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通过对仅适用于湿区裂隙渗流的Darcy定理进行延拓处理,并将潜在溢出面归纳为Signorini型互补边界条件,建立了定义在裂隙网络全域上无压渗流问题的偏微分方程(PDE)提法.为了减小试探函数的选取难度和消除溢出点的奇异性,进一步发展了与PDE提法等价的变分不等式(VI)提法,并给出了离散型变分不等式提法的有限元数值求解格式、迭代算法与计算流程.由于使用了连续型的Heaviside函数代替阶跃型函数,避免了对位于过渡区域裂隙单元进行积分时形成的数值跳跃,从而显著提高了有限元数值求解过程中的稳定性.典型算例的计算结果验证了该方法的有效性和可靠性,并表明基于离散裂隙网络模型的无压渗流分析不但可以较好模拟裂隙岩体渗流的非均质性和优势水流方向,还可以准确预测坡体内部排水结构的渗流量,为裂隙岩体边坡防渗排水系统的优化布置提供科学依据.
By extending the Darcy’s theorem which is only applicable to the seepage of the fractures in the wet zone and classifying the potential overflow surface as Signorini-type complementary boundary conditions, a partial differential equation (PDE) method for the problem of non-pressure seepage in the whole fracture network is established Method.In order to reduce the selection difficulty of the trial function and eliminate the singularity of the overflow point, the method of variational inequality (VI) equivalent to PDE formulation is further developed and the definition of discrete variational inequality is given Meta-numerical solution, iterative algorithm and computational process.Because of using the continuous type of Heaviside function instead of step-type function, it avoids the numerical jump formed when the fracture cell located in the transition region is integrated, thus greatly improving the numerical solution process of finite element The results of typical examples verify the validity and reliability of the proposed method and show that the pressureless seepage flow analysis based on discrete fracture network model can not only simulate the seepage heterogeneity and advantage of fractured rock mass well Water flow direction, but also can accurately predict the seepage flow within the slope drainage body structure, providing scientific for the optimal arrangement of seepage drainage system of rock slope It is.