Method for establishing a model of cascading failure of mountain road network under the influence of rainfall landslides and application thereof

Abstract

The present application relates to the field of complex network cascading failure and urban risk disaster prevention and control, and specifically discloses a method for establishing a mountain road network cascading failure model under the influence of rainfall landslides and its application. The present application can be used to establish a road network cascading failure model under the influence of rainfall landslides, and then be applied to the study of mountain road infrastructure network failure under extreme environment. By comprehensively considering the disturbance form and cascading failure characteristics of rainfall landslides on mountain road network under extreme environment, and based on the nonlinear spatiotemporal distribution characteristics of rainfall landslides and the change of road traffic flow, the present application improves the coupling mapping lattice theory and network seepage theory to construct a rainfall landslide cascading failure model, observes the state change of road network nodes and edge traffic flow, and then judges the situation change of mountain road network under the influence of rainfall landslides. The present application has important significance for improving the disaster risk resistance and emergency collaborative support capability of mountain road traffic infrastructure itself.

Description

Technical Field

[0001] This invention relates to the field of complex network cascading failure and urban risk disaster prevention and control technology, specifically to a method for establishing and applying a cascading failure model of a mountain road network under the influence of rainfall-induced landslides. Background Technology

[0002] With the intensification of global climate change and the continuous increase in the frequency and intensity of extreme disaster events, mountainous areas located in complex geological fault zones face particularly severe disaster risks. The increased frequency of rainfall-induced landslides induced by global warming has made mountainous road and transportation infrastructure networks increasingly vulnerable to these events. In recent years, the temporal and spatial distribution characteristics of rainfall-induced landslide events have attracted widespread attention from researchers, prompting in-depth studies on the mechanisms by which landslides affect critical infrastructure. Since the introduction of cascading failures in network science has garnered even more attention, these studies have contributed to a deeper understanding of the interdependencies within complex systems, revealing that interdependent components within a system can spontaneously evolve to a self-organizing critical state, where even minute disturbances can trigger catastrophic consequences.

[0003] Rainfall-induced landslides, as a special type of disturbance, exhibit nonlinear spatiotemporal distribution characteristics. Due to the complex coupling effects of the natural environment and human activities, the temporal and spatial distribution of rainfall-induced landslides is difficult to predict using simple linear models. Therefore, multi-factor coupled integrated models are often employed for research on dynamic prevention and early warning of risk disasters. This mathematical model can integrate rainfall-induced landslides with mountainous road and transportation infrastructure networks, allowing for the study of the failure characteristics of these networks under rainfall-induced landslide disturbances. This is of great significance for the prevention and mitigation of rainfall-induced landslides. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a method and application for establishing a cascading failure model of a mountain road network under the influence of rainfall-induced landslides, thus solving the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for establishing a cascading failure model of a mountain road network under the influence of rainfall-induced landslides, comprising the following steps: S1. Establishment of a database of rainfall-related landslides; S2. Classification of parameters for rainfall-induced landslides; S3, Calculation of rainfall-induced landslide disturbance model; S4. Analysis of disturbances in the road and transportation infrastructure network in mountainous areas prone to rainfall-induced landslides; S5. Establishment of a failure model for rainfall-induced landslides.

[0006] Preferably, in step S1, a rainfall-type landslide disaster database is established based on NASA's global landslide disaster database, the China Meteorological Data Network, and the Resource, Environment and Science Data Center of the Chinese Academy of Sciences, according to the distribution characteristics, regional climate characteristics, geological environment, and landslide scale of rainfall-type landslide disasters.

[0007] Preferably, in step S2, based on the rainfall-induced landslide disaster database, the analytic hierarchy process (AHP) and the coefficient of determination (COD) method are used to determine the causative factors of rainfall-induced landslides. These factors are divided into five key rainfall-induced landslide induction factors: topographic elevation, average annual rainfall, topographic structure, slope, and lithology. The parameter values ​​of the rainfall-induced landslide induction factors are determined by performing Binary Logistic Regression Analysis using SPSS software.

