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中文核心期刊

三维裂隙网络非稳定渗流分析的变分不等式方法

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

  • 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。

     

    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.

     

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