CE322 Basic Hydrology

Jorge A. Ramírez

Infiltration Computations Example

Assume that the time evolution of the infiltration capacity for a given soil is governed by Horton's equation (Note that this equation assumes an infinite water supply at the surface, that is, it assumes saturation conditions at the soil surface).

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For this soil, the asymptotic or final equilibrium infiltration capacity is fc = 1.25 cm/h; and the initial infiltration capacity is fo = 8 cm/h. The rate of decay of infiltration capacity parameter is k = 3 h-1. For the precipitation hyetograph tabulated below, carry out a complete infiltration analysis, including evaluation of cumulative infiltration and rate of production of precipitation excess, s + v.

 Time  (min) Precipitation  (cm/h) Time  (min) Precipitation  (cm/h) 0 - 10 1.5 40 - 50 4.0 10 - 20 3.0 50 - 60 3.0 20 - 30 8.0 60 - 70 0.8 30 - 40 5.0
1. Compute accumulated precipitation volume as a function of time. The incremental volume over each time period of 10 minutes is:

DP = i Dt

 Time  (min) Precipitation Intensity, i.  (cm/h) Cumulative Precipitation, P (cm) Time  (min) Precipitation Intensity, i.  (cm/h) Cumulative Precipitation, P (cm) 0 - 10 1.5 0.25 40 - 50 4.0 3.583 10 - 20 3.0 0.75 50 - 60 3.0 4.083 20 - 30 8.0 2.083 60 - 70 0.8 4.217 30 - 40 5.0 2.917
2. Compute infiltration capacity using Horton's equation for conditions of unlimited water supply at the surface using equation 1 (Table 1 - Column 2).
3. Compute the accumulated infiltration that would occur under conditions of unlimited water supply at the surface using the following equation 2 (Table 1 - Column 3),

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4. Compare infiltration capacity with precipitation intensity (Figure 1). Observe that during the first 20 minutes of the rainstorm, the infiltration capacity exceeds the precipitation intensity. Thus, during this period, all of the precipitation infiltrates. The actual infiltration rate is (Table 2 - Column 5),

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5. Because the actual infiltration rate is less than the infiltration capacity during the first 20 minutes, the actual infiltration capacity does not decay as predicted by Horton's equation. This is because, as indicated above, Horton's equation assumes that the supply rate exceeds the infiltration capacity from the start of infiltration. Therefore, we must determine the true infiltration capacity at t = 20 min. To do so, first determine the time tp by solving the following equation:

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and then evaluate fp(tp) as follows. The left-hand side of equation 4 represents the accumulated volume of actual infiltration, while the right hand side of equation 4 represents the volume of infiltration that would have accumulated up to time tp if the actual rate of infiltration had been equal to the infiltration capacity.

At t = 20 min the actual volume of accumulated infiltration is:

F(t = 20 min) = (1.5 + 3.0) cm/h (10 min/60 min/h) = 0.75 cm. Substituting this value for F(t) in equation 4 and solving for tp obtain: tp = 0.107 h = 6.41 min. Finally, the true infiltration capacity at 20 minutes is obtained using equation 1 as fp(tp) = 6.15 cm/h = fop. Alternatively, using equations 1 and 2 to eliminate time and express cumulative infiltration as a function of infiltration capacity obtain the following equation,

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6. The rainfall rate at 20 minutes i = 8 cm/h exceeds the corresponding infiltration capacity fop = 6.15 cm/h. Therefore, the actual infiltration rate equals the infiltration capacity, and the decay of infiltration capacity follows Horton's equation with an initial infiltration capacity equal to fop and starting at time t* = 20 min (Table 1 - Column 5 and Table 2 Column 3). That is (see Figure 2 and Figure 3),

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7. Because the precipitation rate exceeds the infiltration capacity, there is excess precipitation available for runoff and depression storage, s + v (Table 2 - Column 6).

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Table 1

 1 2 - Eq. 1 3 - Eq. 2 4 5 - Eq. 6 Time  (min) Infiltration Capacity, fp (cm/h) Cumulative Infiltration, F (cm) Cumulative Precipitation, P  (cm) Actual Infiltration Capacity  (cm/h) 0 8 0 0 10 5.344082 1.093639 0.25 20 3.733186 1.838938 0.75 6.150306 30 2.756129 2.372957 2.083333 4.222186 40 2.163513 2.778829 2.916667 3.052722 50 1.804074 3.106975 3.583333 2.343406 60 1.586063 3.387979 4.083333 1.913184 70 1.453832 3.640389 4.216667 1.652242 80 1.373631 3.875456 1.493972 90 1.324986 4.100005 1.397976 100 1.295481 4.318173 1.339752 110 1.277586 4.532471 1.304437 120 1.266732 4.744423 1.283018

Table 2

 1 2 - Eq. 1 3 - Eq. 6 4 5 - Eq. 3 6 - Eq. 7 Time  (min) Infiltration Capacity, fp (cm/h) Actual Infiltration Capacity  (cm/h) Precipitation Intensity, i (cm/h) Actual Infiltration Rate, f(t) (cm/h) Runoff rate  s + v (cm/h) 0 8.0 8.0 1.5 1.5 0.0 10 5.344082 > 6.15030 3.0 3.0 0.0 20 3.733186 6.150306 8.0 6.15030 1.849694 30 2.756129 4.222186 5.0 4.22218 0.777814 40 2.163513 3.052722 4.0 3.05272 0.947278 50 1.804074 2.343406 3.0 2.34340 0.656594 60 1.586063 1.913184 0.8 0.8 0 70 1.453832 1.652242 80 1.373631 1.493972 90 1.324986 1.397976 100 1.295481 1.339752 110 1.277586 1.304437 120 1.266732 1.283018