A method for improving the resilience of a highway network in a strong earthquake mountainous area

Abstract

The application provides a strong earthquake mountain area highway network resilience improvement decision method, and relates to the technical field of road network disaster prevention. The method comprises the following steps: constructing a road network topology model based on road network data; the road network topology model describes the connection relationship of the road network through an adjacency matrix; fitting and modeling the regional historical seismic ground motion data to obtain a seismic ground motion intensity probability distribution model; determining the vulnerability quantification index of each road section based on the road network topology model and the seismic ground motion intensity probability distribution model; determining the connectivity of each key node in the road network topology model based on the vulnerability quantification index of each road section to obtain a road network connectivity reliability index; constructing a comprehensive resilience index based on the vulnerability quantification index and the road network connectivity reliability index; and using the comprehensive resilience index to generate a resilience improvement decision scheme. The method can improve the accuracy of the seismic resilience of the mountain area highway network by constructing a coupling analysis framework of the road network topology model and the seismic probability model.

Description

Technical Field

[0001] This application relates to the field of road network disaster prevention technology, specifically to a decision-making method for improving the resilience of mountain road networks in strong earthquake-prone mountainous areas. Background Technology

[0002] Due to their unique geological structure and topography, mountainous areas prone to earthquakes are frequently affected by seismic activity, which can easily trigger geological disasters such as landslides, mudslides, and debris flows. This often leads to multiple and scattered road network disruptions. Although some road sections may be interrupted due to localized damage, the impact on the overall road network connectivity is limited because of redundant paths or non-critical locations. However, if a few critical road sections carrying the main traffic flow are interrupted, they may directly sever the connection between multiple sub-road networks, leading to the paralysis of the entire road network.

[0003] In extreme scenarios of post-disaster rescue and relief, on the one hand, the stringent time requirements of the golden rescue window necessitate efficient and precise decision-making; on the other hand, the limitations of post-earthquake resource allocation require controllable and effective decisions regarding road clearing and maintenance. Therefore, under the dual constraints of limited time and controllable costs, how to maximize the overall connectivity and resilience of the road network, especially in extreme scenarios such as rescue and relief, has become a critical issue that urgently needs to be addressed. Existing technologies have limited research on road network resilience, and most studies focus on isolated points within the road network, neglecting the impact of single-point road damage on network connectivity. They fail to fully consider the influence of a single point's location within the road network topology on overall connectivity, leading to unreasonable allocation of treatment resources and hindering the maximization of road network resilience.

[0004] Therefore, there is an urgent need in the existing technology for a decision-making method for improving the resilience of road networks in strong earthquake zones based on road network reliability, so as to achieve the accuracy of reinforcement resource allocation and improve the reliability of regional road network connectivity. Summary of the Invention

[0005] This application provides a decision-making method for improving the resilience of mountain road networks in strong earthquake-prone areas. By constructing a coupled analysis framework of road network topology model and ground motion probability model, the accuracy of the seismic resilience of mountain road networks can be improved.

[0006] In a first aspect, the present invention provides a decision-making method for improving the resilience of a highway network in mountainous areas prone to strong earthquakes, which may include: constructing a highway network topology model based on highway network data; the highway network topology model describes the connection relationship of the highway network through an adjacency matrix, the nodes of the highway network topology model are key nodes of the highway network, and the edges of the highway network topology model are road segments of the highway network; fitting and modeling historical seismic ground motion data in the region to obtain a seismic ground motion intensity probability distribution model; determining the vulnerability quantification index of each road segment based on the highway network topology model and the seismic ground motion intensity probability distribution model; determining the connectivity of each key node in the highway network topology model based on the vulnerability quantification index of each road segment to obtain a highway network connectivity reliability index; constructing a comprehensive resilience index based on the vulnerability quantification index and the highway network connectivity reliability index; and using the comprehensive resilience index to generate a resilience improvement decision scheme.

