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Article(id=1241768039897694225, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1241768035548205179, articleNumber=null, orderNo=null, doi=10.3969/j.issn.0253-6099.2024.01.009, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1692720000000, receivedDateStr=2023-08-23, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773990171645, onlineDateStr=2026-03-20, pubDate=1706716800000, pubDateStr=2024-02-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773990171645, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773990171645, creator=13701087609, updateTime=1773990171645, updator=13701087609, issue=Issue{id=1241768035548205179, tenantId=1146029695717560320, journalId=1235980550691926019, year='2024', volume='44', issue='1', pageStart='1', pageEnd='178', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773990170609, creator=13701087609, updateTime=1773993209826, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241780783011140021, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1241768035548205179, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241780783015334326, tenantId=1146029695717560320, journalId=1235980550691926019, issueId=1241768035548205179, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=39, endPage=43, ext={EN=ArticleExt(id=1241768040312930326, articleId=1241768039897694225, tenantId=1146029695717560320, journalId=1235980550691926019, language=EN, title=Thickness of Horizontal Pillar for Safe Extraction Under Arching Effect of Cemented Backfill, columnId=1236276106018484431, journalTitle=Mining and Metallurgical Engineering, columnName=MINING, runingTitle=null, highlight=null, articleAbstract=

Based on an established three-dimensional analytical model for arching stress of cemented backfill, a calculation formula for vertical load of cemented backfill was obtained. According to a model of four-sided fixed roof and a criterion for ultimate tensile strength of rock mass, a method to determine the thickness of horizontal pillar for safe extraction was obtained. The application practice of horizontal pillar extraction in 612 stope of a lead-zinc mine shows that the vertical stress of cemented backfill calculated with this analytical model is basically consistent with the numerical simulation results, and no plastic zone occurs in the roof in numerical simulation, which verifies that the reserved roof thickness determined by calculation meets the requirement of safe production. The results of stoping process show that the maximum cumulative displacement near the monitoring point is lower than the displacement limit, and the reserved roof tends to be stable. It is concluded that the determined thickness of horizontal pillar is reliable for safe extraction.

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通过建立三维胶结充填体拱应力模型，得到胶结充填体竖向荷载计算公式，并根据四边固支顶板模型和岩体极限抗拉强度准则，得到了水平矿柱回采安全厚度确定方法。在某铅锌矿612采场水平矿柱回采的运用实践表明，解析模型计算的胶结充填体竖向应力与数值模拟结果基本吻合，数值模拟中顶板未出现塑性区，验证了计算确定的保留顶板厚度满足安全生产需求；回采过程监测结果表明，监测点附近的最大累计位移低于极限位移，保留顶板趋于稳定，确定的水平矿柱回采安全厚度具有足够的可靠性。

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叶永飞（1995—），江西赣州人，工程师，主要从事岩石力学方面的研究。E-mail：
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蒋江晨（1978—），湖南邵阳人，高级工程师，主要从事矿山开采设计与研究工作。E-mail：

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蒋江晨（1978—），湖南邵阳人，高级工程师，主要从事矿山开采设计与研究工作。E-mail：

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蒋江晨（1978—），湖南邵阳人，高级工程师，主要从事矿山开采设计与研究工作。E-mail：

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采场结构弹性模量/GPa泊松比内摩擦角/（°）抗拉强度/MPa容重/（N·m-3）黏聚力/MPa
胶结充填体0.390.32300.082 010×9.80.25
接触面——241.60—0.20
顶板矿石93.000.17333.075.34 330×9.812.95
), ArticleFig(id=1241779801510445278, tenantId=1146029695717560320, journalId=1235980550691926019, articleId=1241768039897694225, language=CN, label=表1, caption=

612采场相关物理力学性质

, figureFileSmall=null, figureFileBig=null, tableContent=
采场结构弹性模量/GPa泊松比内摩擦角/（°）抗拉强度/MPa容重/（N·m-3）黏聚力/MPa
胶结充填体0.390.32300.082 010×9.80.25
接触面——241.60—0.20
顶板矿石93.000.17333.075.34 330×9.812.95
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胶结充填体拱效应作用下的水平矿柱回采安全厚度研究
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蒋江晨 1 , 叶永飞 1 , 柳小胜 2
矿冶工程杂志 | 采矿 2024,44(1): 39-43
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矿冶工程杂志 | 采矿 2024, 44(1): 39-43
胶结充填体拱效应作用下的水平矿柱回采安全厚度研究
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蒋江晨1 , 叶永飞1 , 柳小胜2
作者信息
  • 1.中冶长天国际工程有限责任公司，湖南　长沙　410006
  • 2.湖南科技大学　资源环境与安全工程学院，湖南　湘潭　411201

