An evaluation method for effective load transmission capacity of aggregate skeleton based on three-dimensional weighted directed force chain network characteristics

Abstract

The application discloses a kind of based on three-dimensional weighted directed force chain network characteristics of aggregate skeleton effective load capacity evaluation method, specifically is: S1: according to the gradation information of mineral aggregate, assemble mineral mixture three-dimensional digital test piece;For each aggregate in mineral mixture three-dimensional digital test piece Set unique ID;S2: set virtual penetration pressure head on mineral mixture three-dimensional digital test piece, carries out numerical simulation experiment to mineral mixture three-dimensional digital test piece;S3: set force chain chain rule;S4: extract three-dimensional force chain;S5: construct weighted directed force chain network and adjacency matrix;S6: according to adjacency matrix and weighted directed force chain network calculation topological parameter, the effective load capacity of quantitative characterization and evaluation different structure types mineral mixture skeleton structure of weighted directed force chain network structure is carried out.

Description

Technical Field

[0001] This invention belongs to the field of road engineering technology, and in particular relates to a method for evaluating the effective load transfer capacity of mineral skeletons based on the characteristics of three-dimensional weighted directional force chain network. Background Technology

[0002] The skeleton formed by mineral aggregates is the main structure of asphalt mixtures that bears and transmits external loads. Therefore, accurately evaluating the load-transfer capacity of the skeleton structure is crucial for optimizing the skeleton structure and improving the load-bearing capacity of asphalt mixtures from a mechanical perspective. Asphalt mixtures can be considered granular materials, whether analyzed by volume or mass percentage. Force chains are the paths through which granular systems transmit external loads; therefore, researchers have begun to evaluate the load-transfer capacity of the skeleton from the perspective of quantifying force chain characteristics. However, existing methods do not accurately consider the interrelationships between force chains from a network perspective. Especially in three-dimensional granular systems, existing two-dimensional analysis methods cannot accurately reconstruct the spatial distribution characteristics, load-bearing weight, and load transmission direction of force chains, as well as their true structure and dynamic evolution in three-dimensional space. This makes it difficult to accurately evaluate the effective load-transfer capacity of the skeleton structure. Summary of the Invention

[0003] Purpose of the invention: In order to solve the problems existing in the prior art, the present invention provides a method for evaluating the effective load transfer capacity of mineral skeleton based on the characteristics of three-dimensional weighted directional force chain network.

[0004] Technical solution: This invention discloses a method for evaluating the effective load transfer capacity of a mineral skeleton based on the characteristics of a three-dimensional weighted directional force chain network, specifically including the following steps:

[0005] Step S1: Assemble a three-dimensional digital specimen of the mineral mixture according to the gradation information of the mineral aggregate; assign a unique ID to each aggregate in the three-dimensional digital specimen of the mineral mixture;

[0006] Step S2: Set up a virtual penetration head on the three-dimensional digital specimen of the mineral mixture and conduct a numerical simulation experiment on the three-dimensional digital specimen of the mineral mixture;

[0007] Step S3: Set the force chain formation criteria;

[0008] Step S4: Extract the three-dimensional force chain from the three-dimensional digital specimen of the mineral mixture after the experiment, according to the force chain criterion.

[0009] Step S5: Construct a weighted directed force chain network and an adjacency matrix based on the extracted force chains;

[0010] Step S6: Calculate the topological parameters based on the adjacency matrix and the weighted directed force chain network, quantitatively characterize the weighted directed force chain network structure, and evaluate the effective load transfer capacity of different structural types of mineral mixture skeleton structures.

[0011] Furthermore, the force chain criterion also includes the following conditions:

[0012] Rule 1: The normal contact force of the aggregate in the three-dimensional digital specimen of the mineral mixture after the experiment must be greater than the normal contact force threshold.

[0013] Rule 2: In the same force chain, the current aggregate and the next level aggregate are in contact with each other, and the height of the next level aggregate is less than or equal to the height of the current aggregate.

