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Article(id=1236276117435380365, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1236276104999268557, articleNumber=null, orderNo=null, doi=10.3969/j.issn.0253-6099.2025.04.009, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1737648000000, receivedDateStr=2025-01-24, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1772680795296, onlineDateStr=2026-03-05, pubDate=1753977600000, pubDateStr=2025-08-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1772680795296, onlineIssueDateStr=2026-03-05, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1772680795296, creator=13701087609, updateTime=1772680795296, updator=13701087609, issue=Issue{id=1236276104999268557, tenantId=1146029695717560320, journalId=1235980550691926019, year='2025', volume='45', issue='4', pageStart='1', pageEnd='200', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1772680792331, creator=13701087609, updateTime=1772681498687, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1236279067746562719, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1236276104999268557, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1236279067746562720, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1236276104999268557, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=52, endPage=57, ext={EN=ArticleExt(id=1236276118710448812, articleId=1236276117435380365, tenantId=1146029695717560320, journalId=1235980550691926019, language=EN, title=Optimization of Mining Methods for Gently Inclined Phosphate Ore Body Based on Improved AHP-TOPSIS Model, columnId=1236276106018484431, journalTitle=Mining and Metallurgical Engineering, columnName=MINING, runingTitle=null, highlight=null, articleAbstract=

In order to solve the problems of fuzziness, randomness and uncertainty in optimization of mining method by traditional analytic hierarchy process (AHP), some measures, including introducing fuzzy theory, optimizing judgment scale and constructing optimal transfer matrix, were introduced to reduce subjective deviation and enhance the processing ability of uncertain information. Then, based on the combination of improved analytic hierarchy process (AHP) with the technique for order preference by similarity to ideal solution (TOPSIS), a comprehensive evaluation system with multi-level, multi-factor, multi-objective and multi-index characteristics was constructed and applied to the optimization of mining methods for a gently-inclined medium-thick phosphate ore body. The analysis shows that the relative closeness coefficients of those three mining schemes are 0.177 9, 0.822 5 and 0.648 3, respectively. Scheme 2, namely sublevel open stoping with subsequent backfill, is primarily determined as the suitable mining method for the mine. The numerical simulation of Scheme 2 also shows that the maximum surface subsidence in this scheme can be controlled within 72.94 mm, indicating that the mining operation at this stage brings little impact to the surface industrial zone on the mining site.

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为了解决传统层次分析法（AHP）在采矿方法优选过程中的模糊性、随机性和不确定性等问题，引入模糊理论、优化判断标度和构建最优传递矩阵，以减少主观偏差、增强对不确定性信息的处理能力、克服传统AHP的局限。将改进层次分析法与逼近理想解排序法（TOPSIS）相结合，构建了多层次、多因素、多目标、多指标综合评价模型，并应用于某缓倾斜中厚磷矿采矿方法优选。经分析，方案1、方案2、方案3的相对贴近度依次为0.177 9、0.822 5、0.648 3，初步选择方案2（回采联道水平布置的分段空场嗣后充填法）为该矿山的适宜采矿方案。并对方案2进行数值模拟，结果表明，在矿体阶段回采充填后，该方案地表最大沉降量约为72.94 mm，表明阶段开采对矿区地表工业区域影响较小。

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陈帮洪（1998—），男，四川乐山人，硕士研究生，主要从事地下开采方面的研究工作。E-mail：
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武尚荣（1984—），男，云南保山人，高级工程师，主要从事采矿及岩石力学方面的研究工作。E-mail：

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武尚荣（1984—），男，云南保山人，高级工程师，主要从事采矿及岩石力学方面的研究工作。E-mail：

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武尚荣（1984—），男，云南保山人，高级工程师，主要从事采矿及岩石力学方面的研究工作。E-mail：

