Analytical modeling of flow into open drains in a layered soil receiving water from a ponded field
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In this work, an effort is being made to obtain an analytical solution to the problem of groundwater flow into a network of equally spaced ditch drains in a stratified soil underlain by an impervious barrier. The problem is being solved for a few of its variants resulting from different locations of water level in the ditches. All these solutions can tackle both a constant as well as a variable ponding distribution at the surface of the soil. Also, in the first instance, solutions to the problem and its variants are obtained by assuming the flow as two-dimensional in a defined drainage space; this supposition next is been relaxed and the problem with its variants are then solved by considering all the three components of flow in the defined flow space. The separation of variables method along with necessary Fourier expansions are being used to solve all the problems considered for study – the separation of variable method for obtaining solutions to the governing groundwater flow equation corresponding to a problem and the Fourier runs for satisfying the boundary and initial conditions pertaining to the problem. The accuracy of all the solutions is being checked by comparing with the works of others for specific situations; numerical checks on them have also been carried out. All the proposed steady state solutions are new, exact and are valid for all possible variations of parameters associated with them; however, the corresponding transient solutions are approximate in nature and are strictly valid only when the directional conductivities and specific storage of a multi-layered soil satisfy certain pre-defined relations among each other. As a large number of transient ponded drainage situations can be studied even with these imposed restrictions, the proposed transient solutions are also expected to find wide use in studying time dependent behavior of these situations as well. From the study it becomes clear that ponded drainage in a stratified soil is highly influenced by the directional conductivities and specific storage of the constituent layers and that neglecting the stratifications of a layered soil column (i.e., assuming a stratified soil as a single-layered one) may lead to a serious error in reading the hydraulics of flow associated with such a system. It has also become amply clear from the study that ponded drainage of a stratified soil is pretty sensitive to the water head of the recipient drains and also the nature of the ponding distribution at the surface of the soil.
Supervisor: Gautam Barua