Advanced Search
  • 全国中文核心期刊
  • 中国科技核心期刊
  • 美国工程索引（EI）收录期刊
  • Scopus数据库收录期刊
Volume 44 Issue 6
Turn off MathJax
Article Contents
Abstract
References
Related Articles
ZHANG Qi-hua, HU Hui-hua, ZHANG Yu, ZHAO Xue-lian. Comparison of traditional and whole-space stereographic projections in block stability analysis[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(6): 1148-1155. DOI: 10.11779/CJGE202206020
Citation: ZHANG Qi-hua, HU Hui-hua, ZHANG Yu, ZHAO Xue-lian. Comparison of traditional and whole-space stereographic projections in block stability analysis[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(6): 1148-1155. DOI: 10.11779/CJGE202206020
shu

Comparison of traditional and whole-space stereographic projections in block stability analysis

  • 1.

    Badong National Observation and Research Station of Geohazards, China University of Geosciences, Wuhan 430074, China

  • 2.

    Hunan Provincial Communications Planning, Survey and Design Institute Co., Ltd., Changsha 410008, China

  • 3.

    Yangtze River Scientific Research Institute, Wuhan 430010, China

  • 4.

    School of Geography and Information Engineering, China University of Geosciences, Wuhan 430074, China

More Information
  • Received Date: July 08, 2021
  • Available Online: September 22, 2022
    Graphical Abstract
    • Abstract
  • The stereographic projection used in engineering geological analysis is a hemispherical projection: a plane or a straight line in 3-D space is projected to be an arc or a point inside the equatorial circle. This kind of projection is widely used to judge the unstable blocks cut by discontinuities by analyzing the relationship of locations between the intersection of arcs projected by multiple sets of discontinuities and the arc projected by the free surface. Nevertheless, this kind of judgement lacks a rigous theoretical basis. The whole-space stereographic projection proposed in the block theory projects a whole plane and both its upper-half and lower-half space onto the equatorial plane. The removability and failure mode of blocks can be determined by analyzing the location relationship between the joint pyramid projected by multiple sets of discontinuities and the circle projected by the free surface. This approach is complete and accurate in theory. In this study, the shortcomings of the traditional stereographic projection used for slope stability analysis in "Geological engineering handbook" and "Design code for engineering slopes of water resources and hydropower projects" are pointed out by analyzing some specially designed examples, and the reasons for these shortcomings are released. Through the whole-space stereographic projection, the continuous variation of morphology of joint pyramid is exposed, the characteristics of the shape of projection zone projected by flat or sharp blocks are analyzed, and the significance of these issues is explored. Finally, the advantages of the whole-space stereographic projection are summarized, and the simplicity in using and the feasibility for popularization are pointed out.
    • FullText(HTML)
    • References (37)
  • [1]
    石根华. 岩体稳定分析的赤平投影方法[J]. 中国科学, 1977, 7(3): 260–271. https://www.cnki.com.cn/Article/CJFDTOTAL-JAXK197703006.htm

    SHI Gen-hua. Stereographic projection in stability analysis of rock mass[J]. Scientia Sinica, 1977, 7 (3): 260–271. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JAXK197703006.htm
    [2]
    CRUDEN D M. Discussion of G Hocking's paper "a method for distinguishing between single and double plane sliding of tetrahedral wedges"[J]. Int J Rock Mech Min Sci Geomech Abstr, 1978, 15: 217. doi: 10.1016/0148-9062(78)91228-7
    [3]
    廖国华. 赤平投影网的解析原理[J]. 北京钢铁学院学报, 1979, 1(2): 1–17. https://www.cnki.com.cn/Article/CJFDTOTAL-BJKD197902000.htm

    LIAO Guo-hua. Analytical principle of stereographic projection net. [J]. Journal of Beijing Iron and Steel Institute, 1979, 1(2): 1–17. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-BJKD197902000.htm
    [4]
    孙玉科, 古迅. 赤平极射投影在岩体工程地质力学中的应用[M]. 北京: 科学出版社, 1980.