[0007] According to one embodiment of the present invention, the step of fitting and modeling historical ground motion data of a region to obtain a probability distribution model of ground motion intensity includes: fitting the historical ground motion data of the region based on extreme value distribution to determine location parameters and scale parameters that match the historical ground motion data of the region; wherein, the location parameters characterize the baseline level of ground motion intensity in the region, and the scale parameters characterize the fluctuation range of ground motion intensity; constructing a probability density function of the probability distribution model of ground motion intensity based on the location parameters and the scale parameters, wherein the probability density function is used to characterize the distribution characteristics of ground motion intensity.

[0008] According to one embodiment of the present invention, the step of fitting the historical ground motion data of the region based on the extreme value distribution to determine the location parameters and scale parameters that match the historical ground motion data of the region includes: fitting the historical ground motion data of the region based on the extreme value type I distribution to determine the location parameters and scale parameters that match the historical ground motion data of the region.

[0009] According to one embodiment of the present invention, the vulnerability quantification index includes the strong earthquake impact intensity and the road network vulnerability index; the step of determining the vulnerability quantification index of each road segment based on the road network topology model and the seismic motion intensity probability distribution model includes: for each road segment in the road network topology model, determining the strong earthquake impact intensity based on the road network topology model and the seismic motion intensity probability distribution model; and determining the road network vulnerability index based on the disaster resistance performance coefficient of the road segment and the strong earthquake impact intensity.

[0010] According to one embodiment of the present invention, the determination of the connectivity of each key node in the road network topology model based on the vulnerability quantification index of each road segment to obtain the road network connectivity reliability index includes: randomly generating a set of scenarios of road segment failure under earthquake action through a simulation algorithm, and calculating the connectivity of the highway network in the road network topology model based on the inclusion-exclusion principle; and determining the road network connectivity reliability index based on the connectivity of the highway network.

[0011] According to one embodiment of the present invention, the step of calculating the connectivity of the highway network in the road network topology model includes: enumerating all feasible paths between node pairs, independently calculating the connectivity probability for each path to obtain the connectivity between node pairs; and determining the connectivity of the highway network based on the connectivity between all node pairs.

[0012] According to one embodiment of the present invention, the connectivity probability of each path is determined by the reliability of the bridge, the reliability of the tunnel, and the reliability of the roadbed section.

[0013] According to one embodiment of the present invention, determining the road network connectivity reliability index based on the connectivity of the road network includes: determining the road network connectivity reliability index based on the ratio of the minimum time required to repair disconnected nodes to the minimum time required for the overall road network to be connected, and the connectivity of the road network.

[0014] According to one embodiment of the present invention, the step of constructing a comprehensive resilience index based on the vulnerability quantification index and the road network connectivity reliability index includes: normalizing the vulnerability quantification index and the road network connectivity reliability index; determining the weights of the normalized vulnerability quantification index and the road network connectivity reliability index based on the analytic hierarchy process (AHP); and constructing a comprehensive resilience index that includes the normalized reliability index and the average vulnerability index.

[0015] According to one embodiment of the present invention, the method further includes: based on the ranking results of the comprehensive resilience index, locating road segments that are both vulnerable and have an impact on overall connectivity; using an orthogonal enumeration method under the dual constraints of time and cost, calculating the improvement effect of different reinforcement schemes on the comprehensive resilience index, establishing a marginal benefit evaluation model of unit resource input and resilience gain, and determining the target road segments that should be given priority for resilience improvement treatment, wherein the target road segments are the road segments that can bring the greatest global benefits.

[0016] Compared with existing technologies, the beneficial effects of this application are: by constructing a coupled analysis framework of road network topology model and seismic motion probability model, the accuracy of seismic resilience of mountainous highway networks is improved. Specifically, firstly, the actual road network can be abstracted into a node-edge topology structure, and the connection relationships can be quantified through an adjacency matrix. Secondly, by fitting historical earthquake data based on extreme value distribution, a probabilistic model reflecting regional seismic risk can be established. Finally, by integrating road segment vulnerability indicators and network reliability indicators, a comprehensive resilience index can be constructed, which can generate decision-making schemes for prioritizing the reinforcement of highly vulnerable critical road segments, ensuring that limited resources are maximized to improve the overall seismic resistance of the road network. Attached Figure Description

[0017] Figure 1 A schematic diagram illustrating the steps of the decision-making method for improving the resilience of mountain road networks in strong earthquake-prone areas, provided in an embodiment of this application.

