关键柱局部失稳会诱发煤柱群（简称“群柱”）体系的链式失稳及其围岩的联动破坏。关键柱位置的判别是柱式采空区煤岩体链动失稳科学防控的基本前提。本文首先界定了遗留煤柱最小等效宽度的概念，提出了四种确定不同形态遗留煤柱最小等效宽度的方法，优化了遗留煤柱自身强度的计算方法；其次，引入应力扩散的最大距离L，改进了遗留煤柱承担载荷的计算公式；然后，分别确定了待研究区域内各个遗留煤柱的安全系数，并将安全系数最小的遗留煤柱判别为关键柱；最后，形成了遗留群柱中关键柱判别的技术方法，并运用Python语言开发了关键柱智能判别的KPDS软件。结果表明：①最小等效宽度为不同形态遗留煤柱的最小实用承载宽度；内切圆法、最短边法、辅助线法和短轴线法可以用于确定采空区规则/不规则形态遗留煤柱的最小等效宽度。②内切圆法适用于确定横截面为三角形和正多边形遗留煤柱的最小等效宽度；最短边法适用于确定“横截剖面存在最短边且其邻近两边相互平行”遗留煤柱的最小等效宽度；辅助线法适用于确定“横截剖面存在最短边且其两条邻边不相互平行”遗留煤柱的最小等效宽度；短轴线法适用于确定半圆形遗留煤柱、圆形遗留煤柱和椭圆形遗留煤柱的最小等效宽度。③遗留煤柱承担的载荷不只是从属面积上覆岩的载荷，还包括邻近范围覆岩所传递扩散过来的载荷；考虑应力扩散最大距离可以更加准确计算遗留煤柱承担的载荷。④基于最小等效宽度和载荷扩散最大距离，能够确定待研究采空区内安全系数最小的遗留煤柱，可以进一步判别出关键柱，并形成关键柱判别的技术流程。⑤关键柱判别KPDS软件是Key Pillar Determination Software的简称，主要包括：登录界面、参数导入界面、强度计算界面、承载与安全系数计算界面和关键柱判别界面；该软件可以快速智能地判别出遗留群柱体系中关键柱。该研究可以实现遗留群柱体系中关键柱位置的预先超前识别，有望指导遗留群柱链式失稳和围岩联动破坏的科学防控，并进一步促进煤矿岩层控制理论与技术的发展。

The local instability of key pillar will induce the chain failure of coal pillar system and the linkage failure of surrounding rock.Identification of the key pillar’s position is the basic premise for the scientific prevention and control of coal rock mass chain failure in the pillar mining gobs.The concept of minimum equivalent width is defined firstly.Four methods are proposed to determine the minimum equivalent width of residual coal pillar with different shapes.The calculation method of coal pillar’s strength is then optimized.By introducing the maximum transferred distance of stress,the bearing load calculation formula of residual coal pillar is improved.Then,the safety factor of each residual coal pillar in the studied area is obtained,and the residual coal pillar with the minimum safety factor can be identified as the key pillar.Lastly,the technical method of key pillar in the residual pillar system are formed.In addition,the KPDS software are developed based on the Python language to make an intelligent assessment on key pillar.The results show that:① the minimum equivalent width means the minimum practical bearing width of residual coal pillar with different shapes.The inscribed circle method,the shortest side method,the auxiliary line method and the short axis method can be used to determine the minimum equivalent width of regular or irregular residual coal pillar.② The inscribed circle method is suitable for determining the minimum equivalent width of triangular and regular polygon residual coal pillar in the gob.The shortest side method is suitable for determining the minimum equivalent width of residual coal pillar with shortest side and parallel adjacent side in the cross section.The auxiliary line method is suitable for determining the minimum equivalent width of residual coal pillar with shortest side and non parallel adjacent side in the cross section.The short axis method is suitable for determining the minimum equivalent width of semicircular,circular and oval shaped residual coal pillar.③ The load acting on the residual coal pillar not only includes the load of overlying strata in the tributary area,but also involves the transferred load of adjacent overlying strata.Considering the maximum transferred distance of stress,the load of residual coal pillar can be calculated more accurately.④ Based on the minimum equivalent width and the maximum stress transferred distance,the residual coal pillar with the smallest safety factor in the gob can be determined and the key pillar can be further identified.The identification technical process for key pillar can also formed.⑤ KPDS is the abbreviation of Key Pillar Determination Software.It mainly includes:login page,parameter importing page,strength comparison calculation page,safety factor determination page and key pillar identification page.KPDS software can quickly and intelligently identify the key pillar in the residual pillar system.The development of key pillar identification methods and intelligent software can realize the pre distinguishment of key pillar position in the residual pillar system,which is expected to guide the scientific prevention and control of residual coal pillars’ chain failure and surrounding rock’s linkage failure.It can also further promote the rock strata control theory in the coal mining field.

1 基于最小等效宽度的煤柱强度分析

   1.1 内切圆法

   1.2 最短边法

   1.3 辅助线法

   1.4 短轴线法

2 基于载荷扩散距离的煤柱承载分析

3 关键柱判别的技术方法

4 关键柱判别KPDS智能软件与应用

   4.1 KPDS软件的开发环境

   4.2 KPDS软件的核心界面与功能

5 结论