) Figure 5 (a) There is an overlap of AABB between particles A, C, and D, requiring the following precise testing between the aggregates: In three-dimensional space, for regular spheres or ellipsoids, generalized eigenvalues ​​can be used to determine whether they overlap. However, for irregularly shaped aggregates, the contact determination between particles is relatively complex. This invention uses the contact between spherical cluster particles in the discrete element method to determine the contact between irregularly shaped aggregate particles. Within the spherical cluster particles, the contact between the filling spheres is checked to determine whether overlapping occurs between irregular aggregates (e.g., ...). Figure 5 (b) shows that this method can significantly reduce the complexity of contact detection for irregular aggregates. To improve computational efficiency, contact detection between the filling spheres within a single aggregate is not considered; they are treated as ideal rigid bodies. Two irregular aggregates are considered to be in contact if and only if they satisfy... If there is contact between two aggregate particles, the initial sample preparation process will be deemed unsuccessful. ij R represents the distance between the centroids of two spherical particles at the contact point when the aggregate is filled with small spheres; i and R j Let represent the radii of the filling spheres. Overlap is determined between two spherical particles at the contact points of irregular aggregates, and the contact embedment depth δ between the aggregates is: .

[0026] The actual distance between the surfaces of two particles is the surface gap, and the actual distance between the particles at the contact point is the contact gap. When the difference between the contact gap and the reference gap reaches a certain preset value, there is contact between the particles and relative motion occurs. However, when the nominal surface coincides with the workpiece surface, it indicates that the objects are in complete contact, and Newton's second law cannot be applied to particles that are not in contact. When the aggregate expands, the increased volume may lead to increased contact between particles, or even overlap. According to Newton's second law, the contact force will change the motion state (velocity and displacement) of the particles through acceleration, thereby prompting the particles to adjust their positions to eliminate overlap. In the discrete element method, the contact force is usually calculated from the amount of overlap between particles, such as in a linear spring model. middle, The contact force represents the amount of overlap, and its magnitude is related to the amount of overlap; a larger contact force implies a larger overlap. The process of reducing overlap through displacement adjustment is essentially a dynamic equilibrium driven by contact force. In PFC3D, the linear contact stiffness model is widely used for simulating sand and gravel aggregates. This model assumes no slippage or adhesion between particles, only a small contact pressure generated during collisions. This simplified assumption better reflects the actual behavior of sand and gravel aggregates during packing, and compared to other complex models, it has lower computational cost and higher computational efficiency. Therefore, this model is used as a mesoscopic contact model during aggregate loading to eliminate the small overlap between particles caused by expansion (see...). Figure 6 ).

[0027] Because randomly placed particles must meet the condition of no overlap, large gaps will form between the aggregates, leading to increased porosity and making it difficult to achieve a dense state. Therefore, this invention reduces the porosity by first reducing the size of the aggregates before placement, and then restoring them to their actual size after placement. During the dynamic change of the aggregate system volume, the impact of key parameters on the compaction effect needs to be quantitatively evaluated. This invention studies the influence of parameters such as volume reduction ratio, expansion number, and iteration number on controlling particle overlap.

[0028] Figure 7 This is a schematic diagram illustrating the aggregate shrinkage and expansion process during delivery. Figure 7 From left to right: The diagram shows the initial distribution of aggregates in a cubic container under non-overlapping conditions; the expansion stages (expansion coefficient set to 5.0 for enhanced visualization); the elimination of overlap caused by the expansion steps through progressive expansion; and the "overflow" phenomenon where, due to an excessive number of aggregates in the container, some aggregates fail to completely fill the container after expansion. During this process, the aggregates reach equilibrium through positional adjustments and collisions with other aggregates. Finally, in this equilibrium state, two aggregates expanded to their actual size were successfully placed into the container.

