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题名:

 井底煤仓内仓壁变形破坏机理与稳定性控制研究    

作者:

 刘明银    

学号:

 16103304004    

保密级别:

 保密(2年后开放)    

语种:

 chi    

学科代码:

 0819    

学科:

 工学 - 矿业工程    

学生类型:

 博士    

学位:

 工学博士    

学位年度:

 2023    

学校:

 西安科技大学    

院系:

 能源学院    

专业:

 矿业工程    

研究方向:

 岩层控制    

导师姓名:

 伍永平    

导师单位:

 西安科技大学    

提交日期:

 2024-01-12    

答辩日期:

 2023-12-03    

外文题名:

 Study on Deformation Failure Mechanism and Stability Control of the Inner Wall of Shaft Coal Pocket    

关键词:

 井底煤仓 ; 内仓壁 ; 稳定性 ; 散体结构 ; 破坏机理    

外文关键词:

 shaft coal pocket ; inner wall of shaft coal pocket ; stability ; granular structure ; failure mechanism    

摘要:

井底煤仓是煤矿运输系统的重要环节,主要负责井下煤炭的贮存与转运,一旦发生 变形与失稳将直接制约整个矿井的生产。在装煤、卸煤过程中,煤仓内壁受动压(散体 块煤流动与冲击)、静压(满仓、空仓)反复作用,容易出现疲劳损伤,且内壁在频繁 的加载、卸载工况下发生的微破裂监测难度大,导致微裂纹演化成为大裂隙,甚至产生 大变形垮落失稳。因此,开展煤仓内仓壁变形破坏机理及稳定性控制研究对矿井安全生 产具有重要的理论与现实意义。

论文采用理论分析、数值模拟、物理相似模拟、工业试验等相结合的研究方法,分 析井底煤仓损伤破坏特征及影响因素,揭示井底煤仓内仓壁受载、变形及破坏机理,提 出稳定性控制对策。主要研究成果如下:

(1)确定了井底煤仓内仓壁稳定性的主要影响因素。分别为内仓壁自身强度及材 料特性、围岩性质和仓内散体贮料内部承载结构及工作状态。划分了五种仓壁破坏类型, 分别为剪切破坏、拉伸破坏、拉剪组合破坏、冲击破坏和长期磨损破坏。

(2)给出了内仓壁的变形规律和仓内的散体承载结构。建立了井底煤仓内仓壁结 构力学模型,基于厚壁圆筒埋设在无限大弹性体等相关理论,给出了不同工作状态下仓 壁及围岩的应力和位移表达式。揭示了仓内的散体颗粒存在“三维锥壳”承载结构。该 结构的形成和失稳是仓壁产生卸载超压的根本原因,不同的结拱位置对仓壁应力应变分 布有影响,结拱位置越高,相应的仓壁的应力越低,随着结拱位置的升高,相应的仓壁 应变也逐渐减小。给出了仓内散体颗粒流动规律分区,在纵向可划分为“三区”(结构 下方自然流动区、结构上覆压实区和顶部整体流动区)、在水平方向可划分为“两圈” (中心部畅流圈和仓壁侧的缓流圈)。

(3)揭示了内仓壁变形破坏机理。在散体贮料装、卸煤(矸)过程中,仓壁变形 随着循环加载次数的增加而增加,而仓壁强度则衰减,随后出现损伤-裂纹发育-破坏失 稳。仓壁变形呈现出先增加、后稳定、再减小的趋势,确定了内仓壁失稳判定条件。煤 仓内仓壁经历弹性变形、塑性变形、仓壁破坏和承载结构失稳四个阶段。当仓壁主要受 内部散体颗粒载荷作用时,主要发生剪切破坏;当主要受外侧薄弱岩层作用时,主要发生拉伸破坏;二者共同作用时,则为拉剪复合破坏。

(4)给出了井底煤仓内仓壁稳定性控制途径和方法。提出了煤仓内仓壁稳定性的 设计、施工、运营三阶段协同控制技术,指导了现场工程实践,取得了良好的效果。

外文摘要:

Shaft coal pocket is an important segment of the coal mine transportation system,mainly responsible for the storage and transportation of underground coal, and once deformation and instability occur, its stability directly affects the production of the entire mine. In the process of coal loading and unloading, the inner wall of the shaft coal pocket is prone to fatigue damage under the repeated action of dynamic pressure (flow and impact of
bulk coal) and static pressure (full bunker and empty bunker).It is extremely difficult to monitor the micro crack on the inner wall under frequent loading and unloading conditions. So the micro cracks will evolution into large cracks. Then the large deformation collapse instability. Therefore, conducting research on the deformation and failure mechanism and stability control of the inner wall of shaft coal pocket has important theoretical and practical significance for the safety production of mines.

