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Article(id=1322595263127072951, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322595047657296718, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1712592000000, receivedDateStr=2024-04-09, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793260883360, onlineDateStr=2026-10-29, pubDate=1742832000000, pubDateStr=2025-03-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793260883360, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793260883360, creator=13701087609, updateTime=1793260883360, updator=13701087609, issue=Issue{id=1322595047657296718, tenantId=1146029695717560320, journalId=1225396423026438145, year='2025', volume='45', issue='3', pageStart='1', pageEnd='288', issueExtLink='null', onlineDate='null', pubDate='1742832000000', pubDateStr='2025-03-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793260831989, creator='13701087609', updateTime=1793260831989, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=41, endPage=48, ext={EN=ArticleExt(id=1322595263315816632, articleId=1322595263127072951, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=Numerical Simulation and Engineering Verification of Freezing Construction of Vertical Shaft Under Complex Coastal Conditions, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

To study the influence of seepage field on the freezing temperature in the loose accumulation rock group of the intake air shaft in the gold mining area in the northern sea area of Sanshan Island, Laizhou City, based on the flow velocity measurement and the material parameters of the rock group, the COMSOL finite element numerical model was established. The intersection time of the three-circle freezing construction of the vertical shaft and the formation time of the freezing curtain were predicted, and the reliability of the design and numerical simulation of the three-circle freezing construction scheme of the vertical shaft was verified by an engineering example. The results show that due to the high flow velocity of coastal groundwater, the intersection line of the inflow surface is shaped like teeth during the freezing process. The low temperature of the freezing pipe has a significant impact on the downstream under the seepage action, and the freezing curtain develops asymmetrically and shifts to the downstream of seepage. The three-circle freezing design reduces the temperature of the shaft excavation area to below the phase transition temperature of −1 ℃ after 18 days of freezing. In the engineering verification, the intersection time and the freezing curtain formation time are 25 d and 36 d, respectively, which are consistent with the numerical simulation results. The research results can provide reference for similar projects.

, authors=Weifeng HU1, 2, Xiaobing YAN1, 2, Peidong ZHAO2, 3, authorsList=Weifeng HU, Xiaobing YAN, Peidong ZHAO, authorCompany=null, correspAuthors=Xiaobing YAN, 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=1322595267799527641, articleId=1322595263127072951, tenantId=1146029695717560320, journalId=1225396423026438145, language=CN, title=沿海复杂条件立井冻结施工数值模拟与工程验证, columnId=1226462294490657775, journalTitle=矿业研究与开发, columnName=采矿与矿山充填, runingTitle=null, highlight=null, articleAbstract=

为研究莱州市三山岛北部海域金矿区进风井松散堆积物岩组中的渗流场对冻结温度的影响规律，基于流速测定和岩组材料参数，建立COMSOL有限元数值模型，对立井三圈冻结施工的交圈时间和冻结帷幕的形成时间进行预测，并通过工程实例验证立井三圈冻结施工方案设计和数值模拟的可靠性。结果表明：由于沿海地下水流速较大，冻结过程中迎流面交圈线呈“齿状”；冻结管的低温在渗流作用下对下游影响显著，冻结帷幕呈不对称发展且向渗流下游偏移；三圈冻结设计使得立井开挖区域在冻结18 d后温度降低至相变温度–1 ℃以下。工程验证中交圈时间和冻结帷幕形成时间分别为25 d和36 d，与数值模拟结果一致，研究结果可为类似工程提供参考。

, authors=胡伟丰1, 2, 闫小兵1, 2, 赵培东2, 3, authorsList=胡伟丰, 闫小兵, 赵培东, authorCompany=null, correspAuthors=闫小兵, authorNote=

胡伟丰（1992—），男，湖南娄底人，工程师，主要研究方向为地下矿山建设及采矿工程。E-mail:

, correspAuthorsNote=
闫小兵（1985—），男，陕西陇县人，硕士，高级工程师，主要研究方向为地下矿山建设及采矿工程。E-mail:
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胡伟丰（1992—），男，湖南娄底人，工程师，主要研究方向为地下矿山建设及采矿工程。E-mail:

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胡伟丰（1992—），男，湖南娄底人，工程师，主要研究方向为地下矿山建设及采矿工程。E-mail:

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Determination methods and results of groundwater flow velocity

