A granular material liquefaction prediction method based on a persistent homology method

Abstract

The application discloses a granular material liquefaction prediction method based on a persistent homology method. First, according to the mutual contact relation between the particles in the granular system, the original granular system is discretized into a contact force network; then, based on the persistent homology method, the contact force threshold value of each homology invariant in the contact force network is identified through multi-scale homology analysis, the corresponding persistence diagram is constructed, the extraction of key homology structure information and the dimension reduction of the contact force network are realized; subsequently, the distance between two adjacent time persistence diagrams is calculated, and the evolution rate of the contact force network with the shearing process is quantified; further, whether the contact force network evolution rate curve has a mutation point is detected, and if the mutation point exists, it indicates that the contact force network has started to collapse at a high speed, which indicates the occurrence of liquefaction. The application provides a new and effective way for quantitatively characterizing the dynamic behavior of the contact force network of the granular material and establishing the macro-micro cross-scale research of the granular material.

Description

Technical Field

[0001] This invention belongs to the field of mechanics research of particulate matter and relates to a method for predicting the liquefaction phenomenon of particulate materials, specifically a method for predicting the liquefaction of particulate materials based on the continuous cohomology method. Background Technology

[0002] Particulate materials are complex systems composed of a large number of discrete solid particles interacting with each other. They are ubiquitous in engineering construction, industrial production, and all aspects of nature. The widespread natural phenomena of debris flows and landslide dams, the use of blocky materials in civil engineering, and the production of coal and sand all involve the accumulation and movement of particulate materials. Particulate materials exhibit characteristics ranging from discrete to continuous, from microscopic to macroscopic, from disordered to ordered, and from flowing to clogging, making them a key research subject in fundamental disciplines such as physics, materials science, and mechanics. Unlike solids and liquids in the traditional sense, particulate systems, due to their complex microstructure, exhibit complex motion patterns similar to gases, liquids, or solids under different shear states. In 2005, the prestigious academic journal *Science* published a list of 125 of the most challenging scientific problems of the century, one of which was "whether a comprehensive theory of turbulent dynamics and the kinematics of particulate materials can be developed."

[0003] Existing research has identified two failure modes in granular systems subjected to shear stress: localized shear band failure and overall dispersion failure. Localized shear band failure refers to deformation concentrated in a band-like region, while dispersion failure lacks localized concentrated deformation and is difficult to observe in experiments and engineering, resulting in relatively limited research in this area. Recent studies on isovolumetric shear granular systems have revealed that when the system's porosity reaches a certain value, i.e., a certain degree of porosity, a severe instability phenomenon occurs, known as liquefaction of granular materials. This phenomenon is a special case of dispersion failure. Liquefaction occurs extremely rapidly; the granular system instantly loses its load-bearing capacity, becoming a "liquid-like state." Furthermore, the stress state of the system during liquefaction does not reach the plastic limit strength, which undoubtedly poses a significant challenge to predicting liquefaction using traditional modeling methods, necessitating the development of novel liquefaction prediction methods. Through the analysis of numerous cases of geological disasters and failures in water conservancy and geotechnical engineering, it has become increasingly clear that the liquefaction behavior of granular materials is one of the mechanisms underlying geological and engineering disasters such as landslides, debris flows, dam failures, and instability of earth-rock fill. Therefore, research on the prediction and modeling methods for granular material liquefaction has significant theoretical and practical value for geological disaster prevention and mitigation, as well as the safe operation of geotechnical engineering projects.

[0004] On the other hand, particulate materials are essentially disordered stacks of a large number of solid particles. This structural disorder leads to typical spatial heterogeneity in the internal particle contacts, meaning that the orientation and magnitude of contact forces exhibit significant spatial non-uniformity. At the beginning of this century, some scholars first experimentally observed spatially heterogeneous particle contact force networks using optical techniques such as photoelasticity. Subsequent extensive research has suggested that the contact force network of a particulate system is its most fundamental characteristic, and its structure and evolution largely determine the system's macroscopic mechanical response. To further study the structure and evolution of contact force networks, many scholars have artificially defined mesoscopic structures such as force chains and force loops to reflect the evolution of the system's contact force network. This research has significantly promoted the development of particulate matter mechanics. However, these mesoscopic structures are mainly defined from a local perspective, while the contact force network formed by the stacking of particle assemblies is a whole, especially exhibiting heterogeneous topological organization and complex behavioral patterns at different spatial scales. Therefore, the topological structure and evolution of the contact force network should be studied holistically from a system perspective.