The thesis adopts research methods such as theoretical analysis, numerical simulation,physical similarity simulation, and industrial experiments to analyze the damage and failure characteristics and influencing factors of the shaft coal pocket, reveal the loading, deformation, and failure mechanisms of the inner wall of the shaft coal pocket, and propose stability control measures. The main achievements are as follows:

(1) The main factors affecting the stability of the inner wall of shaft coal pocket are determined as follows: the strength and material characteristics of the inner shaft wall, the internal bearing structure of the bulk storage materials in the shaft coal pocket, the properties of surrounding rock, and the operating state of the shaft coal pocket. The failure types of the shaft coal pocket are divided into five categories: shear failure, tensile failure, combined tensile and shear failure, impact failure, and long-term wear failure.

(2) The deformation trend of the inner shaft wall and the loose bearing structure inside the shaft coal pocket are given. A mechanical model of the inner wall structure of the shaft
coal pocket of the well has been established. Based on relevant theories such as thick walled cylinders buried in infinite elastic bodies, expressions for the stress and displacement of the shaft wall and surrounding rock under different working conditions have been given. It hasd been revealed that there exists a "three-dimensional conical shell" load-bearing structure for the dispersed particles in the shaft coal pocket The formation and instability of this structure are the fundamental reasons for the unloading overpressure on the shaft wall. Different arch positions have an impact on the stress and strain distribution of the shaft wall. The higher the arch position, the lower the corresponding stress on the shaft wall. As the arch position increases, the corresponding strain on the inner wall of shaft coal pocket also gradually decreases. The flow patterns of loose particles in the shaft coal pocket are divided into "three zones" in the longitudinal direction (natural flow zone below the structure, compaction zone above the structure, and overall flow zone at the top), and "two circles" in the horizontal direction (smooth flow zone at the center and slow flow circle on the side of the shaft wall).

(3) Revealed the deformation and failure mechanism of the inner wall of shaft coal pocket. During the process of loading and unloading coal (gangue) in bulk storage, the deformation of the shaft wall increases with the increase of cyclic loading times, while the strength of the wall decreases, followed by damage crack development failure instability. The deformation of the shaft wall shows a trend of first increasing, then stabilizing, and then decreasing, which determines the criteria for determining the instability of the inner wall of shaft coal pocket. The inner wall of the shaft coal pocket undergoes four stages: elastic deformation, plastic deformation, failure, and instability of the load-bearing structure inside the bunker. When the shaft wall is mainly subjected to internal granular loading, shear failure mainly occurs; When mainly affected by weak rock layers on the outside, tensile failure mainly occurs; When the two act together, it is a tensile shear composite failure.

(4) The approach and method for controlling the stability of the inner wall of shaft coal pocket are provided. A collaborative control technology for the design, construction, and operation of the stability of the inner wall of shaft coal pocket has been proposed, guiding on-site engineering practice and achieving satisfied application effect.

参考文献:

[1] 伍永平,刘明银,解盘石,郎丁.煤矿井底煤仓内散体颗粒三维结构分析[J].西安科

技大学学报,2021,41(04):592-600.

[2] 刘明银,伍永平.井底煤仓修复设计及工程实践[J].煤炭工程,2017,49(7):14-17.

[3] 谢永存. 井下煤仓仓壁受损修复施工应用[J]. 煤炭与化工, 2017 , 40(12) :

101-103+121.

[4] 史振凡,谢文兵.柴里矿中央煤仓修复改造方法[J].矿山压力与顶板管理,1997,

22(2):71-72.

[5] 姚峰.千吨煤仓快速修复加固施工技术[J].山东煤炭科技,2005,23(5):23-25.

[6] 师同民,范智海.井底煤仓二次锚网索支护加固技术[J].煤炭科学技术,2013,41(07):

54-56+92.

[7] 刘福.井底煤仓破坏机理及治理技术研究[D].重庆:重庆大学硕士学位论文,2008.

[8] 金建春.井底煤仓及上下硐室扩修加固技术[J].科技资讯,2012,10(25):56-57+59.