    • 蒋江晨（1978—），湖南邵阳人，高级工程师，主要从事矿山开采设计与研究工作。E-mail：

通讯作者:

叶永飞（1995—），江西赣州人，工程师，主要从事岩石力学方面的研究。E-mail：
Thickness of Horizontal Pillar for Safe Extraction Under Arching Effect of Cemented Backfill
Jiangchen JIANG1 , Yongfei YE1 , Xiaosheng LIU2
Affiliations
  • 1.Zhongye Changtian International Engineering Co Ltd, Changsha 410006, Hunan, China
  • 2.School of Resources & Environment and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China
出版时间: 2024-02-01 doi: 10.3969/j.issn.0253-6099.2024.01.009
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摘要
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通过建立三维胶结充填体拱应力模型，得到胶结充填体竖向荷载计算公式，并根据四边固支顶板模型和岩体极限抗拉强度准则，得到了水平矿柱回采安全厚度确定方法。在某铅锌矿612采场水平矿柱回采的运用实践表明，解析模型计算的胶结充填体竖向应力与数值模拟结果基本吻合，数值模拟中顶板未出现塑性区，验证了计算确定的保留顶板厚度满足安全生产需求；回采过程监测结果表明，监测点附近的最大累计位移低于极限位移，保留顶板趋于稳定，确定的水平矿柱回采安全厚度具有足够的可靠性。

胶结充填体  /  拱效应  /  水平矿柱  /  薄板理论  /  回采  /  安全厚度

Based on an established three-dimensional analytical model for arching stress of cemented backfill, a calculation formula for vertical load of cemented backfill was obtained. According to a model of four-sided fixed roof and a criterion for ultimate tensile strength of rock mass, a method to determine the thickness of horizontal pillar for safe extraction was obtained. The application practice of horizontal pillar extraction in 612 stope of a lead-zinc mine shows that the vertical stress of cemented backfill calculated with this analytical model is basically consistent with the numerical simulation results, and no plastic zone occurs in the roof in numerical simulation, which verifies that the reserved roof thickness determined by calculation meets the requirement of safe production. The results of stoping process show that the maximum cumulative displacement near the monitoring point is lower than the displacement limit, and the reserved roof tends to be stable. It is concluded that the determined thickness of horizontal pillar is reliable for safe extraction.

