A close-packing method of recycled aggregate based on volume expansion and contraction principle

Abstract

The application discloses a close packing method of recycled aggregate based on a volume expansion and contraction principle, belongs to the technical field of building material preparation, and is mainly applied to gradation optimization and close packing treatment of recycled aggregate in production of building materials such as concrete. The method comprises the following steps: S1, constructing a three-dimensional particle model of recycled aggregate; S2, constructing a recycled aggregate packing model; and S3, gradation optimization. The three-dimensional topographic features of the recycled aggregate, such as irregular shape and prominent edges and corners, are fully considered, and the volume expansion and contraction principle is combined to realize efficient collaborative packing of coarse and fine aggregates, so that the packing density is increased by 8%-12% compared with that of a traditional method, the packing structure is significantly improved, the best feeding proportion and sequence of different particle size aggregates are accurately determined through discrete element method simulation and parameter optimization, the advantages of each particle size are fully brought into play, and the filling effect in concrete is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of building material preparation, and particularly relates to a recycled aggregate close packing method based on a volume expansion and contraction principle. BACKGROUND

[0002] As an important product of resource utilization of construction waste, the application of recycled aggregate in building materials such as concrete has attracted more and more attention. Compared with natural aggregate, recycled aggregate has the characteristics of irregular shape, prominent angularity and high porosity due to complex sources. These characteristics will significantly affect the particle size distribution and close packing state of recycled aggregate, and then play a key role in the performance of recycled aggregate-based building materials.

[0003] In the application research of recycled aggregate, the optimization of particle size distribution and the establishment of close packing model are the core links. Traditional aggregate packing research is mostly based on continuous medium analysis method, focusing on the influence of particle size distribution on packing effect, but ignoring the real three-dimensional topographic features (such as aspect ratio, convexity, etc.) of recycled aggregate. As a numerical calculation and analysis technology based on the discrete characteristics of particles, the discrete element method provides a new way for precise simulation of aggregate packing process. PFC3D (Particle Flow Code in Three-Dimensions) software of ITASCA company is based on this method, which can simulate the close packing process of three-dimensional particles according to the real particle shape of recycled aggregate. Compared with traditional methods, it can more accurately describe the rotation, position change and interaction force between particles.

[0004] At present, although some researches have tried to optimize the packing of recycled aggregate, there are still some deficiencies. The existing packing methods mostly do not fully consider the influence of three-dimensional topographic features (such as shape, angularity, etc.) of recycled aggregate particles in different size ranges on close packing, and it is difficult to accurately construct a close packing model that meets the actual characteristics of recycled aggregate. In terms of particle placement and packing optimization strategy, there is a lack of a method that effectively utilizes the volume expansion and contraction principle to realize the collaborative and efficient packing of recycled coarse and fine aggregates, resulting in limited packing density of recycled aggregate and affecting the performance improvement of subsequent recycled building materials. Therefore, there is an urgent need for a close packing method that considers the three-dimensional topography of recycled aggregate and is based on reasonable placement and packing strategy, in order to optimize the particle size distribution of recycled aggregate, improve its packing density and promote the high-quality resource utilization of recycled aggregate in the construction field. SUMMARY

[0005] Therefore, the present application aims to provide a recycled aggregate close packing method based on the volume expansion and contraction principle, which solves the problem that the existing research on recycled aggregate packing does not fully consider the three-dimensional topographic features and the packing strategy is imperfect. The discrete element method and the volume expansion and contraction principle are used to optimize the full particle size distribution combined with the three-dimensional topography of recycled aggregate (aspect ratio, convexity, etc.), to achieve efficient and collaborative packing of recycled aggregate and improve the density, thereby providing support for its application in building materials.

[0006] To achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0007] The STL format file of recycled fine aggregate and recycled coarse aggregate containing real topography is established by computer tomography and three-dimensional reconstruction, the STL file is imported into the discrete element software, the Bubble-Pack algorithm is used to establish the mathematical model of recycled coarse and fine aggregate particles, the real geometric shape information of the aggregate is restored, and the key parameters such as the degree of overlap (overlap amount) of adjacent spheres, the size ratio (particle size ratio) of the smallest and largest packing spheres, the adhesion degree of small sphere attached surface (radius coefficient), and the control of grid surface number to improve the packing density (optimization coefficient) are controlled.