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Mining and Metallurgical Engineering, 2017, 37(3): 1-5., articleTitle=Mining method choice based on entropy weight-ideal point and stope stability analysis, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1236348228866724191, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, xref=null, ext=[AuthorCompanyExt(id=1236348228875112800, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, companyId=1236348228866724191, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=Kunming Engineering & Research Institute of Nonferrous Metallurgy Co, Ltd, Kunming 650202, Yunnan, China), AuthorCompanyExt(id=1236348228883501410, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, companyId=1236348228866724191, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=昆明有色冶金设计研究院股份公司，云南　昆明　650202)])], figs=[ArticleFig(id=1236348231978897964, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=EN, label=Fig.1, caption=Steps for solving weight vector with improved AHP, figureFileSmall=u8dVYhvEy693sz3FCus0nQ==, figureFileBig=3Y41lr5aYkrpq1LxU3Uubg==, tableContent=null), ArticleFig(id=1236348232075366960, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=CN, label=图1, caption=改进的AHP求解权重向量步骤, figureFileSmall=u8dVYhvEy693sz3FCus0nQ==, figureFileBig=3Y41lr5aYkrpq1LxU3Uubg==, tableContent=null), ArticleFig(id=1236348232180224566, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=EN, label=Fig.2, caption=Evaluation index system for optimizing mining method of gently-inclined and medium-thick phosphate ore body, figureFileSmall=bPlFE223ph3lRcKYb/N/Eg==, figureFileBig=JU6X2B508H+GFrXHN+KFxQ==, tableContent=null), ArticleFig(id=1236348232272499258, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=CN, label=图2, caption=缓倾斜中厚磷矿体采矿方法优选评价指标体系, figureFileSmall=bPlFE223ph3lRcKYb/N/Eg==, figureFileBig=JU6X2B508H+GFrXHN+KFxQ==, tableContent=null), ArticleFig(id=1236348232364773953, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=EN, label=Fig.3, caption=Schematic diagram of mining by Scheme 2, figureFileSmall=gbH87xQ3mofcjUCsDXOtwg==, figureFileBig=6elduZXCypkNURvfIXljzA==, tableContent=null), ArticleFig(id=1236348232431882820, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=CN, label=图3, caption=方案2采矿示意图, figureFileSmall=gbH87xQ3mofcjUCsDXOtwg==, figureFileBig=6elduZXCypkNURvfIXljzA==, tableContent=null), ArticleFig(id=1236348232498991688, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=EN, label=Fig.4, caption=Distribution of maximum principal stress in the dip direction on section of ore body, figureFileSmall=XLVkGCzV7KNPq09YQIAbCw==, figureFileBig=5E+HHRBc782lyA2ClInwLA==, tableContent=null), ArticleFig(id=1236348232574489165, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=CN, label=图4, caption=矿体倾向剖面最大主应力分布, figureFileSmall=XLVkGCzV7KNPq09YQIAbCw==, figureFileBig=5E+HHRBc782lyA2ClInwLA==, tableContent=null), ArticleFig(id=1236348232654180946, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=EN, label=Table 1, caption=

Evaluation indicators of three mining methods

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评价指标体系方案1方案2方案3
准则层指标层
经济性指标T1采矿总成本X1/（元·t－1）51.1941.4243.52
矿石回收率X2/%78.5076.3673.34
矿石贫化率X3/%10.2013.1111.46
技术性指标T2采场生产能力X4/（t·d－1）696.971 060.611 060.61
采切比X5/（m·kt－1）5.204.666.50
方案灵活性与适应性X6468
施工难易度X7846
矿石大块率X8/%688
安全性指标T3顶板安全性X9486
通风条件X10688
), ArticleFig(id=1236348232733872725, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=CN, label=表1, caption=

3种采矿方法评价指标值

, figureFileSmall=null, figureFileBig=null, tableContent=
评价指标体系方案1方案2方案3
准则层指标层
经济性指标T1采矿总成本X1/（元·t－1）51.1941.4243.52
矿石回收率X2/%78.5076.3673.34
矿石贫化率X3/%10.2013.1111.46
技术性指标T2采场生产能力X4/（t·d－1）696.971 060.611 060.61
采切比X5/（m·kt－1）5.204.666.50
方案灵活性与适应性X6468
施工难易度X7846
矿石大块率X8/%688
安全性指标T3顶板安全性X9486
通风条件X10688
), ArticleFig(id=1236348232838730333, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=EN, label=Table 2, caption=