[9] 邵嗣华,苏学友,张应芳,李国胜.大水头煤矿1180 主煤仓快速修复技术[J].煤炭科

技,2017,45(4):4-6+10.

[10] 董荣泉.百米特大立式煤仓抗破坏技术[J].煤炭科学技术,2009,37(12):18-21.

[11] 张国辅.矿山井下煤仓与矿仓(设计和使用)[M].北京:煤炭工业出版社,1983.

[12] 张荣立,何国纬,李铎.采矿工程设计手册[M].北京:煤炭工业出版社,2003:

1743-1751.

[13] GB50215-2015.中华人民共和国国家标准:煤炭工业矿井设计规范[S].2015.

[14] 抚顺设计分院.关于皮带斜井井底煤仓容量应如何确定问题[J].煤矿设计,1957,

3(11):12-17.

[15] 华顺添.对“关于皮带斜井井底煤仓容量应如何确定问题”的补充[J].煤矿设

计,1958,4(08):10-11.

[16] 章立本.井下煤仓容量的分析及计算方法[J].煤炭科学技术,1977,(05):57-58+24.

[17] 龙彦庭.关于确定井底煤仓容量的意见[J].煤矿设计,1981,27(02):2.

[18] 王亮.井下煤仓容量的分析和计算[J].淮南矿业学院学报,1983,3(01):113-122+35.

[19] 刘志河,郝晋生,张海涛,郝海金,程根马,董宪宏.水平煤仓的试验研究[J].煤炭

学报,1995,20(04):371-374.

[20] 刘善荃.井底煤仓快速施工[J].煤炭科学技术,1993,21(05):39-41+55+63.

[21] 王毅,刘志河,李剑刚.基于Petri 网的井下煤仓可靠性分析[J].太原理工大学学报,

2001,32(03):276-278.

[22] 郝兵元,隋刚,康立勋.煤矿井下工作面生产系统可靠性仿真[J].西安科技大学学报,

2008,28(02):367-370+396.

[23] 李饶荣.凉水井煤矿井下主运输系统可靠性分析与改善[D].徐州:中国矿业大学硕

士学位论文,2020.

[24] 胡德斌.矿井煤仓合理配置的计算机模拟研究[D].徐州:中国矿业大学硕士学位论

文,1996.

[25] 孙继平,吴冰.概率哈夫变换在井下煤仓煤位检测中的应用[J].煤炭学报,2004,

29(06):748-751.

[26] 彭飞.煤矿主井装卸系统粘煤堵塞问题研究[D].焦作:河南理工大学硕士学位论文,

2013.

[27] 巩琦,刘建慧,徐晓明.矿井煤仓堵塞的原因和预防浅析[J].煤炭工程,2008,40(10):

68-69.

[28] 薛铜龙.矿井煤仓堵塞的原因分析和解决方法[J].煤炭科学技术,2009,37(03):

71-72+76.

[29] 张鑫磊.大采深大体积瓮形煤仓的支护分析及研究[D].邯郸:河北工程大学硕士

学位论文.2013.

[30] 张超.略谈主井井底增补煤仓的做法[J].煤矿设计,1995,27(09):12-14.

[31] 郑树柱.浅谈大容量圆筒倾斜井底煤仓设计[J].煤炭工程,2006,38(12):28-30.

[32] 郝培业.深仓散体静压力理论研究[J].农业机械学报,1993,24(1):68-72.

[33] 肖国先.料仓内散体流动的数值模拟研究[D].南京:南京工业大学博士学位论

文.2004.

[34] 魏锦平.综放面顶煤压裂规律及成拱机理研究[D].太原:太原理工大学博士学位论

文.2004.

[35] 梁国栋,姜德义,陈兆平.井底煤仓卸载梁纠偏加固治理技术[J].煤矿开采,2008,

13(06):53-55+60.

[36] 于为芹,陈招宣.井底煤仓设计方案比选一例[J].煤炭工程,2011,43(05):4-5.

[37] 高秋野,李林,曾凡彪.井底煤仓及给煤机硐室优化设计[J].煤炭工程,2013,45(S2):

34-35.

[38] 高鹏翔.动压影响下井底主煤仓变形特征及加固技术[J].煤炭技术,2017,36(07):

28-31.

[39] An H.Q.,Wang X.,Fang X.H.Wall normal stress characteristics in an experimental

coal silo[J].Powder Technol.,2021,377(2021):657-665.

