On Infiltration and Infiltration Characteristic Times

In his seminal paper on the solution of the infiltration equation, Philip (1969), https://doi.org/10.1016/b978-1-4831-9936-8.50010-6 proposed a gravity time, t(grav), to estimate practical convergence time and the time domain validity of his infinite time series expansion, TSE, for describing the transient state. The parameter t(grav) refers to a point in time where infiltration is dominated equally by capillarity and gravity as derived from the first two (dominant) terms of the TSE. Evidence suggests that applicability of the truncated two-term equation of Philip has a time limit requiring higher-order TSE terms to better describe the infiltration process for times exceeding that limit. Since the conceptual definition of t(grav) is valid regardless of the infiltration model used, we opted to reformulate t(grav) using the analytic implicit model proposed by Parlange et al. (1982), https://doi.org/10.1097/00010694-198206000-00001 valid for all times and related TSE. Our derived gravity times ensure a given accuracy of the approximations describing transient states, while also providing insight about the times needed to reach steady state. In addition to the roles of soil sorptivity (S) and the saturated (K-s) and initial (K-i) hydraulic conductivities, we explored the effects of a soil specific shape parameter beta, involved in Parlange's model and related to the type of soil, on the behavior of t(grav). We show that the reformulated t(grav) (notably t(grav) = F(beta)S-2/(K-s - K-i)(2), where F(beta) is a beta-dependent function) is about three times larger than the classical t(grav) given by t(grav,Philip) = S-2/(K-s - K-i)(2). The differences between the classical t(grav,Philip) and the reformulated t(grav) increase for fine-textured soils, attributed to the time needed to attain steady-state infiltration and thus i + nfiltration for inferring soil hydraulic properties. Results show that the proposed t(grav) is a better indicator of time domain validity than t(grav,Philip). For the attainment of steady-state infiltration, the reformulated t(grav) is suitable for coarse-textured soils. Still neither the reformulated t(grav) nor the classical t(grav,Philip) are suitable for fine-textured soils for which tgrav is too conservative and t(grav), Philip too short. Using t(grav) will improve predictions of the soil hydraulic parameters (particularly K-s) from infiltration data compared to t(grav,Philip).