[0008] Preferably, step S3 specifically includes the following: The Logistic function is used to determine the disturbance index of rainfall-induced landslide disasters. The calculation method is as follows: Assume that there is a linear relationship between the dependent variable Z and the independent variable b in the disturbance exponent: ; In formula (2) This is the error term of the Logistic function. b m is the independent variable of the function; Let be the regression intercept of the function. These are the partial regression coefficients of the function. It exhibits characteristics of a logistic distribution; in order to calculate its cumulative distribution function, the variable of the function must be less than a specific value: ; The cumulative distribution function in formula (3) and They share the same Logistic distribution characteristics, both converting input values ​​to between 0 and 1; setting... Cumulative distribution function Logistic regression model: ; From formula (4), we can know that when Logistic regression model ,in The cumulative distribution function of the model describes the disturbance characteristics of rainfall-induced landslide disasters. As the inducing factor variables of rainfall-induced landslide disasters increase, the probability of rainfall-induced landslides approaching 1, indicating that rainfall-induced landslide disaster events will definitely occur. Its functional expression is: ; In formula (5), This is a disturbance model for rainfall-induced landslide disasters, and the cumulative distribution function in the model is... This is used to represent the linear relationship between the inducing factors of rainfall-induced landslide disasters. The regression intercept of the function represents the logarithm of the ratio of the probability of a rainfall-induced landslide occurring to the probability of it not occurring. These are the partial regression coefficients of the function. Let be the independent variable of the function, representing the terrain elevation ( ), average annual rainfall ( ), topographic structure ( ),slope( ), lithology ( Inducing factors for rainfall-induced landslides.

[0009] Preferably, step S4 specifically includes the following: Using a rainfall-induced landslide hazard model as an external disturbance in the mountainous road transportation infrastructure network, the disturbance function of points and edges in the initial network is: ; In real-world scenarios, rainfall-induced landslides directly lead to road disruptions. The external disturbances at the midpoints and edges of the network are equivalent to those in a rainfall-induced landslide disturbance model. The external disturbances in the mountainous road transportation infrastructure network are... P The functional relationship is expressed as: ; Road disruptions lead to changes in traffic flow. The product of traffic flow at midpoints and edges of the road network and the amount of external disturbance represents the impact of rainfall-induced landslides on traffic volume in mountainous road infrastructure networks. By observing changes in traffic flow within the network, the impact of rainfall-induced landslides on the network can be intuitively understood. ; In formulas (8) and (9), and This indicates the evolution of the network from never being affected by rainfall-induced landslides to being affected by such disasters. x and y This represents the traffic state quantities of points or edges in the network. Let be the regression intercept of the function. These are the partial regression coefficients of the function. for The independent variable represents the terrain elevation ( ), average annual rainfall ( ), topographic structure ( ),slope( ), lithology ( The inducing factors for rainfall-induced landslides, with Q as an intermediate variable.

[0010] Preferably, step S5 specifically includes: By improving the integration of coupled mapping lattice theory and network seepage theory, a rainfall-induced landslide failure model is constructed; in the spatiotemporal discrete matrix function of the mountain road traffic infrastructure network, the failure model nodes... i The state variables are: ; In formula (10), For network nodes i The coupling strength coefficient, and Representing network nodes i The state variables at time t+1 and time t, when When the node is in a stable state, This indicates that the node is in a failed state; M i For nodes i The degree, N The gamma function represents the total number of network nodes. Represents nodes in the network i and j Functional coupling of traffic flows between them; When a node fails, the edges it connects to also fail; therefore, the state variables of edges in the network depend not only on themselves but also on the two nodes connected to them. In the spatiotemporal discrete matrix function of the mountain road transportation infrastructure network, the failure model of edges... e ij The state variables are represented as: ; In formula (11), p Represents nodes i Other connected nodes, q Represents nodes j Other connected nodes represent all nodes connected to... i Nodes and j When summing pairs of connected nodes, it is necessary to exclude nodes. i and nodes j itself. Connecting edges e ij The coupling strength coefficient, They represent the edges respectively. e ij Adjacent nodes i and j The state quantity at time t and They represent the edges respectively. e ij The state variables at time t+1 and time t; when When the connection is in a stable state, This indicates that the connection is in a failed state, i.e. At that time, ， This indicates that the edge connection is invalid; M i and For nodes i and j The degree, N The gamma function represents the total number of network nodes in the system. and Represents nodes in the network i and j Functional coupling of traffic flow between adjacent edges.