[0008] In the model initialization stage of PFC3D software, the space size and sample size of the calculation model are determined, the aggregate placement space is usually selected as a cube of 100mm×100mm×100mm based on the sample size of concrete, the space size is 300mm×300mm×300mm, the aggregate random generation algorithm is written by fish language, the particle template is selected in the particle library and the position is randomly set during the placement process, 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, the remaining aggregate in the particle library is selected to continue to attempt to generate, until the particles in the space position cannot be placed, the placement of the largest particle size (10.00-20.00mm) is performed first, whether the particles overlap is detected to determine, if not overlapping, the placement is successful, the coordinate information of the particle inner filling small ball is recorded and marked, otherwise the current placement attempt is terminated and the placement is returned to continue, whether the container is full is judged, if there is remaining space, the current particle size segment particles are placed, if it is full, the placement process of the next smaller particle size segment particles is entered, and the cycle is executed until all particle size particles are placed.

[0009] The contact detection firstly uses a screening algorithm and a bounding box algorithm to exclude a large number of non-contact aggregate pairs, and the axis-aligned bounding box is a hexahedral cube corresponding to the global coordinate system and surrounding the particle, whether the bounding box overlaps is determined by comparing the projection lengths of the particle on the X, Y and Z axes, and for irregularly shaped aggregates, the contact between the ball cluster particles in the discrete element method is used to determine whether the overlapping phenomenon occurs between the irregular aggregates, and whether the overlapping phenomenon occurs between the irregular aggregates is determined by checking the contact between the filling small balls; in PFC3D, a linear contact stiffness model is used as the mesoscopic contact model when the aggregate is placed, which is used to eliminate the micro overlap between the particles caused by expansion, the model assumes that there is no slip or bonding effect between the particles, only a small contact pressure is generated when the collision occurs, and the calculation amount is small and the calculation efficiency is high.

[0010] The volume expansion and contraction placement principle reduces the porosity by first reducing the size of the aggregate for placement, and then restoring it to the actual size after the aggregate is placed, so as to reduce the porosity, in order to avoid the problems of large overlap between particles, increased calculation complexity, reduced calculation efficiency and numerical instability of the system caused by directly expanding the particles to the target size at one time, a step-by-step expansion method is used to adjust the size of the particles in stages, and the overlapping phenomenon of the initially generated particles is gradually eliminated.

[0011] The key topographic parameters include the aspect ratio (defined as the ratio of the maximum Feret diameter to the minimum Feret diameter of the particle, reflecting the extension characteristics of the particle) and the convexity (describing the concave degree of the particle by the ratio of the actual volume of the particle to the volume of the convex hull), the analysis shows that as the aspect ratio increases, the coarse aggregate segment screen residue increases, and the fine aggregate segment screen residue decreases, because the arrangement of the long axis of the particle hinders the filling of the fine particles, and the cross-accumulation of the slender particles forms a stable arch structure, which significantly hinders the migration of fine particles; when the convexity decreases, more voids are generated at the corner parts of the particle, which cannot be perfectly embedded and matched with the fine aggregate size, resulting in a decrease in the amount of fine aggregate particles placed, and as the convexity increases, the curve shows that the coarse aggregate segment screen residue decreases and the fine aggregate segment screen residue increases; the gradation distribution obtained based on the volume expansion and contraction method shows significant correlation with the Talbol theoretical curve, the aspect ratio and the convexity are introduced as topographic factors to modify the Talbol model, and the MATLAB software is used to fit the gradation optimization calculation formula considering the topographic parameters, and the least squares method is used to obtain the final formula.

[0012] The beneficial effects of the present application are:

[0013] (1) The three-dimensional topographic characteristics of the irregular shape, the protruding corners and the like of the recycled aggregate are fully considered, the volume expansion and contraction placement principle is combined, the efficient cooperative accumulation of coarse and fine aggregates is realized, the packing density is increased by 8%-12% compared with the traditional method, and the packing structure is significantly improved.

[0014] (2) Through discrete element method simulation and parameter optimization, the optimal feeding ratio and sequence of different particle size aggregates are accurately determined, the advantages of each particle size are fully utilized, and the filling effect in concrete is improved.