[0018] Figure 2 This is a schematic diagram of the road network topology model provided in the embodiments of this application.

[0019] Figure 3 This is a schematic diagram showing the improvement in road network resilience under different reinforcement schemes provided in the embodiments of this application. Detailed Implementation

[0020] The present application will now be described in further detail with reference to experimental examples and specific embodiments. However, this should not be construed as limiting the scope of the subject matter of the present application to the following embodiments. All technologies implemented based on the content of the present application fall within the scope of protection of the present application.

[0021] Unless otherwise specified, the terms "upper," "lower," "left," "right," "center," "inner," "outer," and "side" used in the description of specific embodiments of this application to indicate orientation or positional relationships are based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is usually placed during use. These terms are merely for the purpose of facilitating the description of the solution in this application or simplifying the description in specific embodiments, so as to enable those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on this application.

[0022] In the description of the embodiments of this application, technical terms such as "first" and "second" only distinguish one entity or operation from another, and should not be construed as indicating or implying relative importance or implicitly specifying the number, specific order, or primary or secondary relationship of the indicated technical features. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly defined.

[0023] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0024] Please refer to Figure 1 , Figure 1 A schematic diagram illustrating the steps of the earthquake-prone mountain road network resilience enhancement decision-making method provided in this application embodiment. The method includes the following steps:

[0025] S1. Construct a road network topology model based on road network data.

[0026] The road network data collection includes node data (such as important towns, key intersections, and bridges) and road attribute data (such as road grade and design standards), spatial coordinates, length, and design seismic resistance level of road segments in the strong earthquake zone, as well as historical strong earthquake records (magnitude, focal depth, and damage range) and site conditions (such as topography, geological structure, and soil type). By identifying road networks that may be unstable due to earthquakes and affect road traffic, a road network topology model is constructed based on graph theory. Specifically, the process of constructing the road network topology model based on graph theory involves abstracting key nodes such as intersections and hubs in the highway network as vertices in graph theory, and abstracting the road segments connecting these nodes as edges. Each edge can be assigned a weight attribute to characterize features such as the physical length, travel time, capacity, or reliability of the road segment. By transforming the complex geographical road network into a mathematical graph structure composed of vertex and edge sets, methods such as connectivity analysis, shortest path algorithms, and network flow theory in graph theory can be applied to quantitatively study the performance of the road network under disasters such as earthquakes.

[0027] Please refer to Figure 2 , Figure 2 This is a schematic diagram of a road network topology model provided in an embodiment of this application. The road network topology model describes the road network connections using an adjacency matrix. The starting point of the road network topology model can represent a rescue force assembly point or a material supply center, such as an earthquake command center, emergency material warehouse, or the location of a major medical institution; the ending point corresponds to a disaster-stricken area or a key node requiring guaranteed passage, such as a densely populated area, an important infrastructure site, or an access point to an isolated village. The nodes of the road network topology model are key nodes of the highway network, and the edges of the road network topology model are road segments of the highway network.

[0028] S2. Fit and model the historical ground motion data of the region to obtain the probability distribution model of ground motion intensity.

[0029] In this embodiment of the application, the regional historical ground motion data may include peak ground acceleration (PGA) data recorded by seismic stations over the past 30 years.

[0030] Optionally, S2 can be implemented by: fitting historical ground motion data of the region based on extreme value distribution to determine location parameters and scale parameters that match the historical ground motion data of the region; and constructing a probability density function of the ground motion intensity probability distribution model based on the location parameters and the scale parameters, wherein the probability density function is used to characterize the distribution characteristics of ground motion intensity.

