Establishment method and application of mountainous area road network cascade failure model under rainfall type landslide influence

Abstract

The invention relates to the field of complex network cascading failure and urban risk disaster prevention and control, and particularly discloses an establishment method and application of a mountainous road network cascading failure model under the influence of rainfall-type landslide disasters, and the method can be used for establishing the road network cascading failure model under the influence of rainfall-type landslide disasters. The method is further applied to the failure research of the mountain road infrastructure network in the extreme environment, and by comprehensively considering the disturbance form and cascade failure characteristics of the rainfall-type landslide disaster to the mountain road network in the extreme environment, based on the nonlinear spatial and temporal distribution characteristics of the rainfall-type landslide disaster and the road traffic flow change, the reliability of the mountain road network is improved. By improving a coupling mapping lattice theory and a network seepage theory, a rainfall-type landslide cascade failure model is constructed, state changes of road network nodes and connecting edge traffic flows are observed, and then mountain road network situation changes under the influence of rainfall-type landslide are judged. The method is of great significance in improving the disaster risk resistance and emergency cooperative guarantee capability of the mountain road traffic infrastructure.

Description

Technical Field

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

[0002] With the intensification of global climate change and the continuous increase in the frequency and intensity of extreme disaster events, the disaster risks faced by mountainous areas located in complex geological fault zones are particularly severe. The frequency of rainfall-induced landslide disasters induced by global warming has increased, making the mountain road traffic infrastructure network increasingly vulnerable under the influence of disaster events. In recent years, the distribution characteristics of rainfall-induced landslide disaster events in time and space have attracted extensive attention from researchers, and this attention has promoted in-depth research on the influence mechanism of landslide disasters on key infrastructure. Since the proposal of cascading failure in network science has attracted more attention, these studies have promoted people's in-depth understanding of the interdependent relationships in complex systems, revealing that the constituent units that interact with each other within the system will spontaneously evolve to the self-organized critical state, and even a small perturbation may lead to catastrophic consequences.

[0003] As a special type of perturbation, rainfall-induced landslide disasters have non-linear spatio-temporal distribution characteristics. Due to the complex coupling effect of the natural environment and human activities, it is difficult to predict the occurrence time and spatial distribution of rainfall-induced landslide disasters with a simple linear model. A multi-factor coupling comprehensive model is often used for research on dynamic prevention and control and early warning of risk disasters. Therefore, through this mathematical model, rainfall-induced landslide disasters can be integrated with the mountain road traffic infrastructure network, and it can be used to study the failure characteristics of the mountain road traffic infrastructure network under the perturbation of rainfall-induced landslides, which is of great significance for preventing and mitigating rainfall-induced landslide disasters. Summary of the Invention

[0004] To solve the problems existing in the prior art, the present invention provides a method for establishing and applying a cascading failure model of a mountain road network under the influence of rainfall-induced landslides, and solves the problems mentioned in the above background art.

[0005] To achieve the above object, 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:

[0006] S1. Establishment of a rainfall-induced landslide database;

[0007] S2. Classification of rainfall-induced landslide parameters;

[0008] S3. Calculation of a rainfall-induced landslide perturbation model;

[0009] S4. Analysis of disturbance quantity in the road traffic infrastructure network in mountainous areas affected by rainfall-induced landslide disasters;

[0010] S5. Establishment of rainfall-induced landslide failure model.

[0011] Preferably, in step S1, based on the global landslide disaster database of NASA, the China Meteorological Data Network, and the Resource and Environment Science and Data Center of the Chinese Academy of Sciences, a rainfall-induced landslide disaster database is established according to the distribution characteristics, regional climate characteristics, geological environment, and landslide scale of rainfall-induced landslide disasters.