    SUN Yu-ke, GU Xun. Application of Stereographic Projection in Engineering Geomechanics of Rock Mass[M]. Beijing: Science Press, 1980. (in Chinese)
    [5]
    LUCAS J M. A general stereographic method for determining the possible mode of failure of any tetrahedral rock wedge[J]. International Journal of Rock Mechanics and Mining Sciences and, 1980, 17(1): 57–61. doi: 10.1016/0148-9062(80)90006-6
    [6]
    ÖCAL A, ÖZGENOĞLU A. Determination of sliding mode of tetrahedral wedges in jointed rock slopes[J]. Rock Mechanics and Rock Engineering, 1997, 30(3): 161–165. https://cdmd.cnki.com.cn/Article/CDMD-10491-1015709825.htm
    [7]
    GOODMANR E, SHIG H. Block Theory and Its Application to Rock Engineering[M]. Englewood Cliffs: Prentice-Hall, Inc., 1985
    [8]
    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.

    LIU Jing-hua, LU Zuheng. Block Theory and Its Application to Rock Engineering[M]. Beijing: Water Resources and Electric Power Press, 1988. (in Chinese)
    [9]
    HOEKE, BRAY J W. Rock Slope Engineering[M]. 4th ed. London and New York: Spon Press, 2004.
    [10]
    陈祖煜, 汪小刚, 杨健, 等. 岩质边坡稳定分析原理·方法·程序[M]. 北京: 中国水利水电出版社, 2005.

    CHEN Zu-yu, WANG Xiao-gang, YANG Jian, et al. Rock Slope Stability Analysis—Theory, Methods And Programs[M]. Beijing: China WaterPower Press, 2005. (in Chinese)
    [11]
    《工程地质手册》编委会. 工程地质手册[M]. 5版. 北京: 中国建筑工业出版社, 2018.

    Editorial Committee of Geological Engineering Handbook. Geological Engineering Handbook[M]. 5th ed. Beijing: China Architecture & Building Press, 2018. (in Chinese)
    [12]
    水利水电工程边坡设计规范: SL386—2007[S]. 2007.

    Design Specification For Slope of Water Resources and Hydropower: SL386—2007[S]. 2007. (in Chinese)
    [13]
    LIM S S, YANG H S. An analysis of plane failure of rock slopes by quantified stereographic projection[J]. International Journal of Rock Mechanics and Mining Sciences, 2004, 41: 744-749. doi: 10.1016/j.ijrmms.2004.03.129
    [14]
    KINCAL C. Application of two new stereographic projection techniques to slope stability problems[J]. International Journal of Rock Mechanics and Mining Sciences, 2014, 66: 136–150. doi: 10.1016/j.ijrmms.2014.01.006
    [15]
    罗雪娇, 卢晓春, 李应周, 等. 基于赤平投影的岩质边坡失稳模式分析及程序实现[J]. 三峡大学学报(自然科学版), 2015, 37(3): 48–51. https://www.cnki.com.cn/Article/CJFDTOTAL-WHYC201503012.htm

    LUO Xue-jiao, LU Xiao-chun, LI Ying-zhou, et al. Instability mode analysis and program realization of rock slope based on stereographic projection[J]. Journal of China Three Gorges University (Natural Sciences), 2015, 37(3): 48–51. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-WHYC201503012.htm
    [16]
    丁斌. Unwedge软件在隧洞工程施工地质中的应用研究[J]. 岩土工程技术, 2019, 33(5): 303–306. doi: 10.3969/j.issn.1007-2993.2019.05.012