[40] 马洪涛.大直径大垂高煤仓设计及施工技术[J].煤炭工程,2015,47(10):42-44.

[41] 王志勇,郭俊强,王合涛.井底煤仓上口联合加固技术应用[J].西部探矿工程,2012,

24(10):138+143.

[42] Wu Y.P.,Liu M.Y.,Lv W.Y.,Hu B.S.Mechanical model of underground shaft coal

pocket and deformation of silo wall in coal mines[J].Adv. Civil Eng.,2020,8892091:

1-11.

[43] Wu Y.P.,Liu M.Y.,Xie P.S.,Wang H.W.,Hu B.S. Three dimensional physical

simulation experiment for transparent shaft coal pocket wall in coal mine [J].ACS

Omega,2022,7(19):16442-16453.

[44] Liu M.Y.,Wu Y.P.,Wen Z.C.Study on the flow trend of particles in shaft coal

pocket of coal mine[J].Energy Exploration & Exploitation,2023,41(2):785-801.

[45] 刘明银,温兆翠. 煤矿井底煤仓装卸煤过程中的微振特性研究[J].山西能源学院学

报,2021,34(5):17-19.

[46] 刘明银. 煤矿井底煤仓壁稳定性控制技术研究[J].山西焦煤科技,2021,8:44-46.

[47] 王峥,商守海,高利强,孙磊,卢建宁,薛道荣,等.煤仓清理机器人研发与应用[J].

煤炭科学技术,2022,50(09):215-221.

[48] 宋志安.井下煤仓新型清仓技术[J].矿业工程研究,2010,25(01):59-62.

[49] 王学文,Qin Y.,Tian Y.K.,Yang X.Y.,杨兆建.煤仓内煤散料流动状态与力学

行为影响因素[J].计算力学学报,2016,33(5):773-778.

[50] Q.A.Cui , J.J.Shen.Location Selection of Coal Bunker Based on Particle Swarm

Optimization[C] . In Proceedings of the 19th Int. Conf. Industrial Eng. , 2013 :

1121-1128,Berlin,Heidelberg,Germany,June 2013.

[51] 杨建东.卸矿过程中矿石对溜井井壁碰撞分析研究[D].鞍山:辽宁科技大学硕士学

位论文,2020.

[52] 白庆升,屠世浩,王沉.顶煤成拱机理的数值模拟研究[J].采矿与安全工程学报,

2014,31(02):208-213.

[53] 赵顺波.混凝土结构设计原理[M].上海:同济大学出版社,2004.

[54] 郭志飚,胡江春,杨军,王炯,齐干.地下工程稳定性控制及工程实例[M].北京:

冶金工业出版社,2015.

[55] 郑颖人,孔亮.岩土弹塑性力学[M].北京:中国建筑工业出版社,2010.

[56] Cao H,Jiang L L.Mechanical properties of HPC and numerical simulation of mine shaft

under 3D load[J].Applied Mech. Materials,2015,777:48-51.

[57] H.L.Lv , Y.Ma , S.C.Zhou , et al.Case study on the deterioration and collapse

mechanism and curing technique of RC coal bunkers[J].Procedia Earth Planetary Sci.,

2009(1):606-611.

[58] 程海星,古文哲.井下大直径煤仓设计与施工探究[J].煤炭技术,2023,42(06):80-83.

[59] 徐慧琼,王庆福.基于图像识别的井下煤仓煤位监测系统设计[J].煤炭技术,2022,

41(08):212-214.

[60] Janssen H A.Experiments about pressures of grain in silos[J].Z.des Vereines Deutscher

Ingenieure,1895,39(35):1045-1049.

[61] S.F.Edwards , R.B.S.Oakeshott. The transmission of stress in an aggregate[J].

Physica,1989,38:88-92.

[62] M.M.Khan,G.J.Krige.Evaluation of the structural integrity of aging mine

shafts[J].Eng. Structures,2002,24(7):901-907.

[63] Atewologun & A.O.,Riskoski G.L.,Experimental determination of Janssen's stress

ratio by four methods for soybeans under static conditions[J].Trans.ASAE , 1991 ,

34(5):2193-2198.

[64] W.J.B.vander Bergh,M.R.J.de Lannoy,B.Scarlett.Influence of particle breakage on

the wall friction coefficient of brittle particulate solids:part 2,Application to a silo

design,Powder Technol.,1991,67(3):249-263.

