INFILTRATION METHOD

Infiltration is a component of the general mass balance hydrologic budget. There are several ways/models are commonly used to estimate volume and/or the rate of infiltration of water into a soil. The validity of each of these models should be viewed relative to their consistency with the theoretical infiltration process. The excellent methods are the SCS Method, Darcy’s Law, or most frequently used in engineering practice are Horton Model and Green-Ampt.

HORTON INFILTRATION MODEL

In 1993, Horton suggested that during the early part of a storm (rainfall event) will produce capacity to rapidly declined. Plus, it also tends towards an approximately constant value after a couple of hours for the remainder of the event.

          It is an empirical formula that infiltration capacity starts at a constant rate (fₒ) and is decreasing exponentially with time (t). When the soil saturation level reaches a certain value, the rate of infiltration will level off to the rate fc, which is the minimum asymptotic value of infiltration. In addition, this model is frequently used in engineering practice.

Figure 7: Horton Model Curve

where,

• fp = the infiltration rate capacity potential (depth/time) at some time (mm/hr or cm/hr)
• fc = a final or equilibrium infiltration capacity (mm/hr or cm/hr)
•  fₒ = the initial infiltration capacity (mm/hr or cm/hr)
• k = a constant representing the rate of decrease in the infiltration capacity (decay coefficient) and depends on soil characteristics (1/time)
•  t = time 

Horton Infiltration Model (Cumulative Infiltration)

If water not continuously ponded above the soil column, the potential infiltration fp can be expressed in terms of the cumulative infiltration, F (t), which is the total amount of water entering the soil.

Horton Infiltration Model (Ponding Time)

Time of ponding according to Horton’s model is given by the following equation:

It is the elapsed time between the time rainfall begins and the time water begins to pond on the soil surface.

Example 2.3        :

A catchment soil has the following Horton infiltration parameters: fₒ = 100 mm/h, fc = 20 mm/h and k = 2 / min. Find

a)  What rainfall rate would result in ponding from beginning of the storm? Is the rainfall rate is maintained for 40 minutes, describe the infiltration as a function of time during the storm.

b)  Plot the infiltration capacity curve with time for this catchment and  potential cumulative infiltration for this catchment

Solution     :

a) Using equation 2.5,

b)

Find out the sensitivity of the infiltration capacity curve to different decay coefficients (k) assuming that fₒ = 2.9 in/h and fc = 0.5 in/h. Assume k values = 0.15, 0.30 and 0.45/ hour

GREEN - AMPT MODEL

Green-Ampt Model is based on a simple conceptualization of an infiltrating front in a dry soil with an approximated sharp interface. It is physically based semi-empirical model was first proposed by Green and Ampt (1911) and was put on a firm physical basis by Philip (1954). It sometimes called delta function model is today one of the most realistic model of infiltration.

Figure 8: Sharp Interface

This sharp interface is the wetting front that divides the soil of moisture content θᵢ below from saturated soil with moisture content of θs (equals porosity). The wetting front has penetrated a depth of L in time t since infiltration began. Water is ponded to a depth of H.

Apparently, total cumulative infiltration after time t (since infiltration began) equals:

In addition, we can implement Darcy’s Law where the infiltration rate depends on hydraulic conductivity of the soil along with the head difference, or

Cumulative infiltration F (t) in Green-Ampt model is given by the following equation:

While infiltration rate f (t) is given by the following equation: 

v Equations 2.12 and 2.13 are used under the assumption that water is ponded to a small but negligible depth on the soil surface

When water is applied at rate higher than K (i >K) of the soil, ponding occurs. To find ponding time and the cumulative infiltration at ponding (using Green-Ampt model) use the following equations: 

Example 2.4        :

Compute the infiltration rate and cumulative infiltration after one hour of infiltration into a soil that initially had a water content of 01 and a saturated water content 0f 0.44. The average wetting front capillary pressure head is 16.7 cm and the hydraulic conductivity is 0.65 cm/hr.

Solution     :

1) To find the cumulative infiltration, we have to use the following equation: 

F (t) = 0.65 X 1 + 16.7 X (0.44 - 0.1) ln

                                                  F (t) = 3.167 cm