cemented backfill  /  arching effect  /  extraction of horizontal pillar  /  thin plate theory  /  extraction  /  safe thickness
蒋江晨, 叶永飞, 柳小胜. 胶结充填体拱效应作用下的水平矿柱回采安全厚度研究. 矿冶工程杂志, 2024 , 44 (1) : 39 -43 . DOI: 10.3969/j.issn.0253-6099.2024.01.009
Jiangchen JIANG, Yongfei YE, Xiaosheng LIU. Thickness of Horizontal Pillar for Safe Extraction Under Arching Effect of Cemented Backfill[J]. Mining and Metallurgical Engineering, 2024 , 44 (1) : 39 -43 . DOI: 10.3969/j.issn.0253-6099.2024.01.009
正文
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近年来嗣后胶结充填采矿法得到了广泛应用，胶结充填体下回收水平矿柱的情况越来越多。胶结充填体中存在明显的拱效应，这种“拱效应”先后被Belem[1]、Thompson[2-3]等人通过原位监测手段验证。拱效应是指充填体内形成某种结构使充填体对水平矿柱所产生的压力小于自重的一种力学现象。拱效应的存在为水平矿柱的回收提供了可能。
目前已有很多学者对充填体下水平矿柱的回收进行了研究，研究成果主要从控制回收采场的暴露面积或构筑假顶的角度出发[4-7]，在研究水平矿柱的回收时将水平矿柱所受荷载视为胶结充填体自重，没有考虑胶结充填体的拱效应，所得结果过于保守，导致水平矿柱的回收率较低[8]。
本文着重研究胶结充填体拱效应对水平矿柱回收时采场顶板稳定性的影响。首先，通过建立三维胶结充填体拱应力模型计算获得水平矿柱所受的上部荷载；然后，将水平矿柱保留顶板简化为四边固支的小挠度弹性薄板，并结合极限抗拉强度准则推导出矿柱采场保留顶板的合理厚度，为矿山水平矿柱的安全回收提供理论依据。
1　采场胶结充填体三维拱应力解析模型
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胶结充填体与围岩、矿体刚度差异大，导致自重作用下采场胶结充填体产生不同程度的成拱作用，影响胶结充填体应力分布[9-15]，进而影响其对水平矿柱所产生的荷载。基于Marston法，构建如图1所示的采场胶结充填体三维拱应力模型。
胶结充填体受上下盘围岩以及左右两侧围岩夹制，在自胶结充填体最上部往下任一埋深h处选取胶结充填体微分层单元。可知微分层单元在四周围岩通过接触作用产生的法向力Fn和切向力S（S1、S2、S3、S4）以及上表面传递的压力V、下表面传递的支撑力V+dV、自重W的共同作用下达到静力平衡：
由文献[9]可知，围岩产生的法向应力可按主动土压力计算：
式中Ka为主动土压力系数，，φ为充填体内摩擦角，（°）；σv为微分层竖向应力，MPa。
易知，围岩与胶结充填体间产生胶结接触，因此切向应力为：
式中c为围岩与胶结充填体间的黏聚力，MPa；φ′为围岩与胶结充填体间的内摩擦角，（°）。
由式（3）可求得左、右两侧围岩对微分层单元产生的切向力S1、S3和上、下盘围岩对微分层单元产生的切向力S2、S4分别为：
将式（4）～（5）代入式（1），得：
式中γ为胶结充填体容重，N/m3。
求解式（6），可得：
式中C为常数，由于胶结充填体的脱水沉降，充填体难以接顶，边界条件为，根据边界条件可求得最终竖向应力表达式为：
2　水平矿柱采场顶板稳定性分析
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水平矿柱回采后，上部充填体荷载将由留设的保留顶板支撑，顶板稳定性是决定水平矿柱采场安全的关键所在。顶板、围岩、上部充填体三者形成的力学结构可简化为如图2所示的上部受载的四边固支薄板模型。
根据伽辽金法[16]，顶板挠度可取如下函数：
式中m、n均为系数；amn为待解系数。
顶板的总势能为[17]：
式中U和T分别为顶板的应变能和外力势。
由最小势能原理可得：
由式（12）可求得顶板挠度决定系数amn为：
将求得的amn代入式（10）即可得到顶板的挠度表达式，此时可通过挠度求得顶板内部应力分布：
式中σx为长轴方向应力，MPa；σy为短轴方向应力，MPa。
由岩石物理特性可知，顶板的抗压强度远大于抗拉强度，而顶板的最大拉应力出现在顶板中心，所以水平矿柱采场失稳破坏首先发生在顶板中心处。为使顶板具有足够的稳定性，顶板需预留一定的厚度，以使顶板中的最大拉应力满足：
式中σtmax为式（14）求得的最大拉应力，MPa；k为安全系数，可根据顶板岩体的完整性来选取。
由此，通过式（9）和式（15）即可求出水平矿柱采场保留顶板的厚度。
3　工程实例