[0031] The process of fitting based on extreme value distribution involves using extreme value theory to perform statistical analysis on historical ground motion data, and using statistical methods such as maximum likelihood estimation or moment estimation to back-calculate location parameters and scale parameters from the historical ground motion data. The location parameters determine the central location of the distribution and characterize the baseline level of regional ground motion intensity, while the scale parameters control the dispersion of the distribution and characterize the fluctuation range of ground motion intensity.

[0032] Optionally, extreme value type I, extreme value type II, extreme value type III, etc., can be used to fit the historical ground motion data of the region to determine the location parameters and scale parameters that match the historical ground motion data of the region. This application embodiment uses the extreme value type I distribution as an example for illustration. Using the extreme value type I distribution to fit the historical ground motion data of the region, a ground motion intensity probability distribution model is established, and its probability density function is:

[0033]

[0034] in, For PGA value, For position parameters, Let be the scale parameter, and exp represent the natural exponential function. The physical meaning of the probability density function is that, for any given seismic ground motion intensity 'a', its probability density value can be calculated using this function. Specifically, when assessing the risk of strong earthquake events, the probability value corresponding to PGA ≥ 0.15g can be calculated by integration. This probability mass corresponds to hazard events with seismic intensity VII or higher. By systematically varying the value of 'a' and calculating the corresponding probability density, an earthquake hazard curve reflecting the relationship between seismic ground motion intensity and exceedance probability can be plotted.

[0035] The resulting probability density function reflects the overall statistical regularity of ground motion intensity in the region and predicts the probability of future extreme earthquake events. While establishing the ground motion intensity probability distribution model, the model fit is verified to ensure consistency between the fitted distribution and actual ground motion data. Earthquake hazard curves are plotted by considering earthquake events with intensity VII and above (corresponding to PGA ≥ 0.15g).

[0036] At the quantitative parameter level, the peak ground acceleration (PGA) range corresponding to intensity VII is 0.15g-0.30g (1g=9.8m / s²), where 0.15g is the lower limit threshold of intensity VII, which is also the technical basis for this application to emphasize PGA≥0.15g.

[0037] S3. Based on the road network topology model and the ground motion intensity probability distribution model, determine the vulnerability quantification index of each road segment.

[0038] In some embodiments, the vulnerability quantification index may include the intensity of strong earthquake impact and the road network vulnerability index, and step S3 may specifically include:

[0039] For each road segment in the road network topology model, the intensity of the strong earthquake impact is determined based on the road network topology model and the earthquake motion intensity probability distribution model; the road network vulnerability index is determined based on the disaster resistance performance coefficient of the road segment and the intensity of the strong earthquake impact.

[0040] In this embodiment of the application, the intensity of the strong earthquake impact By integrating three key seismic parameters—magnitude, focal distance, and site liquefaction potential—a single index can be derived using empirical formulas to determine the intensity of strong earthquake impacts on various road sections and quantify the overall intensity of seismic action on specific road segments. For example, lower-grade roads near active faults will exhibit higher seismic activity during strong earthquakes. value.

[0041] After determining the intensity of the strong earthquake's impact, a disaster resistance performance coefficient (k) is determined based on the road segment's seismic resistance level. This coefficient, k, is determined by the road segment's seismic resistance level and essentially reflects the road structure's inherent resilience. This coefficient translates design standards into mathematical parameters; for example, bridges and tunnels designed with higher seismic resistance levels correspond to larger k values. k and... The product of these terms forms the power term of the exponential function, and its magnitude directly determines the steepness of the fragility curve.

[0042] After obtaining the intensity of the strong earthquake impact and the disaster resistance coefficient, the road network vulnerability index can be determined based on the expression for the road network vulnerability index. The expression for the road network vulnerability index is as follows:

[0043]

