Nonlinearity in groundwater flow

Abstract

Since 1856 when Darcy laid the basis for the calculation of the flow of water through sands, researchers have been interested in groundwater flow. Groundwater is essential for agriculture and water supply, but it also plays an important role when soil is used as a construction element, such as for dykes, roads and foundations. The mechanical behaviour of saturated or dry, fine graded or coarse soils are quite different. The theory of groundwater mechanics must be based on the system: water-soil-air. Up to now study has been restricted to mainly saturated and/or undeformable soil. In this thesis the contemporary theory is extended to compressible fluid flow in a semi-saturated deformable porous medium; a water-soil-air mixture, the air in which appears in the form of micro-bubbles. The pore water moves, whereas the soil itself deforms. It is assumed that this deformation behaviour is linear and free of rotations. From a fundamental reconsideration it is shown that the mechanical behaviour of this system can be formulated in a rather simple way taking into account various nonlinear effects. Convective terms and the variation of the permeability related to soil deformation are included. The validity of the formulation derived is discussed. A general solving procedure applying the Mellin transformation technique allows elucidation of the influence of these nonlinear terms on the basis of analytical solutions of some characteristic problems. In the phenomenon of groundwater flow so-called moving boundaries also occur. The free surface of natural groundwater, which actually varies, is such a boundary. This implies that the domain in which the process of porous flow is considered, changes (geometric nonlinearity). This aspect is explained. Transient phreatic porous flow problems can be solved by applying numerical models. In the discussion reference is made to the extensive literature. In conclusion, the following statements hold for nonlinear groundwater flow. In most practical cases the linear theory is sufficiently accurate, nonlinearity becomes manifest in a reduction of the area of influence, and time dependent porous flow problems can be explicitely solved applying a time step much larger than formerly assumed.Hydraulic EngineeringCivil Engineering and Geoscience