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方法地下水流速度/(m/d)备注
涨潮退潮
电导率测试11.9713.38测定时间:2017年4月27日至28日
水流方向:南向北314.82°
垂向流测试6.216.50
放射性同位素示踪8.4710.26
), ArticleFig(id=1322595733899956339, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595263127072951, language=CN, label=表1, caption=

地下水流速度测定方法及结果

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方法地下水流速度/(m/d)备注
涨潮退潮
电导率测试11.9713.38测定时间:2017年4月27日至28日
水流方向:南向北314.82°
垂向流测试6.216.50
放射性同位素示踪8.4710.26
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Freeze hole parameters and layout

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三圈孔冻结布孔圈径/m孔间距/m/冻结孔孔数/个冻结孔深度/m测温孔深度/m水文孔深度/m
主11.41.1533196.6
外12.41.2543142.090、45、4542
内6.01.3351442.0
), ArticleFig(id=1322595734109671541, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595263127072951, language=CN, label=表2, caption=

冻结孔参数与布置情况

, figureFileSmall=null, figureFileBig=null, tableContent=
三圈孔冻结布孔圈径/m孔间距/m/冻结孔孔数/个冻结孔深度/m测温孔深度/m水文孔深度/m
主11.41.1533196.6
外12.41.2543142.090、45、4542
内6.01.3351442.0
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Material parameters of numerical simulation

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自然土壤的初始温度Ts/℃冻结管温度Ti/℃水的导热系数lw/(W/(m·k))冰的导热系数li/(W/(m·k))基质的导热系数lw/(W/(m·k))水的热容Cw/(J/(kg·K))冰的热容Ci/(J/(kg·K))基质的热容Cs/(J/(kg·K))
18–260.62.143.14 1822 060835
水的密度rw/(kg/m3)冰的密度ri/(kg/m3)基质的密度rs/(kg/m3)潜热L/(kJ/kg)孔隙率ep水的动力黏度mw/(Pa·s)固有渗透率kint/m2相变温度Tc/℃
1 0009202 6503340.371.793E-31E-12–1
), ArticleFig(id=1322595734294220919, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322595263127072951, language=CN, label=表3, caption=

数值模拟材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
自然土壤的初始温度Ts/℃冻结管温度Ti/℃水的导热系数lw/(W/(m·k))冰的导热系数li/(W/(m·k))基质的导热系数lw/(W/(m·k))水的热容Cw/(J/(kg·K))冰的热容Ci/(J/(kg·K))基质的热容Cs/(J/(kg·K))
18–260.62.143.14 1822 060835
水的密度rw/(kg/m3)冰的密度ri/(kg/m3)基质的密度rs/(kg/m3)潜热L/(kJ/kg)孔隙率ep水的动力黏度mw/(Pa·s)固有渗透率kint/m2相变温度Tc/℃
1 0009202 6503340.371.793E-31E-12–1
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沿海复杂条件立井冻结施工数值模拟与工程验证
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胡伟丰 1, 2 , 闫小兵 1, 2 , 赵培东 2, 3
矿业研究与开发 | 采矿与矿山充填 2025,45(3): 41-48
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矿业研究与开发 |采矿与矿山充填 2025 , 45 (3) : 41 -48
沿海复杂条件立井冻结施工数值模拟与工程验证
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胡伟丰1, 2 , 闫小兵1, 2 , 赵培东2, 3
作者信息
  • 1.湖南涟邵建设工程（集团）有限责任公司，湖南　长沙　410125
  • 2.宏大爆破工程集团有限责任公司，湖南　长沙　410011
  • 3.中南大学 资源与安全工程学院，湖南　长沙　410083
通讯作者:
闫小兵（1985—），男，陕西陇县人，硕士，高级工程师，主要研究方向为地下矿山建设及采矿工程。E-mail:
作者简介:

胡伟丰（1992—），男，湖南娄底人，工程师，主要研究方向为地下矿山建设及采矿工程。E-mail:

Numerical Simulation and Engineering Verification of Freezing Construction of Vertical Shaft Under Complex Coastal Conditions
Weifeng HU1, 2 , Xiaobing YAN1, 2 , Peidong ZHAO2, 3
Affiliations
  • 1.Hunan Lianshao Construction Engineering (Group) Co., Ltd., Changsha, Hunan 410125, China
  • 2.Hongda Blasting Engineering Group Co., Ltd., Changsha, Hunan 410011, China
  • 3.School of Resources and Safety Engineering, Central South University, Changsha, Hunan 410083, China
出版时间: 2025-03-25
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摘要
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为研究莱州市三山岛北部海域金矿区进风井松散堆积物岩组中的渗流场对冻结温度的影响规律，基于流速测定和岩组材料参数，建立COMSOL有限元数值模型，对立井三圈冻结施工的交圈时间和冻结帷幕的形成时间进行预测，并通过工程实例验证立井三圈冻结施工方案设计和数值模拟的可靠性。结果表明：由于沿海地下水流速较大，冻结过程中迎流面交圈线呈“齿状”；冻结管的低温在渗流作用下对下游影响显著，冻结帷幕呈不对称发展且向渗流下游偏移；三圈冻结设计使得立井开挖区域在冻结18 d后温度降低至相变温度–1 ℃以下。工程验证中交圈时间和冻结帷幕形成时间分别为25 d和36 d，与数值模拟结果一致，研究结果可为类似工程提供参考。

进风井  /  三圈冻结施工  /  渗流速度  /  温度场  /  数值模拟

To study the influence of seepage field on the freezing temperature in the loose accumulation rock group of the intake air shaft in the gold mining area in the northern sea area of Sanshan Island, Laizhou City, based on the flow velocity measurement and the material parameters of the rock group, the COMSOL finite element numerical model was established. The intersection time of the three-circle freezing construction of the vertical shaft and the formation time of the freezing curtain were predicted, and the reliability of the design and numerical simulation of the three-circle freezing construction scheme of the vertical shaft was verified by an engineering example. The results show that due to the high flow velocity of coastal groundwater, the intersection line of the inflow surface is shaped like teeth during the freezing process. The low temperature of the freezing pipe has a significant impact on the downstream under the seepage action, and the freezing curtain develops asymmetrically and shifts to the downstream of seepage. The three-circle freezing design reduces the temperature of the shaft excavation area to below the phase transition temperature of −1 ℃ after 18 days of freezing. In the engineering verification, the intersection time and the freezing curtain formation time are 25 d and 36 d, respectively, which are consistent with the numerical simulation results. The research results can provide reference for similar projects.