Weight vector value determined by improved AHP

, figureFileSmall=null, figureFileBig=null, tableContent=
评价指标准则层准测层权重评价指标指标层权重指标加权权重
经济性指标T10.625 0X10.690 80.431 8
X20.148 80.093 0
X30.160 30.100 2
技术性指标T20.136 5X40.201 80.027 6
X50.245 60.033 5
X60.231 90.031 6
X70.213 80.029 2
X80.106 90.014 6
安全性指标T30.238 5X90.533 30.127 2
X100.466 70.111 3
), ArticleFig(id=1236348232922616417, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=CN, label=表2, caption=

改进的AHP确定的权重向量值

, figureFileSmall=null, figureFileBig=null, tableContent=
评价指标准则层准测层权重评价指标指标层权重指标加权权重
经济性指标T10.625 0X10.690 80.431 8
X20.148 80.093 0
X30.160 30.100 2
技术性指标T20.136 5X40.201 80.027 6
X50.245 60.033 5
X60.231 90.031 6
X70.213 80.029 2
X80.106 90.014 6
安全性指标T30.238 5X90.533 30.127 2
X100.466 70.111 3
), ArticleFig(id=1236348233031668324, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=EN, label=Table 3, caption=

Calculation result of distance and relative closeness coefficient

, figureFileSmall=null, figureFileBig=null, tableContent=
待选采矿方法di+di－Ei+
方案10.110 40.023 90.177 9
方案20.023 70.110 00.822 5
方案30.042 30.078 00.648 3
), ArticleFig(id=1236348233128137320, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=CN, label=表3, caption=

距离和相对贴近度计算结果

, figureFileSmall=null, figureFileBig=null, tableContent=
待选采矿方法di+di－Ei+
方案10.110 40.023 90.177 9
方案20.023 70.110 00.822 5
方案30.042 30.078 00.648 3
), ArticleFig(id=1236348233237189228, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=EN, label=Table 4, caption=

Settlement indicators after mining and filling at different stages

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阶段最大沉降量/m倾斜值i/（mm·m－1）曲率k/（10－3 m－1）ε/（mm·m－1）
10.008 810.0200.0120.014
20.034 820.0280.0180.017
30.057 050.0300.0210.020
40.071 450.0370.0290.030
50.072 940.0420.0340.037
), ArticleFig(id=1236348233367212655, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1236276117435380365, language=CN, label=表4, caption=

不同阶段回采充填后的沉降指标

, figureFileSmall=null, figureFileBig=null, tableContent=
阶段最大沉降量/m倾斜值i/（mm·m－1）曲率k/（10－3 m－1）ε/（mm·m－1）
10.008 810.0200.0120.014
20.034 820.0280.0180.017
30.057 050.0300.0210.020
40.071 450.0370.0290.030
50.072 940.0420.0340.037
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基于改进AHP-TOPSIS评价模型的缓倾斜中厚磷矿采矿方法优选
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武尚荣 , 陈帮洪 , 费志文
矿冶工程杂志 | 采矿 2025,45(4): 52-57
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矿冶工程杂志 | 采矿 2025, 45(4): 52-57
基于改进AHP-TOPSIS评价模型的缓倾斜中厚磷矿采矿方法优选
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武尚荣 , 陈帮洪 , 费志文
作者信息
  • 昆明有色冶金设计研究院股份公司，云南　昆明　650202

    • 武尚荣（1984—），男，云南保山人，高级工程师，主要从事采矿及岩石力学方面的研究工作。E-mail：

通讯作者:

陈帮洪（1998—），男，四川乐山人，硕士研究生，主要从事地下开采方面的研究工作。E-mail：
Optimization of Mining Methods for Gently Inclined Phosphate Ore Body Based on Improved AHP-TOPSIS Model
Shangrong WU , Banghong CHEN , Zhiwen FEI
Affiliations
  • Kunming Engineering & Research Institute of Nonferrous Metallurgy Co, Ltd, Kunming 650202, Yunnan, China
出版时间: 2025-08-01 doi: 10.3969/j.issn.0253-6099.2025.04.009
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摘要
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为了解决传统层次分析法（AHP）在采矿方法优选过程中的模糊性、随机性和不确定性等问题，引入模糊理论、优化判断标度和构建最优传递矩阵，以减少主观偏差、增强对不确定性信息的处理能力、克服传统AHP的局限。将改进层次分析法与逼近理想解排序法（TOPSIS）相结合，构建了多层次、多因素、多目标、多指标综合评价模型，并应用于某缓倾斜中厚磷矿采矿方法优选。经分析，方案1、方案2、方案3的相对贴近度依次为0.177 9、0.822 5、0.648 3，初步选择方案2（回采联道水平布置的分段空场嗣后充填法）为该矿山的适宜采矿方案。并对方案2进行数值模拟，结果表明，在矿体阶段回采充填后，该方案地表最大沉降量约为72.94 mm，表明阶段开采对矿区地表工业区域影响较小。

缓倾斜矿体  /  中厚矿体  /  采矿方法优选  /  层次分析法  /  TOPSIS  /  分段空场嗣后充填法  /  地表沉降

In order to solve the problems of fuzziness, randomness and uncertainty in optimization of mining method by traditional analytic hierarchy process (AHP), some measures, including introducing fuzzy theory, optimizing judgment scale and constructing optimal transfer matrix, were introduced to reduce subjective deviation and enhance the processing ability of uncertain information. Then, based on the combination of improved analytic hierarchy process (AHP) with the technique for order preference by similarity to ideal solution (TOPSIS), a comprehensive evaluation system with multi-level, multi-factor, multi-objective and multi-index characteristics was constructed and applied to the optimization of mining methods for a gently-inclined medium-thick phosphate ore body. The analysis shows that the relative closeness coefficients of those three mining schemes are 0.177 9, 0.822 5 and 0.648 3, respectively. Scheme 2, namely sublevel open stoping with subsequent backfill, is primarily determined as the suitable mining method for the mine. The numerical simulation of Scheme 2 also shows that the maximum surface subsidence in this scheme can be controlled within 72.94 mm, indicating that the mining operation at this stage brings little impact to the surface industrial zone on the mining site.