[0011] On the other hand, to achieve the above objectives, the present invention also provides the following technical solution: an application of a cascading failure model of a mountain road network under the influence of rainfall-induced landslides, dividing the entire application scenario into the time of disaster occurrence and the time after disaster occurrence: Following a rainfall-induced landslide: Treating rainfall-induced landslides as external disturbances to the network, the mountainous road and transportation infrastructure network nodes... i and connecting edges e ij The cascading failure model is represented as: ; In formulas (12) and (13), Indicates the time when a rainfall-induced landslide disaster occurs. and Indicates the network node at the time of the disaster i and connecting edges e ij The absolute value in the formula is used to ensure that the state variables of nodes and edges are non-negative. When rainfall-induced landslides occur: These landslides are considered external disturbances to the network, affecting mountainous road and transportation infrastructure network nodes. i and connecting edges e ij The cascading failure model is represented as: ; In formulas (14) and (15), t represents the number of nodes in the network when a rainfall-induced landslide occurs. i and connecting edges e il State variables; chaotic logistic mapping function and and The product of these values ​​indicates that rainfall-induced landslides increase the probability of failure of nodes and connections in mountainous road networks. When node i variables This indicates that more nodes in the network will fail, and the edges connected to them will be removed. The state variables of the removed nodes and edges will tend towards infinity, and the traffic flow of these nodes and edges will shift to adjacent nodes and edges, increasing the traffic load on adjacent nodes and edges; therefore, the connection... e ij The state quantity at the time of a disaster is determined by two factors: one is the adjacent edges. e ip and e jq Connected nodes i and j The traffic flow variables at time t-1 are twofold: first, the probability of occurrence of rainfall-induced landslide disasters.

[0012] The beneficial effects of this invention are as follows: The method of this invention can be used to establish a cascading failure model of road networks under the influence of rainfall-induced landslide disasters, and then applied to the study of the failure of mountain road infrastructure networks in extreme environments. By comprehensively considering the disturbance forms and cascading failure characteristics of rainfall-induced landslide disasters on mountain road networks under extreme environments, and based on the nonlinear spatiotemporal distribution characteristics of rainfall-induced landslide disasters and changes in road traffic flow, a cascading failure model of rainfall-induced landslides is constructed by improving coupled mapping lattice theory and network seepage theory. The state changes of road network nodes and connecting traffic flows are observed, thereby judging the status changes of mountain road networks under the influence of rainfall-induced landslides. This invention is of great significance for improving the ability of mountain road transportation infrastructure to resist disaster risks and provide emergency collaborative support. It can provide scientific basis and technical support for the prevention and mitigation of the impact of extreme environmental disasters, and contribute to building a safe, stable, and sustainable society. Attached Figure Description

[0013] Figure 1 This is a schematic diagram illustrating the process of establishing a cascading failure model for a mountain road network under the influence of rainfall-induced landslides. Detailed Implementation

[0014] 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, and 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.

[0015] Please see Figure 1This invention provides a technical solution: a method for establishing a cascading failure model of a mountain road network under the influence of rainfall-induced landslides, comprising the following steps: S1. Establishment of a rainfall-based landslide database.

[0016] Based on NASA's global landslide disaster database, the China Meteorological Data Network, and the Resource, Environment and Science Data Center of the Chinese Academy of Sciences, a rainfall-induced landslide disaster database was established according to the distribution characteristics, regional climate characteristics, geological environment, and landslide scale of rainfall-induced landslide disasters.