Intake air shaft  /  Three-circle freezing construction  /  Seepage velocity  /  Temperature field  /  Numerical simulation
胡伟丰, 闫小兵, 赵培东. 沿海复杂条件立井冻结施工数值模拟与工程验证. 矿业研究与开发, 2025 , 45 (3) : 41 -48 .
Weifeng HU, Xiaobing YAN, Peidong ZHAO. Numerical Simulation and Engineering Verification of Freezing Construction of Vertical Shaft Under Complex Coastal Conditions[J]. Mining Research and Development, 2025 , 45 (3) : 41 -48 .
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0　引言
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冻结施工是一种利用人工制冷技术将地下水冻结成冰墙，从而实现地下工程支护和防水的方法，具有施工周期短、适应性强、安全可靠等优点，被广泛应用于地铁、隧道、基坑、矿井等工程[1-3]。随着矿产资源开发利用的深入，深部矿床和滨海矿区等复杂地质水文条件下的资源开采越来越普遍[4-5]。因此，立井冻结施工在复杂地质条件下的矿产资源开采上具有更加广阔的前景。以莱州市三山岛北部海域超大型金矿床开采为例，该海域矿区发现的黄金资源储量高达470多吨，平均埋深超过2 000 m，且全部位于海底。要开采此类矿床，势必需要沿海建设超深矿井，然而沿海地区的地层多为深厚的松散沉积地层，普通凿井法将无法实现其开采。冻结法施工是此类地层立井施工的必然选择，对沿海复杂水文条件下的开采施工具有重要的现实意义。
立井冻结施工涉及多相流动、传热传质、相变等复杂的物理过程。薛红梅等[6]指出冻结温度监测系统对冻结施工参数的准确控制至关重要，提出了煤矿建井的冻结施工智能测温系统，并成功在多个工程实践中运用。王天亮等[7]通过搭建微缩模型，研究了地下水渗流速度对冻结施工的影响，从冻结壁厚度和交圈时间等多角度分析了流速的影响效果。近年来，冻结施工的数值模拟成为一种有效分析和优化冻结方案的手段[8]。冻结施工的数值模拟主要包括冻结温度场、冻结应力场、冻结变形场、冻结渗流场等的模拟，而冻结温度场的演化能够反映出冻结帷幕的形成过程。ZHANG等[9]通过模型试验和数值模拟分析了基坑工程中冻结施工温度场的演化规律，根据冻结帷幕的承压情况提出冻结管设计准则。
冻结温度场是冻结施工的基础，影响着冻结施工过程中地层强度等力学性能，进而影响施工的可行性[10]。陈红蕾等[11]运用ANSYS有限元软件对回风立井冻结温度场进行了平面热传导模拟，优化了温控孔设计。冻结温度场的数值模拟需要考虑冻结介质的热物性参数、冻结管的布置、冻结介质的流速和温度、地下水的流动和温度等因素[8,12]，现有的立井冻结施工数值模拟对地下水渗流的考虑仍存在不足，未能反映渗流速度对冻结温度场的影响[11,13-14]。同时，众多学者运用ANSYS和ABAQUS等软件对地铁工程冻结施工开展数值模拟研究且成果显著，而对运用COMSOL软件模拟立井冻结施工的研究较少。
因此，本文针对沿海复杂水文条件下的立井冻结施工，运用多种方法精确测量地下水渗流速度，通过COMSOL软件对设计的三圈冻结施工方案的冻结温度场进行数值模拟，分析最大渗流速度下冻结温度场演化规律，并对高渗流速度下冻结施工交圈和冻结帷幕形成作出预测。研究结果可为立井冻结施工提供参考。
1　工程概况
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1.1　施工区域位置
莱州市瑞海矿业有限公司拟建进风井位于莱州市区北26 km，莱州湾东南岸边，三山岛街道西岭村北2 km，莱州市三山岛北部海域金矿区东侧。进风井井口中心平面坐标：X=4 142 793,Y=40 499 057,Z=4.94。该井设计深度为1 530 m，井径为6.5 m，井筒净面积为33.183 m2，掘进面积为41.854~55.418 m2，井颈段高度为85 m。井颈段支护方式为内外壁双层钢筋砼支护，其中外壁砼支护厚度为550 mm，内壁砼支护厚度为400 mm，内外层砼支护井壁之间铺设1.5 mm厚的单层聚乙烯塑料板隔水层。
1.2　水文地质条件