gently inclined ore body  /  medium-thick ore body  /  mining method optimization  /  analytic hierarchy process (AHP)  /  TOPSIS  /  sublevel open stoping with subsequent backfill  /  surface subsidence
武尚荣, 陈帮洪, 费志文. 基于改进AHP-TOPSIS评价模型的缓倾斜中厚磷矿采矿方法优选. 矿冶工程杂志, 2025 , 45 (4) : 52 -57 . DOI: 10.3969/j.issn.0253-6099.2025.04.009
Shangrong WU, Banghong CHEN, Zhiwen FEI. Optimization of Mining Methods for Gently Inclined Phosphate Ore Body Based on Improved AHP-TOPSIS Model[J]. Mining and Metallurgical Engineering, 2025 , 45 (4) : 52 -57 . DOI: 10.3969/j.issn.0253-6099.2025.04.009
正文
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近年来，数学模型、物理模型、系统工程方法、数值模拟和深度神经网络等技术广泛应用于采矿方法优化和评估中，取得了良好的应用效果[1-3]。
在开采过程中，埋深较大的缓倾斜薄至中厚矿体会面临地压释放困难、采场作业条件恶劣等显著挑战，针对该类矿体，选择适宜的采矿方法具有重要的现实意义。采矿方法选择是一个涉及技术、经济、施工、安全等多因素、多目标的复杂决策过程。传统的基于经验与类比的方法往往存在较大的模糊性、随机性和不确定性[4]。为应对这一挑战，学者们致力于建立更科学的决策体系：文献[5]基于模糊理论和决策多交互方法，构建了涵盖技术可行性、安全状况、经济效益和管理复杂性等维度的采矿方法选择指标体系；文献[6]应用AHP-Fuzzy综合优选方法，系统考量了采矿成本、地压管理难度、矿石贫化率、千吨采切比、施工难易程度、采场生产能力、矿石损失率、方法灵活适应性及通风条件等9项关键指标。由于传统层次分析法（AHP）中决策方法不一致性，建立的判断矩阵一致性检验计算繁琐，且一致性检验无法通过。基于此，在前人采矿方法优选研究的基础上，本文提出通过转移矩阵构建一致性判断矩阵，将改进的AHP与逼近理想解排序法（TOPSIS）相结合，采用改进AHP-TOPSIS评价模型获得权重向量值，以获得不用通过一致性检验的指标权重值，并应用于某缓倾斜中厚磷矿充填采矿方法优选过程，结合数值模拟验证充填回采效果，为缓倾斜中厚矿体的安全高效开采提供参考。
1　矿山概况
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某缓倾斜中厚磷矿为大型磷块岩矿床，矿层总体上呈面状分布，呈南-北向分布，长2.3 km，宽1.5 km，分布面积约3.2 km2。矿区内矿层露头仅在南侧有少量出露，海拔标高为1 870 m；矿区矿层分布最高标高1 985 m，最低标高1 000 m，相对高差约985 m；矿层最小埋深0 m，最大埋深1 407 m。矿体倾角15.2°～25.3°，平均倾角21°，厚度5.39～24.6 m，平均厚14.67 m，P2O5平均品位为21.22%。矿体顶板为白云岩，岩石坚固性系数为5.96；矿体为磷块岩，岩石坚固性系数为7.15；矿体底板为泥质白云岩，岩石坚固性系数为8.10。矿区是以岩溶含水层充水为主、顶底板直接充水、水文地质条件中等的矿床。围岩与矿体底板的接触关系明显，但与顶板的逐渐变质蚀变关系不明显。随着开采强度增加，矿石资源继续向下移动，矿体倾角变缓，矿石搬运困难。
2　采矿方法优选模型构建
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2.1　基于改进的AHP确定权重向量
AHP是一种结合了定性和定量方法的多标准、多目标、多方案的决策分析方法。在实际采矿方法选择过程中，由于专家在决策中的主观性，尤其是在因素指标较多的情况下，难以一次性构建满足一致性要求的判断矩阵。改进的AHP可以在不调整专家初始数据的情况下重构判断矩阵并计算权重向量。它不仅可以避免多次专家调查所造成的支出浪费，而且还可以减少通过调整判断矩阵所造成的重复计算。采用改进的AHP求解权重向量的过程如图1所示。