[0029] During particle expansion, directly expanding particles to the target size all at once can lead to significant overlap between particles, increasing computational complexity, reducing efficiency, and causing numerical instability. To avoid this, a step-by-step expansion method is employed, gradually eliminating initial particle overlap by adjusting particle size in stages. Compared to one-time expansion, step-by-step expansion increases particle volume gradually with smaller steps, ensuring the contact forces between particles are rebalanced at each stage. This method helps avoid excessive contact forces, reducing violent oscillations caused by such forces and effectively preventing system instability or numerical divergence. During calculation, particle movement is explicitly driven by dynamics within each cycle, gradually eliminating overlap. Simultaneously, particle velocity and contact forces are adjusted to accelerate system equilibrium. In this mode, particle velocity is gradually reduced to prevent instability caused by excessive velocity. Furthermore, velocity is reset to zero each cycle to prevent continuous particle motion due to inertia, thus avoiding computational divergence caused by initial overlap and preventing particles from overflowing the wall due to excessive velocity. When the system stiffness changes (e.g., the particle contact state changes), the step size is automatically adjusted to maintain a balance between computational accuracy and efficiency, ensuring the stability and convergence of the computation process. The volume reduction ratio, number of expansions, number of iterations, and cycle time for adjusting particle velocity and contact force are shown in Table 1, ultimately obtaining the minimum porosity of the system. The equilibrium calculation cycle means recalculating after every 1000 steps.

[0030] Table 1. Parameter settings for the shrinkage-expansion method Figure 8 This demonstrates the changes in the packing of recycled aggregate before and after expansion treatment. Figure 8 (a) shows the original aggregate state, which exhibits obvious void distribution characteristics and significant voids between particles. Figure 8 (b) shows the expanded state. When the aggregate volume expands to its actual size, the contact between particles increases, resulting in a dense arrangement. The porosity of the aggregate before expansion was 36%, and the porosity of the packing system after expansion decreased to 21%. The dynamic adjustment of the aggregate position is achieved through particle volume expansion, thereby effectively reducing the porosity. Comparing this porosity with that obtained from existing gradation optimization models (as shown in Table 2), the results indicate that the shrinkage expansion method used in this invention can achieve dense packing of recycled coarse and fine aggregates.

[0031] Table 2 Comparison of porosity in different literature Considering the influence of three-dimensional particle morphology parameters of recycled aggregates on their close packing, the aspect ratio (aspect ratio) and convexity (convexity ratio) are two key parameters that can independently characterize particle morphology. The aspect ratio, defined as the ratio of the maximum to the minimum Feretta diameter, effectively reflects the particle's elongation characteristics; the convexity ratio describes the degree of concavity in the particle by the ratio of its actual volume to the volume of its convex hull.

[0032] Figure 9 The results of random feeding of aggregate particles with aspect ratios of 1.0, 2.0, and 2.5 are shown. The number of aggregate particles of each size is shown in Table 3.

[0033] Table 3 Number of particles deployed in each segment with different aspect ratios (1) Figure 9 (a) The results of filling ellipsoidal aggregates in the 10.00~20.00mm particle size range according to size stepwise. When only three different aspect ratio ellipsoidal aggregates with particle sizes of 10.00~20.00mm are used, the volume can reach 31.1% in the space when the aspect ratio is 1.0, and the volume reaches the maximum of 32.4% when the aspect ratio is 2.5. (2) Figure 9(b) Presents the results of a feeding test using ellipsoidal aggregates with particle sizes ranging from 4.75 to 20.00 mm, after being filled in stages according to particle size. Comparative analysis of the feeding results for ellipsoidal aggregates with different aspect ratios revealed that as the aspect ratio of the ellipsoidal aggregates increases, the actual volume percentage in the system shows a significant decreasing trend. The volume percentage gradually decreases from an initial 50.7% to 45.5%; when the aspect ratio reaches 2.5, the volume percentage further decreases to 43.4%, with the spherical aggregate with an aspect ratio of 1.0 exhibiting the largest volume percentage, reaching 50.7%. (3) Figure 9 (c) The results of filling ellipsoidal aggregates in the particle size range of 2.36~20.00mm in stages according to particle size, gradually decreasing from 68.4% to 64.7% of the total volume. When the aspect ratio is 2.5, the volume decreases to 60.1%. Among them, the volume of spherical aggregates with an aspect ratio of 1.0 is the largest, at 68.4%. (4) Figure 9 (d) shows the results of filling ellipsoidal aggregates in the particle size range of 1.18~20.00mm in stages according to particle size. The filling volume gradually decreased from 73.9% to 72.1%, and when the aspect ratio was 2.5, the filling volume decreased to 70.5%. Among them, the spherical aggregates with an aspect ratio of 1.0 had the largest filling volume of 73.9%. (5) Figure 9 (e) shows the results of filling ellipsoidal aggregates in the 0.6~20.00mm particle size range according to their size. From the final actual volume ratio of the three aggregates, it can be seen that as the aggregate particle size range continues to expand, the amount of smaller aggregates will gradually decrease. When the aspect ratio is 1.0, only about 8.5% of the aggregates in the 0.60~1.18mm particle size range are filled. When the aspect ratio is 2.0, only about 6.8% of the aggregates in the 0.60~1.18mm particle size range are filled. When the aspect ratio is 2.5, only about 6.1% of the aggregates in the 0.60~1.18mm particle size range are filled.

