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A Variational Inequality Formulation For Unconfined Seepage Problems In Porous Media

机译：多孔介质中无限制渗流问题的变分不等式公式

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In the existing variational inequality formulations for the unconfined seepage problem in porous media, the seepage point, namely the exit point of the free surface, is a singular point and how to locate the seepage point exactly has been an open issue. By generalizing Darcy's law applied solely to the saturated zone in an earth dam to the entire dam including the no-flow zone, a new variational inequality formulation is presented. The new formulation imposes a boundary condition of Signorini's type on the potential seepage boundary and the seepage point turns out to be such a point that makes both inequalities in Signorini's complementary condition become equalities. Singularity of the seepage point is accordingly eliminated. A strategy is developed for overcoming the mesh-dependency in the finite element implementation.
机译：在针对多孔介质中无侧限渗流问题的现有变分不等式公式中，渗流点（即自由表面的出口点）是奇异点，如何准确定位渗流点一直是一个未解决的问题。通过将仅适用于土坝饱和区的达西定律推广到包括无流量区在内的整个水坝，提出了一种新的变分不等式公式。新的公式在潜在的渗流边界上施加了Signorini类型的边界条件，并且渗流点被证明是使Signorini互补条件中的两个不等式变为相等的点。相应地消除了渗漏点的奇异性。开发了一种策略来克服有限元实现中的网格依赖性。

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