[0012] Preferably, in step S2, based on the rainfall-induced landslide disaster database, by using the analytic hierarchy process and the determination coefficient method, the disaster-causing factors of rainfall-induced landslides are determined, and they are divided into 5 key rainfall-induced landslide induction factors, namely terrain elevation, annual average rainfall, terrain structure, slope, and lithology. The parameter values of the rainfall-induced landslide induction factors are determined through Binary Logistic regression analysis by SPSS software.

[0013] Preferably, in step S3, it specifically includes the following:

[0014] Use the Logistics function to determine the disturbance index of rainfall-induced landslide disasters, and the calculation method is as follows:

[0015] Assume that there is a linear relationship between the dependent variable Z and the independent variable b in the disturbance index:

[0016]

[0017] It can be obtained from formula (1):

[0018]

[0019] In formula (2) is the error term of the Logistics function, b m is the independent variable of the function; α is the regression intercept of the function, and β m is the partial regression coefficient of the function, has the Logistics distribution characteristic. In order to calculate its cumulative distribution function, the variable of the function is less than a specific value:

[0020]

[0021] The cumulative distribution function F in formula (3) and have the same Logistics distribution characteristic, and both convert the input value to between 0 and 1; set F i as the Logistics regression model of the cumulative distribution function F:

[0022]

[0023] It can be known from formula (4) that when Logistics regression model F i ∈ [0, 1], where F i The cumulative distribution function feature of the model is used to describe the disturbance feature of rainfall-induced landslide disasters. As the variable of the inducing factor of rainfall-induced landslide disasters increases, it will cause the probability of rainfall-induced landslides to approach 1, indicating that the rainfall-induced landslide disaster event will definitely occur. Its function expression is:

[0024]

[0025] In formula (5), P i Is the disturbance model of rainfall-induced landslide disasters, and the cumulative distribution function in the model Is used to represent the linear relationship of the inducing factors of rainfall-induced landslide disasters. α is the regression intercept of the function, indicating the logarithm of the ratio of the probability of rainfall-induced landslides occurring or not; β m Is the partial regression coefficient of the function, b m Is the independent variable of the function, representing the inducing factors of rainfall-induced landslides such as terrain elevation (b1), average annual rainfall (b2), terrain structure (b3), slope (b4), and lithology (b5).

[0026] Preferably, in step S4, it specifically includes the following:

[0027] Taking the rainfall-induced landslide disaster model as the external disturbance quantity in the mountain road traffic infrastructure network, in the initial network, the functions of the points and connecting edges in the mountain road traffic infrastructure network being disturbed are:

[0028]

[0029] In the real scenario, rainfall-induced landslide disasters will directly cause road interruptions. The external disturbance quantity of points and connecting edges in the network is equivalent to the rainfall-induced landslide disturbance model. The functional relationship of the external disturbance quantity P in the mountain road traffic infrastructure network is expressed as:

[0030]

[0031] Road interruptions will cause changes in traffic flow. The product of the traffic flow of points and connecting edges in the road network and the external disturbance quantity represents the impact of rainfall-induced landslide disasters on the traffic volume in the mountain road traffic infrastructure network. By observing the changes in traffic flow in the network, the impact of rainfall-induced landslides on the network can be intuitively felt:

[0032]

[0033] In Formulas (8) and (9), x→Qx and y→Qy represent the evolution process of the network from never being affected by rainfall-induced landslide disasters to being affected. x and y represent the traffic state variables of the nodes or connecting edges in the network. α is the regression intercept of the function, and β m is the partial regression coefficient of the function, and b m is the independent variable of the function, representing the inducing factors for the occurrence of rainfall-induced landslides such as terrain elevation (b1), average annual rainfall (b2), terrain structure (b3), slope (b4), and lithology (b5). Q is the intermediate variable.

