矿柱强度(Pillar Strength and Design)文献聚合
1 引言
房柱采矿法的矿柱设计(包括硬岩和软岩)一直是采矿岩石力学不断发展和进化的研究课题，特别是随着数值模拟技术和概率设计的应用，对矿柱的强度和破坏机理有了更深入的了解。为了对目前矿柱设计方法进行一个系统的State-of-the-Art的回顾，有必要对矿柱设计的文献实现聚合。这个笔记简要描述了文献聚合的过程。
矿柱变形破坏类型
2 从GeotechSet数据集中提取
GeotechSet数据集中包含着一个用于数据生成的<岩石力学>数字图书馆，首先从这个图书馆中提取矿柱设计的数据。下图所示的是提取出数据的原始文献。这些文献中既包括了最经典的采矿岩石力学专著，也包括了一些矿柱设计的杂志论文和学位论文。
3 从Endnote和Mendeley中提取
使用coal pillar design关键词从Endnote的Web of Science数据库中提取相关文献，共提取出592篇论文。此外，也从Mendeley中提取出部分论文。有一点需要说明的是，Mendeley不能直接输出为txt文档，因此先保存为xml文件，然后在Endnote中输入，再输出为txt文件。
矿柱断裂和破坏发展过程
4 矿柱强度经验公式
下面简要总结可得到的矿柱强度经验公式，按提出年代排序如下。根据我个人的记忆，其中Salamon and Munro (1967)和Wilson (1972, 1983)公式是最广为接受的设计方法，因为这是我当年作研究生论文时最常见到的名字。
Bunting (1911)
Zern (1928)
Greenwald (1941)
Gaddy (1956)
Salamon and Munro (1967)
Obert and Duvall (1967)
Cook (1971)
Wagner (1974)
Wilson (1972, 1983)
Hustrulid (1976)
Bieniawski (1981)
Pariseau (1982)
Agapito and Hardy (1982)
Das (1986)
Mark-Bieniawski (1988)
Madden (1991)
Sheorey (1992)
Maleki (1992)
Mark (1997)
Gale (1999)
硬岩矿柱的经验强度公式
5 矿柱强度的数值模拟
自从上世纪80年代开始，数值模拟技术逐渐在矿柱设计中得到了应用。其中最流行的数值模拟技术是FLAC/FLAC3D和UDEC/3DEC，特别是近年来随着SRM合成岩体以及新的岩体本构关系(应变软化损伤模型)的发展，数值模拟在矿柱设计中将发挥越来越多的作用。
矿柱应力演化的数值模拟
6 参考文献
[1] Mark, C. and G. M. Molinda (2005). "The Coal Mine Roof Rating (CMRR) - A decade of experience." International Journal of Coal Geology.
[2] Mark, C. and G. M. Molinda (2007). "Development and application of the coal mine roof rating (CMRR)." Proceedings of the International Workshop on Rock Mass Classification in Underground Mining.
[3] Carter, T.G. 1992. A new approach to surface crown pillar design. Proc. 16th. Canadian Rock Mechanics Symposium, Sudbury, 75-83.
[4] Kersten, R. W. O. (2019). "An alternative pillar design methodology." Journal of the Southern African Institute of Mining and Metallurgy 119(5): 471-478.
[5] Medhurst, T. P. (1999). "Highwall mining: practical estimates of coal-seam strength and the design of slender pillars." Transactions of the Institution of Mining and Metallurgy Section a-Mining Industry 108: A161-A171.
[6] Medhurst, T. P. and E. T. Brown (1998). "A study of the mechanical behaviour of coal for pillar design." International Journal of Rock Mechanics and Mining Sciences 35(8): 1087-1105.
[7] McKinnon, S. D., D. Harding and K. Birnie. “Crown Pillar Design at INCO's South Mine,” in NARMS-TAC2002: Mining and Tunnelling Innovation and Opportunity, Vol. 2, pp. 1041-1048. R. Hammah et al., eds. Toronto: University of Toronto Press (2002).
[8] Pariseau, W. G. and W. K. Sorensen (1979). "3D mine pillar design information from 2D FEM analysis." International Journal for Numerical and Analytical Methods in Geomechanics 3(2): 145-157.
[9] Pariseau, W. G. (1981). "Inexpensive but technically sound mine pillar design analysis." International Journal for Numerical and Analytical Methods in Geomechanics 5(4): 429-447.
[10] Fama, M. E. D., et al. (1995). "2-Dimensional and 3-Dimensional Elastoplastic Analysis for Coal Pillar Design and Its Application to Highwall Mining." International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 32(3): 215-225.
[11] Cording EJ, Hashash YMA, Oh J. (2015) Analysis of pillar stability of mined gas storage caverns in shale formations Engineering Geology. 184: 71-80.
[12] Esterhuizen, G. S., 2000. Jointing effects on pillar strength. Morgantown, West Virginia University.
[13] Esterhuizen, G. S., 2014. Extending empirical evidence through numerical modelling in rock engineering design. Journal of the Southern African Institute of Mining and Metallurgy, 114(10), pp. 755-764.
[14] Esterhuizen, G. S., Dolinar, D. R. & Ellenberger, J. L., 2011. Pillar strength in underground stone mines in the United States.. International Journal of Rock Mechanics and Mining Sciences, Volume 48, pp. 42-50.
[15] Malan, D. F. & Napier, J. A., 2011. The design of stable pillars in the Bushveld Complex mines: a problem solved?. The Journal of The Southern African Institute of Mining and Metallurgy, Volume 111, pp. 821-836.
[16] Martin, C. & Maybee, W. G., 2000. The strength of hard-rock pillars. International Journal of Rock Mechanics & Mining Sciences, pp. 1239-1246.
[17] Salamon, M. D. & Munro, A. H., 1967. A study of the strength of coal pillars. Journal of the South African Institute of Mining and Metallurgy, pp. 55-67.
煤矿长壁开采近似矿柱载荷的方法
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Bonded Particle Model (BPM)