[0015] (3) Improve the quality of recycled aggregates, expand their application in construction engineering, reduce the dependence on natural aggregates, promote large-scale resource utilization of construction waste, and help alleviate resource shortage and environmental pollution problems.

[0016] (4) This method is not only suitable for recycled aggregates, but also can be applied to other types of aggregate packing optimization after adjustment, and can be combined with advanced material preparation technology to further expand the application range and effect.

[0017] Other advantages, objects and features of the present application will be set forth in the following specification, and in part will be apparent from the application itself or from the practice of the application, and will be learned by practice of the application by those skilled in the art. The objects and other advantages of the present application can be realized and obtained by the following description. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to make the purpose, technical scheme and beneficial effects of the present application clearer, the present application provides the following drawings for illustration:

[0019] Figure 1 The figure is a schematic diagram of the three-dimensional modeling process and ball cluster model of the recycled aggregate of the present application;

[0020] Figure 2 The figure is a schematic diagram of the three-dimensional modeling process and ball cluster model of the recycled aggregate of the present application;

[0021] (a) is a model diagram of 0.60~1.18mm particle size;

[0022] (b) is a model diagram of 1.18~2.36mm particle size;

[0023] (c) is a model diagram of 2.36~4.75mm particle size;

[0024] (d) is a model diagram of 4.75~10.00mm particle size;

[0025] (e) is a model diagram of 10.00~20.00mm particle size;

[0026] Figure 3 The figure is a model domain and sample size of the present application;

[0027] Figure 4 The figure is a process of randomly feeding aggregates of the present application;

[0028] (a) is a particle size of 10.00~20.00mm;

[0029] (b) is 4.75~20.00mm particle size;

[0030] (c) is 2.36~20.00mm particle size;

[0031] (d) is 1.18~20.00mm particle size;

[0032] (e) is 0.60~20.00mm particle size;

[0033] Figure 5 The contact detection two-dimensional schematic diagram of the granule of the present application:

[0034] (a) is the schematic diagram of spherical granule, (b) is the schematic diagram of spherical cluster granule;

[0035] Figure 6 The aggregate overlap elimination process of the present application;

[0036] (a) is the schematic diagram of the position state before the aggregate overlap elimination;

[0037] (b) is the schematic diagram of the position state after the aggregate overlap elimination;

[0038] Figure 7 The aggregate expansion process flow chart of the present application;

[0039] Figure 8 The comparison of the real morphology regenerated aggregate before and after the accumulation expansion of the present application;

[0040] Figure 9 The random placement result of the granule with different aspect ratios of the present application;

[0041] Figure 10 The polyhedral structure unit with different convexities of the present application;

[0042] Figure 11 The random placement result of the granule with different convexities of the present application;

[0043] Figure 12 The cumulative sieve residue curve of the granule with different aspect ratios of the present application;

[0044] Figure 13 The cumulative sieve residue curve of the granule with different convexities of the present application;

[0045] Figure 14 The cumulative sieve residue curve of the granule with different gradation models of the present application;

[0046] Figure 15 The distribution diagram of the predicted value and the residual value of the present application;

[0047] (a) is the real value and the predicted value when the aspect ratio is 1.0;

[0048] (b) the real value and the predicted value for the aspect ratio of 1.5;

[0049] (c) the real value and the predicted value for the aspect ratio of 2.0;

[0050] (d) the real value and the predicted value for the aspect ratio of 2.5;

[0051] (e) the real value and the predicted value for the convexity of 0.815;

[0052] (f) the real value and the predicted value for the convexity of 0.874;

[0053] (g) the real value and the predicted value for the convexity of 0.959;

[0054] (h) the real value and the predicted value for the real topography. DETAILED DESCRIPTION

[0055] As shown in Figures 1-15 , the application first constructs a three-dimensional particle model of recycled aggregate, and establishes STL format files of 255 recycled fine aggregates and 100 recycled coarse aggregates containing real topography through computer tomography and three-dimensional reconstruction. The STL files are imported into the discrete element software, and finally the application establishes a mathematical model of recycled fine and coarse aggregate particles through the Bubble-Pack algorithm, restores the real geometric shape information of the aggregate, and the modeling process is as shown in Figure 1 .