[0014] Rule 3: The included angle α between the normal contact points of two adjacent aggregates is less than or equal to θ, where θ is the angle threshold.

[0015] Rule 4: The number of aggregate particles in a force chain must be greater than or equal to N, where N is a positive integer;

[0016] Rule 5: Select the next level aggregate based on the included angle α between adjacent normal contacts. Specifically: If there are multiple next level aggregates with the current aggregate whose included angle α between their normal contacts satisfies Rule 3, then select the aggregate with the smallest included angle α. If there are cases where α is equal, then select the aggregate with the largest normal contact force.

[0017] Furthermore, the expression for the included angle α between normal contacts is as follows:

[0018]

[0019] Where A, B, and C are all aggregates, and B is the next level of aggregate after A, and C is the next level of aggregate after B; Let be the direction vector pointing from the centroid of aggregate A to the centroid of aggregate B. Let be the direction vector from the centroid of aggregate B to the centroid of aggregate C.

[0020] Furthermore, the normal contact force threshold is the average of all normal contact forces.

[0021] Furthermore, step S4 specifically includes:

[0022] Step 4.1: Based on the normal contact force threshold, retain the aggregates that meet criterion 1, and sort the aggregates in descending order of height;

[0023] Step 4.2: Identify the initial aggregate starting from the highest point; mark the initial aggregate as visited aggregate; denote the initial aggregate as A;

[0024] Step 4.3: Determine if there exists a next-level aggregate that satisfies criterion 2 with aggregate A. If it exists, proceed to step 4.4; otherwise, proceed to step 4.2.

[0025] Step 4.4: Determine whether all the next-level aggregates of aggregate A have been traversed. If so, go to step 4.2; otherwise, select an aggregate from the untraversed aggregates as the current aggregate, denoted as aggregate B.

[0026] Step 4.5: Based on criteria 2, 3, and 5, find the next-level aggregate of aggregate B. If found, record the next-level aggregate of aggregate B as aggregate C, and mark aggregate B and aggregate C as visited aggregates, then proceed to step 4.6; if not found, determine whether the current number of force chains satisfies criterion 4. If yes, store the current force chain in the force chain set, and then determine whether there are still aggregates that satisfy the force chain formation criteria. If there are, proceed to step 4.4; if not, the force chain search is complete; if the current number of force chains does not satisfy criterion 4, determine whether there are still aggregates that satisfy the force chain formation criteria. If there are, proceed to step 4.4; if not, the force chain search is complete.

[0027] Step 4.6: Take aggregate C as the new current aggregate, update the direction vector, and then go to step 4.5.

[0028] Furthermore, the construction of the weighted directed force chain network in step S5 specifically involves: removing invalid force chains, then using the aggregate particles in the remaining force chains as network nodes, and considering two adjacent aggregates in the same force chain as interconnected; projecting the normal contact force corresponding to the two interconnected network nodes onto the line connecting the centroids of the two corresponding aggregates to obtain two scalars, and using the sum of these two scalars as the weight of the connecting edge; the direction of the connecting edge is from top to bottom; for each force chain, sequentially traversing its adjacent aggregate pairs, which are considered as an edge in the network.

[0029] Furthermore, the invalid force chains include force chains with a length less than a preset threshold, repetitive force chains, and force chains with abnormal aggregate IDs.

[0030] Furthermore, the construction of the adjacency matrix in step S5 specifically involves:

[0031] Step 5.1: Read the total number N of network nodes in the weighted directed force chain network; each network node corresponds to a unique aggregate ID.

[0032] Step 5.2: Map all network nodes to consecutive integer indices from 1 to N, and construct a bidirectional mapping table, including a forward mapping from the original ID to the index and a reverse mapping from the index to the original ID;

[0033] Step 5.3: Using a sparse matrix format, initialize an N×N Boolean adjacency matrix to record the connection relationships between nodes in the network, with all initial values ​​set to 0;

[0034] Step 5.4: Map the network nodes to the corresponding elements in the adjacency matrix; assign the weights and directions of the network nodes to the corresponding elements in the adjacency matrix;

[0035] Step 5.5: Normalize the adjacency matrix.