[0005] Contact force networks essentially fall under the category of complex networks. In recent years, graph theory and related methods have been widely used to study the topological structure and evolution of contact force networks in particulate materials. This primarily includes extracting the force chain structure of the system through community detection methods, predicting interparticle contact forces, and detecting failure paths. As a fundamental tool in graph theory and topological data analysis, persistent cohomology methods provide a theoretical framework based on algebraic topology for quantitatively studying the dynamic behavior of complex networks by quantifying the persistence of topological invariants. The topological properties of topological invariants, which do not change with continuous deformation of the network structure, are considered key characteristics of persistent cohomology, mainly including connected components, loops, and voids. In recent years, persistent cohomology and related methods have shown broad application prospects in various fields such as materials science, biology, and natural language processing.

[0006] Therefore, it is necessary to design a particulate material liquefaction prediction method based on the continuous cohomology method to overcome the above problems. Summary of the Invention

[0007] This invention provides a method for predicting particulate material liquefaction based on the continuous coherence method, in order to solve the problem that related technologies only study the evolution of mesoscopic structures from a local perspective, and cannot quantitatively characterize the dynamic behavior of contact force networks and predict particulate material liquefaction from a global perspective.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0009] A method for predicting liquefaction of particulate materials based on a continuous cohomology approach includes the following steps:

[0010] Step S1. Based on the contact relationships between particles in the particle system, discretize the original particle system into a contact force network;

[0011] Step S2. Based on the continuous cohomology method, through multi-scale topology analysis, the contact force thresholds for the generation and disappearance of each topological invariant in the contact force network are identified, and the corresponding continuous graph is constructed to achieve the extraction of key topological structural information and dimensionality reduction of the contact force network.

[0012] Step S3. Calculate the distance between the duration graphs of two adjacent time points to quantify the evolution rate of the contact force network with the shear process;

[0013] Step S4. Detect whether there is a sudden change point in the evolution rate curve of the contact force network. If a sudden change point is detected, it indicates that the contact force network has begun to collapse at an accelerated rate, which indicates the occurrence of liquefaction.

[0014] Preferably, step S1 specifically comprises:

[0015] For a given particle system, first determine the contact relationship between each particle and its neighboring particles, including whether they are in contact and the contact force level. Based on the above contact relationship, treat each particle in the system as a node in the contact force network. If there is contact between two particles, add an edge between the corresponding two nodes. This edge contains the contact force level information.

[0016] Preferably, the width of the edge is used to represent the magnitude of different contact forces, and the larger the width of the edge, the greater the contact force between the two corresponding particles.

[0017] Preferably, step S2 includes the following sub-steps:

[0018] Step S2.1. First, select the maximum value of the contact force among all particles in the system as the contact force threshold. Select the nodes and edges whose contact force is greater than the contact force threshold to construct a contact force sub-network. Then, extract each topological invariant from the contact force sub-network, including connected components and contact loops.

[0019] Step S2.2. Continuously reduce the contact force threshold and repeat the above operation; during this process, it can be observed that each topological invariant appears or disappears as the contact force threshold decreases;

[0020] Step S2.3. Simultaneously record the contact force threshold when each topological invariant appears or disappears. Based on this, construct the corresponding persistence graph to achieve the extraction of key topological structure information and dimensionality reduction of the contact force network.

[0021] Preferably, the contact force thresholds are all based on the average value of all contact forces in the system as the basic unit of the contact force threshold.

[0022] Preferably, step S3 specifically includes:

[0023] During the shearing process of the granular system, the aforementioned persistence graph is constructed at each time step. The Wasserstein Distance is used to calculate the distance between the persistence graphs of two adjacent time steps. This distance quantifies the evolution rate of the contact force network between these two adjacent time steps, thus obtaining the evolution rate curve of the contact force network with the shearing process.

[0024] Preferably, the distance between the duration graphs of two adjacent time points is calculated, and the specific calculation formula is as follows:

[0025]

[0026] Where PD and PD′ represent the continuous graphs at two consecutive time points, WD(PD,PD′) is the distance between the continuous graphs at two adjacent time points, φ(PD,PD′) represents the point-to-point mapping from continuous graph PD to continuous graph PD′, for a point p in continuous graph PD, φ(p) represents the corresponding point in continuous graph PD′ after mapping φ, and d(p,φ(p)) represents the distance between the two points.

