三维裂隙网络非稳定渗流分析的变分不等式方法

叶祖洋; 姜清辉; 姚池; 周创兵

doi:10.6052/0459-1879-13-055

三维裂隙网络非稳定渗流分析的变分不等式方法

叶祖洋^1,2,
姜清辉^1,2, ,,
姚池²,
周创兵^1,2

1.
武汉大学土木建筑工程学院, 武汉 430072
2. 水资源与水电工程科学国家重点实验室, 武汉 430072

基金项目: 国家重点基础研究发展计划(2011CB013503), 国家自然科学基金(51079110)和中央高校基本科研业务费专项资金(2012206020214)资助

详细信息

通讯作者:
姜清辉，教授，主要研究方向：岩土力学数值方法与边坡稳定分析. Email：jqh1972@yahoo.com.cn

中图分类号: O357.3
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出版历程
- 收稿日期: 2013-02-28
- 修回日期: 2013-05-30
- 刊出日期: 2013-11-17

A VARIATIONAL INEQUALITY APPROACH FOR NON-STEADY SEEPAGE FLOW THROUGH THREE-DIMENSIONAL FRACTURE NETWORK

1.
School of Civil Engineering, Wuhan University, Wuhan 430072, China
2. State Key Laboratory of Water Resources and Hydropower Engineering, Wuhan 430072, China

Funds: The project was supported by the National Basic Research Program of China (2011CB013503), and the National Natural Science Foundation of China (51079110), and the Fundamental Research Funds for the Central Universities (2012206020214).

摘要

摘要: 为了求解裂隙岩体有自由面非稳定渗流问题，将Darcy定律延拓至整个研究区域，使得潜在溢出边界条件满足Signorini型边界条件，建立了三维裂隙网络非稳定渗流问题的抛物型变分不等式（parabolic variational inequality，PVI）提法，并证明其与偏微分方程（partial differential equation，PDE）提法的等价性，从而将自由面上的流量条件以及潜在溢出边界上的互补条件转化成自然边界条件，降低该问题求解难度。同时给出了基于PVI提法的有限元数值求解方法，通过与交叉裂隙模型理论解的对比分析，证明了该方法的正确性。最后将该方法对含复杂三维裂隙网络的边坡进行非稳定渗流分析，计算结果表明该方法对于复杂裂隙网络求解具有较强的可靠性和适应性。
- 三维裂隙网络 /
- 非稳定渗流 /
- 自由面 /
- 变分不等式
Abstract: To solve non-steady seepage flow problems with free surface in fractured rock masses, Darcy's law is extended to the entire domain. A parabolic variational inequality (PVI) formulation, in which a Signorini's type of boundary condition enforced on the potential seepage surface, is established for transforming the flux condition on the potential seepage surface into natural boundary conditions, and then proved to be equivalent to the partial differential equation (PDE) formulation, and then the difficulty in solving this problem is reduced. Finite element numerical solution of the PVI formulation is proposed, and the validity of the numerical approach is verified by comparison of theoretical and calculated results for cross fracture model. Finally, the proposed approach is applied for non-steady seepage flow behaviors in a complex fractured rock slope, and the calculation results validate the reliability and robustness of this method well.
- three-dimensional fracture networks /
- non-steady seepage flow /
- free surface /
- variational inequality

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参考文献(17)

刘中,张有天.有自由面三维裂隙网络渗流分析.水利学报,1996, 6(6): 34-47 (Liu Zhong, Zhang Youtian. Analysis of free seepage problems in three dimensional network of fracture. Journal of Hydraulic Engineering, 1996, 6(6): 34-47 (in Chinese))

王恩志.岩体裂隙的网络分析及渗流模型. 岩石力学与工程学报, 1993, 8(12): 214-221 (Wang Enzhi. Network analysis and seepage model of fractured rockmass. Chinese Journal of Rock Mechanics and Engineering, 1993, 8(12): 214-221 (in Chinese))

