Quasilinearised infiltration and the boundary element method

Abstract

A general numerical method is presented for solving the problem of quasilinearised steady infiltration from two-dimensional or axisymmetric surface cavities and from a general cavity buried at an arbitrary depth in either a two- or three-dimensional homogeneous semi-infinite porous medium. For constant diffusivity, this technique can be used to solve time dependent problems. With some modifications, the procedure is also capable of solving the coupled saturated-unsaturated problem that results when water head inside the cavity is not neglected. Numerical results are compared to known analytical results for the cases of a shallow circular pond, and a circular cylindrical cavity and a spherical cavity buried in an infinite medium. Further steady state results ignoring the water head in the cavity are presented graphically, illustrating the effect of an upper surface on the flux from a circular cavity and also the effect of an upper surface on the size of the effective wetted region. The dependence of the flux on geometry, gravity and capillarity is investigated for twodimensional surface cavities. These results provide important extensions to previous analytical results. The problem of time dependent quasilinearised infiltration with constant diffusivity from a small axisymmetric shallow flat pond is also examined. The variation of flux with time is illustrated for a range of the dimensionless pond radius s likely to be found in many small ring infiltrometer experiments. The time taken for the flux to reach near steady state and its dependence on s is investigated. Results for coupled saturated-unsaturated systems are presented for buried twodimensional circular cylindrical cavities and various two-dimensional circular surface cavities with non-zero head. The effects of the size of the cavity and the soil type on the flux from the cavity, the size of the saturated zone and the size of the effective wetted region are studied. Comparisons with previous analytical and numerical results, in which the water head in the cavity was neglected, indicate the severe errors that this approximation introduces into the calculation of the flux and the flow field. In particular it is shown that the percentage error in the flux from a buried circular cylinder with water head neglected increases from 20% to 220% as the dimensionless cavity size s increases from 0.1 to 1. Also when the head is neglected there is no saturated zone, but when the head is included for the buried circular cylinder the saturated zone extends to a depth of approximately 7.9 times the cavity radius for s = 1.