    DING Bin. Application study of unwedge at construction geology during tunnel excavation[J]. Geotechnical Engineering Technique, 2019, 33(5): 303–306. (in Chinese) doi: 10.3969/j.issn.1007-2993.2019.05.012
    [17]
    康志亮, 周顺田, 朱永生, 等. 基于赤平投影方法的周宁抽蓄电站边坡块体破坏模式识别[J]. 人民珠江, 2020, 41(3): 59–65. doi: 10.3969/j.issn.1001-9235.2020.03.011

    KANG Zhi-liang, ZHOU Shun-tian, ZHU Yong-sheng, et al. Recognition of failure mode of slope block failure mode in Zhouning pumped storage station based on stereographic projection method[J]. Pearl River, 2020, 41(3): 59–65. (in Chinese) doi: 10.3969/j.issn.1001-9235.2020.03.011
    [18]
    Rocscience Ltd. SWEDGE-probabilistic Analysis of the Geometry and Stability of Surface Wedges[EB]/OL. 2001. www.rocscience.com.
    [19]
    JIANG Q H, LIU X H, WEI W, et al. A new method for analyzing the stability of rock wedges[J]. International Journal of Rock Mechanics and Mining Sciences, 2013, 60: 413–422. doi: 10.1016/j.ijrmms.2013.01.008
    [20]
    郑俊, 邓建辉. 岩石边坡块体稳定性的运动学分析及其应用[M]. 杭州: 浙江大学出版社, 2017.

    ZHENG Jun, DENG Jian-hui. Kinematic Analysis of Block Stability of Rock Slope and Its Application[M]. Hangzhou: Zhejiang University Press, 2017. (in Chinese)
    [21]
    SHI Gen-hua. A geometric method for stability analysis of discontinuous rocks[J]. Science in China, Ser A, 1982, 25(3): 318–336.
    [22]
    XUE J, SONG X, MIAO Q, et al. 3D graphical visualization for block theory[C]//51st US Rock Mechanics/Geomechanics Symposium, 2017, San Francisco.
    [23]
    GOODMAN R E, SHIG H, WILLAM B. Calculation of support for hard jointed rock using the keyblock principle[C]//Proc 23th US Symposium on Rock Mechanics, 1982, Berkeley.
    [24]
    任放. 三峡枢纽船闸高边坡岩石切割体的几何构形与锚固基础[J]. 长江科学院院报, 1988, 5(4): 1–11. https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB198804000.htm

    REN Fang. The geometrical feature and supporting base of blocks cut of ship lock high side slope of the three-gorge project[J]. Journal of Yangtze River Scientific Research Institute, 1988, 5(4): 1–11. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB198804000.htm
    [25]
    傅鹤林, 周昌达. 块体理论分析峒室的稳定性[J]. 长沙矿山研究院季刊, 1991, 11(4): 66–72. https://www.cnki.com.cn/Article/CJFDTOTAL-KYYK199104010.htm

    FU He-lin, ZHOU Chang-da. Use block theory to analyze cave stability[J]. Quarterly of CIMR, 1991, 11(4): 66–72. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-KYYK199104010.htm
    [26]
    HATZOR Y, GOODMAN R E. Application of block theory and the critical key block concept to tunneling: two case histories[C]//Proceedings of ISRM Conference on Fractured and Jointed Rock Mass. 1992. Luke Tahoe.
    [27]
    KOTTENSTETTE J T. Block theory techniques used in arch dam foundation stability analysis[J]. International Journal of Rock Mechanics and Mining Sciences, 1997, 34(3/4): 1–19.
    [28]
    OHNISHI Y, NⅡDA H, RYU M, et al. An application of key block analysis to large section tunnel excavation[C]//The Fourth International Conference on Analysis of Discontinuous Deformation, 2001.
    [29]
    GOODMAN R E, POWELL C. Investigations of blocks in foundations and abutments of concrete dams[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2003, 129(2): 105–116. doi: 10.1061/(ASCE)1090-0241(2003)129:2(105)
    [30]
    方宏伟, 李荐华, 黄幼民. 全空间赤平投影在伦潭水利工程中的应用[J]. 华北水利水电学院学报, 2008, 29(6): 75–77. https://www.cnki.com.cn/Article/CJFDTOTAL-HBSL200806023.htm