[0036] Furthermore, the topology parameters in step S6 include: node out-degree, kernel degree, and average path length;

[0037] Node out-degree The expression is as follows:

[0038]

[0039] Among them, w ij Let w be the value of the element in the i-th row and j-th column of the adjacency matrix. ij If δ(w) > 0, then δ(w) ij ) = 1, otherwise δ(w) ij = 0; N is the total number of nodes in the weighted directed force chain network;

[0040] The expression for the average path length L is as follows:

[0041]

[0042] Where, d ij It is the sum of the weights of all nodes in the shortest path from node i to node j in a weighted directed force chain network.

[0043] Beneficial Effects: This invention can extract the weighted directed force chain network from the mineral skeleton, accurately quantifying the load-bearing strength and load transfer direction of the force chains. Simultaneously, based on the extracted weighted directed network, various network topology parameters can be extracted for quantitative evaluation of the effective load transfer capacity of the mineral skeleton structure. This overcomes the limitations of existing two-dimensional methods, which cannot accurately characterize the true distribution of force chains in three-dimensional space, the load-bearing weight of the force chains, and neglect the directionality of load transfer, thus hindering a comprehensive and accurate evaluation of the true effective load transfer capacity and dynamic evolution of the skeleton structure. Attached Figure Description

[0044] Figure 1 Grading curves for AC-10, SMA-10, and OGFC-10;

[0045] Figure 2 Figure 1 shows the digital specimen diagrams of mineral mixtures; Figure 2 shows the digital specimen diagram of AC-10 grade mineral mixture, Figure 3 shows the digital specimen diagram of SMA-10 grade mineral mixture, and Figure 4 shows the digital specimen diagram of OGFC-10 grade mineral mixture.

[0046] Figure 3This is a schematic diagram of the included angle between the normal contact points of the force chain;

[0047] Figure 4 Figure (a) shows the particle size distribution of the force chain network in the mineral mixture; Figure (b) shows the particle size distribution of the force chain network in the AC-10 grade mineral mixture, Figure (c) shows the particle size distribution of the force chain network in the SMA-10 grade mineral mixture, and Figure (c) shows the particle size distribution of the force chain network in the OGFC-10 grade mineral mixture.

[0048] Figure 5 This is a flowchart of the construction process for the force chain network and adjacency matrix. Detailed Implementation

[0049] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0050] This embodiment uses AC-10, SMA-10, and OGFC-10 grade mixtures as examples. The curves of these three mixtures are shown below. Figure 1 As shown.

[0051] This invention provides a method for evaluating the effective load transfer capacity of a mineral skeleton based on the characteristics of a three-dimensional weighted directional force chain network, specifically including the following steps:

[0052] Step S1: Based on the gradation information of the mineral aggregate, assemble a three-dimensional digital specimen of the mineral mixture. The specimen drawing is shown below. Figure 3 As shown;

[0053] Step S2: Set up a virtual penetration head on the digital specimen of the mineral mixture, and conduct a numerical simulation experiment on the digital specimen to obtain aggregate information and contact information;

[0054] Step S3: Based on the aggregate information and the contact information between aggregates, set the force chain formation criteria;

[0055] Step S4: Based on the force chain criterion, extract the three-dimensional force chain to obtain the force chain information and the corresponding aggregate information, and set the composition criteria for the weighted oriented force chain network;

[0056] Step S5: Based on the force chain information and the composition criteria of the weighted directed force chain network, construct the weighted directed force chain network and the corresponding adjacency matrix;

[0057] Step S6: Calculate the topological parameters based on the adjacency matrix, quantitatively characterize the weighted directional force chain network structure, and evaluate the effective load transfer capacity of mineral mixture skeleton structures of different structural types.