[0017] S2. Classification of parameters for rainfall-induced landslides.

[0018] Based on a database of rainfall-induced landslide disasters, the analytic hierarchy process (AHP) and coefficient of determination (COD) method were used to determine the causative factors of rainfall-induced landslides. These factors were categorized into five key inducing factors: topographic elevation, average annual rainfall, topographic structure, slope, and lithology. The parameter values ​​of these inducing factors were determined using binary logistic regression analysis with SPSS software.

[0019] S3, calculation of rainfall-induced landslide disturbance model.

[0020] The Logistic function is used to determine the disturbance index of rainfall-induced landslide disasters. The calculation method is as follows: Assume that there is a linear relationship between the dependent variable Z and the independent variable b in the disturbance exponent: ; In formula (2) This is the error term of the Logistic function. b m is the independent variable of the function; intercept, The partial regression coefficients of the function, It exhibits characteristics of a logistic distribution; in order to calculate its cumulative distribution function, the variable of the function must be less than a specific value: ; The cumulative distribution function in formula (3) and They share the same Logistic distribution characteristics and can both convert input values ​​to a range of 0 to 1; setting Cumulative distribution function Logistic regression model: ; From formula (4), we can know that when Logistic regression model ,in The cumulative distribution function of the model can be used to describe the disturbance characteristics of rainfall-induced landslide disasters. As the inducing factor variables of rainfall-induced landslide disasters increase, the probability of rainfall-induced landslides approaching 1, indicating that rainfall-induced landslide disaster events will definitely occur. Its functional expression is: ; In formula (5), This is a disturbance model for rainfall-induced landslide disasters, and the cumulative distribution function in the model is... This is used to represent the linear relationship between the inducing factors of rainfall-induced landslide disasters. The regression intercept of the function represents the logarithm of the ratio of the probability of a rainfall-induced landslide occurring to the probability of it not occurring. These are the partial regression coefficients of the function. Let be the independent variable of the function, representing the terrain elevation ( ), average annual rainfall ( ), topographic structure ( ),slope( ), lithology ( Inducing factors for rainfall-induced landslides.

[0021] S4. Disturbance analysis of road traffic infrastructure network in mountainous areas prone to rainfall-induced landslides.

[0022] Using a rainfall-induced landslide hazard model as an external disturbance in the mountainous road transportation infrastructure network, the disturbance function of points and edges in the initial network is: ; In real-world scenarios, rainfall-induced landslides directly lead to road disruptions. The external disturbances at the midpoints and edges of the network are equivalent to those in a rainfall-induced landslide disturbance model. The external disturbances in the mountainous road transportation infrastructure network are... P The functional relationship is expressed as: ; Road disruptions lead to changes in traffic flow. The product of traffic flow at midpoints and edges of the road network and the amount of external disturbance represents the impact of rainfall-induced landslides on traffic volume in mountainous road infrastructure networks. By observing changes in traffic flow within the network, the impact of rainfall-induced landslides on the network can be intuitively understood. ; In formulas (8) and (9), and This indicates the evolution of the network from never being affected by rainfall-induced landslides to being affected by such disasters. x and y This represents the traffic state quantities of points or edges in the network. The regression coefficients of the function are . These are the partial regression coefficients of the function. for The independent variable represents the terrain elevation ( ), average annual rainfall ( ), topographic structure ( ),slope( ), lithology ( The inducing factors for rainfall-induced landslides, with Q as an intermediate variable.

[0023] S5. Establishment of a failure model for rainfall-induced landslides.