    FANG Hong-wei, LI Jian-hua, HUANG You-min. Application of stereographic projection of vector in luntan water project[J]. Journal of North China Institute of Water Conservancy and Hydroelectric Power, 2008, 29(6): 75–77. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HBSL200806023.htm
    [31]
    梁宁, 伍法权, 刘彤, 等. 块体理论赤平解析法在锦屏二级水电站皮带机隧洞稳定分析中的应用[J]. 工程地质学报, 2009, 17(3): 383–388. doi: 10.3969/j.issn.1004-9665.2009.03.017

    LIANG Ning, WU Fa-quan, LIU Tong, et al. Application of block theory based stereo-analytical method to stability analysis of conveyor tunnel at Jinping ⅱ hydropower station[J]. Journal of Engineering Geology, 2009, 17(3): 383–388. (in Chinese) doi: 10.3969/j.issn.1004-9665.2009.03.017
    [32]
    张子新, 廖一蕾. 基于块体理论赤平解析法的地下水封油库围岩稳定性分析[J]. 岩石力学与工程学报, 2010, 29(7): 1339–1347. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201007008.htm

    ZHANG Zi-xin, LIAO Yi-lei. Stability anaysis of surrounding rock mass of water-tight oil storage using block theory based on stereo-analytical method[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(7): 1339–1347. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201007008.htm
    [33]
    张奇华. 岩体块体理论的应用基础研究[M]. 武汉: 湖北科学技术出版社, 2010.

    ZHANG Qi-hua. Fundamental Research on Application of Rock Mass Block Theory[M]. Wuhan: Hubei Science & Technology Press, 2010. (in Chinese)
    [34]
    吴豪伟, 蔡美峰. 块体理论赤平解析法的节理裂隙岩体破坏预测分析[J]. 中国矿业, 2011, 20(3): 57–60. doi: 10.3969/j.issn.1004-4051.2011.03.016

    WU Hao-wei, CAI Mei-feng. Analysis on prediction of failure of fractured rock mass by stereo-analytical method based on block theory[J]. China Mining Magazine, 2011, 20(3): 57–60. (in Chinese) doi: 10.3969/j.issn.1004-4051.2011.03.016
    [35]
    彭红胜, 徐光黎, 李志鹏, 等. 全空间赤平投影法在公路边坡稳定性分析中的应用[J]. 中外公路, 2015, 35(4): 48–52. https://www.cnki.com.cn/Article/CJFDTOTAL-GWGL201504012.htm

    PENG Hong-sheng, XU Guang-li, LI Zhi-peng, et al. Application of stereographic projection in stability analysis of road slope[J]. Journal of China & Foreign Highway, 2015, 35(4): 48–52. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GWGL201504012.htm
    [36]
    邬爱清. 基于关键块体理论的岩体稳定性分析方法及其在三峡工程中的应用[J]. 长江科学院院报, 2019, 36(2): 1–7. https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB201902004.htm

    WU Ai-qing. Series methods of analyzing rock mass stability based on key block theory and their applications to Three Gorges project[J]. Journal of Yangtze River Scientific Research Institute, 2019, 36(2): 1–7. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB201902004.htm
    [37]
    张奇华, 张煜, 李利平, 等. 块体理论在地下洞室围岩稳定分析中的应用进展[J]. 隧道与地下工程灾害防治, 2020, 2(4): 9–18. https://www.cnki.com.cn/Article/CJFDTOTAL-SDZH202004002.htm

    ZHANG Qi-hua, ZHANG Yu, LI Li-ping, et al. Advances in application of block theory to stability analysis of rock mass surrounding Caverns[J]. Hazard Control in Tunnelling and Underground Engineering, 2020, 2(4): 9–18. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SDZH202004002.htm
    • Related Articles