[0058] The aggregate information in step S2 includes: aggregate coordinates, aggregate number, and aggregate group number; the contact information is the contact information between aggregates, which includes: normal contact force, coordinates of two mutually contacting aggregates, ID, and coordinates of the midpoint of the line connecting the two aggregates.

[0059] The force chain criterion in step S3 includes the following conditions:

[0060] Rule 1: The normal contact force between aggregates must be greater than the normal contact force threshold.

[0061] Rule 2: The next level of aggregate is the aggregate that is in contact with the current aggregate in this force chain and whose height is less than or equal to the height of the current aggregate;

[0062] Rule 3: The included angle α between two adjacent normal contacts forming a force chain of mineral mixtures is less than or equal to θ, where θ is the angle value;

[0063] Rule 4: The number of aggregate particles constituting the force chain must be greater than or equal to N, where N is a positive integer;

[0064] Rule 5: Select the next-level aggregate based on the included angle α between adjacent normal contacts. Specifically: if multiple next-level aggregates have included angle α between their normal contacts and the current aggregate that satisfies Rule 3, then select the aggregate with the smaller included angle α. If multiple next-level aggregates have included angle α between their normal contacts and the current aggregate that are equal, then select the aggregate with the larger normal contact force as the next-level aggregate.

[0065] The included angle α between adjacent normal contacts is as follows: Figure 3 As shown, its expression is as follows:

[0066]

[0067] In the formula: Let be the direction vector from the centroid of aggregate A to the centroid of aggregate B. Let be the direction vector from the centroid of aggregate B to the centroid of aggregate C. B is the next-level aggregate after A, and C is the next-level aggregate after B.

[0068] The force chain extraction process in step S4 is as follows:

[0069] Step ①: Obtain the normal contact force in all contacts. The preset contact force threshold is the average normal contact force of all contacts. Based on the normal contact force threshold, retain the contact information and aggregate information that meet criterion 1.

[0070] Step 2: Based on the Z coordinate of the aggregate, prioritize identification starting from the aggregate at higher elevations. Select the starting aggregate A and mark aggregate A as visited to prevent looping. If there are no unvisited particles, the force chain extraction is complete.

[0071] Step 3: Obtain the adjacent aggregates with Z coordinates lower than the current aggregate A through contact information. If there are no adjacent aggregates, return to step 2. Otherwise, select adjacent aggregate B as the candidate aggregate, calculate the current direction vector, and remove aggregate B from the set of adjacent aggregates.

[0072] Step 4: Set a preset normal angle threshold θ. Based on the contact information, obtain the adjacent aggregates of the current aggregate B, calculate the direction vectors of the current aggregate B and the adjacent aggregate C, and calculate the angle between them and the direction vectors of the previous step (the direction vectors of aggregate A and aggregate B). According to the preset angle threshold, if the angle threshold is met, proceed to step 5. If it is not met or there are no adjacent particles C, determine whether the number of aggregates in the current force chain meets criterion 4. If it is met, store the force chain in the force chain set and return to step 3. Otherwise, return directly to step 3. Among the aggregates C that meet the angle θ, prioritize the node with the smallest angle α. If there are multiple aggregates with the same angle, select the aggregate with the largest contact force as the extension direction (that is, meet criterion 5).

[0073] Step 5: Select the adjacent aggregate C as the new current aggregate B, update the direction vector and repeat step 4, continue to extend the force chain until the force chain retrieval is completed, record the complete force chain to the force chain set and return to step 3.

[0074] The criteria for constructing the weighted directed force chain network in step S4 include:

[0075] Requirement 1: The aggregate particles in the force chain are used as network nodes;

[0076] Requirement 2: The connection relationship between nodes is determined by the existence of force chains between aggregates. If a force chain exists between particles, the two nodes are considered connected; otherwise, they are considered disconnected (that is, the network nodes corresponding to two adjacent aggregates within the same force chain are considered connected).