[0034] Preferably, in step S5, it specifically includes:

[0035] By improving the integration of the coupled map lattice theory and the network percolation theory, a rainfall-induced landslide failure model is constructed. In the spatio-temporal variable discrete matrix function of the mountain road traffic infrastructure network, the state variable of failure model node i is:

[0036]

[0037] In Formula (10), ε1 is the coupling strength coefficient of network node i, and x i (t + 1) and x i (t) represent the state variables of network node i at time t + 1 and time t respectively. When x i (t + 1) ∈ [0, 1], it means the node is in a stable state. When x i (t + 1) ∈ [1, ∞], it means the node is in a failed state; M i is the degree of node i, N is the total number of network nodes, and the gamma function F ij f[x j (t)] represents the functional coupling of the traffic flow between nodes i and l in the network;

[0038] When a node fails, the connected edge will also fail. Therefore, the state variable of the edge in the network not only depends on itself but also is affected by the two nodes it is connected to. In the spatio-temporal variable discrete matrix function of the mountain road traffic infrastructure network, the state variable of failure model edge e ij is expressed as:

[0039] y il (t + 1) = max

[0040]

[0041] In Formula (11), p represents the other nodes connected to node i, q represents the other nodes connected to node j. When summing over all node pairs connected to nodes i and j, nodes i and j themselves need to be excluded. ε2 is the coupling strength coefficient of edge e ij and xi (t), x j (t) respectively represent the states of the adjacent nodes i and j of the connecting edge e ij at time t, and y il (t + 1) and y il (t) respectively represent the states of the connecting edge e ij at time t + 1 and time t; when y il (t + 1) ∈ [0, 1], it means the connecting edge is in a stable state, and when y il (t + 1) ∈ [1, ∞], it means the connecting edge is in a failed state, that is, x i (t) > 1 or x j (t) > 1, then y il (t + 1) > 1, indicating that the connecting edge fails; M i and M j are the degrees of nodes i and l, N is the total number of nodes in the system network, and the gamma function F ip f[y ip (t)] and F jq f[y jq (t)] represent the functional coupling of traffic flow between adjacent connecting edges of nodes i and l in the network.

[0042] On the other hand, to achieve the above object, the present invention also provides the following technical solution: An application of a cascading failure model for a mountain road network under the influence of rainfall-induced landslides, which divides the entire application scenario into before and after the disaster:

[0043] Before the occurrence of the rainfall-induced landslide disaster: The cascading failure model of the mountain road traffic infrastructure network nodes i and connecting edge e ij is expressed as:

[0044]

[0045] In formulas (12) and (13), t0 represents the time before the occurrence of the rainfall-induced landslide disaster, t0 + 1 and t0 represent the state quantities of network nodes i and connecting edge e ij before the disaster, and the absolute value in the formula is to ensure that the state quantities of nodes and connecting edges are non-negative;

[0046] After the occurrence of the rainfall-induced landslide disaster: Regarding the rainfall-induced landslide disaster as an external perturbation to the network, the cascading failure model of the mountain road traffic infrastructure network nodes i and connecting edge e ij is expressed as:

[0047]

[0048] In formulas (14) and (15), t represents the time when the rainfall-induced landslide disaster occurs, and nodes i and connecting edge e ilState variable; chaotic Logistic mapping function f[y il (t - 1)] and f[x i (t - 1)] and the product with [1 + exp(α + β i b)], indicating that rainfall-induced landslide disasters will increase the failure probabilities of nodes and links in the mountain road traffic network;

[0049] When the variable x i (t) of node i > 1, it means that there will be more node failures in the network, and the links connected to it will all be removed. The state variables of the removed nodes and links will tend to infinity, and the traffic flows of these nodes and links will also transfer to adjacent nodes and links, increasing the traffic load of adjacent nodes and links. Therefore, the state variable of link e ij during the disaster occurrence is determined by two factors. One is the traffic flow variables of adjacent links e ip and e jq and the connected nodes i and j at time t - 1, and the other is the occurrence probability of rainfall-induced landslide disasters.

