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Aiming at the problem that the slope is easy to lose stability in the mining of ionic rare earth mines, and the traditional stability criterion method is difficult to quantify the uncertainty of dynamic multi-field coupling, a slope stability evaluation model based on game theory and cloud model was constructed. According to the four principles of uniqueness, purpose, feasibility and observability, a multi-dimensional evaluation index system covering geomechanical parameters, leaching process, slope geological conditions, hydrometeorological characteristics and regional geological characteristics was constructed. The game theory was used to optimize the subjective weight determined by the fuzzy analytic hierarchy process (FAHP) and the objective weight determined by the entropy weight method, so as to realize the collaborative weighting of subjective and objective weights. The cloud model was introduced to quantify the membership degree of slope stability, and the expectation, entropy and super entropy were used to characterize the random fuzziness of parameter values. An ionic rare earth mining area in southern Jiangxi was taken as an example for industrial application. The results show that the comprehensive stability scores of 1#, 2# and 3# slopes in the mining area are 74.8 (sub-unstable), 58.9 (relatively stable) and 99.3 (unstable), respectively, which are consistent with the actual observation results and the calculation results of the improved AHP method. Compared with the traditional limit equilibrium method, the potential risks can be found in advance. It is verified that the game theory-cloud model can provide reliable discriminant results and has high-risk sensitivity. The research results provide a theoretical basis for the dynamic control of slope stability of ionic rare earth mines.

, authors=Jianlong Liao, Hongjun Sun, Yi Wan, authorsList=Jianlong Liao, Hongjun Sun, Yi Wan, authorCompany=null, correspAuthors=Hongjun Sun, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1321866347320038215, articleId=1321866346808333125, tenantId=1146029695717560320, journalId=1225396423026438145, language=CN, title=基于博弈论云模型的离子型稀土矿原地浸出采场边坡稳定性评价, columnId=1226462295417598973, journalTitle=矿业研究与开发, columnName=矿山安全与环保, runingTitle=null, highlight=null, articleAbstract=

针对离子型稀土矿开采中边坡易失稳、传统稳定性判据方法难以量化动态多场耦合不确定性的难题,构建了基于博弈论与云模型的边坡稳定性评价模型。依据唯一性、目的性、可行性和可观测性4个原则,构建涵盖地质力学参数、浸矿工艺、边坡地质条件、水文气象特征及区域地质特征的多维度评价指标体系;采用博弈论优化融合模糊层次分析法(FAHP)确定的主观权重与熵权法确定的客观权重,实现主、客观权重的协同赋权;引入云模型量化边坡稳定性隶属度,利用期望、熵和超熵表征参数取值的随机模糊性。以赣南某离子型稀土矿区为例进行工业应用,结果表明:该矿区1#、2#、3#边坡综合稳定性评分分别为74.8(次不稳定)、58.9(较稳定)和99.3(不稳定),与现场实际观测结果和改进AHP法计算结果一致,较传统极限平衡法能提前发现潜在风险,验证了博弈论-云模型可得出可靠的判别结果且具有较高的风险敏感性。研究结果为离子型稀土矿边坡稳定性动态管控提供了理论依据。

, authors=廖健龙, 孙洪军, 万奕, authorsList=廖健龙, 孙洪军, 万奕, authorCompany=null, correspAuthors=孙洪军, authorNote=

廖健龙(1997—),男,广东河源人,硕士研究生,主要从事边坡稳定性相关研究工作。E-mail:

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孙洪军(1973—),男,辽宁阜新人,博士,教授,主要从事岩土工程相关教学与科研工作。E-mail:
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廖健龙(1997—),男,广东河源人,硕士研究生,主要从事边坡稳定性相关研究工作。E-mail:

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廖健龙(1997—),男,广东河源人,硕士研究生,主要从事边坡稳定性相关研究工作。E-mail:

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基于博弈论云模型的离子型稀土矿原地浸出采场边坡稳定性评价
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廖健龙 , 孙洪军 , 万奕
矿业研究与开发 | 矿山安全与环保 2026,46(5): 91-100
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矿业研究与开发 |矿山安全与环保 2026 , 46 (5) : 91 -100
基于博弈论云模型的离子型稀土矿原地浸出采场边坡稳定性评价
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廖健龙 , 孙洪军 , 万奕
作者信息
  • 辽宁工业大学 土木建筑工程学院,辽宁 锦州市 121001
通讯作者:
孙洪军(1973—),男,辽宁阜新人,博士,教授,主要从事岩土工程相关教学与科研工作。E-mail:
作者简介:

廖健龙(1997—),男,广东河源人,硕士研究生,主要从事边坡稳定性相关研究工作。E-mail:

Slope Stability Evaluation of In-Situ Leaching Stope for Ionic Rare Earth Mines Based on Game Theory-Cloud Model
Jianlong Liao , Hongjun Sun , Yi Wan
Affiliations
  • School of Civil and Architectural Engineering, Liaoning University of Technology, Jinzhou, Liaoning 121001, China
出版时间: 2026-05-25
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针对离子型稀土矿开采中边坡易失稳、传统稳定性判据方法难以量化动态多场耦合不确定性的难题,构建了基于博弈论与云模型的边坡稳定性评价模型。依据唯一性、目的性、可行性和可观测性4个原则,构建涵盖地质力学参数、浸矿工艺、边坡地质条件、水文气象特征及区域地质特征的多维度评价指标体系;采用博弈论优化融合模糊层次分析法(FAHP)确定的主观权重与熵权法确定的客观权重,实现主、客观权重的协同赋权;引入云模型量化边坡稳定性隶属度,利用期望、熵和超熵表征参数取值的随机模糊性。以赣南某离子型稀土矿区为例进行工业应用,结果表明:该矿区1#、2#、3#边坡综合稳定性评分分别为74.8(次不稳定)、58.9(较稳定)和99.3(不稳定),与现场实际观测结果和改进AHP法计算结果一致,较传统极限平衡法能提前发现潜在风险,验证了博弈论-云模型可得出可靠的判别结果且具有较高的风险敏感性。研究结果为离子型稀土矿边坡稳定性动态管控提供了理论依据。

离子型稀土矿  /  博弈论-云模型  /  多场耦合  /  指标权重  /  边坡稳定性

Aiming at the problem that the slope is easy to lose stability in the mining of ionic rare earth mines, and the traditional stability criterion method is difficult to quantify the uncertainty of dynamic multi-field coupling, a slope stability evaluation model based on game theory and cloud model was constructed. According to the four principles of uniqueness, purpose, feasibility and observability, a multi-dimensional evaluation index system covering geomechanical parameters, leaching process, slope geological conditions, hydrometeorological characteristics and regional geological characteristics was constructed. The game theory was used to optimize the subjective weight determined by the fuzzy analytic hierarchy process (FAHP) and the objective weight determined by the entropy weight method, so as to realize the collaborative weighting of subjective and objective weights. The cloud model was introduced to quantify the membership degree of slope stability, and the expectation, entropy and super entropy were used to characterize the random fuzziness of parameter values. An ionic rare earth mining area in southern Jiangxi was taken as an example for industrial application. The results show that the comprehensive stability scores of 1#, 2# and 3# slopes in the mining area are 74.8 (sub-unstable), 58.9 (relatively stable) and 99.3 (unstable), respectively, which are consistent with the actual observation results and the calculation results of the improved AHP method. Compared with the traditional limit equilibrium method, the potential risks can be found in advance. It is verified that the game theory-cloud model can provide reliable discriminant results and has high-risk sensitivity. The research results provide a theoretical basis for the dynamic control of slope stability of ionic rare earth mines.

Ionic rare earth mine  /  Game theory-cloud model  /  Multi-field coupling  /  Index weight  /  Slope stability
廖健龙, 孙洪军, 万奕. 基于博弈论云模型的离子型稀土矿原地浸出采场边坡稳定性评价. 矿业研究与开发, 2026 , 46 (5) : 91 -100 .
Jianlong Liao, Hongjun Sun, Yi Wan. Slope Stability Evaluation of In-Situ Leaching Stope for Ionic Rare Earth Mines Based on Game Theory-Cloud Model[J]. Mining Research and Development, 2026 , 46 (5) : 91 -100 .
  • 2022年辽宁省研究生联合培养示范基地项目(YJD202204)
  • 2023年辽宁省教育厅高等学校基本科研项目(JYTMS20230865)
  • 2024年辽宁省科技计划联合计划项目(2024011314-JH2/1026)
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  • 接收时间:2025-05-18
  • 首发时间:2026-10-27
  • 出版时间:2026-05-25
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  • 收稿日期:2025-05-18
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2022年辽宁省研究生联合培养示范基地项目(YJD202204)
2023年辽宁省教育厅高等学校基本科研项目(JYTMS20230865)
2024年辽宁省科技计划联合计划项目(2024011314-JH2/1026)
作者信息
    辽宁工业大学 土木建筑工程学院,辽宁 锦州市 121001

通讯作者:

孙洪军(1973—),男,辽宁阜新人,博士,教授,主要从事岩土工程相关教学与科研工作。E-mail:
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2种不同金属材料的力学参数
科
Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)
属
Genus
种数
Number of
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占总种数比例
Percentage of total
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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