工程勘察钻孔钻深将井筒在深度1 065.09 m的范围内自上而下分为4个工程岩组，如图1所示。一层为松散堆积物岩组，位于0.00~45.20 m，厚度为45.20 m，主要由砂土、黏性土组成，顶部为回填物，上部为近岸沉积物，中部为滨海沉积物，下部为陆相冲洪积物；二层为基岩风化带岩组，位于45.20~72.69 m，厚度为27.49 m，自上而下由变辉长岩的强风化带、中风化带和微风化带组成；三层为上部变辉长岩岩组，位于72.69~802.04 m，厚度为729.35 m，主体岩性为变辉长岩（原定名斜长角闪岩），岩石谱系属新太古代马连庄序列栾家寨单元（Ar3vMl）；四层为下部变辉长岩夹花岗岩岩组，位于802.04~1 065.09 m，厚度为263.05 m，主体岩性为变辉长岩，其中有多条二长花岗岩脉穿插，厚度为0.30~16.12 m，脉体与变辉长岩界线或截然或渐变，产状或顺延或斜切片麻理，成分或较纯或与基体岩石同化、混染。
根据地质钻孔勘探编录、孔内简易水文观测以及抽水试验获得的数据，划分了3种类型含水层，分别为第四系松散岩类孔隙含水层、基岩风化裂隙含水层、构造裂隙含水层。进一步划出4个含水层组，分别与4个工程岩组相对应。各含水层组间既有一定的水力联系，又各自相对成带。松散堆积物透水层厚度为45.20 m，主要由九层砂土、五层黏性土组成。其中粉质黏土、黏土为不透水层，粉砂、细砂为较弱透水层，中砂、粗砂为较强透水层。钻孔位于海岸，地下水直接与海水连通，受潮汐、波浪和海产养殖抽取地下水的影响，造成该含水层组水位变化较快且水位浮动较大，试验测得的渗透系数为0.401 40 m/d。基岩弱风化含水层组包括强-中-微风化变辉长岩。埋深为45.20~72.69 m，标高为−40.26~−67.75 m，厚度为27.49 m。地下水类型属基岩风化/构造裂隙水，水力性质为微承压水。
2　冻结施工参数设计
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2.1　渗流速度测定
施工点临近海岸，存在大量水产养殖的抽水井，且受到受潮汐影响，水位、地下水流速等变化较大，水文条件极其复杂。对水文孔内水流速度采用常规的染色剂示踪法进行测定，测得20~24 m矿层水流速度为37.63 m/d,24~34 m矿层水流速度为62.9 m/d，测定结果远远超出规范中规定的水流速度5 m/d。为合理设计冻结参数和保证冻结施工安全，采取更可靠、更高精度的方法，对水文孔内20 m、30 m、40 m等3个不同位置的水流速度重新测定。测量方法及结果见表1。
海水涨潮时，地下水流速度最大为11.97 m/d，退潮时为13.38 m/d，即最大渗流速度为13.38 m/d。该施工区域地下水流速度大，水文地质条件极其复杂，冻结难度大。因此，冻结施工设计三圈孔冻结施工方案，即采用主冻结孔冻结全深，在主孔内外分别设一圈辅助冻结孔，长度为松散堆积物透水层厚度。其中内圈辅助孔布置于井筒开挖范围内。三圈冻结施工示意如图2所示。
2.2　冻结施工参数计算
2.2.1　冻结壁厚度计算
控制层（松散堆积物透水层）底板埋深H为45.20 m，小于100 m，故采用无限长厚壁圆筒公式计算冻结壁厚度，即Lame公式[17]。
式中：E为冻结壁厚度，m；rw为井筒掘砌半径，取4.2 m;[σ]为冻土极限抗压强度，取2.21 MPa;n为安全系数，取2;p为地压值，取0.588 MPa。
计算得出冻结壁厚度为1.94 m。立井冻结施工开挖区的外围冻结壁设计平均温度为−8 ℃。
2.2.2　冻结孔圈径计算
主冻结孔布置圈直径D0的计算公式为：
式中：D′1为冲积层和基岩中井筒最大掘进直径，取8.2 m;Q′f为冲积层和基岩段的冻结孔允许偏斜率，取0.3%;h0为井筒冻结深度，m。
主冻结孔深度h0为96.6 m，则主冻结孔布置圈径直径为11.18 m。
2.2.3　冻结孔孔数计算
主冻结孔孔数由冻结孔圈径D0和开孔间距Ls决定。当冻结深度小于300 m时，依据施工经验，冻结孔开孔间距为1.10~1.20 m，设计取1.153 m。故冻结孔孔数N=πD0/Ls，计算得出进风井主冻结孔孔数为31个。内外辅助冻结孔参数与冻结孔布置参数设计如表2和图3所示。
3　冻结过程传热数值模拟
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沿海立井冻结施工受渗流和传热的影响。为解决地下水流速度超出规范的问题，确保一次冻结到位，顺利开挖井筒，运用COMSOL软件进行温度场演变数值模拟研究。冻结温度场的演变伴随相变传热，因此有必要对数值模拟进行工况简化：
（1）不考虑应力和应变，且自然土壤均为饱和状态，即水填满土壤的整个空隙空间；
（2）冷却液温度直接加载在冷冻管外壁，忽略冷冻管与冷却液之间的热交换；
（3）只考虑热传导，对流和辐射忽略不计。