[0050] The beneficial effects of the present invention are as follows: The method of the present invention can be used to establish a road network cascading failure model under the influence of rainfall-induced landslide disasters, and then apply it to the research on the failure of mountain road infrastructure networks in extreme environments. By comprehensively considering the disturbance form and cascading failure characteristics of rainfall-induced landslide disasters on mountain road networks in extreme environments, based on the non-linear spatio-temporal distribution characteristics of rainfall-induced landslide disasters and the changes in road traffic flows, an improved coupled map lattice theory and network percolation theory are used to construct a rainfall-induced landslide cascading failure model, observe the state changes of traffic flows of road network nodes and links, and then judge the changes in the situation of mountain road networks under the influence of rainfall-induced landslides. The present invention has important significance for improving the ability of mountain road traffic infrastructure to resist disaster risks and emergency collaborative support by itself, can provide a scientific basis and technical support for prevention and mitigation under the influence of extreme environment disasters, and make contributions to building a safe, stable and sustainable development society. Brief Description of the Drawings

[0051] Figure 1 It is a schematic flow chart of the method for establishing a mountain road network cascading failure model under the influence of rainfall-induced landslides. Detailed Embodiment

[0052] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0053] Please refer toFigure 1 , the present invention provides a technical solution: a method for establishing a cascading failure model of mountain road networks affected by rainfall-induced landslides, including the following steps:

[0054] S1. Establishment of a rainfall-induced landslide database.

[0055] Based on the NASA global landslide disaster database, the China Meteorological Data Network, and the Resource and Environment Science and Data Center of the Chinese Academy of Sciences, a rainfall-induced landslide disaster database is established according to the distribution characteristics, regional climate characteristics, geological environment, and landslide scale of rainfall-induced landslides.

[0056] S2. Classification of rainfall-induced landslide parameters.

[0057] Based on the rainfall-induced landslide disaster database, by using the analytic hierarchy process and the determination coefficient method, the disaster-causing factors of rainfall-induced landslides are determined and divided into 5 key rainfall-induced landslide induction factors: terrain elevation, annual average rainfall, terrain structure, slope, and lithology. The parameter values of the rainfall-induced landslide induction factors are determined through Binary Logistic regression analysis using SPSS software.

[0058] S3. Calculation of the rainfall-induced landslide disturbance model.

[0059] The Logistics function is used to determine the disturbance index of rainfall-induced landslide disasters, and the calculation method is as follows:

[0060] Assume that there is a linear relationship between the dependent variable Z and the independent variable b in the disturbance index:

[0061]

[0062] It can be obtained from formula (1):

[0063]

[0064] In formula (2) is the error term of the Logistics function, b m is the independent variable of the function; α is the regression intercept of the function, β m is the partial regression coefficient of the function, has the Logistics distribution characteristics. In order to calculate its cumulative distribution function, the variable of the function is less than a specific value:

[0065]

[0066]

[0067] In formula (3), the cumulative distribution function F and have the same Logistics distribution characteristics and can convert the input values to between 0 and 1; set F i as the Logistics regression model of the cumulative distribution function F:

[0068]

[0069] It can be known from formula (4) that when Logistics regression model F i ∈[0, 1], where F i the characteristics of the cumulative distribution function of the model can be used to describe the disturbance characteristics of rainfall-induced landslide disasters. As the variable of the inducing factor of rainfall-induced landslide disasters increases, it will lead to the probability of rainfall-induced landslides approaching 1, indicating that the rainfall-induced landslide disaster event will definitely occur. Its function expression is:

[0070]

[0071] In formula (5), P i is the disturbance model of rainfall-induced landslide disasters, and the cumulative distribution function in the model is used to represent the linear relationship of the inducing factors of rainfall-induced landslide disasters. α is the regression intercept of the function, representing the logarithm of the ratio of the probability of rainfall-induced landslides occurring or not; β m is the partial regression coefficient of the function, and b m is the independent variable of the function, representing the inducing factors of rainfall-induced landslides such as topographic elevation (b1), annual average rainfall (b2), topographic structure (b3), slope (b4), and lithology (b5).

