基于平面弹性复变函数中的保角变换方法,考虑衬砌的支护滞后效应,并认为衬砌与围岩完全接触,提出了带有衬砌的非圆形水工隧洞在原始地应力和内水压力共同作用下的应力与位移解析解,且求解过程中采用幂级数法简化计算。以马蹄形隧洞为例,用ANSYS进行数值计算,并与解析解进行对比验证;计算隧洞围岩开挖边界和衬砌内外边界的切向正应力以及围岩与衬砌之间的接触应力;讨论在不同侧压力系数、位移释放系数和内水压力下围岩与衬砌的应力分布规律。结果显示:解析解与数值解吻合较好;位移释放系数和内水压力对衬砌及围岩的应力分布影响显著,当位移释放系数和内水压力较大时,在衬砌内边界将出现拉应力区。研究结果为非圆形水工隧洞的围岩与衬砌的应力与位移分析提供了可行方法。
Abstract
In association with the conformal transformation method of plane elastic complex function,the analyticalsolutions of stress and displacement for a non-circular lined tunnel subjected to in-situ stress and internal water pressure are derived. The support delay and the full contact between surrounding rock-mass and lining are taken into consideration. The power series method is used to simplify the calculation process. With a horseshoe tunnel as an example,the analytical solutions are verified by numerical results. Furthermore,the tangential stresses along the excavation boundary and the inner and outer boundaries of the lining,as well as the contact stresses along the interface of the lining-surrounding rock mass are calculated. Besides,the stress distributions of the surrounding rock mass and the lining under different lateral pressure coefficients,displacement release coefficients and internal water pressures are discussed. The results show that the analytical solution is in good agreement with the numerical solution,and the displacement release coefficient and internal water pressure have significant influence on the stress distributions of the lining and surrounding rock mass. Great values of displacement release coefficient and internal water pressure will give rise to tensile stress along the inner boundary of the lining.
关键词
非圆形隧洞 /
支护滞后 /
保角变换 /
静水压力 /
应力与位移分析 /
解析解
Key words
non-circular tunnel /
support delay /
conformal transformation /
hydrostatic pressure /
stress and displacement analysis /
analytical solution
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] MUSKHELISHVILI N I. Some Basic Problems of the Mathematical Theory of Elasticity[M]. Groningen: P.Noordhoff Ltd.,1953.
[2] 吕爱钟,张路青.地下隧洞力学分析的复变函数方法[M]. 北京:科学出版社,2007.
[3] 施高萍,祝江鸿,李保海,等. 矩形巷道孔边应力的弹性分析[J].岩土力学,2014,35(9):2587-2593.
[4] 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.
[5] EXADAKTYLOS G E,STAVROPOULOU M C. A Closed-form Elastic Solution for Stresses and Displacements Around Tunnels[J]. International Journal of Rock Mechanics & Mining Sciences,2002,39(7):905-916.
[6] EXADAKTYLOS G E,LIOLIOS P A,STAVROPOULOU M C. A Semi-analytical Elastic Stress-Displacement Solution for Notched Circular Openings in Rocks[J]. International Journal of Solids & Structures,2003,40(5): 1165-1187.
[7] WANG M B,LI S C. A Complex Variable Solution for Stress and Displacement Field Around a Lined Circular Tunnel at Great Depth[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2009,33(7):939-951.
[8] LU 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 & Mining Sciences, 2014,70(9):69-81.
[9] 吕爱钟,覃 媛,陈虹宇. 马蹄形隧洞考虑支护滞后过程的应力分析[J]. 岩土力学,2014, 35(增1):42-48.
[10]张黎明, 李 鹏, 孙林娜,等. 考虑地下水渗流影响的衬砌隧洞弹塑性分析[J]. 长江科学院院报, 2008, 25(5):84-87.
[11]陈振民. 地应力对圆形压力隧洞衬砌应力的影响[J]. 江西水专学报,1984:23-30.
[12]LU A Z,ZHANG L Q,ZHANG N. Analytic Stress Solutions for a Circular Pressure Tunnel at Pressure and Great Depth Including Support Delay[J]. International Journal of Rock Mechanics & Mining Sciences, 2011,48(3):514-519.
[13]李云鹏,刘怀恒. 典型洞室工作面端部围岩变形特征的有限元分析[J]. 西安矿业学院学报,1988,8(2):1-8.
[14]ZHU W S,LIN S S, ZHU J Q, et al. Some Practical Cases of Back Analysis of Underground Opening Deform Ability Concerning Time and Space Effects[C]∥ Proceedings of the Sixth International Conference on Rock Mechanics. Montreal,August 30-September 10,1987:1325-1356.
[15]吕爱钟. 非圆形硐室封闭整体式支护映射函数确定的新方法[J]. 岩土工程学报,1995,17(4):38-44.
[16]吕爱钟,蒋斌松,尤春安. 位移反分析有限元网格划分范围的研究[J]. 土木工程学报,1999,32(1):26-30.
PDF(3960 KB)
