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Analytic Modeling of Impermeable and Resistant Barriers
Author(s) -
Fitts Charles R.
Publication year - 1997
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.1997.tb00088.x
Subject(s) - boundary (topology) , boundary value problem , flux (metallurgy) , aquifer , nonlinear system , flow (mathematics) , mathematical analysis , mathematics , mechanics , geometry , geotechnical engineering , geology , physics , groundwater , materials science , quantum mechanics , metallurgy
Superpositioned analytic functions are used to efficiently and accurately model ground‐water flow fields containing thin barriers such as slurry walls and sheet‐pile walls. Barriers are modeled as a series of straight‐line segments strung together to create irregularly shaped open or closed boundaries with zero thickness. The complex analytic functions employed provide perfect continuity of flow across the boundary while approximating normal flux boundary conditions along the boundary. Along an impermeable boundary the normal flux is specified as zero, and along a resistant (leaky) barrier the normal flux is proportional to a specified resistance parameter and the potential difference across the boundary. Solution of a given flow problem requires solving a system of equations with one equation per boundary corner. These equations are linear for impermeable boundaries and for resistant boundaries in confined aquifers or single‐strata unconfined aquifers. In other cases, the boundary condition equations associated with resistant barriers can be nonlinear and a new technique for iterative solution is employed. Implementation of these techniques in a computer program is tested and it is demonstrated by modeling various configurations of flow funneled into a gap between two barriers.