[0072] S4. Analysis of the disturbance quantity in the mountain road traffic infrastructure network of rainfall-induced landslide disasters.

[0073] Taking the rainfall-induced landslide disaster model as the external disturbance quantity in the mountain road traffic infrastructure network, in the initial network, the functions of the points and connecting edges in the mountain road traffic infrastructure network being disturbed are:

[0074]

[0075] In the real scenario, rainfall-induced landslide disasters will directly cause road interruptions. The external disturbance quantities of points and connecting edges in the network are equivalent to the rainfall-induced landslide disturbance model. The functional relationship of the external disturbance quantity P in its mountain road traffic infrastructure network is expressed as:

[0076]

[0077] Road interruptions can lead to changes in traffic flow. The product of the traffic flow at the nodes and links in the road network and the external disturbance quantity represents the impact of rainfall-induced landslide disasters on the traffic volume in the mountain road traffic infrastructure network. By observing the changes in traffic flow in the network, the impact of rainfall-induced landslides on the network can be intuitively felt:

[0078]

[0079] In formulas (8) and (9), x→Qx and y→Qy represent the evolution process of the network from being unaffected by rainfall-induced landslide disasters to being affected. x and y represent the traffic state quantities of the nodes or links in the network. α is the regression coefficient of the function, and β m is the partial regression coefficient of the function, and b m is the independent variable of the function, representing the inducing factors for the occurrence of rainfall-induced landslides such as terrain elevation (b1), annual average rainfall (b2), terrain structure (b3), slope (b4), and lithology (b5). Q is an intermediate variable.

[0080] S5. Establishment of the rainfall-induced landslide failure model.

[0081] By improving the integration of the coupled map lattice theory and the network percolation theory, a rainfall-induced landslide failure model is constructed. In the spatio-temporal variable discrete matrix function of the mountain road traffic infrastructure network, the state quantity of failure model node i is:

[0082]

[0083] In formula (10), ε1 is the coupling strength coefficient of network node i, x i (t + 1) and x i (t) represent the state quantities of network node i at time t + 1 and time t respectively. When x i (t + 1) ∈ [0, 1], it indicates that the node is in a stable state. When x i (t + 1) ∈ [1, ∞], it indicates that the node is in a failure state; M i is the degree of node i, N is the total number of network nodes, and the gamma function F ij f[x j (t)] represents the functional coupling of the traffic flow between nodes i and l in the network;

[0084] When a node fails, the connected link will also fail. Therefore, the state quantity of the link in the network not only depends on itself but also is affected by the two nodes it is connected to. In the spatio-temporal variable discrete matrix function of the mountain road traffic infrastructure network, the state quantity of failure model link e ij is expressed as:

[0085] y il (t + 1) = max

[0086]

[0087] In formula (11), p represents other nodes connected to node i, q represents other nodes connected to node j. When summing over all node pairs connected to nodes i and j, nodes i and j themselves need to be excluded. ε2 is the coupling strength coefficient of edge e ij , x i (t), x j (t) respectively represent the state variables of adjacent nodes i and j at time t of edge e ij . y il (t + 1) and y il (t) respectively represent the state variables of edge e ij at time t + 1 and time t; when y il (t + 1) ∈ [0, 1], it means the edge is in a stable state. When y il (t + 1) ∈ [1, ∞], it means the edge is in a failed state, that is, x i (t) > 1 or x j (t) > 1, then y il (t + 1) > 1, indicating that the edge has failed; M i and M j are the degrees of nodes i and l, N is the total number of nodes in the system network, and the gamma function F ip f[y ip (t)] and F jq f[y jq (t)] represent the functional coupling of traffic flow between adjacent edges of nodes i and l in the network.