[0034] The dodecahedron possesses a clear and regular edge and face structure, and this unique angularity gives it a high degree of geometric symmetry. Therefore, this invention involves indenting different symmetrical faces of the dodecahedron to the same degree to characterize the change in convexity. The shortest axis is the distance between the vertices of two opposite indented faces, and the longest axis is the distance from one vertex to the symmetrical vertex of the dodecahedron. The aspect ratio is the ratio of the longest axis to the shortest axis. Convexity is defined as the ratio of the volume of the polyhedron after indentation to the volume of the dodecahedron itself; while keeping the aspect ratio constant, the convexity changes to varying degrees. Figure 10 Polyhedral structural units with different convexity ratios are shown.

[0035] Figure 11 The results of random placement of aggregates with convexity ratios of 0.815, 0.876, and 0.959 are shown. Table 4 shows the number of random placements of aggregates with different convexity ratios.

[0036] Table 4. Number of particles deployed in each segment with different convexities. (1) Figure 11 (a) The results of feeding aggregates in the 10.00~20.00mm particle size range according to the particle size stepwise. By comparing the feeding results of three different aggregates with different convexity, it can be seen that when only three different aggregates with particle sizes of 10.00~20.00mm are fed, the bulk density of coarse aggregates increases as the convexity decreases. Particles with a convexity of 0.959 can successfully feed 38.3% of the feeding volume within a fixed volume space. (2) Figure 11 (b) The results of aggregate placement in the 4.75~20.00mm particle size range, arranged in order of particle size. Comparison of placement data for aggregates with different convexity ratios revealed a significant upward trend in the actual volume percentage of the aggregate in the system as the convexity ratio increased. The volume percentage gradually increased from an initial 51.2% to 58.5%. In the test samples, spherical aggregates with a convexity ratio of 0.959 exhibited the best packing effect, reaching a peak volume percentage of 58.5%.

[0037] (3) Figure 11 (c) The results of gradually increasing the aggregate size in the range of 2.36~20.00mm according to the particle size, from 60.7% to 67.5% of the total volume, and the total volume increases to 67.5% when the convexity is 0.959; (4) Figure 11 (d) shows the results of gradually increasing the volume of aggregates in the 1.18~20.00mm particle size range according to their size. The volume gradually increased from 71.5% to 73.8%, with the largest volume of spherical aggregates with a convexity of 0.959 being 73.8%. (5) From Figure 11 As shown in (e), the results of the aggregate filling in the 0.6~20.00mm particle size range according to the particle size can be found that the larger the convexity, the lower the final porosity, which can reach 20.6%.

[0038] The final actual volume percentages of the three aggregates show that as the aggregate size range increases, the amount of smaller aggregates added gradually decreases. A convexity ratio of 0.959, due to its high symmetry and regular geometry, achieves a high packing density. During close packing, the contact points between particles are evenly distributed, resulting in low porosity. Therefore, relatively less coarse aggregate is required to achieve a close packing state. Concave surfaces increase the irregularity of the particle surface, forming local uneven structures. This geometric feature interferes with the directional alignment of particles, reducing the packing density. To achieve a close packing state, more coarse aggregate is needed to fill the remaining voids caused by irregular contact. Concave surfaces significantly enhance particle irregularity, leading to complex interlocking structures and localized voids between particles. It has the lowest packing density and requires the most fine aggregate to achieve a close packing state. Therefore, as the convexity ratio increases, the proportion of fine aggregate increases.

