The one‐dimensional quasi‐linear intercept on cumulative infiltration graphs

The asymptotic time behavior of one‐dimensional infiltration of water into a class of idealized soils is determined theoretically. First, we assume that all flows are one dimensional and investigate transient behavior between a steady initial state and another final steady state. Second, soil properties are idealized by making the quasi‐linear assumption of J. R. Philip (1969) that relative permeability is related exponentially to capillary pressure, which linearizes the flow terms. Third, and least importantly, we also assume later that changes in volumetric water content vary as a power of relative permeability. The transient flow equations then reduce to a nonlinear parabolic equation with relative permeability as the primary variable. One‐dimensional cumulative infiltration is then asymptotically a linear function of time, whose gradient depends on the saturated soil conductivity and whose intercept equals the change in field capacity (or near surface volumetric water content) divided by the quasi‐linear inverse length parameter. The equations for both the gradient and intercept for this asymptotic linear function are independent of time and independent of the relationship between volumetric water content and relative permeability. Finally, the three assumptions above imply that the time constant, representative of the duration needed to attain near steady conditions, essentially equals the sum of a term independent of the initial conditions, plus a term depending only on differences between the initial and final conditions.