[0056] The Bubble-Pack algorithm is to approximate the shape of irregular aggregate by a sphere. The more the number of spheres, the more accurately the target particle shape can be fitted by the sphere cluster particles, and it has flexibility and adaptability for complex shaped aggregate. The approximation effect of sphere combination on irregular aggregate is optimized by adjusting four key parameters:

[0057] (1) Overlap: control the degree of overlap of adjacent spheres, the larger the value, the smoother the particle surface. When the overlap is 0, two spheres only contact at a certain point and do not overlap. When the overlap is 180, one sphere is contained in the other sphere, and the spheres are completely overlapped.

[0058] (2) Particle size ratio: determines the size ratio of the smallest and largest filling spheres, and affects the uniformity of small sphere filling in the particle.

[0059] (3) Radius coefficient: adjusts the fit degree of small sphere attached surface.

[0060] (4) Optimization coefficient: control the number of grid surfaces to improve the filling density.

[0061] By adjusting these parameters in coordination, the generated sphere combination can more realistically simulate the geometric morphological characteristics of the aggregate. The present application selects ratio (particle size ratio) = 0.3, distance (overlap amount) = 160, radfactor (radius factor) = 2.0, and refinenum (optimization factor) = 1 to represent the shape of the recycled coarse and fine aggregate. Based on the Bubble-Pack algorithm, the recycled coarse and fine aggregate model of different particle segments is established as shown in Figure 2 .

[0062] Then the recycled aggregate accumulation model is constructed. In the model initialization stage of PFC3D software, the spatial size (domain) and sample size (wall) of the calculation model are determined. The sample size of the concrete is usually 100mmx100mmx100mm. In order to ensure the accuracy of the calculation, the present application selects the aggregate placement space as a cube of 100mmx100mmx100mm, and the spatial size is 300mmx300mmx300mm. As shown in Figure 3 The model boundary should be set within the spatial size. The area outside the model does not participate in any force and displacement calculation, and the generation of particles and wall boundary is not allowed.

[0063] The aggregate random generation algorithm is written by fish language. The random placement step is as shown in Figure 4 . The particle template is selected in the particle library and the position is randomly set during the placement process, and it is ensured that there is no overlap between the particles. The program will generate particles in turn. If a new particle cannot be generated at a certain position, the program will select the remaining aggregate in the particle library to continue to try to generate, until the particles in the space position cannot be placed. First, the placement of the largest particle (10.00~20.00mm) is performed. Whether the particles overlap is detected to determine whether the placement is successful. If there is no overlap, the coordinate information of the particle is recorded and marked as successful placement. Otherwise, the current placement attempt is terminated and the placement is continued. Then it is judged whether the container is full. If there is still space for the current aggregate placement in the container, the current particle size segment is continued to be placed. If it is full, the placement process of the next smaller particle size segment is entered. The above steps are executed in a loop until all particle size particles are placed. Finally, the particle random placement accumulation model is output as shown in Figure 4 .

[0064] Contact detection is needed in each step of the initial packing and the subsequent dynamic expansion process to prevent the interference between particles. Compared with the whole packing system, each aggregate only contacts with the surrounding aggregates, i.e. there is no overlap between a certain aggregate and the majority of particles in the packing system. Therefore, the screening algorithm is used to exclude these large number of non-contact aggregates. In the discrete element method, the bounding box algorithm is an effective and fast method to initially exclude non-contact aggregates. For irregular aggregates, the axis-aligned bounding box is generally used, which is widely used in the contact detection of discrete element particles. The axis-aligned bounding box is a hexahedral box that encloses the particle and corresponds to the global coordinate system, which can compactly enclose the whole 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 projection length of the particles in the X, Y, Z axes. If the projections of the bounding boxes do not overlap in a certain direction coordinate axis, it is determined that the two bounding boxes do not overlap, i.e. there is no overlap between the two aggregates (such as Figure 5 The projections of the bounding boxes of particle A and particle B in x-axis in (a) do not overlap). If there is overlap between the two bounding boxes in the projection direction (such as Figure 5 There is overlap between particle A and particles C and D in (a)), the following accurate detection between aggregates is needed:

[0065] In three-dimensional space, for regular spheres or ellipsoids, the generalized eigenvalue can be used to judge whether they are coincident. However, for irregularly shaped aggregates, the contact judgment between particles is relatively complex. The present application is based on the contact between the ball cluster particles in the discrete element method to judge the contact between the irregularly shaped aggregate particles. In the ball cluster particles, the contact between the filling balls is checked to judge whether the overlap occurs between the irregular aggregates (such as Figure 5 (b) shown), which can significantly reduce the complexity of contact detection of irregular aggregates. In order to improve the calculation efficiency, the contact detection between the filling balls in a single aggregate is not considered, which is regarded as an ideal rigid body. Two irregular aggregates are in contact only when the condition is met, at which time the initial packing process is judged to be unsuccessful.d ij The distance between the centers of two spherical particles when the contact point between the filling balls in the aggregate is indicated; R i and R j respectively represent the radius of the filling ball. The overlap between the two spherical particles at the contact point of the irregular aggregates is judged, and the contact embedding depth δ between the aggregates is: .

[0066] The actual distance between two particle surfaces is the surface gap, and the actual distance between 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, the particles are in contact and relative motion occurs. However, when the nominal surface coincides with the workpiece surface, it indicates that the object is in full contact, and Newton's second law cannot be applied to particles that are not in contact. When the aggregate expands, the increase in volume can cause an increase in contact between particles, and even overlap. According to Newton's second law, the contact force changes 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 overlap between particles, such as in the linear spring model represents the overlap, the contact force is related to the overlap, and a larger contact force means a larger overlap, and the process of reducing overlap through displacement adjustment is essentially a contact force-driven kinetic equilibrium. In PFC3D, a linear contact stiffness model is widely used in the simulation of sand and gravel aggregates. This model assumes that there is no slip or bonding between particles, and only a small contact pressure occurs when a collision occurs. This simplified assumption is more consistent with the actual behavior of sand and gravel aggregates during the stacking process, and compared to other complex models, this model has a smaller computational load and higher computational efficiency. Therefore, this model is used as the mesoscopic contact model for aggregate placement to eliminate the small overlap between particles caused by expansion (see Figure 6 ).

[0067] Because the randomly placed particles need to meet the non-overlapping condition, large gaps will form between the aggregates, leading to an increase in void ratio and making it difficult to achieve a dense state. Therefore, the present invention reduces the void ratio by first reducing the size of the aggregate for placement, and then restoring it to its actual size after the aggregate placement is complete. In the process of dynamic volume change of the aggregate system, it is necessary to quantitatively evaluate the influence of key parameters on the densification effect. The present invention studies the influence of parameters such as volume reduction ratio, expansion times, and iteration times on the control of particle overlap.

[0068] Figure 7 The figure shows the placement of the aggregate shrinkage and expansion process. Figure 7 From left to right are the initial distribution state diagram of the aggregate in the cubic container under the non-overlapping condition; the expansion stage diagram (the expansion coefficient is set to 5.0 to enhance the visualization effect); the diagram showing that the overlap phenomenon caused by the expansion step can be eliminated through step-by-step expansion; and the diagram showing that due to the excessive number of aggregates in the container, the aggregates cannot completely fill the inside of the container after expansion, resulting in the "overflow" phenomenon of some aggregates. In this process, the aggregates reach an equilibrium state through position adjustment and collision with other aggregates. Finally, 2 aggregates expanded to the actual size are successfully placed in the container in the equilibrium state.

