Analytical Analysis of Non-Circular Hydraulic Lined Tunnels Under Smooth Contact With Transversely Isotropic Rock Mass
-
摘要: 提出了横观各向同性岩体中的非圆形水工衬砌隧洞在各向同性衬砌与岩体处于光滑接触条件下的解析方法.基于复变函数理论,通过建立两种介质在光滑接触边界上的力和位移连续关系以及衬砌自由边界的水压力边界条件,考虑衬砌支护滞后效应并使用幂级数解法获得解析解.针对倾斜结构面岩体中的马蹄形水工衬砌隧洞,使用解析和数值方法验证了解析解的正确性,获得了岩体各向异性和不同洞内水压力对衬砌和围岩接触边界,以及衬砌自由边界上应力和位移分布的影响规律.Abstract: An analytical method for non-circular hydraulic lined tunnels in transversely isotropic rock mass was proposed, with the lining under the smooth contact condition with surrounding rock mass. Based on the complex variable theory, continuous conditions for stresses and displacements at the contact boundary and water pressure boundary condition at the lining free boundary were established. In view of the lining support delay effect and with the power series method, the analytical solution was acquired. Aimed at a horseshoe-shaped lined tunnel constructed in transversely isotropic rock mass with inclined structural face, the correctness of this method was validated by analytical check and numerical comparison. Distributions of stress and displacement at the contact boundary and lining free boundary under the effects of anisotropic property and water pressures were discussed.
-
[1] LEKHNITSKII S G. Anisotropic Plates [M]. New York: Gordon and Breach Science Publishers, 1968. [2] CHAUHAN M M, SHARMA D S. Stresses in finite anisotropic plate weakened by rectangular hole[J]. International Journal of Mechanical Sciences, 2015,101/102: 272-279. [3] L Aizhong, ZHANG Ning, ZHANG Xiaoli, et al. Analytic method of stress analysis for an orthotropic rock mass with an arbitrary-shaped tunnel[J]. International Journal of Geomechanics,2015,15(4): 04014068. [4] MANH H T, SULEM J, SUBRIN D. A closed-form solution for tunnels with arbitrary cross section excavated in elastic anisotropic ground[J]. Rock Mechanics & Rock Engineering,2015,48(1): 277-288. [5] 刘淑红, 王自豪, 甄卫刚. 深埋公路隧洞围岩应力和位移分布的复变函数解[J]. 应用数学和力学, 2018,39(5): 548-557.(LIU Shuhong, WANG Zihao, ZHEN Weigang. Complex variable function solutions for stress and displacement distributions in surrounding rock of deep buried highway tunnels[J]. Applied Mathematics and Mechanics,2018,39(5): 548-557.(in Chinese)) [6] 周凤玺, 曹小林. 深埋隧洞围岩应力的精确解与近似解的对比分析[J]. 应用数学和力学, 2017,38(10): 1166-1179.(ZHOU Fengxi, CAO Xiaolin. Comparison between exact solutions and approximate solutions of deep tunnels[J]. Applied Mathematics and Mechanics,2017,38(10): 1166-1179.(in Chinese)) [7] 祝江鸿. 隧洞围岩应力复变函数分析法中的解析函数求解[J]. 应用数学和力学, 2013,34(4): 345-354.(ZHU Jianghong. Analytic functions in stress analysis of the surrounding rock for caverns with the complex variable theory[J]. Applied Mathematics and Mechanics,2013,34(4): 345-354.(in Chinese)) [8] BOBET A. Lined circular tunnels in elastic transversely anisotropic rock at depth[J]. Rock Mechanics & Rock Engineering,2011,44(2): 149-167. [9] Lü A Z, ZHANG N, WANG S J, et al. Analytical solution for a lined tunnel with arbitrary cross sections excavated in orthogonal anisotropic rock mass[J]. International Journal of Geomechanics,2017,17(9): 04017044. [10] 王少杰, 吕爱钟, 张晓莉. 正交各向异性岩体中非圆形水工隧洞的解析解[J]. 岩土力学, 2018,39(12): 149-159,168.(WANG Shaojie, L Aizhong, ZHANG Xiaoli. Analytical solution for the non-circular hydraulic tunnel buried in the orthotropic rock mass[J]. Rock and Soil Mechanics,2018,39(12): 149-159,168.(in Chinese)) [11] Lü A Z, ZHANG N, KUANG L. Analytic solutions of stress and displacement for a non-circular tunnel at great depth including support delay[J]. International Journal of Rock Mechanics and Mining Sciences,2014,70(9): 69-81. [12] PACHOUD A J, SCHLEISS A J. Stresses and displacements in steel-lined pressure tunnels and shafts in anisotropic rock under quasi-static internal water pressure[J]. Rock Mechanics & Rock Engineering,2016,49(4): 1263-1287. [13] BOBET A, YU H. Full stress and displacement fields for steel-lined deep pressure tunnels in transversely anisotropic rock[J]. Tunnelling and Underground Space Technology,2016,56: 125-135. [14] Lü A Z, ZHANG N, QIN Y. Analytical solutions for the stress of alined non-circular tunnel under full-slip contact conditions[J]. International Journal of Rock Mechanics and Mining Sciences,2015,79: 183-192. [15] WANG S J, L A Z, TAO J Y, et al. Analytical solution for an arbitrary-shaped tunnel with full-slip contact lining in anisotropic rock mass[J]. International Journal of Rock Mechanics and Mining Sciences,2020,128: 104276. [16] 陈子荫. 围岩力学分析中的解析方法[M]. 北京: 煤炭工业出版社,1994.(CHEN Ziyin. Analytical Method in Mechanics Analysis of Surrounding Rock [M]. Beijing: China Coal Industry Publishing House, 1994.(in Chinese)) [17] MUSKHELISHVILI N I. Some Basic Problems of the Mathematical Theory of Elasticity [M]. Groningen: Springer, 1977. [18] 于学馥, 郑颖人. 地下工程围岩稳定分析[M]. 北京: 煤炭工业出版社, 1983.(YU Xuefu, ZHEN Yingren. Stability Analysis of Surrounding Rock in Underground Works [M]. Beijing: China Coal Industry Publishing House, 1983.(in Chinese))
点击查看大图
计量
- 文章访问数: 845
- HTML全文浏览量: 180
- PDF下载量: 367
- 被引次数: 0