BLOCK THEORY OF LIMITED TRACE LENGTHS AND ITS APPLICATION TO PROBABILITY ANALYSIS OF BLOCK SLIDING OF
SURROUNDING ROCK
HAO Jie1，SHI Kebin1，CHEN Gongmin2，BAI Xianjun2
(1. College of Water Conservancy and Civil Engineering，Xinjiang Agricultural University，Urumqi，Xinjiang 830000，China；
2. Gezhouba Xinjiang Engineering Co.，Ltd.，Urumqi，Xinjiang 830000，China)
Abstract：The key block theory assumes that the rock masses are crossed over completely by structural planes，which is in conflicting with the fact that the lengths of traces of structural planes are finite，leading to the overestimation of the number of key blocks and the underestimation of the safety factor in calculations. The edge lengths of key blocks and the actual lengths of traces were thus computed according to the stereo-analytical method of block theory. The key block probability was redefined as absolute key block probability，relative key block probability and non-key block probability according to the probability theory of traces of structural planes. Calculations on the example of an equilateral triangular pyramid showed that when the ratio of length of trace to edge was larger than 100，the absolute key block probability was nearly 1.0 and structural planes could be considered to cross through rock mass in this case. If the ratio of length of trace to edge was equal to 1.5，the relative key block probability reached 0.75 and if the ratio of length of trace to edge was greater than 7.5，the non-key block probability was close to 0. The safety factor of the underground cavern at Bulungl-Gongur hydropower station was 3.145 according to the stability analysis of key block theory and was 4.591–5.233 based on the absolute key block probability，increased 46.0%–66.4%.
郝 杰1，侍克斌1，陈功民2，白现军2. 有限长迹线块体理论及其在围岩块体滑落概率分析中的应用[J]. 岩石力学与工程学报, 2014, 33(7): 1471-1478.
HAO Jie1，SHI Kebin1，CHEN Gongmin2，BAI Xianjun2. BLOCK THEORY OF LIMITED TRACE LENGTHS AND ITS APPLICATION TO PROBABILITY ANALYSIS OF BLOCK SLIDING OF
SURROUNDING ROCK. , 2014, 33(7): 1471-1478.
[1] STAGG K G，ZIENKIEWICZ O C. Rock mechanics in engineering practice[M]. New York：John Wiley and Sons，1969：12–85.
[2] CUNDALL P A. A computer model for simulating progressive，large scale movements in blocky rock systems[C]// Proceedings of the International Symposium on Rock Fracture，ISRM. Nancy：[s. n.]，1971：23–29.
[3] GOODMAN R E. Methods of geological engineering in discontinuous rock[M]. New York：John Wiley and Sons，1976：22–53.
[4] 石根华. 岩体稳定分析的赤平投影方法[J]. 中国科学，1977，5(3)：260–271.(SHI Genhua. Based on analysis of stereographic projection of rock mass stability[J]. Science in China，1977，5(3)：260–271.(in Chinese))
[5] 石根华. 岩体稳定分析的几何方法[J]. 中国科学，1981，(4)：487–495. (SHI Genhua. Rock mass stability analysis of geometric method[J]. Science in China，1981，(4)：487–495.(in Chinese))
[6] GOODMAN R E，SHI G H. Block theory and its applications to rock engineering[M]. Englewood Cliffs：Prentice-Hall，1985：11–48.
[7] 黄正加，邬爱清，盛 谦. 块体理论在三峡工程中的应用[J]. 岩石力学与工程学报，2001，20(5)：648–652.(HUANG Zhengjia，WU Aiqing，SHENG Qian. Usage of block theory in the Three Gorges Projects[J]. Chinese Journal of Rock Mechanics and Engineering，2001，20(5)：648–652.(in Chinese))
[8] 张奇华，邬爱清，石根华. 关键块体理论在百色水利枢纽地下厂房岩体稳定性分析中的应用[J]. 岩石力学与工程学报，2004，23(15)：2 609–2 614.(ZHANG Qihua，WU Aiqing，SHI Genhua. Application of key block theory to analysis of rock stability for underground plant in Baise hydraulic project[J]. Chinese Journal of Rock Mechanics and Engineering，2004，23(15)：2 609–2 614.(in Chinese))
[9] 朱 晟，张发明，庞正江，等. 西龙池抽水蓄能电站地下厂房随机块体稳定性分析[J]. 岩石力学与工程学报，2005，24(14)：2 513– 2 517.(ZHU Sheng，ZHANG Faming，PANG Zhengjiang. Stability analysis of random block rock of underground power houses of Xilongchi pumped storage plant[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(14)：2 513–2 517.(in Chinese))
[10] 杨 庆，杨 钢，王忠昶，等. 块体理论在荒沟抽水蓄能电站地下厂房系统硐室群围岩稳定性分析中的应用[J]. 岩石力学与工程学报，2007，26(8)：1 618–1 624.(YANG Qing，YANG Gang，WANG Zhongchang. Application of block theory to surrounding rock stability of underground caverns in Huanggou pumped storage station[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(8)：1 618–1 624.(in Chinese))
[11] 谢全敏，朱瑞赓，程 康. 可疑关键块体成为真正关键块体的概率分析[J]. 武汉工业大学学报，1998，20(3)：98–100.(XIE Quanmin，ZHU Ruigeng，CHENG Kang. Probilistic analysis of a suspected keyblock forming a complete keyblock[J]. Journal of Wuhan University of Technology，1998，20(3)：98–100.(in Chinese))
[12] 赵 文. 块体理论中关键块滑落的概率分析[J]. 中国有色金属学报，1998，8(2)：356–359.(ZHAO Wen. Probability analysis for falling of key block in block theory[J]. The Chinese Journal of Nonferrous Metals，1998，8(2)：356–359.(in Chinese))
[13] 张子新，孙 钧. 三峡高边坡关键分形块体的概率分析[J]. 同济大学学报，1998，26(3)：335–339.(ZHANG Zixin，SUN Jun. Probability analysis of key fractal blocks in the high slope of the Three Gorges of the Yangtze River[J]. Journal of Tongji University，1998，26(3)：335–339.(in Chinese))
[14] 许 研，王述红，朱浮声. 大跨度岩体隧道工程块体滑落的概率分析[J]. 东北大学学报：自然科学版，2003，24(6)：593–596.(XU Yan，WANG Shuhong，ZHU Fusheng. Probabilistic analysis of blocks sliding of large-span tunnel[J]. Journal of Northeastern University：Natural Science，2003，24(6)：593–596.(in Chinese))
[15] 刘锦华，吕祖珩. 块体理论在工程岩体稳定分析中的应用[M]. 北京：水利电力出版社，1988：30–59.(LIU Jinhua，LU Zuheng. Application of block theory to the engineering rock mass stability analysis[M]. Beijing：Water Conservancy and Electric Power Press，1988：30–59.(in Chinese))
[16] 张子新. 分形块体理论及其在岩体稳定分析中的应用[博士学位论文][D]. 徐州：中国矿业大学，1994.(ZHANG Zixin. Fractal block theory and application on stability analysis of rock mass[Ph. D. Thesis][D]. Xuzhou：China University of Mining and Technology，1994.(in Chinese))
[17] PRIEST S D，HUDSON J A. Estimation of discontinuity spacing and trace length using scanline surveys[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1981，18(3)：183–197.
2014, Vol. 33 