[65] John Brown.Numerical analysis of silo discharge[D].Lund University,2008.

[66] D.M.Walker.An approximate theory for pressure and arching in hoppers[J].Chem.

Engng.Sci.,1966,21:975-997.

[67] J.K.Walters.A theoretical analysis of stresses in silos with vertical walls[J].Chem.

Engng.Sci.,1973,28:13-21.

[68] A.W.Jenike,J.R.Johanson,J.W,Carson. Bin loads-part 2[J].Concepts.Jnl Engng

Industry,Trans ASME,1973,95(1):1-5.

[69] M.L.Reimbert,A.M.Reimbert.Silos:Theory and Practice[M].Clausthal,Ger.:Trans.

Tech. Publications,1976.

[70] C.Wu,J.Luo,R.J.Tian,et al.The effect of Mud-shale hydration on rock mechanic

parameters[J].Journal of Oil,Gas Technol.,2012,34(04):147-150.

[71] B. Shen.Coal mine roadway stability in soft rock: a case study[J].Rock Mech. Rock

Eng.,2014,47(06):2225-2238.

[72] H.Basarir , Y.Sun , G.Li.Gateway stability analysis by global-local modeling

approach[J].Int.J.RockMech.Min.Sci.,2019,113(01):31-40.

[73] T.Gentzis , N.Deisman , R.J.Chalaturnyk.A method to predict geomechanical

properties and model well stability in horizontal boreholes[J].Int.J.Coal Geol.,2009,

78(02):149-160.

[74] Yang S.Q.,Chen M.,Jing H.W.,Chen K.F.,Meng B.A case study on large

deformation failure mechanism of deep soft rock roadway in Xin'An coal mine ,

China[J].Eng.Geol.,2017,217:89-101.

[75] Kang Y.S.,Liu Q.S.,Gong G.Q.,Wang H.C. Application of a combined support

system to the weak floor reinforcement in deep underground coal mine[J].

Int.J.RockMech.Min.Sci.,2014,71:143-150.

[76] Liang S.,Elsworth D.,Li X.H.,Fu X.H.,Sun B.Y.,Yao Q.L. Key strata

characteristics controlling the integrity of deep wells in longwall mining

areas[J].Int.J.Coal Geol.,2017,172:31-42.

[77] Cheng M.,Fu X.H.,Kang J.Q.,Tian Z.B.,Shen Y.Y. Experimental study on the

change of the pore-fracture structure in mining-disturbed coal-series strata : an

implication for cbm development in abandoned mines[J]. Energy & Fuels,2021,35(02):

1208-1218.

[78] Yin B.,Kang T.H.,Kang J.T. Experimental and mechanistic research on enhancing

the strength and deformation characteristics of Fly-Ash-Cemented filling materials

modified by electrochemical treatment[J]. Energy & Fuels,2018,32(03):3614-3626.

[79](苏)Г.К.КЛЕЙН,著.散体结构力学[M].陈大鹏,王荣鋆,徐文焕,项忠权,

范文田,译.北京:人民铁道出版社,1960.

[80] 杨维好,崔广心,周国庆,李毅,陈先德,吕恒林.特殊地层条件下井壁破裂机理

与防治技术的研究(之一)[J].中国矿业大学学报,1996,25(4):1-5.

[81] 吕恒林,杨维好,程锡禄,周国庆,陈先德,李毅.特殊地层条件下井壁破裂机理

与防治技术的研究(之二)[J].中国矿业大学学报,1997,26(2):1-4.

[82] 吕恒林,崔广心.深厚表土中井壁结构破裂的力学机理[J].中国矿业大学学报.1999,

28(6):539-543.

[83] 崔广心.深厚表土中竖井井壁的外载[J].岩土工程学报.2003,25(3):294-298.

[84] 赵光思.厚表土立井井壁受力状态及其演变规律研究[D].徐州:中国矿业大学博

士学位论文,2009.

[85] 程桦,刘吉敏,荣传新,姚直书.变断面深厚表土钻井井壁竖向结构稳定性[J].煤

炭学报,2008,33(12):1351-1357.

[86] 姚直书,程桦,居宪博.深厚冲积层井筒修复内层钢板高强钢纤维混凝土复合井壁

研究及应用[J].煤炭学报,2017,42(09):2295-2301.

