Analysis of Early‐Time and Steady State Single‐Ring Infiltration Under Falling Head Conditions

Abstract

The prediction of infiltration of water into field soils requires measurements of the field-saturated hydraulic conductivity (Kfs) and the matric flux potential corresponding to field saturation (qbm). We develop analytical solutions for (1) early-time, onedimensional infiltration into slowly permeable soils such as clay liners under the conditions of an initial constant head followed by a falling head phase and (2) steady state, threedimensional infiltration into permeable soils under the condition of steady state flow at a constant head followed by falling head conditions. Kfs and qbm govern the shape of both solutions. The parameters are simultaneously identifiable, unique, and stable within the early-time solution; however, there is a limited range in which the parameters of the steady state solution are unique. Laboratory and field experiments based on both solutions gave physically realistic best fit parameter values using the solutions in inversion procedures. Field measurements gave an excellent correlation between Kfs from steady state constant head and falling head techniques. The correlation between qbm values was somewhat lower. Introduction Most field procedures for determining field-saturated hydraulic conductivity, Kfs(L T-•) and the mattic flux potential corresponding to field saturation, (•m (L2T-1), (e.g., well permeameters, ring infiltrometers, tension infiltrometers) measure flow under constant ponded head and steady state flow conditions. Constant head conditions have traditionally been used because constant head devices are simple and easy to maintain experimentally and because the analyses are usually relatively easy to invert. A difficulty with this approach, however, is that insufficient information is obtained from the measurement of steady state flow under one constant head to evaluate both Kfs and •)m [Elrick and Reynolds, 1992a, b]. Either one parameter, such as a* (a* = Kf•/rbm), must be measured or estimated independently [e.g., Elrick et al., 1989] or steady state flow measurements need to be taken for two or more ponded heads [e.g., Elrick and Reynolds, 1992b]. If a* is estimated, however, some error can result [e.g., Reynolds et al., 1992], and if steady state measurements are taken at two or more heads, soil heterogeneity can cause a large percentage of invalid (i.e., negative) and unrealistic Kfs and l•m values [Elrick and Reynolds, 1992b; Reynolds et al., 1992]. Infiltration under both early-time falling head conditions and steady state falling head conditions can provide, however, information from which both Kfs and qbm can be uniquely obtained (for the most part) with reasonable accuracy. By "early-time falling head" (EFH) Paper number 95WR01139. 0043-1397/95/95WR-01139505.00conditions we mean that water is rapidly ponded on the infiltration surface and the initial rate of fall of the water level is measured. By "steady state falling head" (SFH) we mean that infiltration is initially allowed to come to steady state under constant ponded head conditions and then the head is a...

Saturated Soil Hydraulic Conductivity

“…The iterative fitting procedure requires an initial guess value for each parameter, and measurement errors coupled with bad first guesses can give incorrect best fit values. Elrick et al (1995) suggested that the slope, m, of the early data of ln[H(t)] versus t gives a guess value of K fs : K fs ¼ mXG r ð2:104Þ Equation (2.104) was derived from the pressure head component of falling-head infiltration and it is expected to provide a sufficiently accurate initial guess of K fs , provided that m is obtained when the perturbing effects of soil capillarity and gravity, i.e. the second and third term, respectively, on the right hand side of Eq.…”

“…(2.105) can be obtained from Eq. (2.103), developed by Elrick et al (1995) for a steady-state falling-head process, under the assumptions that the cross-sectional area of the infiltrometer's cylindrical water reservoir coincides with the infiltration surface and the dimensionless shape factor can be estimated with the approximate relationship of Reynolds and Elrick (1990), i.e. G % G e ¼ 0.316(d/r) + 0.184.…”

“…(2.103), are minimal. Elrick et al (1995) established a field comparison between the Two Ponding Depth (TPD) approach and the steady-state fallinghead analysis by sampling a silty-clay soil at 12 locations. Initially, steady constant-head infiltration was obtained at two successively ponded heads (0.11 and 0.34 m).…”

“…In particular, the method by Touma et al (2007) and the Simplified method based on the Beerkan Infiltration run (Bagarello et al 2013b(Bagarello et al , 2014b) rely on the so-called Beerkan experimental protocol and they consider the transient phase of an infiltration process under a constant head of water on the soil surface, theoretically equal to zero. With the Steady-State Falling-Head method by Elrick et al (1995) and the Bottomless Bucket method by Nimmo et al (2009), a falling-head infiltration process has to be established. These methods are described in this section.…”

Measuring Water Transmission Parameters in Vadose Zone Using Ponded Infiltration Techniques

“…For constant head procedures see Elrick and Reynolds (1992) and Vauclin et al (1994). For falling head procedures see Elrick et al (1995Elrick et al ( , 2002. APPLIED ENGINEERING INVESTIGATIONS: Applied engineering investigations often require only "ball park" estimates of K fs .…”