[0069] ​In the process of particle expansion, if the particles are directly expanded to the target size at one time, it will cause a large overlap between the particles, not only increasing the complexity of the calculation, but also significantly reducing the calculation efficiency, and causing numerical instability of the system. In order to avoid this problem, a step-by-step expansion method is adopted, which adjusts the size of the particles in stages, and gradually eliminates the overlap of the initially generated particles. Compared with one-time expansion, step-by-step expansion can gradually increase the volume of the particles in small steps, so that the contact force between the particles can be rebalanced at each stage. This method helps to avoid excessive contact force between particles, reduce the violent shock caused by excessive contact force, and effectively avoid the instability or numerical divergence of the system. During the calculation process, the particle motion is advanced by explicit dynamics within the execution period, and the overlap is gradually eliminated. At the same time, the speed and contact force of the particles are adjusted in time to speed up the system to reach equilibrium. In this mode, the system gradually reduces the particle speed to prevent instability caused by excessive speed. In addition, the speed is cleared once every cycle to prevent particles from moving continuously due to inertia, thereby avoiding the calculation divergence problem caused by initial overlap and the overflow of particles from the wall due to excessive speed. When the stiffness of the system changes (such as the change of particle contact state), the step size is automatically adjusted to balance between calculation accuracy and efficiency, ensuring the stability and convergence of the calculation process. The volume reduction ratio, expansion times, and iteration times, as well as the cycle period of adjusting the particle speed and contact force are shown in Table 1, and the minimum porosity of the system is finally obtained. The meaning of the balance calculation period is to clear and recalculate every 1000 steps.

[0070] Table 1: Parameter settings related to the shrinkage expansion method

[0071]

[0072] Figure 8 The change process of the recycled aggregate before and after the expansion treatment is shown. Figure 8 (a) is the original aggregate state, and the structure presents obvious void distribution characteristics, and there is significant void between the particles. Figure 8 (b) is the state after expansion, when the volume of the aggregate is expanded to the actual size, the contact between the particles increases, and the arrangement characteristics are dense. The porosity of the aggregate before expansion is 36%, and the porosity of the aggregate after expansion is reduced to 21%. By expanding the volume of the particles, the position of the aggregate is dynamically adjusted, thereby effectively reducing the porosity. Compared with the porosity obtained by the existing grading optimization model (as shown in Table 2), the results show that the shrinkage expansion method adopted by the present application can realize the close packing of recycled coarse and fine aggregates.

[0073] Table 2: Comparison of porosities in different documents

[0074]

[0075] Considering the influence of three-dimensional particle morphology characteristic parameters of recycled aggregate on its close packing, the shape quantification index-aspect ratio and the angularity quantification index-convexity are two key parameters that can independently represent the particle morphology. Among them, the aspect ratio is defined as the ratio of the maximum Feret diameter to the minimum Feret diameter, which can effectively reflect the extension characteristics of the particle; the convexity describes the degree of concave of the particle through the ratio of the actual volume of the particle to the volume of the convex hull.

[0076] Figure 9 The random throwing results of aggregate particles with aspect ratios of 1.0, 2.0 and 2.5 are shown. The number of aggregate particles of each size range is shown in Table 3.

[0077] Table 3 Number of particles of each size range with different aspect ratios

[0078]

[0079] (1) Figure 9 (a) is the throwing result of ellipsoidal aggregate in the size range of 10.00-20.00 mm filled step by step according to the size of the particle grade. Only three different aspect ratio ellipsoidal aggregates of 10.00-20.00 mm particle size are thrown. When the aspect ratio is 1.0, the throwing volume in the space range can reach 31.1%, and when the aspect ratio is 2.5, the throwing volume reaches the maximum, i.e. 32.4%;

[0080] (2) Figure 9 (b) shows the throwing test results of ellipsoidal aggregate in the size range of 4.75-20.00 mm filled step by step according to the size of the particle grade. By comparing and analyzing the throwing results of different aspect ratio ellipsoidal aggregates, it is found that as the aspect ratio value of the ellipsoidal aggregate increases, the actual throwing volume ratio in the system shows a significant downward trend. The volume ratio decreases from the initial 50.7% to 45.5%; when the aspect ratio reaches 2.5, the throwing volume ratio further decreases to 43.4%, among which the spherical aggregate with aspect ratio 1.0 has the maximum throwing volume ratio, reaching 50.7%;

[0081] (3) Figure 9 (c) is the throwing result of ellipsoidal aggregate in the size range of 2.36-20.00 mm filled step by step according to the size of the particle grade. The throwing volume decreases from 68.4% to 64.7%, and when the aspect ratio is 2.5, the throwing volume decreases to 60.1%, among which the spherical aggregate with aspect ratio 1.0 has the maximum throwing volume of 68.4%;