何杨,柴军瑞,唐志立等.三维裂隙网络非稳定渗流数值分析.水动力学研究与进展A辑, 2007, 5(22): 338-344 (He Yang, Chai Junrui, Tang Zhili, et al. Numerical analysis of 3D unsteady seepage through fracture network in rock mass. Journal of Hydrodynamics, 2007, 5(22): 338-344 (in Chinese))

毛昶熙,陈平,李祖贻等.裂隙岩体渗流计算方法研究.岩土工程学报,1991, 13(6):1-10 (Mao Changxi,Chen Ping,Li Zuyi, et a1. Research on fractured rock mass seepage calculation method.Chinese Journal of Geotechnical Engineering, 1991, 13(6): 1-10 (in Chinese))

王恩志.裂隙网络地下水流数值模型及非连通裂隙网络水流的研究.水文地质工程地质, 1992, 1(19): 12-14 (Wang Enzhi. Numerical model of groundwater flow in fracture networks and water flow in disconnected fracture networks. Hydrogeology and Engineering Geology, 1992, 1(19): 12-14 (in Chinese))

Jing LR, Ma Y, Fang ZL. Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(3): 343-355

张奇华,邬爱清.三维任意裂隙网络渗流模型及其解法.岩石力学与工程学报, 2010, 4(29): 720-730 (Zhang Qihua, Wu Aiqing. Three-dimensional arbitrary fracture network seepage model and its solution. Chinese Journal of Rock Mechanics and Engineering, 2010, 4(29): 720-730 (in Chinese))

Wilson CR, Witherspoon PA. Steady state flow in rigid networks of fractures. Water Resources Research, 1974, 10(2): 328-335

张有天.岩石水力学与工程. 北京:中国水利水电出版社,2005 (Zhang Youtian. Rock Hydraulic and Engineering. Beijing: China Water Power Press, 2005 (in Chinese))

Zheng H, Liu DF, Lee CF, et al. A new formulation of Signorini's type for seepage problems with free surfaces. International Journal for Numerical Methods in Engineering, 2005, 64: 1-16

Chen YF, Hu R, Zhou CB, et al. A new parabolic variational inequality formulation of Signorini's condition for non-steady seepage problems with complex seepage control systems. International Journal for Numerical Methods in Engineering, 2011, 35: 1034-1058

Jiang QH, Ye ZY, Yao C, et al. A new variational inequality formulation for unconfined seepage flow through fracture networks. Science China: Technological Sciences, 2012, 11: 3090-3101

姚池,姜清辉,叶祖洋等. 裂隙网络无压渗流分析的初流量法. 岩土力学, 2012, 6(33): 1896-1903 (Yao Chi, Jiang Qinghui, Ye Zuyang, et al. Initial flow method for unconfined seepage problems of fracture networks. Rock and Soil Mechanics, 2012, 6(33): 1896-1903 (in Chinese))

Jiang QH, Yao C, Ye ZY, et al. Seepage flow with free surface in fracture networks. Water Resources Research, DOI: 10.1029/2012WR011991

Zheng TS, Li L, Xu QY. An iterative method for the discrete problems of a class of elliptical variational inequalities. Applied Mathematics and Mechanics, 1995, 16(4): 351-358

张蔚榛. 地下水非稳定流计算和地下水资源评价. 北京: 科学出版社, 1983 (Zhang Weizhen. Unsteady Groundwater Flow Calculation and Groundwater Resources Evaluation. Beijing: Science Press, 1983 (in Chinese))

张奇华,邬爱清.随机结构面切割下的全空间块体拓扑搜索一般方法.岩石力学与工程学报, 2007, 10(26): 2043-2048 (Zhang Qihua, Wu Aiqing. General methodology of spatial block topological identification with stochastic discontinuities cutting. Chinese Journal of Rock Mechanics and Engineering, 2007, 10(26): 2043-2048 (in Chinese))