  • Related Articles

    [1]LIANG Xiaomin, GU Xiaoqiang, ZHAI Chongpu, WEI Deheng. Anisotropic wave velocities of granular materials and microscopic fabric using X-ray computed tomography[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(7): 1398-1407. DOI: 10.11779/CJGE20230425
    [2]ZHANG He-nian, CHEN Liang, LI Xiong-wei, XI Pei-sheng, MU Lin, HU Cai-yun. Ratio and mechanism of activated magnesium oxide carbonized raw earth block materials[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(S2): 233-236. DOI: 10.11779/CJGE2021S2055
    [3]YAO Jun-kai, YE Yang-sheng, WANG Peng-cheng, CHEN Feng, CAI De-gou. Subgrade heave of sulfate attacking on cement-stabilized filler[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(4): 782-788. DOI: 10.11779/CJGE201904024
    [4]XU Xiao-li, GAO Feng, ZHANG Zhi-zhen, ZHANG Chuan-hu. Energy and structural effects of granite after high temperature[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(5): 961-968. DOI: 10.11779/CJGE201405022
    [5]ZHOU Qiao-yong, XIONG Bao-lin, YANG Guang-qing, LIU Wei-chao. Microstructure of low liquid limit silt[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(zk2): 439-444.
    [6]YU Hui, DING Xuan-ming, KONG Gang-qiang, ZHENG Chang-jie. Comparative FEM analysis of deformation properties of expressway widening projects with cast-in-situ X-shaped concrete piles and circular pile[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(zk2): 170-176.
    [7]WANG Cheng-hu, WANG Hong-cai, LIU Li-peng, SUN Dong-sheng, ZHAO Wei-hua. Effects of high temperatures on mechanical performance of basaltic tuff and mechanism analysis[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(10): 1827-1835.
    [8]Micro-experiments on a soft ground improved by cement-mixed soils with gypsum additive[J]. Chinese Journal of Geotechnical Engineering, 2010, 32(8).
    [9]Full scale model tests on vertical bearing characteristics of cast-in-place X-section piles[J]. Chinese Journal of Geotechnical Engineering, 2010, 32(6).
    [10]WU Yanqing, CAO Guangzhu, DING Weihua. Permeability experiment of sandstone under variable seepage pressures by using X-ray CT real-time observation[J]. Chinese Journal of Geotechnical Engineering, 2005, 27(7): 780-785.
    • Supplements (0)

  • Cited by

    Periodical cited type(4)

    1. 王大兵，黄郁东，韩振中，徐考，崔文海，周苏华. 基于贝叶斯逻辑回归模型的边坡稳定性预测. 市政技术. 2023(10): 173-180 .
    2. 曾锃，赵树祥，葛龙进，潘卫平，李敏，殷国峰. 罗闸河二级水电站拱坝右岸边坡变形破坏机制研究及治理后评估. 岩土工程学报. 2021(S1): 171-175 . 本站查看
    3. 夏增选，李萍，曹博，李同录，沈伟，康海伟. 边坡可靠度的Bayes估计及后验稳健性. 河海大学学报(自然科学版). 2020(03): 238-244 .
    4. 谢永利，刘新荣，晏长根，杨忠平，李家春，周志军，岳夏冰. 特殊岩土体工程边坡研究进展. 土木工程学报. 2020(09): 93-105 .

    Other cited types(18)

Catalog

    Get Citation
    PDF
    XML
    Article views (174) PDF downloads (97) Cited by(22)
    Related
    Copyright © 2010 Editorial By Chinese Journal of Geotechnical Engineering 苏ICP备05007122号-11公安联网备案号：32010602011255
    Editorial Office address：34 Hujuguan,Nanjing 210024,ChinaPostal Code：210024Tel：025-85829534，85829556E-mail: ge@nhri.cn

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return