[0027] Preferably, the formula for calculating the distance d(p,φ(p)) between two points is:

[0028] d(p,φ(p))=max(|f birth,p -f birth,φ(p) |,|f death,p -f death,φ(p) |)

[0029] Among them, f birth,p and f death,p f represents the contact force threshold at the birth and death of the topological invariant at point p, respectively. birth,φ(p) and f death,φ(p) These represent the contact force thresholds at the birth and death of the topological invariant corresponding to point φ(p), respectively.

[0030] Preferably, step S4 specifically includes: using the Bernaola Galvan segmentation algorithm to detect whether there are abrupt change points in the curve. If there are abrupt change points in the curve, it indicates that the contact force network has accelerated its collapse, which indicates the occurrence of liquefaction. Otherwise, it indicates that the particulate material will not liquefy.

[0031] Compared with the prior art, this application has the following beneficial effects:

[0032] (1) This invention provides a method for predicting the liquefaction of particulate materials based on the continuous coherence method;

[0033] (2) The method provided by this invention can achieve comprehensive and effective extraction of various topological invariants in the contact force network, effectively describe the topological structure of the contact force network, and provide a method for extracting the topological features of complex systems for related research on other amorphous systems.

[0034] (3) The method provided by this invention can quantitatively study the dynamic evolution of the contact force network from a system and overall perspective, providing a new and effective way to predict the liquefaction phenomenon of particulate materials.

[0035] (4) Due to the high-dimensional complexity of the contact force network of particulate materials, previous studies on constructing constitutive models of particulate materials have been unable to consider the evolution of the contact force network. Therefore, the method provided by this invention can provide a reference for establishing constitutive models of particulate materials that take into account the evolution of the contact force network. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This invention provides a method for predicting the liquefaction of particulate materials based on a continuous coherence method.

[0038] Figure 2 This is a schematic diagram of the original particle system provided in an embodiment of the present invention;

[0039] Figure 3 This is a macroscopic stress-strain curve obtained from a particle shearing experiment provided in an embodiment of the present invention;

[0040] Figure 4 This is a schematic diagram of the contact force network of the particle system provided in the embodiment of the present invention;

[0041] Figure 5 This is a graph showing the change of the contact force network as a function of the contact force threshold provided in this embodiment of the invention;

[0042] Figure 6 This is a continuous contact force network graph obtained based on the continuous coherence method provided in this embodiment of the invention;

[0043] Figure 7 This is a graph showing the evolution rate of the contact force network as a function of the shearing process, provided in an embodiment of the present invention. Detailed Implementation

[0044] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0045] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] This invention provides a method for predicting particulate material liquefaction based on a continuous coherence approach. This method can solve the problem in related technologies that only study the evolution of mesoscopic structures from a local perspective, and cannot quantitatively characterize the dynamic behavior of contact force networks and predict particulate material liquefaction from a global perspective.

[0047] See Figure 1 As shown in the figure, a method for predicting the liquefaction of particulate materials based on the continuous coherence method is provided in an embodiment of the present invention, which may include the following steps:

[0048] Step S1. Based on the contact relationships between particles in the particle system, discretize the original particle system into a contact force network;

[0049] Step S2. Based on the continuous cohomology method, through multi-scale topology analysis, the contact force thresholds for the generation and disappearance of each topological invariant in the contact force network are identified, and the corresponding continuous graph is constructed to achieve the extraction of key topological structural information and dimensionality reduction of the contact force network.

[0050] Step S3. Calculate the distance between the duration graphs of two adjacent time points to quantify the evolution rate of the contact force network with the shear process;

[0051] Step S4. Detect whether there is abrupt change in the evolution rate curve of the contact force network. If an abrupt change is detected, it indicates that the contact force network has begun to accelerate its collapse, foreshadowing the occurrence of liquefaction. The specific process is as follows:

[0052] 1. Conduct discrete element numerical simulations or physical experiments on particulate materials. Simulation or experimental parameters should be determined based on specific circumstances. (See attached...) Figure 2 As shown, a given pristine particle system is subjected to various shearing forces, such as biaxial shear, uniaxial shear, and isovolute shear. During the shearing process, the variation trend of the macroscopic deviatoric stress with the macroscopic shear strain is first recorded. (See attached diagram.) Figure 3As shown, in the particle system used in this embodiment of the invention, the macroscopic deviatoric stress gradually decreases to 0 during the shearing process, indicating that the system completely loses its load-bearing capacity at that point, i.e., liquefaction has occurred. Furthermore, it is necessary to record the position information of each particle in the system at each moment and its contact relationship with other particles. The position information refers to the coordinate position of each particle in space, and the contact relationship mainly includes whether each particle is in contact with its surrounding particles and the level of contact force, etc.