[0082] (4) Figure 9(d) for 1.18~20.00mm particle size range of ellipsoidal aggregate by particle size step by step filling of the results of the delivery, delivery volume 73.9% gradually reduced to 72.1%, when the aspect ratio is 2.5, the delivery volume is reduced to 70.5%, wherein the aspect ratio of 1.0 spherical aggregate delivery volume is the largest 73.9%;

[0083] (5) Figure 9 (e) for 0.6~20.00mm particle size range of ellipsoidal aggregate by particle size step by step filling of the results of the delivery, from the three aggregate final true delivery volume ratio can be seen, with the continuous expansion of the aggregate particle size range, the subsequent small particle size aggregate delivery quantity will gradually decrease, when the aspect ratio is 1.0, 0.60~1.18mm particle size range of aggregate is only about 8.5% delivery, when the aspect ratio is 2.0, 0.60~1.18mm particle size range of aggregate is only about 6.8% delivery, when the aspect ratio is 2.5, 0.60~1.18mm particle size range of aggregate is only about 6.1% delivery.

[0084] The regular dodecahedron has clear and regular edge and face structure, and the unique edge and corner of the structure makes it show high symmetry in geometric shape. Therefore, the same degree of recess processing is performed on different symmetry faces of the regular dodecahedron to represent the change of convexity. The shortest axis is the distance between the vertices of two opposite recessed faces, and the longest axis is the distance from one vertex to the symmetric vertex of the regular dodecahedron. The aspect ratio is the ratio of the longest axis to the shortest axis. The convexity is defined as the ratio of the volume of the recessed polyhedron to the volume of the regular dodecahedron. The convexity changes to different degrees while keeping the aspect ratio unchanged. Figure 10 The polyhedral structure units with different convexities are shown.

[0085] Figure 11 The random delivery results of the particles with convexities of 0.815, 0.876 and 0.959 are shown. Table 4 shows the random delivery numbers of the aggregates with different convexities.

[0086] Table 4: The number of particles in each particle segment with different convexities

[0087]

[0088] (1) Figure 11 (a) for 10.00~20.00mm particle size range of aggregate by particle size step by step filling of the delivery results, by comparing the delivery results of three different convexity aggregates, it can be seen that: only 10.00~20.00mm particle size of three different convexity aggregates are delivered, with the decrease of convexity, the bulk density of coarse aggregate increases, the volume of particles with convexity of 0.959 delivered successfully in a fixed volume of space can reach 38.3% of the delivery volume;

[0089] (2) Figure 11 (b) is the result of the feeding of the aggregate in the size range of 4.75-20.00 mm filled by size. By comparing the feeding data of different convexity aggregates, it is found that with the increase of the convexity value of the aggregate, the actual volume ratio in the system presents a significant upward trend. The volume ratio gradually increases from the initial 51.2% to 58.5%. Among the test samples, the spherical aggregate with a convexity of 0.959 shows the best stacking effect, and the feeding volume ratio reaches a peak of 58.5%.

[0090] (3) Figure 11 (c) is the result of the feeding of the aggregate in the size range of 2.36-20.00 mm filled by size, which gradually increases from 60.7% to 67.5%, and the feeding volume increases to 67.5% when the convexity is 0.959;

[0091] (4) Figure 11 (d) is the result of the feeding of the aggregate in the size range of 1.18-20.00 mm filled by size, and the feeding volume gradually increases from 71.5% to 73.8%, among which the spherical aggregate with a convexity of 0.959 has the largest feeding volume of 73.8%;

[0092] (5) From Figure 11 (e) shows the result of the feeding of the aggregate in the size range of 0.6-20.00 mm filled by size. It can be found that the larger the convexity, the lower the void ratio finally achieved, which can reach 20.6%.

[0093] From the actual feeding volume ratio of the three aggregates, it can be seen that with the continuous expansion of the aggregate size range, the subsequent feeding quantity of small size aggregate gradually decreases. When the convexity is 0.959, due to its high symmetry and regular geometric shape, a higher packing density can be achieved. In the process of close packing, the contact points between particles are uniformly distributed, and the void ratio is low. Therefore, when reaching the state of close packing, the amount of coarse aggregate to be fed is relatively small. The concave surface increases the irregularity of the particle surface, forming a local concave-convex structure. This geometric feature will interfere with the directional arrangement of particles, reducing the packing density. In order to achieve the state of close packing, more coarse aggregate needs to be fed to fill the remaining voids caused by irregular contact. The concave surface significantly enhances the irregularity of the particles, resulting in complex interlocking structure and local arching phenomenon between particles. Its packing density is the lowest, and the most fine aggregate needs to be fed to achieve the state of close packing. Therefore, with the increase of convexity, the proportion of fine aggregate increases.