[0024] By improving the integration of coupled mapping lattice theory and network seepage theory, a rainfall-induced landslide failure model is constructed; in the spatiotemporal discrete matrix function of the mountain road traffic infrastructure network, the failure model nodes... i The state variables are: ; In formula (10), For network nodes i The coupling strength coefficient, and Representing network nodes i The state variables at time t+1 and time t, when When the node is in a stable state, This indicates that the node is in a failed state; M i For nodes i The degree, N The gamma function represents the total number of network nodes. Represents nodes in the network i and j Functional coupling of traffic flows between them; When a node fails, the edges it connects to also fail; therefore, the state variables of edges in the network depend not only on themselves but also on the two nodes connected to them. In the spatiotemporal discrete matrix function of the mountain road transportation infrastructure network, the failure model of edges... e ij The state variables are represented as: ; In formula (11), p Represents nodes i Other connected nodes, q Represents nodes j Other connected nodes represent all nodes connected to... i Nodes and j When summing pairs of connected nodes, it is necessary to exclude nodes. i and nodes jitself. Connecting edges e ij The coupling strength coefficient, They represent the edges respectively. e ij Adjacent nodes i and j The state quantity at time t and They represent the edges respectively. e ij The state variables at time t+1 and time t; when When the connection is in a stable state, This indicates that the connection is in a failed state, i.e. At that time, ， This indicates that the edge connection is invalid; M i and For nodes i and j The degree, N The gamma function represents the total number of network nodes in the system. and Represents nodes in the network i and j Functional coupling of traffic flow between adjacent edges.

[0025] Based on the same inventive concept as the above-described method embodiments, this application also provides an application of a cascading failure model of a mountain road network under the influence of rainfall-induced landslides, dividing the entire application scenario into the time of disaster occurrence and the time after disaster occurrence: Following a rainfall-induced landslide: Treating rainfall-induced landslides as external disturbances to the network, the mountainous road and transportation infrastructure network nodes... i and connecting edges e ij The cascading failure model is represented as: ; In formulas (12) and (13), Indicates the time when a rainfall-induced landslide disaster occurs. and Indicates the network node at the time of the disaster i and connecting edges e ij The absolute value in the formula is used to ensure that the state variables of nodes and edges are non-negative. When rainfall-induced landslides occur: These landslides are considered external disturbances to the network, affecting mountainous road and transportation infrastructure network nodes. i and connecting edges e ijThe cascading failure model is represented as: ; In formulas (14) and (15), t represents the number of nodes in the network when a rainfall-induced landslide occurs. i and connecting edges e il State variables; chaotic logistic mapping function and and The product of these values ​​indicates that rainfall-induced landslides increase the probability of failure of nodes and connections in mountainous road networks. When node i variables This indicates that more nodes in the network will fail, and the edges connected to them will be removed. The state variables of the removed nodes and edges will tend towards infinity, and the traffic flow of these nodes and edges will shift to adjacent nodes and edges, increasing the traffic load on adjacent nodes and edges; therefore, the connection... e ij The state quantity at the time of a disaster is determined by two factors: one is the adjacent edges. e ip and e jq Connected nodes i and j The traffic flow variables at time t-1 are twofold: first, the probability of occurrence of rainfall-induced landslide disasters.

[0026] In summary, through the above steps, the cascading failure process of the mountain road traffic infrastructure network under the influence of rainfall-induced landslide disasters can be simulated by using formulas (12) to (15). The operation process of node failure is as follows: Set the nodes of the mountain road traffic infrastructure network to a stable state and ensure that the state variables are distributed in the range of 0 to 1. When a rainfall-induced landslide disaster occurs, the state variables of the road network nodes are analyzed by formula (14) to determine the failed nodes. After the disaster occurs, the failed nodes in the stable road network state will propagate the traffic flow to their adjacent nodes. The node failure process caused by the traffic flow is calculated by formula (12), and the cycle continues until the entire network node fails.

[0027] The operation process for edge failure is as follows: Set the edges of the mountain road traffic infrastructure network to a stable state and ensure that the state variables are distributed within the range of 0 to 1. When a rain-induced landslide occurs, calculate the failed edges in the road network using formula (15). After the disaster occurs, the failed edges in the stable road network state will propagate traffic flow to their adjacent edges. After the road network state stabilizes, calculate the state variables of the traffic flow of each edge using formula (14), and repeat this process until the entire network edge fails.