[0044] in, The index represents the vulnerability of the road network, and k represents the disaster resistance coefficient. The intensity is affected by strong earthquakes. (The relationship between k and...) When the product is small, The vulnerability index grows approximately linearly; as the seismic load intensifies, Va gradually approaches 1, indicating complete road section damage. This nonlinear relationship accurately simulates the seismic performance characteristics of highway networks. Specifically, under low-intensity seismic action (corresponding to the "minor earthquake" condition), the vulnerability index shows a slow increasing trend, reflecting the design state where the structure remains intact. When a moderate-intensity earthquake occurs (corresponding to the "moderate earthquake" condition), the slope of the index curve increases, simulating the structure entering a repairable damage stage. When encountering a strong earthquake (corresponding to the "major earthquake" condition), the function value asymptotically approaches 1 but never reaches it, precisely reflecting the safety baseline of avoiding overall collapse despite severe structural damage. Through this index, the performance differences of road sections with different seismic resistance levels under the same seismic load can be quantitatively compared.

[0045] S4. Based on the vulnerability quantification index of each road segment, determine the connectivity of each key node in the road network topology model to obtain the road network connectivity reliability index.

[0046] In some embodiments, step S4 may specifically include:

[0047] A set of scenarios of road segment failure under earthquake action is randomly generated by simulation algorithm, and the connectivity of the highway network in the road network topology model is calculated based on the inclusion-exclusion principle; the road network connectivity reliability index is determined based on the connectivity of the highway network.

[0048] For example, Monte Carlo simulation can be used to calculate the connectivity between nodes. The specific implementation process of Monte Carlo simulation includes:

[0049] First, random scenario generation is performed. Based on the seismic intensity probability distribution model and road segment vulnerability index, a random number generator simulates the failure states of each road segment. Each simulation is equivalent to a virtual earthquake test, where whether each road segment fails depends on its corresponding failure probability value—a uniformly distributed random number in the interval [0,1] is generated. If this number is less than the road segment failure probability, the road segment is considered failed; otherwise, it remains intact. A large number of earthquake scenarios are generated independently and repeatedly to ensure coverage of various possible disaster combinations. Second, connectivity is determined. For each scenario generated in simulation, a breadth-first search or depth-first search algorithm from graph theory is used to check whether there is at least one intact path between the specified start and end points. If it exists, the simulation is recorded as successful; otherwise, it is recorded as a failure. This step transforms the complex probability problem into a discrete graph connectivity judgment problem, achieving fast state detection through an efficient graph traversal algorithm. Finally, probability convergence calculation is performed. The number of successful connections in all simulations is counted. When the number of simulations is large enough, the ratio of the number of successful connections to the total number of connections will converge to the theoretical connectivity probability. According to the law of large numbers, tens of thousands of simulations are typically required to stabilize the results within an acceptable error range. The final connectivity probability value comprehensively reflects the randomness of earthquake risk and the complexity of network topology, providing quantitative input for subsequent resilience assessment.

[0050] Furthermore, the methods for calculating the connectivity of the highway network in the road network topology model based on the inclusion-exclusion principle include:

[0051] All feasible paths between node pairs are enumerated, and the connectivity probability of each path is calculated independently to obtain the connectivity between node pairs; the connectivity of the highway network is determined based on the connectivity between all node pairs.

[0052] The connectivity probability of each path is determined by the reliability of bridges, tunnels, and roadbed sections. The expression for the connectivity of the highway network is as follows:

[0053]

[0054]

[0055] Where P(s,t) represents the connectivity of the road network, k represents all passable paths in the road network, i1, i2...ik are the path numbers of the passable paths, and Pij represents the connectivity of the ij-th passable path. For bridge reliability, For tunnel reliability, denoted as denoted as , where n is the reliability coefficient of the roadbed section.

[0056] Furthermore, determining the road network connectivity reliability index based on the connectivity of the road network can specifically include: determining the road network connectivity reliability index based on the ratio of the minimum time required to repair disconnected nodes to the minimum time required for the overall road network to be connected, and the connectivity of the road network.

[0057] Based on historical earthquake data and road attribute data, probabilistic statistical methods and structural mechanics analysis methods are used to calculate the probability of damage to each road segment under different earthquake intensities, thereby obtaining the road segment reliability. By analyzing the damage situation of road segments with similar attributes in historical earthquakes, a relationship model between the probability of road segment damage and earthquake intensity and road attributes is established. Then, based on the earthquake intensity that may be encountered in strong earthquake zones, the probability of damage to each road segment is calculated.