[0077] The weighting and orientation of the weighted directional force chain network in step S4 of requirement 3 are defined as the scalar sum of the forces (normal contact forces) between two aggregates that are greater than the average contact force, projected onto the line connecting the centroids of the two aggregates, and the direction from the upper aggregate to the lower aggregate, with the vertical load direction (downward along the Z-axis) being the dominant direction.

[0078] like Figure 5 As shown, the implementation method of the weighted directed force chain network and adjacency matrix in step S5 includes:

[0079] A1: Based on the force chains identified in steps ①-⑤, extract the aggregate information of the weighted directed force chain network and read the chain data in the aggregate information; read the original force chain data, remove invalid chains of length 1, duplicate chains, and data containing abnormal IDs, and count the total number N of all unique aggregate IDs after reading, as the number of nodes in the network; the digital specimen diagram of the weighted directed force chain network is shown below. Figure 4 As shown.

[0080] A2: Re-number the unique aggregate IDs after cleaning, mapping them to consecutive integer indices from 1 to N, and construct a bidirectional mapping table, including a forward mapping from the original ID to the index and a reverse mapping from the index to the original ID. Sort by original ID in ascending order to ensure consistency in data processing and result reproduction. Used for rapid location and reconstruction of aggregate positions in subsequent matrix construction;

[0081] A3: Uses a sparse matrix format, initializes an N×N Boolean adjacency matrix where N is the number of nodes. All initial values ​​are set to "0" to record the connections between nodes in the network, and matrix space is pre-allocated.

[0082] A4: For each force chain, sequentially traverse its adjacent aggregate pairs, treating them as edges in the network. In the adjacency matrix, mark the positions of the corresponding node pairs with the scalar and magnitude of the contact force between the aggregate pairs, indicating the force chain connection relationship and load transmission strength between the two nodes. Based on the spatial location of the aggregates, determine the directionality of the edges: the direction is from the upper aggregate to the lower aggregate, and from the aggregate with the larger z-axis coordinate to the aggregate with the smaller z-axis coordinate, thus reflecting the load transmission path. After sequentially traversing and assigning values ​​to all force chains, the complete weighted directed force chain network and its adjacency matrix can be obtained.

[0083] A5: After the edge construction is completed, the adjacency matrix is ​​normalized to ensure that all elements on the main diagonal are "0" and to eliminate possible self-loop connections; if there are duplicate edges during the network construction process, you can choose to keep them once or perform edge counting.

[0084] A6: The final generated adjacency matrix and aggregate ID index mapping table should be standardized and saved. It is recommended that the adjacency matrix be output in compressed binary format, and the mapping table can be saved in .csv format to ensure readability and subsequent retrieval. Simultaneously, record basic information about the network construction process, including the number of nodes, edges, number of isolated nodes, and connectivity. The process of constructing a weighted directed force chain network is as follows: Figure 4 As shown.

[0085] The topology parameters in step S6 include: node out-degree, kernel degree, and average path length, and the specific calculation formulas are shown in formulas (2) to (4):

[0086]

[0087] In the formula: w is the out-degree of node i, the number of edges from node i to other nodes. ij Let be the element in the i-th row and j-th column of the adjacency matrix. If w ij >0 indicates that a direction exists and is taken as 1 without considering weight; otherwise, it is taken as 0. N is the total number of nodes in the network.

[0088] Coreness(i) = max{k∈N} + |i∈k-core(G)} (3)

[0089] In the formula: Coreness(i) is the kernel degree value of node i, and the directed k-core subgraph of the weighted directed network of k-core(G) is a maximal connected subgraph in which the out-degree of all nodes is not less than k.

[0090]

[0091] In the formula: L is the average path length of the network, representing the average shortest distance between any two nodes, and d ij Let be the sum of the node weights in the shortest path from node i to node j. That is, the minimum sum of the weights of the edges on the path between the two nodes.

[0092] In this embodiment, the calculation results of the topology parameters of the weighted directional force chain network for different mineral skeletons are shown in Table 1.