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某铅锌矿采用分段凿岩阶段空场嗣后充填采矿法和大直径深孔侧向崩矿阶段空场嗣后充填采矿法进行回采，造成-70 m、-120 m等6个中段留有较多的水平矿柱，水平矿柱均为矿体，共有200余万吨矿量，经济价值高，需对这一部分矿体进行回收。在水平矿柱回收之前已完成分级尾砂胶结充填，充填区域如图3所示。由于水平矿柱回采是在胶结充填下进行，形成复杂的采空区环境，顶板作为直接承载结构，其稳定性关系着水平矿柱回采能否顺利进行。
现以612采场水平矿柱（图4）作为实例，对胶结充填体下水平矿柱采场顶板稳定性进行分析。
612采场上部的512采场内胶结充填体高42 m、长35 m、宽7.5 m，612采场水平矿柱厚度为8 m，充填体灰砂比1∶6，相关物理力学性质见表1。
3.1　解析模型的数值验证
为验证采场胶结充填体三维拱应力解析模型的可靠性，利用有限差分软件FLAC3D构建与解析模型相对应的数值模型，如图5所示。
模拟时假设采场围岩为各向同性且服从线弹性模型，水平矿柱服从摩尔-库伦模型。通过模拟中的监测点和式（9）得到如图6所示的胶结充填体不同埋深h的竖向应力σv分布曲线。从图6可以看出，虽然解析解和数值模拟结果存在一定差异，但两者整体吻合较好，验证了胶结充填体三维拱应力解析模型的可靠性。从图6还可以看出，解析解和数值解均小于覆重法结果，说明拱效应可以明显减小胶结充填体内部的竖向应力。
3.2　水平矿柱回采厚度确定
易知顶板最大拉应力在顶板中心下表面短轴方向（y方向）。顶板厚度与最大拉应力σtmax的关系如图7所示。从图7可以发现，随着顶板厚度增加，顶板中的最大拉应力逐渐减少。图7还列出了以覆重法计算胶结充填体荷载得到的最大拉应力与顶板厚度的关系曲线，覆重法确定的顶板临界厚度为2.755 m，本文确定的顶板临界厚度为1.123 m，本文考虑充填体拱效应作用所需的顶板厚度明显小于覆重法所需顶板厚度。图8为顶板取临界厚度时下表面长轴（x方向）、短轴（y方向）方向的应力分布图。从图8可以发现，顶板最大拉应力出现在顶板中部，短轴方向最大拉应力明显大于长轴方向最大拉应力。
在612采场水平矿柱的实际回采中，取安全系数k=1.3，实际顶板厚度为1.5 m，即实际回收水平矿柱厚度为6.5 m，沿矿体厚度（b=7.5 m）持续推进，每次暴露长度为12 m，具体如图9所示。为了进一步验证顶板的安全性，对回采过程进行了数值模拟，发现回采过程中顶板未出现塑性区域。在612采场水平矿柱的实际回收过程中，顶板和上中段充填体未发生垮塌，即以上确定的顶板厚度能保证回采作业的安全进行。
3.3　工程验证
为了验证水平矿柱开采后保留顶板的稳定性，在612水平矿柱采场顶板处埋设ZLGH-20型钻孔位移计监测顶板位移变化情况，结果见图10。监测结果表明，顶板中心处监测点A最大累计位移值为0.45 mm，端部监测点B最大累计位移值为0.03 mm，均小于极限位移量，顶板在回采过程中未发生垮塌、冒落，验证了理论分析结果的可靠性。
4　结论
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1）将采场胶结充填体三维拱应力解析模型与顶板力学模型结合，得到顶板竖向应力求解公式，从而得到水平矿柱采场顶板厚度确定方法，为水平矿柱的安全回收提供理论依据。
2）以某铅锌矿612采场水平矿柱回采为例，对胶结充填体所产生的垂直应力进行求解，并将其代入顶板模型中，得到顶板临界厚度为1.5 m。
3）解析模型计算的胶结充填体竖向应力与数值模拟结果基本吻合，水平矿柱回采过程中顶板未出现塑性区，计算确定的顶板保留厚度能满足安全生产需求。
4）位移监测结果表明，监测点A、B最大累计位移量均小于极限位移量，顶板在回采过程中保持稳定，验证了理论分析结果的可靠性。
基金
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  • 2023年度湖南省自然科学基金项目区域联合基金项目(2023JJ50356)
文献
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doi: 10.3969/j.issn.0253-6099.2024.01.009
  • 接收时间：2023-08-23
  • 首发时间：2026-03-20
  • 出版时间：2024-02-01
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  • 收稿日期：2023-08-23
基金
2023年度湖南省自然科学基金项目区域联合基金项目(2023JJ50356)
作者信息
    1.中冶长天国际工程有限责任公司，湖南　长沙　410006
    2.湖南科技大学　资源环境与安全工程学院，湖南　湘潭　411201

通讯作者:

叶永飞（1995—），江西赣州人，工程师，主要从事岩石力学方面的研究。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
species		 占总种数比例
Percentage of total
species (%)
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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