مهدی رحمتی

In his seminal paper on the solution of the infiltration equation, Philip (1969) proposed a gravity time, tgrav, to estimate practical convergence time and the time domain validity of his infinite time series expansion, TSE, for describing the transient state. The parameter tgrav 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 expansion. 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 tgrav is valid regardless of the infiltration model used, we opted to reformulate tgrav using the analytic implicit model proposed by Parlange et al. (1982) 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 (Ks) and initial (Ki) hydraulic conductivities, we explored the effects of a soil specific shape parameter β, involved in Parlange’s model and related to the type of soil, on the behavior of tgrav. We show that the reformulated tgrav (notably t_grav= F(β)S^2⁄((K_s-K_i )^2,) where F(β) is a β-dependent function) is about three times larger than the classical tgrav given by t_(grav,Philip)=S^2⁄(K_s-K_i )^2 . The differences between the classical tgrav,Philip and the reformulated tgrav increase for fine-textured soils, attributed to the time needed to attain steady-state infiltration and thus infiltration for inferring soil hydraulic properties. Results show that the proposed tgrav is a better indicator of time domain validity than tgrav,Philip. For the attainment of steady-state infiltration, the reformulated tgrav is suitable for coarse-textured soils. Still neither