[0058]

[0059] Where R represents the reliability of passage. The minimum time required to repair a disconnected node. The minimum time required for the overall road network to be operational is defined as the required timeframe. Traffic reliability R characterizes the overall guarantee of maintaining effective connectivity of the road network while considering the timeliness of emergency repairs. This assessment method expands structural reliability from a binary judgment of whether or not it has failed to a continuous assessment of the duration of failure. It reflects the functional value differences of different road segments during emergency phases through time thresholds and provides a quantitative basis for prioritizing the allocation of emergency repair resources.

[0060] S5. Construct a comprehensive resilience index based on the vulnerability quantification index and the road network connectivity reliability index.

[0061] In this embodiment, the comprehensive resilience index is used to generate a resilience improvement decision scheme. Step S5 may specifically include: normalizing the vulnerability quantification index and the road network connectivity reliability index; determining the weights of the normalized vulnerability quantification index and the road network connectivity reliability index based on the analytic hierarchy process, and constructing a comprehensive resilience index that includes the normalized reliability index and the average vulnerability index.

[0062] The normalization preprocessing involves normalizing the road network vulnerability and reliability indices to the [0, 1] interval. The weights of the normalized vulnerability quantification index and the road network connectivity reliability index can be determined using the analytic hierarchy process (AHP). This can be achieved by constructing a judgment matrix to quantify the relative importance of each index. In practice, this can be done by pairwise comparisons between the two criteria layers of "disaster resistance" and "network function" based on the work of earthquake experts, traffic planners, and emergency management personnel, to determine the reliability weight α and vulnerability weight β.

[0063] The comprehensive resilience index is formed through algebraic combination. The expression for the comprehensive resilience index, constructed from the reliability weight α and the fragility weight β, is as follows:

[0064] Where A is the normalized reliability index and B is the average fragility index. It emphasizes the positive contribution of high-reliability road sections to system resilience. This approach emphasizes the negative impact of highly vulnerable road sections. The asymmetric approach, which directly weights reliability and then compensates for vulnerability, makes the index more sensitive to changes in network connectivity, aligning with the core requirement of ensuring smooth traffic flow in emergency situations. When the Z-value is close to 1, it indicates that the road network possesses both high reliability and low vulnerability; when Z approaches 0, the early warning system faces significant risks. This index dynamically couples structural performance and network function through weighted analysis, avoiding the limitations of isolated evaluations and ensuring a linear correlation between index changes and actual engineering needs. Resilience enhancement schemes generated based on this index can accurately identify combinations of highly vulnerable and low-reliability road sections that contribute the least to the Z-value, providing a quantitative basis for the optimal allocation of limited resources.

[0065] Furthermore, this application embodiment also provides a step for generating a resilience improvement decision scheme for a mountainous road network based on a comprehensive resilience index. Specifically, it may include: locating road segments that are both vulnerable and have an impact on overall connectivity based on the ranking results of the comprehensive resilience index; calculating the improvement effect of different reinforcement schemes on the comprehensive resilience index using an orthogonal enumeration method under the dual constraints of time and cost; establishing a marginal benefit evaluation model of unit resource input and resilience gain; and determining the target road segments that should be given priority for resilience improvement treatment, wherein the target road segments are those that can bring the greatest global benefits.

[0066] For example, the location of critical road segments is obtained based on the multidimensional ranking results of the comprehensive resilience index. Pareto front analysis can be used to identify critical paths with insufficient structural disaster resistance and significant impact on network topology. The intersection of these two methods forms a set of highly vulnerable and high-impact road segments. These segments typically exhibit characteristics such as seismic resistance levels below the regional fortification standard, location in network cut sets, and lack of effective alternative paths. For instance, if a low-grade bridge in a mountainous area connects two seismically isolated islands, its failure will lead to road network fragmentation, thus constituting a typical intervention target.

