WANG Yong-fu, WANG Cheng, TANG Xiao-song. Slip Line Solution for Circular Tunnels Based on the Non-Associated Flow Rule[J]. Applied Mathematics and Mechanics, 2013, 34(12): 1285-1290. doi: 10.3879/j.issn.1000-0887.2013.12.007
 Citation: WANG Yong-fu, WANG Cheng, TANG Xiao-song. Slip Line Solution for Circular Tunnels Based on the Non-Associated Flow Rule[J]. Applied Mathematics and Mechanics, 2013, 34(12): 1285-1290.

# Slip Line Solution for Circular Tunnels Based on the Non-Associated Flow Rule

##### doi: 10.3879/j.issn.1000-0887.2013.12.007
• Publish Date: 2013-12-16
• The slip line equation for circular tunnels had been solved by Soviet scholars in the middle of 20th century, and widely used in China. But the assumption that the angle between the slip line and the velocity vector was 45°-φ/2 in the derivation had been wrong. Theoretically, that angle was related to the flow rule adopted. The plastic slip line equation of circular tunnels and the formula of horizontal fracture depth were derived based on both the associated flow rule and non-associated flow rule. Proved by previous model test, the slip line solution based on the non-associated flow rule is recommended for application.
•  [1] 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.(YU Xue-fu, ZHENG Ying-ren, LIU Huai-heng, FANG Zheng-chang. The Stability Analysis of Surrounding Rock of Underground Engineering [M]. Beijing: China Coal Industry Publishing House,1983.(in Chinese)) [2] 王思敬, 杨志法, 刘竹华. 地下工程岩体稳定分析[M]. 北京: 科学出版社, 1984.(WANG Si-jing, YANG Zhi-fa, LIU Zhu-hua. The Stability Analysis of Underground Engineering [M]. Beijing: Science Press, 1984.(in Chinese)) [3] 郑颖人, 孔亮. 岩土塑性力学[M]. 北京: 中国建筑工业出版社, 2010.(ZHENG Ying-ren, KONG Liang. Geotechnical Plastic Mechanics [M]. Beijing: China Architecture & Building Press, 2010.(in Chinese)) [4] 郑颖人, 王敬林, 朱小康. 关于岩土材料滑移线理论中速度解的讨论——广义塑性理论的应用[J]. 水利学报, 2001(6): 1-7.(ZHENG Ying-ren, WANG Jing-lin, ZHU Xiao-kang. Discussion on velocity solution of slip line theory for geotechnical materials—the application of generalized plastic theory[J]. Journal of Hydraulic Engineering,2001(6): 1-7.(in Chinese)) [5] 郑颖人, 邓楚键, 王敬林. 基于非关联流动法则的滑移线场及上限法研究[J]. 中国工程科学, 2010,12(8): 56-69.(ZHENG Ying-ren, DENG Chu-jian, WANG Jing-lin. The study of slip line field and upper bound method based on the non-associated flow rule[J]. Engineering Sciences,2010,12(8): 56-69.(in Chiense)) [6] Bobryakov A P, Revuzhenko A F. Experimental simulation of spiral slip lines on granular materials[J]. Journal of Mining Science,2009,45(2): 99-104. [7] Liu F Q, Wang J H. A generalized slip line solution to the active earth pressure on circular retaining walls[J]. Computers and Geosciences,2008,35(2): 155-164. [8] 郑颖人, 徐浩, 王成, 肖强. 隧洞破坏机理及深浅埋分界标准研究[J]. 浙江大学学报（工学版）, 2010,44(10): 1851-1856, 1875.(ZHENG Ying-ren, XU Hao,WANG Cheng, XIAO Qiang. Research on the failure mechanism of tunnel and dividing line standard between shallow and deep bury[J]. Journal of Zhejiang University(Engineering Science),2010,44(10): 1851-1856, 1875.(in Chinese)) [9] Dawson E M, Roth W H, Drescher A. Slope stability analysis by strength reduction[J]. Geotechnique,1999,49(6): 835-840. [10] 郑颖人, 赵尚毅. 有限元强度折减法在土坡与岩坡中的应用[J]. 岩石力学与工程学报, 2004,23(19): 3381-3388.(ZHENG Ying-ren, ZHAO Shang-yi. Application of strength reduction on FEM in soil and rock slope[J]. Chinese Journal of Rock Mechanics and Engineering,2004,23(19): 3381-3388.(in Chinese)) [11] Chen W F. Limit Analysis and Soil Plasticity [M]. Berlin: Elsevier Scientific Press, 1975. [12] 朱以文, 吴春秋, 蔡元奇. 基于滑移线场理论的边坡滑裂面确定方法[J]. 岩石力学与工程学报, 2005,24(15): 2609-2616.(ZHU Yi-wen, WU Chun-qiu, CAI Yuan-qi. Determination of slip surface in slope based on theory of slip line field[J]. Chinese Journal of Rock Mechanics and Engineering,2005,24(15): 2609-2616.(in Chinese)) [13] 肖大平. 滑移线法求解极限承载力问题的一些进展[J]. 岩土工程学报, 1998,20(4): 25-29.( XIAO Da-ping .Progress in slip lines method to solve the bearing capacity problem[J]. Chinese Journal of Geotechnical Engineering,1998,20(4): 25-29.(in Chinese)) [14] 顾金才, 苏锦昌. 在静荷载作用下的均质岩体中砂浆锚杆支护洞室受力特点及破坏形态模型试验研究——喷锚支护作用机理研究内容之一[C]//第一届全国岩石力学数值计算及模型试验讨论会论文集. 中国岩石力学与工程学会, 1986: 288-293.(GU Jin-cai, SU Jin-chang. Model testing study on the behaviour and failure shape of grouted rockbolts reinforced opening under static loading[C]//The First National Conference on Numerical Calculation and Model Test of Rock Mechanics Symposium . Chinese Society for Rock Mechanics and Engineering, 1986: 288-293.(in Chinese))

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142