Lab infiltration measurement, Horton's equation

Laboratory measurement of infiltration

Infiltration of soil can be measured in the laboratory using an undisturbed soil core or packed soil column in a transparent cylinder (permeameter).

1. Take an undisturbed soil sample in a metal cylinder (or pack a column of the soil to the field density). Fit a perforated base with filter paper.
2. Saturate the sample slowly from below, then place it in the apparatus.
3. Pond water on the soil surface at a constant head using a Mariotte bottle.
4. Record the volume of water entering the soil (drop in Mariotte bottle) at fixed time intervals.
5. Infiltration rate $f = \dfrac{\Delta V}{A\,\Delta t}$, where $A$ is the cross-section area of the column.
6. Continue until the rate becomes constant (the final infiltration capacity $f_c$).

   Mariotte bottle
      |   |
   ___|___|___  constant head
   |  ~~~~~  |
   |  soil   |  column
   |_________|
   ===filter==
      | drip
      v  measuring cylinder

Horton's equation

Horton (1933) observed that infiltration capacity decreases exponentially with time from an initial value $f_0$ toward a constant value $f_c$:

$$f_t = f_c + (f_0 - f_c)e^{-kt}$$

where $f_t$ = infiltration capacity at time $t$ (cm/h), $f_0$ = initial capacity, $f_c$ = final (equilibrium) capacity and $k$ = decay constant (h$^{-1}$) depending mainly on soil and vegetation.

  f
  |\ f0
  | \
  |  \___
  |      ----___
  |             ------ fc
  +--------------------- t

Features:

• Valid only when rainfall intensity exceeds $f$ (ponded surface).
• Cumulative infiltration: $F_t = f_c t + \dfrac{f_0 - f_c}{k}\left(1 - e^{-kt}\right)$.
• Constants are found from infiltrometer data by plotting $\ln(f-f_c)$ against $t$.