Degree Name

Master of Science (Hons.)


Department of Mathematics


Infiltration is the process whereby water enters soil through the surface. This can be a naturally occurring process, such as in rainfall, or can be artificially induced in engineering or agricultural applications. In most cases, fluid is infiltrated into soil that is unsaturated. As water infiltrates drier unsaturated soil, the water molecules fill the smallest soil pores where they are bound tighdy by capillary forces. In the transition to saturated soil, the capillary forces become less dominant and free water appears. Surface ponding is characterised by the appearance of this free water pooHng on the surface of the soil and can occur even if the soil is dry at depth. Surface ponding is an important hydrological phenomenon with applications relevant to many fields from agriculture to civil engineering. With excessive irrigation techniques, once arable soils become water logged, the rising water table brings with it geological salts which kill vegetation rendering fertile soils effectively useless. However, ponding is a desirable phenomenon in areas of water catchment. Before the emergence of highly versatile nonlinear analytic solution techniques for groundwater flow, reasonably accurate estimations for ponding times were available only with the use of numerical methods. Prior to this the linear and quasi linear models were applied to the problem of groundwater flow with mixed results. An estimation for the time to surface ponding for a variety of one and two dimensional infiltration patterns is found using a number of analytic and numerical solution methods. It is found and is observable in the field that as the wetted proportion of the soil surface and the rate of surface infiltration increase the time to surface ponding decreases. It is found that this effect dominates over the spatial pattern of irrigation.