Estimating of soil sorptivity ( S ) and saturated hydraulic conductivity ( K s ) parameters by field infiltration tests are widespread due to the ease of the experimental protocol and data treatment. The analytical equation proposed by Haverkamp et al. (1994) allows the modeling of the cumulative infiltration process, from which the hydraulic parameters can be estimated. This model depends on both initial and final values of the soil hydraulic conductivity, initial soil sorptivity, the volumetric water content increase ( ∆ θ ), and two infiltration constants, the so-called β and γ parameters. However, to reduce the number of unknown variables when inverting experimental data, constant parameters such as β and γ are usually prefixed to 0.6 and 0.75, respectively. In this study, the values of these constants are investigated using numerical infiltration curves for different soil types and initial soil water contents for the van Genuchten-Mualem (vGM) soil hydraulic model. Our approach considers the long-time expansions of the Haverkamp model, the exact soil properties such as S , K s , and initial soil moisture to derive the value of the β and γ parameters for each specific case. We then generated numerically cumulative infiltration curves using Hydrus 3-D software and fitted the long-time expansions to derive the value of the β and γ parameters. The results show that these parameters are influenced by the initial soil water content and the soil type. However, for initially dry soil conditions, some prefixed values can be proposed instead of the currently used values. If an accurate estimate of S and K s is the case, then for coarse-textured soils such as sand and loamy sand, we propose the use of 0.9 for both constants. For the remaining soils, the value of 0.75 can be retained for γ . For β constant, 0.75 and 1.5 values can be considered for, intermediate permeable soils (sandy loam and loam) and low permeable soils (silty loam and silt), respectively. We clarify that the results are based on using the vGM model to describe the hydraulic functions of the soil and that the results may differ, and the assumptions may change for other models.

In his seminal paper on solution of the infiltration equation, Philip (1957) proposed a gravity time, tgrav, to estimate practical convergence time of his infinite time series expansion, TSE. The parameter tgrav refers to a point in time where infiltration is dominated equally by capillarity and gravity derived from the first two (dominant) terms of the TSE expansion. Evidence that higher order TSE terms describe the infiltration process better for longer times. Since the conceptual definition of tgrav is valid regardless of the infiltration model used, we opted to reformulate tgrav using the analytic approximation proposed by Parlange et al. (1982) valid for all times. In addition to the roles of soil sorptivity (S) and saturated (Ks) and initial (Ki) hydraulic conductivities, we explored effects of a soil specific shape parameter β on the behavior of tgrav. We show that the reformulated tgrav (notably tgrav= F(β) S^2/(Ks - Ki)^2 where F(β) is a β-dependent function) is about 3 times larger than the classical tgrav given by tgrav, Philip= S^2/(Ks - Ki)^2. The differences between original tgrav, Philip and the revised tgrav increase for fine textured soils. Results show that the proposed tgrav is a better indicator for convergence time than tgrav, Philip. For attainment of the steady-state infiltration, both time parameters are suitable for coarse-textured soils, but not for fine-textured soils for which tgrav is too conservative and tgrav, Philip too short. Using tgrav will improve predictions of the soil hydraulic parameters (particularly Ks) from infiltration data as compared to tgrav, Philip.

Infiltration into hydrophobic soils has been widely observed, quantified and documented in many situations and several climates (DeBano, 2000; Angulo-Jaramillo et al., 2016).The modelling of water infiltration into soils with hydrophobic properties is often performed by modifying the unsaturated hydraulic parameters of soils, but only rarely taking into account explicitly the water-repellency. In this study, we model water infiltration in hydrophobic soils considering explicitly the contact angle as the measurement of water repellency, with the geometrical pore model proposed by Hammecker et al. (2004).This microscopical approach showed good agreement with macroscopical models and with experimental data. The model was used to evaluate the conditions for unstable flow with fingering features.