该冻结施工涉及3个不同性质的地层，而最上层松散堆积物岩组为软弱地层，是施工难点。此外，根据渗流速度监测结果，松散堆积物岩组地下水流向主要为水平方向。因此，为控制建模参数一致和降低建模对算力的要求，采用二维简化模型对松散堆积物岩组进行数值模拟。根据需要求解的立井冻结施工问题，确定用到的COMSOL软件物理场接口为达西定律和多孔介质传热[18]。
3.1　控制方程
3.1.1　热传导方程
温度场中水冰相变的热传导方程可表示为：
式中：ρ为流体密度，kg/m3；Cp为恒压流体热容，J/(kg·K)，与水的热容Cw相等；(ρCp)e为恒压条件下的有效体积热容，J/(kg·K);u为地下水渗流速度矢量，m/s;T为温度，K;Q为热源；keff为多孔介质的有效导热率，W/(m·K);t为时间，s。
3.1.2　连续性方程
水与冰的连续性方程为：
式中，ε为孔隙率。
当多孔介质中的渗流水满足达西定律时，渗流速度即为达西速度，即：
式中：kint为多孔介质固有渗透率，m2;k0为冻结前的渗透率，m2;kr为相对渗透率，m2;p为流体压强，Pa;μ为流体黏度系数，Pa·s。
将孔隙率ε和相对渗透率kr定义为内置相变温度变量的函数，从而将相变与多孔介质传热相耦合。
3.1.3　相变潜热方程
多孔介质中渗透水发生相变转化为冰时产生潜热，潜热的释放视为材料热容的一部分，如式(6)所示。
式中：Ca为表观热容，J/(kg·K)；Ci和Cw分别是冰和水的热容，J/(kg·K)；L为水相变的潜热，kJ/kg;Tc是水相变为冰的温度变化，K。
3.2　数值模型参数配置
3.2.1　模型网格划分
根据工程实况，对地质条件差的松散堆积物岩组进行建模分析，利用软件自带建模和网格划分功能，模型长×宽为40 m×30 m，网格划分如图4所示。3个测温孔的坐标分别为C1(13.4,15)、C2(27.1,15)、C3(20,8.15)；图中红色路径为流速方向上沿直径走向的温度监测线（颜色标识见电子版）。
工程上冷冻管直径为0.108 m，冷冻管中冷冻液温度视为直接作用在冷冻管表面的温度，为–26 ℃。自然土壤初始温度为18 ℃。对于模型边界条件设置，地下水渗流上方位边界设置为恒温边界和水力边界，下方位边界设置为水力为0的边界。将三圈冷冻管及其表面设置为初始冻结温度，即−26 ℃，其余面设置为绝热边界。上下游边界的水力差由渗流速度等效转换，并驱动地下水的流动。
3.2.2　材料参数设置
研究区域数值模型划分为3种材料，分别为多孔介质基体、水和冰。研究区域地层土壤视为饱和介质，则土壤和流体的性质不随时间变化。数值模拟材料参数见表3。
3.3　模拟结果分析
通过临海立井三圈冻结施工有限元模型，得到温度场中渗流速度矢量箭头和相变温度等温线云图，对三圈冻结施工交圈时间和冻结壁发展进行预测研究。选取积极冻结5 d、10 d、25 d和36 d的模拟结果进行分析，相变温度为−1 ℃，冻结壁温度为−8 ℃。积极冻结5 d和10 d的温度场及相变温度等温线如图5所示。
由图5可知，冻结区域由冻结孔向四周发展，较大的渗流速度导致下游温度降低明显快于上游，这与渗流通过初期冻结孔间隙流速变大有关（红色箭头的大小表示达西速度大小，颜色标识见电子版），且垂直流速方向的冻结区域发展速度快于流速方向，相变区域(黑色线圈为相变温度−1 ℃)在冻结10 d时已完成联结。
积极冻结25 d和36 d的温度场及相变温度等温线如图6 所示。由图6 可知，冻结施工在第 25天完成交圈，由于流速较大，冻结过程中迎流面呈现明显的“齿状”，交圈范围在齿间最薄弱。立井开挖区域渗流场随冻结时间的增加而逐渐消失(圈内红色箭头消失), 当冻结36 d时，从等温线图中可以看出，已形成完整的冻结壁，等温线的间距为主冻结孔与外圈冻结孔间距的2.3倍，表明平均温度为−8 ℃、厚度为2.3 m的冻结壁已经形成。随着三圈冻结孔上游冻结壁的形成，冻结管的低温向下游传导得更快，表现为冻结壁在下游有一个尾部冻结区域。
测温点C1、C2和C3的温度变化规律如图7所示，冻结圈外侧温度降低速度由快到慢依次是渗流下游、垂直流速方向、渗流上游。由图7可知，积极冻结期间，温度降低最慢的渗流上游在25 d后，温度也能降低到相变温度−1 ℃以下。冻结圈流速方向上，沿直径走向的温度变化如图8所示。由图8可知，三圈冻结施工立井开挖区域(横轴上−4.2 m到4.2 m范围)在18 d后温度降低至相变温度以下，能够快速冻结。且横轴上，36 d后平均温度在−8 ℃以下的区域呈现不对称分布，即在较大渗流速度下，冻结壁非均匀对称发展，最终冻结壁形成位置向流速下游偏移。
冻结时间为50 d时，冻结帷幕范围进一步扩大，冻结孔范围内大部分区域温度为−8 ℃，如图9和图10所示。由图9和图10可知，冻结初期尽快降低盐水温度，进行三圈冻结孔积极冻结，能够实现井筒早日开挖，并使井筒连续掘砌施工。