[0039] Based on the above results of the closest packing, cumulative sieve residue curves of recycled aggregate under the influence of various parameters were established. The cumulative sieve residue curves for different aspect ratios are shown below. Figure 12 As shown in the figure, when the aspect ratio is 1.0, the cumulative sieve residue curve shows a continuous and gentle upward trend. The increase in sieve residue is uniform in the coarse particle segment, while the slope of the curve increases slightly in the fine particle segment. This indicates that spherical particles achieve uniform distribution through equiaxed characteristics, with small differences in filling size across different particle segments. As the aspect ratio increases, the sieve residue in the coarse particle segment increases, while the sieve residue in the fine particle segment decreases. This is because the long axis alignment of the particles hinders the filling of fine particles, and the slender particles form a stable arch structure through cross-stacking, significantly hindering the migration of fine particles.

[0040] like Figure 13 The figure shows the cumulative sieve residue curves for different crown ratios. As can be observed from the figure, when the crown ratio is 0.815, the cumulative sieve residue curve exhibits a continuous and gentle upward trend. In the coarse particle segment, the increase in sieve residue is relatively uniform; while in the fine particle segment, the slope of the curve increases slightly. As the crown ratio gradually increases, the curve shows that the sieve residue in the coarse particle segment decreases, while the sieve residue in the fine particle segment increases. This is because when the crown ratio decreases, more voids are generated at the edges of the particles. These voids cannot perfectly fit and match the size of the fine aggregate, thus reducing the amount of fine aggregate particles that can be added.

[0041] The Fuller gradation curve is a theoretical particle size distribution model proposed by Willard Fuller and Sanders Thompson in the 20th century. In the formula: CPFT represents the cumulative sieve residue (%) of particles smaller than d; d represents the size of the sieve aperture or the particle size (in mm). This indicates the maximum particle size of the aggregate (in mm). The core idea is to continuously distribute particles from the maximum to the minimum particle size, and the quantity of each particle size can just fill the voids of the previous particle size, ultimately maximizing the aggregate bulk density and minimizing the porosity.

[0042] The Talbol gradation curve is a further improvement on the Fuller curve. Talbol proposed that the proportion of coarse and fine aggregate particles can be flexibly controlled by adjusting the coefficients to adapt to the special requirements of different engineering projects for aggregate gradation, so that the gradation model conforms to the actual material properties. In the formula: CPFT represents the cumulative sieve residue (%) of particles smaller than d; d represents the size of the sieve aperture or the particle size (in mm). This indicates the maximum particle size of the aggregate (in mm); n represents the distribution modulus, which typically ranges from 0.3 to 0.7. Dinger and funk, based on the Andreasen model, considered the influence of minimum particle size on the compaction of the packing system, and further optimized and improved the original model, proposing a modified MAA model: In the formula: CPFT (%) represents the cumulative sieve residue of particles smaller than d; d (in mm) represents the size of the sieve opening or the particle size. (Unit: mm) indicates the maximum particle size of the aggregate in the packing system; (Unit: mm) represents the minimum particle size of aggregate in the packing system; n represents the distribution modulus.

[0043] Based on the MAA model, Yu Zhouliang considered the morphological characteristics of recycled sand particles and introduced an aspect ratio characteristic factor to correct the n value in the model, proposing a modified MAA model: In the formula: CPFT (%) represents the cumulative sieve residue of particles smaller than d; d (in mm) represents the size of the sieve opening or the particle size. (Unit: mm) indicates the maximum particle size of the aggregate in the packing system; (Unit: mm) represents the minimum particle size of aggregate in the packing system; n represents the distribution modulus. This represents the ratio of the longest axis to the shortest axis among the three axes of aggregate in a packing system. The value is greater than or equal to 1.

[0044] The above research shows that the aspect ratio and convexity have a significant impact on close packing. The cumulative sieve residue curves obtained by comparing different gradation design methods are shown below. Figure 14 The gradation distribution obtained based on the volume expansion / contraction method and the Talbol theoretical curve. A significant correlation was observed. In the formula: CPFT represents the cumulative sieve residue (%) of particles smaller than d; d represents the sieve aperture size or particle size (mm); dmax This indicates the maximum particle size of the aggregate (mm); n represents the distribution modulus, which typically ranges from 0.3 to 0.7.

[0045] The cumulative sieve residue deviation of the two aggregates showed little difference compared to other models. This indicates that the traditional Talbol model can well characterize the skeleton formation of coarse aggregates and the filling behavior of fine aggregates in aggregate voids, but its theoretical assumptions do not consider the influence of particle morphology on particle size distribution.