[87] 何有巨,经来旺.深立井围岩稳定性分析[J].中国矿业,2006,15(6):61-64.

[88] 蔡海兵,姚直书,荣传新.钢纤维混凝土弧板井壁结构的力学特性[J].煤炭学报,

2010,35(01):46-50.

[89] 徐海洋,桂和荣,孙本魁.任楼煤矿副井井筒变形破坏机理研究与防治[J].宿州

学院学报,2016,31(12):112-119.

[90] 王传武.副井井筒的破坏机理和变形规律的研究[D].淮南:安徽理工大学硕士学

位论文,2015.

[91] 奚家米.深厚富水软岩井筒冻结壁力学特性及应用研究[D].西安:西安科技大学

博士学位论文,2011.

[92] 张丁丁.兖州矿区第四系厚松散层沉降特性研究[D].西安:西安科技大学博士学

位论文,2015.

[93] 梁博.新庄煤矿风立井考虑冻结壁解冻井壁的稳定性影响分析[D].西安:西安科

技大学硕士学位论文,2015.

[94] 李博融.白垩系地层冻结井筒岩石物理力学特性及温度场研究[D].西安:西安科

技大学博士学位论文,2016.

[95] 鲁治城,宋选民,李宏斌,刘兵晨,周钰博.姚家山矿千米立井围岩稳定及井壁

支护厚度的理论预测研究[J].太原理工大学学报.2014,45(06):807-812.

[96] 刘兵晨.姚家山矿千米立井井壁稳定性及支护技术研究[D].太原:太原理工大学

硕士学位论文,2012.

[97] 康红普,林健,杨景贺,吴拥政,高富强.松软破碎井筒综合加固技术研究与实

践[J].采矿与安全工程学报,2010,27(4):447-452.

[98] 张建俊.深立井不稳定软岩段井壁破裂机理与防治技术研究[D].阜新:辽宁工程

技术大学博士学位论文.2014.

[99] 王猛,汤国水,王东,霍丙杰.井筒围岩应力分布及支护强度相似模拟[J].辽宁

工程技术大学学报,2009,28(S1):51-53.

[100] 闫国宁.钻井井壁漂浮下沉竖向稳定性控制技术研究[D].阜新:辽宁工程技术大

学硕士学位论文.2014.

[101] 王渭明,路林海.正交各向异性复合井壁应力变形分析与应用[J].力学与实践,

2009,31(1):52-56.

[102] 蒋斌松,张平,桕雪云.立井井壁的计算理论[J].岩石力学与工程学报.2003,

22(Sl):2183-2186.

[103] 侯俊友.深厚表土中复合井壁受力及结构形式研宄[D].焦作:河南理工大学硕士

学位论文,2012.

[104] 葛晓光.底部含水层疏水时表土层的流变作用及井壁受力模型[J].煤炭学报,2001,

26(2):137-140.

[105] 刘环宇,陈卫忠,王争鸣.兖州矿区立井井筒破坏机制的理论分析[J].岩石力学

与工程学报,2007,26(S1):2620-2626.

[106] 宋朝阳,纪洪广,孙利辉.高地应力深立井井筒围岩应力演化与变形规律及支护

分析[J].煤炭工程,2016,48(10):45-48.

[107] 谢洪彬.立井井筒基岩段井壁破坏原因分析[J].煤炭科学技术,2000,28(4):

367-370.

[108](美)乔纳斯A·朱卡斯,等,著.碰撞动力学[M].张志云,丁世用,魏传忠,译.

北京:兵器工业出版社,1989.

[109] 陈育民,徐鼎平.FLAC/FLAC3D 基础与工程实例[M].北京:中国水利水电出版

社,2013.

[110] 石崇,张强,王盛年.颗粒流(PFC5.0)数值模拟技术[M].北京:中国建筑工业出

版社,2016.

[111] 于学馥,郑颖人,刘怀恒,方正昌.地下工程围岩稳定分析[M].北京:煤炭工业出

版社,1983.

[112] 黄克智.板壳理论[M].北京:清华大学出版社,1987.

[113](苏)考洛特金(Я.И.Короткин),等,著.板与圆筒形壳的弯曲及稳定性船舶结

构力学[M].陈铁云,等译.北京:高等教育出版社.

[114] 贾喜荣.岩石力学与岩层控制[M].徐州:中国矿业大学出版社,2010.

中图分类号:

 TD325    

开放日期:

 2026-01-13    

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