[0028] It should be noted that, in this document, 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. Unless otherwise specified, 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.

[0029] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” as used in the embodiments of this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0030] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0031] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0032] The terms "first" and "second" used in the embodiments are merely to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first" and "second" can be interchanged in a specific order or sequence where permitted. It should be understood that the objects distinguished by "first" and "second" can be interchanged where appropriate so that the embodiments described herein can be implemented in an order other than those illustrated or described herein.

[0033] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for establishing a cascading failure model of a mountain road network under the influence of rainfall-induced landslides, characterized in that, Includes the following steps: S1. Establishment of a rainfall-based landslide database; S2. Classification of parameters for rainfall-induced landslides; S3, Calculation of rainfall-induced landslide disturbance model; S4. Disturbance analysis of road transportation infrastructure networks in mountainous areas prone to rainfall-induced landslides; specifically including the following: Using a rainfall-induced landslide hazard model as an external disturbance in the mountainous road transportation infrastructure network, the disturbance function of points and edges in the initial network is: ; In real-world scenarios, rainfall-induced landslides directly lead to road disruptions. The external disturbances at the midpoints and edges of the network are equivalent to those in a rainfall-induced landslide disturbance model. The external disturbances in the mountainous road transportation infrastructure network are... P The functional relationship is expressed as: ; Road disruptions lead to changes in traffic flow. The product of traffic flow at midpoints and edges of the road network and the amount of external disturbance represents the impact of rainfall-induced landslides on traffic volume in mountainous road infrastructure networks. By observing changes in traffic flow within the network, the impact of rainfall-induced landslides on the network can be intuitively understood. ; In formulas (8) and (9), and This indicates the evolution of the network from never being affected by rainfall-induced landslides to being affected by such disasters. x and y This represents the traffic state quantities of points or edges in the network. The regression intercept of the function is . These are the partial regression coefficients of the function. Let be the independent variable of the function, representing the terrain elevation ( ), average annual rainfall ( ), topographic structure ( ),slope( ), lithology ( The inducing factors for rainfall-induced landslides, with Q as an intermediate variable; S5. Establishment of a rainfall-induced landslide failure model, specifically including: By improving the integration of coupled mapping lattice theory and network seepage theory, a rainfall-induced landslide failure model is constructed; in the spatiotemporal discrete matrix function of the mountain road transportation infrastructure network, the failure model nodes... i The state variables are: ; In formula (10), For network nodes i The coupling strength coefficient, and Representing network nodes i The state variables at time t+1 and time t, when When the node is in a stable state, This indicates that the node is in a failed state; M i For nodes i The degree, N The gamma function represents the total number of network nodes. Represents nodes in the network i and j Functional coupling of traffic flows between them; When a node fails, the edges it connects also fail; therefore, the state variables of edges in the network depend not only on themselves but also on the two nodes connected to them. In the spatiotemporal discrete matrix function of the mountain road transportation infrastructure network, the failure model of edges... e ij The state variables are represented as: ; In formula (11), p Represents nodes i Other connected nodes, q Represents nodes j Other connected nodes; Connecting edges e ij The coupling strength coefficient, They represent the edges respectively. e ij Adjacent nodes i and j The state quantity at time t and They represent the edges respectively. e ij The state variables at time t+1 and time t; when When the connection is in a stable state, This indicates that the connection is in a failed state, i.e. At that time, ， This indicates that the edge connection is invalid; M i and For nodes i and j The degree, N The gamma function represents the total number of network nodes in the system. and Represents nodes in the network i and j Functional coupling of traffic flow between adjacent edges.

2. The method for establishing a cascading failure model of a mountain road network under the influence of rainfall-induced landslides according to claim 1, characterized in that: In step S1, a rainfall-type landslide disaster database is established based on NASA's global landslide disaster database, the China Meteorological Data Network, and the Resource Environment Science and Data Center of the Chinese Academy of Sciences, according to the distribution characteristics, regional climate characteristics, geological environment, and landslide scale of rainfall-type landslide disasters.