[0046] Therefore, the aspect ratio and convexity are introduced as morphology factors to modify the Talbol model. Based on the least squares polynomial fitting principle, the morphology parameter gradation optimization calculation formula is as follows: .

[0047] In the formula, This indicates the maximum particle size of the aggregate in the packing system, and AR represents the aspect ratio of the particles. Indicates the convexity of the particles. , , and These are different constants.

[0048] Coefficient of determination R 2 The goodness of fit of the reaction model, R 2 The range is 0-1; the closer to 1, the better the variable fits the overall data and the better its explanatory power for the dependent variable. The calculation formula is shown in the equation: In the formula, Let be the actual observed value of the dependent variable at the i-th observation point. For the first The predicted value of the dependent variable for each observation point. The sum of squared residuals is the average of the observed values ​​of the dependent variable, m represents the number of observation points, and RSS is the sum of squared residuals, corresponding to the formula... .

[0049] Calibration Determination Coefficient Adjusted-R 2 It is used to evaluate the quality of the regression equation. As the number of independent variables increases, R0 increases. 2 The main purpose of continuously increasing the sample size is to offset the impact of sample size on R. 2 The effect of this is calculated using the formula shown in the equation: (Where: N is the number of samples, and P is the number of features.) The above formula was fitted using MATLAB software, and the least squares method was used to obtain the optimization calculation formula considering the morphological parameters: .

[0050] The actual values ​​and predicted values ​​of the cumulative sieve residue curves obtained from particles with different aspect ratios, convexities, and true morphologies are compared, and their numerical distributions are as follows: Figure 15 As shown. The aspect ratio and convexity of the actual aggregate are both taken as average values ​​and substituted into the formula: Calculations were performed. The model fit index verified the reliability of the formula fit, with the coefficient of determination R² reaching 0.9967, indicating that the model can explain 99.67% of the variation in the response variable. The adjusted coefficient of determination, adjusted for degrees of freedom, was 0.9954, and the small difference from the R² value (Δ=0.0013) reflects that the model did not exhibit overfitting.

[0051] This invention fully considers the irregular shape and protruding edges of recycled aggregates in three dimensions, and combines this with the principle of volume expansion and contraction to achieve efficient and coordinated packing of coarse and fine aggregates. The packing density is increased by 8%-12% compared to traditional methods, significantly improving the packing structure. Through discrete element method simulation and parameter optimization, the optimal packing ratio and order of different aggregate sizes are accurately determined, giving full play to the advantages of each size and improving the filling effect in concrete. This improves the quality of recycled aggregates, expands their application in construction engineering, reduces dependence on natural aggregates, promotes the large-scale resource utilization of construction waste, and helps alleviate resource shortages and environmental pollution problems. This method is not only applicable to recycled aggregates, but can also be applied to the packing optimization of other types of aggregates after adjustment. It can also be combined with advanced material preparation technology to further expand the scope of application and effects.

[0052] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A method for close packing of recycled aggregate based on the principle of volume expansion and contraction, characterized in that, Includes the following steps: S1. Construct a three-dimensional particle model of recycled aggregate: Recycled aggregate is reconstructed in three dimensions using computer tomography (CT) technology to obtain an STL format file containing the true morphology of recycled aggregate. The STL format file is imported into discrete element software, and a three-dimensional particle model of recycled aggregate is established using the Bubble-Pack algorithm. The three-dimensional particle model is then input into a particle library. S2. Constructing a recycled aggregate packing model: In PFC3D software, set the size of the aggregate delivery space, proportionally reduce the size of the three-dimensional particle model in the particle library, and select three-dimensional particle models from the particle library in descending order of particle size to deliver them into the aggregate delivery space. During the delivery process, the position of the three-dimensional particle model is randomly set, and there is no overlap between particles, until all particles of each size have been delivered. Then restore the size of the three-dimensional particle model to the actual size to obtain the recycled aggregate packing model. S3. Gradation Optimization: Based on the gradation distribution obtained from the recycled aggregate packing model, the aspect ratio and convexity are introduced as morphology factors to modify the Talbol model. The gradation optimization calculation formula considering morphology parameters is fitted using MATLAB software, and the final formula is obtained using the least squares method to achieve close packing.

