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).

(1)

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),

    (2)

  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), 

    (3)

  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:

    (4)

    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,

    (5)

  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),

    (6)
     

  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).

(7)

 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