[0094] Based on the above closest packing results, the cumulative sieve residue curve of recycled aggregate under the influence of various parameters is established, and the cumulative sieve residue curves of different aspect ratios are as follows Figure 12As 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.

[0095] 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.

[0096] 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.

[0097] 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.

[0098] 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: , where CPFT (%) represents the cumulative percentage of particles having a size less than d; d (unit: mm) represents the size of the sieve or the particle size; (unit: mm) represents the maximum particle size of the aggregate in the packing system; (unit: mm) represents the minimum particle size of the aggregate in the packing system; n represents the distribution modulus.

[0099] Yuzhou Liang considered the morphology characteristics of recycled sand particles based on the MAA model, introduced the aspect ratio characteristic factor to modify the n value in the model, and proposed the modified MAA model: , where CPFT (%) represents the cumulative percentage of particles having a size less than d; d (unit: mm) represents the size of the sieve or the particle size; (unit: mm) represents the maximum particle size of the aggregate in the packing system; (unit: mm) represents the minimum particle size of the aggregate in the packing system; n represents the distribution modulus. represents the ratio of the longest axis to the shortest axis of the aggregate in the packing system, with a value greater than or equal to 1.

[0100] From the above research, it can be known that the aspect ratio and convexity have a significant impact on close packing. By comparing the cumulative sieve residue curves obtained by different grading design methods, it can be seen that Figure 14 The grading distribution obtained based on the volume shrinkage method shows a significant correlation with the Talbol theoretical curve . In the formula: CPFT represents the cumulative percentage of particles having a size less than d; d represents the size of the sieve or the particle size (mm); d max represents the maximum particle size of the aggregate (mm); n represents the distribution modulus, usually with a value range of 0.3-0.7.

[0101] The cumulative sieve residue deviation of the two aggregates is relatively small compared to other models. This shows that the traditional Talbol model can better represent the skeleton formation of coarse aggregate and the filling of fine aggregate voids, but the theoretical assumptions do not consider the influence of particle morphology on particle grading.

[0102] Therefore, the aspect ratio and convexity are introduced as morphology factors to modify the Talbol model. According to the least squares polynomial fitting principle, the morphology parameter grading optimization calculation formula is set as follows:

[0103] .

[0104] In the formula, represents the maximum particle size of the aggregate in the packing system, AR represents the aspect ratio of the particle, represents the convexity of the particle, , , and These are different constants.

[0105] 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:

[0106]

[0107] 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... .

[0108] 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:

[0109] (Where: N is the number of samples, and P is the number of features.)

[0110] 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: .

[0111] 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.

[0112] The application fully considers the three-dimensional appearance characteristics of the recycled aggregate, such as irregular shape, sharp corners and protrusions, and realizes efficient collaborative accumulation of coarse and fine aggregates by combining the volume expansion and contraction principle, the accumulation density is increased by 8%-12% compared with the traditional method, and the accumulation structure is significantly improved; through discrete element method simulation and parameter optimization, the optimal feeding ratio and sequence of different particle size aggregates are accurately determined, the advantages of each particle size are fully utilized, and the filling effect in concrete is improved; the quality of recycled aggregate is improved, the application of recycled aggregate in construction engineering is expanded, the dependence on natural aggregate is reduced, the large-scale resource utilization of construction waste is promoted, and the problems of resource shortage and environmental pollution are alleviated; the method is not only suitable for recycled aggregate, but also can be applied to other types of aggregate accumulation optimization after adjustment, and can be combined with advanced material preparation technology to further expand the application range and effect.

[0113] Finally, it should be pointed out that the above preferred embodiments are only used to illustrate the technical solutions of the present application and are not limiting, although the present application has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present application.

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 spheres 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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