2.1.1　构建比较矩阵
比较矩阵A如式（1）所示，矩阵A中元素aij是评价指标中元素xi对元素xj的相对重要性。
2.1.2　构建一致性判断矩阵
为了避免初始比较矩阵的不一致性，引入改进的AHP[6]，并利用最优传递矩阵的概念得到了一次指标权重值。其定义和存在的关系如下。
定义1：设矩阵Am×n，集合U=（1，2，…，n）。若aij=1/aji，且aij=aik·ajk，i，j，k∈U，则矩阵A是一致性判断矩阵。
定义2：设矩阵Am×n，矩阵Bm×n，bij=lgaij，i，j，k∈U，U=（1，2，…，n）。若矩阵A是一致性判断矩阵，那么bij=－bji，且bij=bik+bkj，则矩阵B被称为矩阵A的传递矩阵；相反，如果B是A的传递矩阵，那么A就是一致性判断矩阵。
定义3：矩阵Bm×n、Cm×n，若bij=－bji，则矩阵B的最优传递矩阵C满足，i，j，k∈U，U=（1，2，…，n）。
2.2　改进AHP-TOPSIS综合评价模型的构建
利用TOPSIS来定义正理想解和负理想解，并根据方案与理想解的接近程度来评价该方案的优越性。一般优越方案是接近正理想解、远离负理想解。
2.2.1　建立初始判断矩阵
假设有m个备选方案P1，P2，…，Pm，所有方案的集合为P=｛P1，P2，…，Pm｝；每个方案的评价指标集合设为X，X=｛X1，X2，…，Xn｝，每个方案对应的评价指标可表示为xij（i=1，2，…，m；j=1，2，…，n），则xij表示第i方案的第j个评价指标。初始判断矩阵P表达式[7]为：
2.2.2　标准化决策矩阵的建立
由于评价对象具有复杂性，且各评价指标存在不兼容性，需对评价指标进行无量纲处理。其中，成本型指标因“数值越小越优”，先通过式（3）取倒数转化为“数值越大越优”的效益型指标，再进行标准化处理[8]。效益型指标因“数值越大越优”，直接采用式（4）进行标准化处理；经上述操作，最终得到标准化决策矩阵Q（见式（5））。
式中：xij是矩阵P的元素；表示矩阵P中j列的最大值；qij、qij′均为标准化决策矩阵Q的元素。
2.2.3　加权标准化决策矩阵的构建
将上述标准化决策矩阵Q与各指标对应的权重wi相乘，得到加权标准化矩阵R：
2.2.4　待选方案贴近度计算
加权标准化决策矩阵的理想解按式（7）[9]计算。
式中：R+、R－分别为正、负理想解；表示矩阵R中第j列的最大值；表示矩阵R中第j列的最小值。评价对象与理想解之间的距离按式（8）[10]计算：
式中：和分别为评价对象与正理想解和负理想解之间的距离；和分别为R+和R－的元素。每个评价对象与正理想解之间的距离向量为：
由组成的矩阵E为综合评价矩阵。在相同的一级指标下，接近1为优，接近0为差，可以通过进度值的递减排列来初步判断评价对象的优缺点。
3　实例应用
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3.1　方案初选及综合评价指标体系建立
根据矿体产状和开采技术条件，初步提出以下3种较为可行的充填采矿方案：方案1为上向点柱式分层充填法；方案2为回采联道水平布置的分段空场嗣后充填法；方案3为回采联道倾斜布置的分段空场嗣后充填法。根据采矿方法初选分析，方案1回收率、贫化率高，但安全性和生产效率低，方案2和方案3安全性高、成本低、生产效率低，但贫化率高。相比于方案2，方案3回收率高，但采切工程量大。因此需要进一步综合考虑技术、经济和安全性等条件，优选出合适的采矿方法。
根据改进的AHP的基本原理，参考前人对采矿方法评价指标体系的研究，建立了缓倾斜中厚磷矿体采矿方法优选评价指标体系，如图2所示。
评价体系中X1、X2、X3、X4、X5、X8为定量指标，可根据标准的采矿方法图、参考类似矿山实例及所获得的相关专家意见进行综合估算[7]。评价体系中的X6、X7、X9、X10为定性指标。评价等级分为非常好、好、一般、差、非常差5个等级，依次对应10、8、6、4、2打分值。最终得到3种充填采矿方法的评价指标值如表1所示。
3.2　指标权重确定
总成本取决于采矿技术条件、充填开采方法、机械化水平、管理水平等。确定开采方法后，采矿总成本在短时间内变化不大，而矿石回收率和贫化率指数对矿山的经济效益影响较大[11]。
根据AHP基本原理和文献[8]，结合当地政策和矿山企业生产经营情况，与相关专家学者讨论，确定标准层指标T、经济性指标T1、技术性指标T2、安全性指标T3的初始比较矩阵为：
由改进的AHP[9]得到的权重向量值如表2所示。通过表2的准则层权重及指标层权重即可得到各指标的加权权重，以便后续对指标进行综合评价。