4　工程应用
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为在冻结初期尽快降低盐水温度，进行积极冻结，冻结制冷系统设计如下。
（1）通过计算，井筒冻结需冷量为1.36×106 kcal/h，冻结管散热量为4.8×105 kcal/h。
（2）冻结系统设置一个制冷站，采用盐水制冷系统，总装机标准制冷量为1.92×106 kcal/h，配备4台JYSLG20F型制冷机，2台DBNL3-200型冷却塔。
（3）选用2台10Sh-9型盐水泵，使用1台，备用1台。单孔盐水流量均为12 m3/h，总盐水流量为372 m3/h。
（4）根据盐水总流量，选用Φ299 mm×8 mm的无缝钢管作为盐水干管及配集液圈，一去一回。供液管选用Φ60 mm×5 mm的聚乙烯塑料管。
（5）选用2台10SH-13A型冷却水循环泵，以满足300 m3/h的冷却水总循环量，选用2台200QJ32-26/2型水泵，以保证30 m3/h的新水补充量。
为降低冻结孔钻孔偏差对实际冻结效果的影响，钻孔测斜采用JDT-5型陀螺仪。定向及测斜采用JDT-3K型陀螺仪定向、随钻可提式导向器和5LZ146-7.0型螺杆钻。
完成冻结孔钻孔施工，在冷冻站设备安装调试运行后，5月6日正式开始进行积极冻结。积极冻结期间，4台制冷机全开，确保了制冷量时刻充足。冷冻过程中实时监测盐水进水、回水，水文孔和测温孔的温度，发现温度异常变化并及时分析原因，调整冷冻系统运行参数，以确保积极冻结期的盐水温度为−26~−28 ℃。5月31日，井筒冻结孔交圈。6月11日，冻结壁温度达到设计平均温度，冻结壁形成，井筒开始试挖，且试挖效果良好。经过33 d的施工，一次性通过了施工难度最高的松散沉积地层及强风化地层，为井筒后续顺利施工打下了坚实的基础。
综上，三交圈冻结施工数值模拟和工程应用在交圈时间和冻结壁形成时间上的结果相符，表明数值模拟结果可靠。
5　结论
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矿区进风井距离海岸线不足30 m, 井筒开口处于沿海沉积地层中，且地下水流速大。本研究设计了三圈孔冻结施工方案，借助数值模拟对冻结过程的温度场演变进行预测，并通过工程应用验证预测结果。得到的主要结论如下。
（1）通过多种方法准确测量地下水流速度，并建立多孔介质数值模型，分析渗流对三圈冻结施工传热的影响。
（2）根据理论公式和经验公式设计出冻结施工参数，并结合矿区岩土参数开展数值模拟，达西速度矢量箭头的演化表明，冻结25 d后，立井开挖区域渗流消失，即冻结施工交圈；从−8 ℃等温线的间距发展判断出冻结壁设计厚度形成时间为36 d。
（3）流速方向上沿直径走向的温度情况表明，沿海区域较大的渗流速度造成冻结壁的形成位置向下游偏移，研究结果为工程实践提供了必要参考。
（4）三圈冻结施工实例应用中的温度监测表明，数值模拟结果可靠，但更加精准的模型预测有待充分考虑不同岩层性质等参数的影响。
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  • 中南大学研究生创新资助项目(2022XQLH080)
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2025年第45卷第3期
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  • 接收时间：2024-04-09
  • 首发时间：2026-10-29
  • 出版时间：2025-03-25
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  • 收稿日期：2024-04-09
基金
中南大学研究生创新资助项目(2022XQLH080)
作者信息
    1.湖南涟邵建设工程（集团）有限责任公司，湖南　长沙　410125
    2.宏大爆破工程集团有限责任公司，湖南　长沙　410011
    3.中南大学 资源与安全工程学院，湖南　长沙　410083

通讯作者:

闫小兵（1985—），男，陕西陇县人，硕士，高级工程师，主要研究方向为地下矿山建设及采矿工程。E-mail:
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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
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