[0093] Table 1

[0094] Grading type out degree nuclear Average path length AC10 1.702 2.049 83.36 SMA10 1.778 2.089 115.55 OGFC10 1.749 2.086 124.41

[0095] As shown in Table 1, the degree value of the mineral mixture AC10 is the lowest, followed by OGFC10, while SMA10 has the highest degree value. This indicates that compared with mineral mixtures OGFC10 and SMA10, AC10 has a weaker interlocking degree between aggregates. Regarding the core density, AC10 has the lowest core density, indicating that its aggregate contact is mostly edge contact, with a smaller core skeleton area. OGFC10 and SMA10 have higher core densities, indicating that their networks contain more structural core aggregates. These aggregates are in close contact, forming a mutually interlocking and supporting skeleton framework, thus creating a certain degree of skeleton force transmission channels. Regarding the average path length, AC10 has the shortest, followed by SMA10, while OGFC10 has the longest average path length. This indicates that compared with skeleton-type mineral mixtures, AC10 has the shortest load transfer path length, and its skeleton exhibits a weaker effective load transfer capacity.

[0096] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

Claims

1. A method for evaluating the effective load transfer capacity of a mineral skeleton based on the characteristics of a three-dimensional weighted directional force chain network, characterized in that, Specifically, the steps include the following: Step S1: Assemble a three-dimensional digital specimen of the mineral mixture according to the gradation information of the mineral aggregate; assign a unique ID to each aggregate in the three-dimensional digital specimen of the mineral mixture; Step S2: Set up a virtual penetration head on the three-dimensional digital specimen of the mineral mixture and conduct a numerical simulation experiment on the three-dimensional digital specimen of the mineral mixture; Step S3: Set the force chain formation criteria; Step S4: Extract the three-dimensional force chain from the three-dimensional digital specimen of the mineral mixture after the experiment, according to the force chain criterion. Step S5: Construct a weighted directed force chain network and an adjacency matrix based on the extracted force chains; Step S6: Calculate the topological parameters based on the adjacency matrix and the weighted directional force chain network, quantitatively characterize the weighted directional force chain network structure, and evaluate the effective load transfer capacity of different structural types of mineral mixture skeleton structures. The construction of the weighted directed force chain network in step S5 is specifically as follows: remove invalid force chains, then use the aggregate particles in the remaining force chains as network nodes, and consider two adjacent aggregates in the same force chain as interconnected; project the normal contact force corresponding to the two interconnected network nodes onto the line connecting the centroids of the two corresponding aggregates to obtain two scalars, and use the sum of these two scalars as the weight of the connecting edge; the direction of the connecting edge is from top to bottom; for each force chain, traverse its adjacent aggregate pairs in turn, and consider them as an edge in the network; The specific steps for constructing the adjacency matrix in step S5 are as follows: Step 5.1: Read the total number N of network nodes in the weighted directed force chain network; each network node corresponds to a unique aggregate ID; Step 5.2: Map all network nodes to consecutive integer indices from 1 to N, and construct a bidirectional mapping table, including a forward mapping from the original ID to the index and a reverse mapping from the index to the original ID; Step 5.3: Using a sparse matrix format, initialize an N×N Boolean adjacency matrix to record the connection relationships between nodes in the network. Set all initial values ​​to 0. Step 5.4: Map the network nodes to the corresponding elements in the adjacency matrix; assign the weights and directions of the network nodes to the corresponding elements in the adjacency matrix; Step 5.5: Normalize the adjacency matrix.