[0088] Based on the same inventive concept as the above method embodiment, the embodiment of the present application also provides an application of a cascading failure model for mountain road networks under the influence of rainfall-induced landslides, dividing the entire application scenario into before and after the disaster:

[0089] Before the rainfall-induced landslide disaster: The cascading failure model of mountain road traffic infrastructure network nodes i and edge e ij is expressed as:

[0090]

[0091] In formulas (12) and (13), t0 represents the moment before the rainfall-induced landslide disaster, t0 + 1 and t0 represent the state variables of network node i and edge e ij before the disaster. The absolute value in the formula ensures the non-negativity of the state variables of nodes and edges;

[0092] After the occurrence of rainfall-induced landslide disasters: Regarding the rainfall-induced landslide disasters as external disturbances to the network, the nodes i and edges e of the mountain road traffic infrastructure network ij The cascading failure model is expressed as:

[0093]

[0094] In Formulas (14) and (15), t represents the state variables of nodes i and edges e in the network when the rainfall-induced landslide disaster occurs il The chaotic Logistic mapping functions f[y il (t - 1)] and f[x i (t - 1)] multiplied by [1 + exp(α + β i b)] indicate that the rainfall-induced landslide disaster will increase the failure probability of nodes and edges in the mountain road traffic network

[0095] When the variable x of node i i (t) > 1, it means that there will be more node failures in the network, and the edges connected to them will all be removed. The state variables of the removed nodes and edges will tend to infinity, and the traffic flows of these nodes and edges will also transfer to adjacent nodes and edges, increasing the traffic load of adjacent nodes and edges. Therefore, the state variable of edge e ij at the time of the disaster is determined by two factors. One is the traffic flow variables of adjacent edges e ip and e jq and the connected nodes i and j at time t - 1, and the other is the occurrence probability of the rainfall-induced landslide disaster

[0096] To sum up, through the above steps, finally, by using Formulas (12) to (15), the cascading failure process of the mountain road traffic infrastructure network under the influence of rainfall-induced landslide disasters can be simulated. 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 within the range of 0 to 1. When the rainfall-induced landslide disaster occurs, analyze the state variables of the road network nodes through Formula (14) to determine the failed nodes. After the disaster, the stable road network state transfers the traffic flow of the failed nodes to their adjacent nodes, and calculates the node failure process caused by the traffic flow through Formula (12), and repeats until all the network nodes fail

[0097] The operation process of 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 the rainfall-induced landslide disaster occurs, calculate the failed edges in the road network by using Formula (15). After the disaster, the stable road network state transfers the traffic flow of the failed edges to their adjacent edges, and calculates the state variables of the traffic flows of each edge through Formula (14) after the road network state is stable, and repeats until all the network edges fail

[0098] It should be noted that in this text, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "including one..." does not exclude the presence of additional identical elements in the process, method, article or device including said element.

[0099] The terms used in the embodiments of the present invention are for the purpose of describing specific embodiments only and are not intended to limit the present invention. The singular forms "a", "the" and "said" used in the embodiments of the present invention and the appended claims are also intended to include the plural forms unless the context clearly dictates otherwise.

[0100] It should be understood that the term "and / or" used herein is merely a description of the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " herein generally represents an "or" relationship between the associated objects before and after.

[0101] Depending on the context, the word "if" as used herein may be interpreted as "when", "while", "in response to determining", or "in response to detecting". Similarly, depending on the context, the phrase "if determined" or "if detecting (stated condition or event)" may be interpreted as "when determined", "in response to determining", "when detecting (stated condition or event)", or "in response to detecting (stated condition or event)".

[0102] The "first / second" mentioned in the embodiments is only to distinguish similar objects and does not represent a specific order for the objects. It can be understood that the "first / second" can be interchanged in a specific order or sequence when permitted. It should be understood that the objects distinguished by "first / second" can be interchanged under appropriate circumstances so that the embodiments described herein can be implemented in an order other than those illustrated or described herein.

[0103] 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 recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall 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: The steps include: S1. Establishment of rainfall-induced landslide database; S2, classification of rainfall-type landslide parameters; S3, rainfall-type landslide disturbance model calculation; S4. Analysis of disturbance volume in road traffic infrastructure network in mountainous areas with rainfall-induced landslide hazards; S5. Establishment of rainfall-induced landslide failure model.