3. The method for establishing a cascading failure model of a mountain road network under the influence of rainfall-induced landslides according to claim 1, characterized in that: In step S2, based on the rainfall-induced landslide disaster database, the analytic hierarchy process (AHP) and the coefficient of determination method are used to determine the causative factors of rainfall-induced landslides. These factors are divided into five key rainfall-induced landslide induction factors: topographic elevation, annual average rainfall, topographic structure, slope, and lithology. The parameter values ​​of the rainfall-induced landslide induction factors are determined by performing Binary Logistic Regression Analysis using SPSS software.

4. The method for establishing a cascading failure model of a mountain road network under the influence of rainfall-induced landslides according to claim 1, characterized in that: Step S3 specifically includes the following: The Logistic function is used to determine the disturbance index of rainfall-induced landslide disasters. The calculation method is as follows: Assume that there is a linear relationship between the dependent variable Z and the independent variable b in the disturbance exponent: ; In formula (2) This is the error term of the Logistic function. b m is the independent variable of the function; The regression intercept of the function is . These are the partial regression coefficients of the function. It exhibits characteristics of a logistic distribution; in order to calculate its cumulative distribution function, the variable of the function must be less than a specific value: ; The cumulative distribution function in formula (3) and They share the same Logistic distribution characteristics, both converting input values ​​to between 0 and 1; setting... Cumulative distribution function Logistic regression model: ; From formula (4), we can know that when Logistic regression model ,in The cumulative distribution function of the model describes the disturbance characteristics of rainfall-induced landslide disasters. As the inducing factor variables of rainfall-induced landslide disasters increase, the probability of rainfall-induced landslides approaching 1, indicating that rainfall-induced landslide disaster events will definitely occur. Its functional expression is: ; In formula (5), This is a disturbance model for rainfall-induced landslide disasters, and the cumulative distribution function in the model is... This is used to represent the linear relationship between the inducing factors of rainfall-induced landslide disasters. The regression intercept of the function represents the logarithm of the ratio of the probability of a rainfall-induced landslide occurring to the probability of it not occurring. These are the partial regression coefficients of the function. Let be the independent variable of the function, representing the terrain elevation ( ), average annual rainfall ( ), topographic structure ( ),slope( ), lithology ( Inducing factors for rainfall-induced landslides.

5. An application of the failure model obtained by the method for establishing a cascading failure model of a mountain road network under the influence of rainfall-induced landslides according to any one of claims 1-4, characterized in that: The entire application scenario is divided into two parts: during a disaster and after a disaster. Following a rainfall-induced landslide: Treating rainfall-induced landslides as external disturbances to the network, the mountainous road and transportation infrastructure network nodes... i and connecting edges e ij The cascading failure model is represented as: ; In formulas (12) and (13), Indicates the time when a rainfall-induced landslide disaster occurs. and Indicates the network node when the disaster occurs. i and connecting edges e ij The absolute value in the formula is used to ensure that the state variables of nodes and edges are non-negative. When rainfall-induced landslides occur: Mountainous road transportation infrastructure network nodes i and connecting edges e ij The cascading failure model is represented as: ; In formulas (14) and (15), t represents the number of nodes in the network when a rainfall-induced landslide occurs. i and connecting edges e il State variables; chaotic logistic mapping function and and The product of these values ​​indicates that rainfall-induced landslides increase the probability of failure of nodes and connections in mountainous road networks. When node i variables This indicates that more nodes in the network will fail, and the edges connected to them will be removed. The state variables of the removed nodes and edges will tend towards infinity, and the traffic flow of these nodes and edges will shift to adjacent nodes and edges, increasing the traffic load on adjacent nodes and edges; therefore, the connection... e ij The state quantity at the time of a disaster is determined by two factors: one is the adjacent edges. e ip and e jq Connected nodes i and j The traffic flow variables at time t-1 are twofold: first, the probability of occurrence of rainfall-induced landslide disasters.

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