[0067] The implementation process of the orthogonal enumeration optimization algorithm includes: establishing a decision variable space, discretizing the reinforcement intensity of each road segment into several selectable levels (such as light / medium / full reinforcement) to form a multi-dimensional combination scheme; constructing an objective function, using "comprehensive resilience index improvement / (cost × time)" as the optimization index to ensure that the evaluation criteria take into account both effectiveness and efficiency; and finally, using orthogonal experimental design to reduce the amount of computation, and deriving the global approximate optimal solution through the simulation results of some representative combinations.

[0068] Marginal benefit assessment models can quantify the differences in reinforcement benefits among different road sections by calculating the increase in resilience index per unit of resource input, thereby enabling dynamic adjustment of resource allocation strategies. For example, priority can be given to road sections with the highest marginal benefits, and once their reliability reaches a threshold, the remaining resources can be automatically redirected to suboptimal targets. This adaptive mechanism can maximize the overall resilience improvement under total budget constraints. For instance, if a tunnel reinforcement investment of 10,000 yuan can increase the Z-value by 0.15, while a roadbed section can only increase it by 0.02, then the tunnel project will be prioritized.

[0069] Once the basic reliability standard is met, reinforcement of that section is stopped, and a reinforcement plan is derived. Simultaneously, the optimal decision plan is calculated and output using road network status, reinforcement intensity, and resource allocation as indicators, with the goal of maximizing the overall ratio of resilience index improvement to cost and repair time. Please refer to [link / reference]. Figure 3 , Figure 3 This is a schematic diagram showing the improvement in road network resilience under different reinforcement schemes provided in the embodiments of this application.

[0070] This line graph visually compares the performance of three different toughness enhancement schemes over time. The horizontal axis represents the complete cycle from initial to final standardized time, while the vertical axis uses a logarithmic scale to display the toughness enhancement value. This coordinate choice facilitates the observation of performance differences across different orders of magnitude. The blue curve for Scheme 3 consistently remains at the highest position, indicating that its toughness enhancement effect is superior to other schemes at all time points, especially maintaining a significant advantage in the mid-to-late stages. The green curve for Scheme 2 is generally at a mid-level, while the red curve for Scheme 1 shows relatively weak performance with the smallest enhancement. The differences between the curves of each scheme are mainly reflected in the enhancement magnitude and sustainability: Scheme 3 not only has a rapid initial enhancement rate but also maintains a high level in the mid-to-late stages; Scheme 2 performs well initially but shows weak subsequent growth; Scheme 1 shows relatively limited overall enhancement. This comparative result demonstrates that Scheme 3 has significant technical advantages over traditional methods and can provide more scientific guidance for the seismic reinforcement of mountain road networks in strong earthquake-prone areas.

[0071] In the decision-making method for improving the resilience of mountain highway networks in strong earthquake-prone areas provided in this application, the accuracy of the seismic resilience of mountain highway networks is improved by constructing a coupled analysis framework of a road network topology model and a seismic motion probability model. Firstly, the actual road network can be abstracted into a node-edge topology structure, and the connection relationships can be quantified through an adjacency matrix. Secondly, historical earthquake data can be fitted based on extreme value distribution to establish a probabilistic model reflecting regional earthquake risk. Finally, by integrating road segment vulnerability indicators and network reliability indicators, a comprehensive resilience index is constructed, which can generate a decision scheme for prioritizing the reinforcement of highly vulnerable key road segments, ensuring that limited resources are maximized to improve the overall seismic resistance of the road network.

[0072] Based on the same concept, embodiments of this application also provide a computer device, which may include a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the methods described above.

[0073] Based on the same concept, embodiments of this application also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the methods described above.