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 is characterized in that: In step S1, based on NASA's global landslide hazard database, China Meteorological Data Network, and the Resource and Environmental Science and Data Center of the Chinese Academy of Sciences, a rainfall-type landslide hazard database is established according to the distribution characteristics of rainfall-type landslide hazards, regional climate characteristics, geological environment, and landslide scale.

3. The method for establishing a cascading failure model of a mountain road network under the influence of rainfall-induced landslide according to claim 1 is characterized in that: In step S2, based on the rainfall-induced landslide hazard database, the analytic hierarchy process and the determination coefficient method are used to determine the rainfall-induced landslide hazard factors, which are divided into five key rainfall-induced landslide inducing factors: terrain elevation, average annual rainfall, terrain structure, slope and lithology. Binary Logistic regression analysis is performed using SPSS software to determine the parameter values ​​of the rainfall-induced landslide inducing factors.

4. The method for establishing a cascading failure model of a mountain road network under the influence of rainfall-induced landslide according to claim 1 is characterized in that: In step S3, the specific steps include: The Logistic function is used to determine the disturbance index of rainfall-type 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 index: From formula (1), we can get: In formula (2) is the error term of the Logistics function, b m is the independent variable of the function; α is the regression intercept of the function, β m is the partial regression coefficient of the function, With the characteristics of the Logistics distribution, in order to calculate its cumulative distribution function, the function's variable is less than a specific value: The cumulative distribution function F in formula (3) is The Logistics distribution characteristics are the same as those of the two models, and both convert the input values ​​to between 0 and 1. i Logistics regression model with cumulative distribution function F: From formula (4), we can know that when Logistics regression model F i ∈[0, 1], where F i The cumulative distribution function characteristics of the model are used to describe the disturbance characteristics of rainfall-type landslide disasters. As the variables of rainfall-type landslide disaster induction factors increase, the probability of rainfall-type landslides approaching 1, indicating that rainfall-type landslide disasters are bound to occur. Its function expression is: In formula (5), P i is the rainfall-induced landslide hazard disturbance model, and the cumulative distribution function in the model is It is used to express the linear relationship of the factors inducing rainfall-type landslide disasters. α is the regression intercept of the function, which represents the logarithmic value of the ratio of the probability of rainfall-type landslide occurrence to non-occurrence. β m is the partial regression coefficient of the function, b m are the independent variables of the function, representing the inducing factors of rainfall-induced landslides, including terrain elevation (b1), average annual rainfall (b2), terrain structure (b3), slope (b4), and lithology (b5).

5. The method for establishing a cascading failure model of a mountain road network under the influence of rainfall-induced landslide according to claim 1 is characterized by: In step S4, the specific steps include: The rainfall-type landslide disaster model is used as the external disturbance in the mountain road traffic infrastructure network. In the initial network, the function of the disturbance of the midpoints and edges of the mountain road traffic infrastructure network is: In real scenarios, rainfall-induced landslide disasters will directly lead to road interruption. The external disturbance amount of the network midpoint and edge is equivalent to the rainfall-induced landslide disturbance model. The functional relationship of the external disturbance amount P in the mountainous road traffic infrastructure network is expressed as: Road interruption will lead to changes in traffic flow. The product of the traffic flow at the midpoint and edge of the road network and the external disturbance represents the impact of rainfall-type landslide disasters on the traffic volume in the mountain road traffic infrastructure network. By observing the changes in traffic flow in the network, we can intuitively feel the impact of rainfall-type landslides on the network: In formulas (8) and (9), x→Qx and y→Qy represent the evolution of the network from never being affected by rainfall-type landslide disaster to being affected by disaster, x and y represent the traffic state quantity of the network midpoint or edge, α is the regression intercept of the function, and β m is the partial regression coefficient of the function, b m is the independent variable of the function, representing the inducing factors of rainfall-induced landslides, including terrain elevation (b1), average annual rainfall (b2), terrain structure (b3), slope (b4), and lithology (b5), and Q is the intermediate variable.