[0053] 2. Construct the contact force network of the particle system. (See attached diagram) Figure 4 As shown, each particle in the particle system is treated as a node in the contact force network. Based on the recorded particle position information and contact relationships, an edge is added between two nodes in contact, and this edge contains information about the contact force level. Figure 4 In this model, the width of the edges represents the magnitude of different contact forces; a wider edge indicates a stronger contact force between the two corresponding particles. Based on this, the original particle system can be discretized into a contact force network.

[0054] 3. Construct a continuity graph of the contact force network based on the continuity cohomology method. (See attached diagram) Figure 4 As shown, the contact force network of particulate materials exhibits a highly heterogeneous distribution in space. To quantify the topological structure and evolution of this complex network, based on the idea of ​​continuous homology, we focus on the emergence and disappearance of topological invariants in the contact force network with different contact force thresholds.

[0055] The specific steps are as follows:

[0056] a. First, select the maximum value of the contact force among all particles in the system as the contact force threshold. Then, select nodes and edges in the contact force network whose contact forces are greater than the contact force threshold to construct a contact force subnetwork. Next, extract the topological invariants from this contact force subnetwork, including connected components and contact loops. A connected component refers to a connected structure formed by connecting several nodes through edges, and a contact loop refers to a closed-loop structure formed by connecting several nodes through edges.

[0057] b. Continuously decrease the contact force threshold mentioned above, and repeat the above operation. (See attached diagram) Figure 5 As shown, the average value F0 of all contact forces in the system is used as the basic unit of the contact force threshold. When the contact force threshold is large, many isolated connected components begin to appear in the contact force subnetwork, but no contact loops have yet appeared. As the contact force threshold decreases, more isolated connected components begin to appear in the contact force subnetwork, and then these isolated connected components begin to merge, while a large number of contact loops begin to appear. In the above process, it can be observed that each topological invariant is born or dies as the contact force threshold decreases, and the contact force threshold at the time of the birth or death of each topological invariant is recorded.

[0058] c. Based on the contact force threshold recorded at the birth or death of each topological invariant, a contact force network continuity diagram is plotted, with the contact force threshold at birth as the X-axis data and the contact force threshold at death as the Y-axis data. (See attached diagram) Figure 6 As shown, each point in the continuity graph represents the contact force threshold corresponding to the birth and death of a topological invariant.

[0059] Based on this, a continuous graph of the contact force network can be constructed using the continuous cohomology method.

[0060] 4. Calculate the distance between the persistence graphs of two adjacent time points to quantify the evolution rate of the contact force network. During the shearing process of the granular system, a persistence graph of the contact force network is constructed at each time point. The persistence graph encodes the information of the birth and death of each topological invariant, representing the most essential feature of the contact force network. Therefore, quantifying the distance between the persistence graphs of the contact force network of two adjacent time points is equivalent to quantifying the evolution rate of the contact force network at the corresponding time point. The Wasserstein distance is used to calculate the distance between the persistence graphs of two adjacent time points. The specific calculation formula is as follows:

[0061]

[0062] Where PD and PD′ represent the continuous graphs at two consecutive time points, WD(PD,PD′) is the distance between the two continuous graphs, and φ(PD,PD′) represents the point-to-point mapping from continuous graph PD to continuous graph PD′. Since there may be multiple possible combinations of point-to-point mappings, the final selected distance is the minimum value among all possible mappings. For a point p in continuous graph PD, φ(p) represents its corresponding point in continuous graph PD′ after mapping φ. The formula for calculating the distance d(p,φ(p)) between these two points is:

[0063] d(p,φ(p))=max(|f birth,p -f birth,φ(p) |,|f death,p -f death,φ(p) |) (2)

[0064] Among them, f birth,p and f death,p f represents the contact force threshold at the birth and death of the topological invariant at point p, respectively. birth,φ(p) and f death,φ(p) These represent the contact force thresholds at the birth and death of the topological invariant corresponding to point φ(p), respectively.

[0065] Based on the above calculation process, the following can be obtained: Figure 7 The graph shows the evolution rate of the contact force network as shear strain increases.

