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Keywords = cusp mutation theory

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28 pages, 7252 KB  
Article
Study on the Deformation Energy Evolution Characteristics and Instability Prediction Model of Weak Surrounding Rock in Tunnels
by Chuang Sun, Zhengyang Xu, Jianjun Zhang, Yunbo Pu, Qi Tao, Ye Zhou, Xibin Guan and Tianhao Liu
Appl. Sci. 2025, 15(19), 10478; https://doi.org/10.3390/app151910478 - 27 Sep 2025
Cited by 3 | Viewed by 806
Abstract
This study focuses on tunnel construction in fault fracture zones and systematically investigates the energy evolution and damage catastrophe mechanisms of surrounding rock during excavation, based on energy conservation principles and cusp catastrophe theory. A tunnel instability prediction and support optimization framework integrating [...] Read more.
This study focuses on tunnel construction in fault fracture zones and systematically investigates the energy evolution and damage catastrophe mechanisms of surrounding rock during excavation, based on energy conservation principles and cusp catastrophe theory. A tunnel instability prediction and support optimization framework integrating energy damage evolution and intelligent optimization algorithms was developed. Field tests, rock mechanics experiments, and Discrete Fracture Network (DFN) numerical simulations reveal the intrinsic relationships among energy input, dissipation, damage accumulation, and instability under complex geological conditions. Particle Swarm Optimization–Back Propagation (PSO-BP) is applied to optimize tunnel support parameters. Model performance is evaluated using the Mean Absolute Error (MAE), Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and R-squared (R2). The results show that upon reaching structural mutation zones, the system damage variable (ds), displacement, and dissipated energy increase abruptly, indicating critical instability. Numerical simulation and catastrophe feature analysis demonstrate that energy-related damage accumulation is effectively suppressed, the system damage variable decreases significantly, and crown stability is greatly enhanced. These findings provide a theoretical basis and practical reference for optimizing tunnel support design and controlling instability risks in complex geological settings. Full article
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26 pages, 6219 KB  
Article
A Multi-Method Approach to the Stability Evaluation of Excavated Slopes with Weak Interlayers: Insights from Catastrophe Theory and Energy Principles
by Tao Deng, Xin Pang, Jiwei Sun, Chengliang Zhang, Daochun Wan, Shaojun Zhang and Xiaoqiang Zhang
Appl. Sci. 2025, 15(13), 7304; https://doi.org/10.3390/app15137304 - 28 Jun 2025
Cited by 1 | Viewed by 935
Abstract
As open-pit mining extends to greater depths, slope stability is becoming a critical factor in ensuring safe production. This issue is particularly pronounced in geological settings with weak interlayers, where sudden slope failures are more likely to occur, demanding precise and reliable stability [...] Read more.
As open-pit mining extends to greater depths, slope stability is becoming a critical factor in ensuring safe production. This issue is particularly pronounced in geological settings with weak interlayers, where sudden slope failures are more likely to occur, demanding precise and reliable stability assessment methods. In this study, a typical open-pit slope with weak interlayers was investigated. Acoustic testing and ground-penetrating radar were employed to identify rock mass structural features and delineate loose zones, enabling detailed rock mass zoning and the development of numerical simulation models for stability analysis. The results indicate that (1) the slope exhibits poor overall integrity, dominated by blocky to fragmented structures with well-developed joints and significant weak interlayers, posing a severe threat to stability; (2) in the absence of support, the slope’s dissipated energy, displacement, and plastic zone volume all exceeded the failure threshold (Δ < 0), and the safety factor was only 0.962, indicating a near-failure state; after implementing support measures, the safety factor increased to 1.31, demonstrating a significant improvement in stability; (3) prior to excavation, the energy damage index (ds) in the 1195–1240 m platform zone reached 0.82, which dropped to 0.48 after reinforcement, confirming the effectiveness of support in reducing energy damage and enhancing slope stability; (4) field monitoring data of displacement and anchor rod forces further validated the stabilizing effect of the support system, providing strong assurance for safe mine operation. By integrating cusp catastrophe theory with energy-based analysis, this study establishes a comprehensive evaluation framework for slope stability under complex geological conditions, offering substantial practical value for deep open-pit mining projects. Full article
(This article belongs to the Special Issue Slope Stability and Earth Retaining Structures—2nd Edition)
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19 pages, 2724 KB  
Article
Extraction of Catastrophe Boundary and Evolution of Expressway Traffic Flow State
by Dayi Qu, Haomin Liu, Hui Song and Yiming Meng
Appl. Sci. 2022, 12(12), 6291; https://doi.org/10.3390/app12126291 - 20 Jun 2022
Cited by 6 | Viewed by 2785
Abstract
As the main road type in an urban traffic system, the increasingly severe congestion of the expressway restricts social and economic development. It is essential to explore the evolution law of congestion and dissipation to ensure the efficient operation of the expressway. In [...] Read more.
As the main road type in an urban traffic system, the increasingly severe congestion of the expressway restricts social and economic development. It is essential to explore the evolution law of congestion and dissipation to ensure the efficient operation of the expressway. In order to accurately grasp the evolution law of the expressway traffic flow state, this paper selects the expressway weaving section, which is a traffic flow frequency-changing area, to study the traffic operation state, change process, and evolution law, and determine the traffic state discrimination standard. The simulation analysis was carried out using the traffic simulation platform, Vissim software. The simulation results showed an apparent catastrophe phenomenon in the mutual transformation between free and congestion flow. The spectral clustering analysis algorithm was used to accurately extract the boundary of traffic state mutation, combined with the cusp catastrophe theory, to study and analyze the traffic flow state at different times and positions, thus completely displaying the evolution characteristics of traffic flow state. The research results provide an essential theoretical basis for formulating control measures of expressway traffic flow and strategies for traffic congestion dissipation. Full article
(This article belongs to the Section Transportation and Future Mobility)
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