3.3　各因素和指标的综合评价
根据式（2）构造初始判断矩阵P。在各方案的综合评价指标体系中，X1、X3、X5、X7、X8属于成本指标，X2、X4、X6、X9、X10属于效益指标，通过式（3）～（5）得到标准化矩阵Q，利用式（6）加权表2中指标权重，得到标准化加权判断矩阵R。
根据式（7）计算加权归一化矩阵的理想解，得到加权标准化矩阵的正理想解和负理想解。
根据式（8）、（9）分别计算每个待优选采矿方法到正、负理想解的距离di+、di－和相对贴近度Ei+，计算结果如表3所示。
根据表3结果，方案2到正理想解的距离最小，到负理想解的距离最大，相对贴近度最大，说明方案2切割工程量小、回收率高、安全性高。因此，选择方案2作为本文缓倾斜中厚磷矿适宜的采矿方案。
3.4　工业试验
方案2采矿示意图如图3所示，矿块沿走向布置，矿块长50～100 m，矿块宽度为矿体厚度。分段高度20 m，矿块间沿走向和倾向留隔离矿柱，矿柱宽度4～6 m。采用凿岩台车凿岩，4 m3柴油铲运机出矿。采场回采结束后，采用废石及尾砂对采空区进行充填，废石采用汽车运输，运输至充填平巷从充填井充入采空区。
该方法已在矿山中进行了试验。根据首采区域现场试验数据统计，方案2主要技术经济指标为：采场生产能力1 100 t/d，回收率85.7%，矿石贫化率12.34%，采切比4.5 m/kt，回采和充填总成本42元/t，达到预期效果。
4　优选采矿方法数值模拟
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深部矿体开采采矿方法选择还需考虑地压管理及地表沉降控制。根据方案2，基于矿区地形地质条件及岩体力学参数建立三维数值模型，对阶段矿体回采及采空区充填开展数值模拟，按照1 790～1 930 m（阶段1）、1 590～1 770 m（阶段2）、1 390～1 570 m（阶段3）、1 190～1 370 m（阶段4）、1 030～1 170 m（阶段5）的开采顺序进行回采充填数值模拟计算，截取阶段1回采充填后矿体倾向剖面最大主应力分布，如图4所示，不同阶段回采充填后的沉降指标如表4所示。
根据图4和表4可以看出，分段矿体赋存区域最大主应力值约为22.5 MPa，矿山地表沉降总体呈现前期和后期变化较小、中期变化较大的规律。但总体而言，矿山围岩条件相对较好，矿区回采充填后地表沉降相对较小。矿区矿体回采过程中地表最大沉降量约为72.94 mm，在矿体回采过程中对矿区地表工业场地影响较小，留设保安矿柱能够保证地表工业场地的安全。
5　结论
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1）提出通过最优传递矩阵构建一致性判断矩阵，减少主观偏差，增强对不确定性信息的处理能力，以克服传统AHP确定权重的局限，在实际采矿方法优选的应用中取得了较好效果。
2）以某缓倾斜中厚磷矿为例，建立了采矿方法优选的AHP-TOPSIS综合决策模型。方案1、方案2、方案3的相对贴近度分别为0.177 9、0.822 5、0.648 3，方案2（回采联道水平布置的分段空场嗣后充填法）的相对贴近度最大，选择方案2作为该矿体适宜的采矿方案。
3）通过数值模拟得到，方案2在矿体阶段回采充填后，地表最大沉降量约为72.94 mm，表明阶段开采对矿区地表工业区域的影响较小。设置合理的保安矿柱能够有效保障地表工业场地的安全稳定。
文献
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2025年第45卷第4期
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doi: 10.3969/j.issn.0253-6099.2025.04.009
  • 接收时间：2025-01-24
  • 首发时间：2026-03-05
  • 出版时间：2025-08-01
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  • 收稿日期：2025-01-24
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    昆明有色冶金设计研究院股份公司，云南　昆明　650202

通讯作者:

陈帮洪（1998—），男，四川乐山人，硕士研究生，主要从事地下开采方面的研究工作。E-mail：
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