[0066] 5. Detecting abrupt changes in the evolution curve of the contact force network. Based on the evolution rate curve of the contact force network with increasing shear strain, the Bernaola-Galvan algorithm is used to detect abrupt changes. The Bernaola-Galvan algorithm, based on heuristic segmentation, can quickly obtain information such as abrupt changes from non-stationary time series. The presence of abrupt changes indicates that the contact force network is undergoing accelerated collapse, predicting the occurrence of liquefaction of the particulate material; conversely, the absence of abrupt changes indicates that the contact force network is undergoing stable evolution, and the system is not at risk of liquefaction. (See attached diagram) Figure 7 As indicated by the arrows, after probing the aforementioned contact force network evolution rate curve using the Bernaola-Galvan algorithm, two abrupt change points were indeed found in the evolution curve. This indicates that the particle system used in this invention will experience accelerated collapse and liquefaction of the contact force network during subsequent shearing. This can be seen from the attached diagram. Figure 3 The results provide evidence that the present invention has good implementation effect and can indeed achieve quantitative description of the dynamic evolution of the contact force network of particulate materials and prediction of macroscopic liquefaction behavior.

[0067] In the description of this invention, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this invention can be understood according to the specific circumstances.

[0068] It should be noted that in this invention, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0069] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for predicting the liquefaction of particulate materials based on a continuous cohomology approach, characterized in that, Includes the following steps: Step S1. Based on the contact relationships between particles in the particle system, discretize the original particle system into a contact force network; Step S2. Based on the persistent cohomology method, through multi-scale topology analysis, identify the contact force thresholds for the generation and disappearance of each topological invariant in the contact force network, construct the corresponding persistent graph, and realize the extraction of key topological structural information and dimensionality reduction of the contact force network; including the following sub-steps: Step S2.

1. For the obtained contact force network, select the maximum value among all particle contact forces in the system as the contact force threshold, select the nodes and edges whose contact forces are greater than the contact force threshold to construct a contact force sub-network, and then extract each topological invariant from the contact force sub-network, including connected components and contact loops; Step S2.

2. Continuously decrease the contact force threshold mentioned above, and repeat the above operation; during this process, it can be observed that each topological invariant appears or disappears as the contact force threshold decreases; Step S2.

3. Simultaneously record the contact force threshold when each topological invariant appears or disappears. Based on this, construct the corresponding persistence graph to achieve the extraction of key topological structure information and dimensionality reduction of the contact force network. Step S3. Calculate the distance between the duration graphs of two adjacent time points to quantify the evolution rate of the contact force network with the shear process; including: During the shearing process of the granular system, a persistence graph is constructed at each time step. The Wasserstein Distance is used to calculate the distance between two adjacent persistence graphs. This distance quantifies the evolution rate of the contact force network between these two adjacent time steps, resulting in the evolution rate curve of the contact force network as a function of the shearing process. The specific formula for calculating the distance between two adjacent persistence graphs is as follows: in, and A continuity graph representing two consecutive moments. The distance between two consecutive time-duration graphs is denoted as . Represented by a continuous graph To the continuous graph Point-to-point mapping for continuous graphs One point , This represents its mapping In the continuous graph The corresponding point in Represents the distance between two points; Distance between two points The calculation formula is: in, and Represent The contact force threshold at which the corresponding topological invariants are created and destroyed. and Represent The contact force threshold at which point-corresponding topological invariants are born and disappear; Step S4. Detect whether there is a sudden change point in the evolution rate curve of the contact force network. If a sudden change point is detected, it indicates that the contact force network has begun to collapse at an accelerated rate, which indicates the occurrence of liquefaction.

2. The method for predicting liquefaction of particulate materials based on the continuous cohomology method according to claim 1, characterized in that, Step S1 specifically involves: For a given particle system, first determine the contact relationship between each particle and its neighboring particles, including whether they are in contact and the contact force level. Based on the above contact relationship, treat each particle in the system as a node in the contact force network. If there is contact between two particles, add an edge between the corresponding two nodes. This edge contains the contact force level information.

3. The method for predicting liquefaction of particulate materials based on the continuous cohomology method according to claim 2, characterized in that, The width of the edge represents the magnitude of different contact forces; the wider the edge, the greater the contact force between the two particles.

4. The method for predicting liquefaction of particulate materials based on the continuous cohomology method according to claim 1, characterized in that, The contact force thresholds are all based on the average value of all contact forces in the system.

5. The method for predicting liquefaction of particulate materials based on the continuous cohomology method according to claim 1, characterized in that: Step S4 specifically includes: using the Bernaola Galvan segmentation algorithm to detect whether there are abrupt change points in the curve. If there are abrupt change points in the curve, it indicates that the contact force network has accelerated its collapse, which indicates the occurrence of liquefaction. Otherwise, it indicates that the particulate material will not liquefy.

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