2. The method for close packing of recycled aggregate based on the principle of volume expansion and contraction as described in claim 1, characterized in that: In S1, the Bubble-Pack algorithm approximates the shape of irregular aggregates using spheres. It optimizes the approximation effect of the sphere combination on irregular aggregates by adjusting four key parameters: Overlap Amount: Controls the degree of overlap between adjacent spheres. The larger the value, the smoother the particle surface. When the overlap amount is 0, the two spheres only contact each other at a certain point and there is no overlap. When the overlap amount is 180, one sphere is contained inside the other sphere, and the spheres completely overlap. Particle size ratio: determines the size ratio between the smallest and largest filled spheres; Radius coefficient: Adjusts the fit of the sphere to the surface it is attached to; Optimization factor: Controlling the number of mesh faces increases fill density.

3. The method for close packing of recycled aggregate based on the principle of volume expansion and contraction as described in claim 1, characterized in that: In S2, the largest particle size is first added. The process is determined by detecting whether there is overlap between particles. If there is no overlap, the addition is considered successful, and the coordinate information of the sphere inside the particle is recorded and marked as successful addition. Otherwise, the current addition is terminated and the process is returned to continue adding particles. Then, it is determined whether the container is full. If there is still space inside the container for the current aggregate addition, the current particle size segment is added. If the container is full, the process of adding the next smaller particle size segment is started. The above steps are repeated until all particle sizes have been added.

4. The method for close packing of recycled aggregate based on the principle of volume expansion and contraction as described in claim 1, characterized in that: During the initial shrinkage and expansion of recycled aggregate to its actual size, contact detection between particles is required, including the following steps: The axis-aligned bounding box method is used to detect the overlap between two axis-aligned bounding boxes by comparing the projected lengths of the particles on the X, Y, and Z axes. If the projections of the bounding boxes do not overlap on a certain coordinate axis, it is determined that the two bounding boxes do not overlap, that is, there is no overlap between the two aggregates. If the two bounding boxes overlap in the projection direction, the following precise detection is required between the aggregates: By checking the contact between the filler spheres, it can be determined whether there is overlap between irregular aggregates. Two aggregates meet the following requirements. There is contact between the two aggregates, d ij R represents the distance between the centroids of two spherical particles when the aggregate is filled with spherical particles at their contact point; i and R j These represent the radii of the filled sphere, respectively. In this case, the initial deployment is considered unsuccessful.

5. The method for close packing of recycled aggregate based on the principle of volume expansion and contraction as described in claim 1, characterized in that: In PFC3D software, the linear contact stiffness model is selected as the microscopic contact model when aggregate is added to eliminate particle overlap caused by expansion.

6. The method for close packing of recycled aggregate based on the principle of volume expansion and contraction as described in claim 1, characterized in that: In the process of restoring the size of the 3D particle model to its actual size, a step-by-step expansion method is adopted. By adjusting the size of the particles in stages, the overlapping phenomenon of the initially deployed particles is gradually eliminated. During the expansion process, the particle motion is propelled by explicit dynamics within the execution cycle, and overlap is gradually eliminated. At the same time, the particle velocity and contact force are adjusted to accelerate the system to reach equilibrium. The velocity is reset to zero once per cycle. When the system stiffness changes, the step size is adjusted to finally obtain the minimum porosity of the system.

7. The method for close packing of recycled aggregate based on the principle of volume expansion and contraction as described in claim 6, characterized in that: The initial shrinkage ratio of recycled aggregate during the initial feeding process was 0.

8. During the expansion process to restore the actual size, the number of expansion iterations was 50, and the volume of each expansion was 0.448%.

8. The method for close packing of recycled aggregate based on the principle of volume expansion and contraction as described in claim 1, characterized in that: The gradation optimization calculation formula considering morphological parameters described in S3 is as follows: In the formula, This indicates the maximum particle size of the aggregate in the packing system, and AR represents the aspect ratio of the particles. Indicates the convexity of the particles. , , and These are different constants.

9. A method for close packing of recycled aggregate based on the principle of volume expansion and contraction as described in claim 1, characterized in that: The final formula described in S3 is as follows: In the formula, This indicates the maximum particle size of the aggregate in the packing system, and AR represents the aspect ratio of the particles. This represents the convexity of the particle.

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