2. The method for evaluating the effective load transfer capacity of a mineral skeleton based on the characteristics of a three-dimensional weighted directional force chain network, as described in claim 1, is characterized in that... The force chain criterion includes the following conditions: Rule 1: The normal contact force of the aggregate in the three-dimensional digital specimen of the mineral mixture after the experiment must be greater than the normal contact force threshold. Rule 2: In the same force chain, the current aggregate and the next level aggregate are in contact with each other, and the height of the next level aggregate is less than or equal to the height of the current aggregate. Criterion 3: The included angle between the normal contact surfaces of two adjacent aggregates Less than or equal to , Angle threshold; Rule 4: The number of aggregate particles in a force chain must be greater than or equal to N, where N is a positive integer; Rule 5, based on the included angle between adjacent normal contacts Selecting the next level of aggregate specifically involves: if there are multiple angles between the normal contact points of the next level of aggregate and the current aggregate. If criterion 3 is satisfied, then the minimum normal contact angle is selected. The corresponding aggregate, if it exists If the forces are equal, select the aggregate with the largest normal contact force.

3. The method for evaluating the effective load transfer capacity of a mineral skeleton based on the characteristics of a three-dimensional weighted directional force chain network, as described in claim 2, is characterized in that... Angle between normal contacts The expression is as follows: ； Where A, B, and C are all aggregates, and B is the next level of aggregate after A, and C is the next level of aggregate after B; Let be the direction vector pointing from the centroid of aggregate A to the centroid of aggregate B. Let be the direction vector from the centroid of aggregate B to the centroid of aggregate C.

4. The method for evaluating the effective load transfer capacity of a mineral skeleton based on the characteristics of a three-dimensional weighted directional force chain network, as described in claim 2, is characterized in that... The normal contact force threshold is the average value of all normal contact forces.

5. The method for evaluating the effective load transfer capacity of a mineral skeleton based on the characteristics of a three-dimensional weighted directional force chain network, as described in claim 2, is characterized in that... Step S4 specifically involves: Step 4.1: Based on the normal contact force threshold, retain the aggregates that meet criterion 1, and sort the aggregates in descending order of height; Step 4.2: Identify the initial aggregate starting from the highest point; mark the initial aggregate as visited aggregate; denote the initial aggregate as A; Step 4.3: Determine if there exists a next-level aggregate that satisfies criterion 2 with aggregate A. If it exists, proceed to step 4.4; otherwise, proceed to step 4.

2. Step 4.4: Determine whether all the next-level aggregates of aggregate A have been traversed. If so, go to step 4.2; otherwise, select an aggregate from the untraversed aggregates as the current aggregate, denoted as aggregate B. Step 4.5: Based on criteria 2, 3, and 5, find the next-level aggregate of aggregate B. If found, record the next-level aggregate of aggregate B as aggregate C, and mark aggregate B and aggregate C as visited aggregates, then proceed to step 4.6; if not found, determine whether the current number of force chains satisfies criterion 4. If yes, store the current force chain in the force chain set, and then determine whether there are still aggregates that satisfy the force chain formation criteria. If there are, proceed to step 4.4; if not, the force chain search is complete; if the current number of force chains does not satisfy criterion 4, determine whether there are still aggregates that satisfy the force chain formation criteria. If there are, proceed to step 4.4; if not, the force chain search is complete. Step 4.6: Take aggregate C as the new current aggregate, update the direction vector, and then go to step 4.

5.

6. The method for evaluating the effective load transfer capacity of a mineral skeleton based on the characteristics of a three-dimensional weighted directional force chain network, as described in claim 1, is characterized in that... The invalid force chains include force chains with a length less than a preset threshold, repetitive force chains, and force chains with abnormal aggregate IDs.

7. The method for evaluating the effective load transfer capacity of a mineral skeleton based on the characteristics of a three-dimensional weighted directional force chain network, as described in claim 1, is characterized in that... The topology parameters in step S6 include: node out-degree, kernel degree, and average path length; Node out-degree The expression is as follows: ； in, The adjacency matrix is ​​the first... Line number The value of the element in the column, if ,but =1, otherwise N represents the total number of nodes in the weighted directed force chain network. Average path length The expression is as follows: ； in, It is the sum of the weights of all nodes in the shortest path from node i to node j in a weighted directed force chain network.

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