[0074] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for improving the resilience of a highway network in a strong earthquake mountainous area, characterized in that, The method comprises the following steps: constructing a road network topology model based on road network data; the road network topology model describes the connection relationship of the road network through an adjacency matrix, the nodes of the road network topology model are key nodes of the highway network, and the edges of the road network topology model are road sections of the highway network; fitting and modeling regional historical ground motion data to obtain a ground motion intensity probability distribution model; determining a vulnerability quantization index of each road section based on the road network topology model and the ground motion intensity probability distribution model; determining the connectivity of each key node in the road network topology model based on the vulnerability quantization index of each road section to obtain a road network connectivity reliability index; constructing a comprehensive resilience index based on the vulnerability quantization index and the road network connectivity reliability index; the comprehensive resilience index is used to generate a resilience improvement decision scheme; wherein the determination of the connectivity of each key node in the road network topology model based on the vulnerability quantization index of each road section to obtain the road network connectivity reliability index comprises: randomly generating a set of road section failure scenarios under the action of an earthquake through a simulation algorithm, and calculating the connectivity of the highway network in the road network topology model based on the inclusion-exclusion principle; determining the road network connectivity reliability index based on the connectivity of the highway network. wherein the determination of the road network connectivity reliability index based on the connectivity of the highway network comprises: determining the road network connectivity reliability index based on the ratio of the minimum time required for repairing a disconnected node to the minimum time required for the overall road network to be connected, and the connectivity of the highway network. The road network connectivity reliability index comprises a traffic reliability index, and the calculation method of the traffic reliability index comprises: Wherein, Pij is the connectivity of the ithjth connected path, R is the traffic reliability, The minimum time required for disconnecting node repair, The minimum time required for requiring the overall road network to be connected.

2. The method of claim 1, wherein, The fitting and modeling of the regional historical ground motion data to obtain the ground motion intensity probability distribution model comprises: fitting the regional historical ground motion data based on an extreme value distribution to determine a location parameter and a scale parameter that are consistent with the regional historical ground motion data; wherein the location parameter represents a reference level of regional ground motion intensity, and the scale parameter represents a fluctuation range of ground motion intensity; constructing a probability density function of the ground motion intensity probability distribution model based on the location parameter and the scale parameter, the probability density function being used to represent the distribution characteristics of ground motion intensity.

3. The method of claim 2, wherein, The fitting of the regional historical ground motion data based on an extreme value distribution to determine a location parameter and a scale parameter that are consistent with the regional historical ground motion data comprises: fitting the regional historical ground motion data based on an extreme value type I distribution to determine a location parameter and a scale parameter that are consistent with the regional historical ground motion data.

4. The method of claim 1, wherein, The vulnerability quantization index comprises a strong earthquake influence intensity and a road network vulnerability index. The determination of the vulnerability quantization index of each road section based on the road network topology model and the ground motion intensity probability distribution model comprises: for each road section in the road network topology model, determining the strong earthquake influence intensity based on the road network topology model and the ground motion intensity probability distribution model; determining the road network vulnerability index based on the disaster resistance performance coefficient of the road section and the strong earthquake influence intensity.

5. The method of claim 1, wherein, The step of calculating the connectivity of the highway network in the road network topology model comprises: enumerating all feasible paths between node pairs, independently calculating the connectivity probability for each path, and obtaining the connectivity between node pairs; determining the connectivity of the road network based on the connectivity between all node pairs.

6. The method of claim 5, wherein the method further comprises: The connectivity probability of each path is determined by the bridge reliability, the tunnel reliability, and the subgrade section reliability.

7. The method of claim 1, wherein, The method further comprises: normalizing the vulnerability quantification index and the road network connectivity reliability index; determining the weights of the normalized vulnerability quantification index and the road network connectivity reliability index based on the analytic hierarchy process, and constructing a comprehensive resilience index containing the normalized reliability index and the average vulnerability index.

8. The method of claim 1-7, wherein, The method further comprises: locating the road sections that have both vulnerability and influence on the overall connectivity based on the ranking result of the comprehensive resilience index; under the double constraints of time and cost, calculating the promotion effect of different reinforcement schemes on the comprehensive resilience index by using the orthogonal enumeration method, establishing a marginal benefit evaluation model of unit resource investment and resilience gain, and determining the target road section for which the resilience improvement processing should be prioritized, the target road section being the road section that can bring the maximum global benefit.

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