Asymptotic Behavior of Infiltration in Soils Containing Cracks or Holes

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Abstract
An asymptotic, one‐dimensional Green‐Ampt model of infiltration into a soil containing regularly spaced vertical cracks, or a cylindrical soil column containing a central hole, is derived from a complete two‐dimensional or axisymmetric Green‐Ampt analysis by summing an asymptotic expansion for the infiltration rate valid at large times when the wetting front has become horizontal. The model is shown to be accurate at intermediate times when the front is not necessarily horizontal and corresponds to one‐dimensional infiltration initiated from a plane lying below the soil surface at a depth which depends only on the geometry and which lies between zero and the crack (hole) depth. When applicable, model predictions of infiltration rate and cumulative infiltration obtained for cylindrical holes, like those previously obtained for cracks, agreed well with corresponding results based on finite difference solutions of the saturated‐unsaturated flow equations, differences being in the range of 2–9%.

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