6. The method for establishing a cascading failure model of a mountain road network under the influence of rainfall-induced landslide according to claim 1 is characterized by: In step S5, it specifically includes: By improving the integration of coupled mapping lattice theory and network percolation theory, a rainfall-induced landslide failure model is constructed; in the spatiotemporal variable discrete matrix function of the mountain road traffic infrastructure network, the state quantity of the failure model node i is: In formula (10), ε1 is the coupling strength coefficient of network node i, x i (t+1) and x i (t) represents the state of network node i at time t+1 and time t respectively. i (t+1)∈[0,1] indicates that the node is in a stable state. i (t+1)∈[1,∞] indicates that the node is in a failed state; M i is the degree of node i, N is the total number of network nodes, and the gamma function F ij f[x j (t)] represents the functional coupling of traffic flow between nodes i and l in the network; When a node fails, the connected edge will also fail; therefore, the state of the edge in the network depends not only on itself, but also on the two nodes connected to it. In the spatiotemporal variable discrete matrix function of the mountain road traffic infrastructure network, the failure model edge e ij The state quantity is expressed as: y il (t+1)=max In formula (11), p represents other nodes connected to node i, q represents other nodes connected to node j; ε2 is the edge e ij The coupling strength coefficient, x i (t),x j (t) respectively represent the edge e ij The state of adjacent nodes i and j at time t, y il (t+1) and y il (t) respectively represent the edge e ij The state quantity at time t+1 and time t; when y il (t+1)∈[0,1] indicates that the edge is in a stable state. il (t+1)∈[1,∞] indicates that the edge is in an invalid state, that is, x i (t)>1 or x j When (t)>1, then y il (t+1)>1, indicating edge failure; M i and M j is the degree of nodes i and l, N is the total number of system network nodes, and the gamma function F ip f[y ip (t)] and F jq f[y jq (t)] represents the functional coupling of traffic flow between adjacent edges of nodes i and l in the network.

7. An application of a failure model established by the method for establishing a cascading failure model of a mountain road network under the influence of a rainfall-induced landslide according to any one of claims 1 to 6, characterized in that: The entire application scenario is divided into pre-disaster and post-disaster: Before a rainfall-induced landslide disaster occurs: Node i and edge e of a mountain road traffic infrastructure network ij The cascading failure model is expressed as: In formula (12) and formula (13), t0 represents the time before the rainfall landslide disaster occurs, t0+1 and t0 represent the network node i and edge e before the disaster occurs. ij The absolute value in the formula is to ensure that the state quantities of nodes and edges are non-negative; After the rainfall-type landslide disaster occurs: Considering the rainfall-type landslide disaster as an external disturbance of the network, the node i and the edge e of the mountain road traffic infrastructure network ij The cascading failure model is expressed as: In formulas (14) and (15), t represents the relationship between node i and edge e in the network when a rainfall-type landslide disaster occurs. il The state quantity of the chaotic Logistic mapping function f[y il (t-1)] and f[x i (t-1)] and [1+exp(α+β i b)], indicating that rainfall-induced landslide disasters will increase the failure probability of nodes and edges in mountain road traffic networks; When the variable x of node i i (t)>1, which means that more nodes will fail in the network, and the edges connected to them will be removed. The state of the removed nodes and edges will tend to infinity, and the traffic flow of these nodes and edges will also be transferred to the adjacent nodes and edges, increasing the traffic load of the adjacent nodes and edges. Therefore, the edge e ij The state quantity when a disaster occurs is determined by two factors: the adjacent edge e ip and e jq The first is the traffic flow variable between the connected nodes i and j at time t-1, and the second is the probability of occurrence of rainfall-type landslide disasters.

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