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 f_{c} = 1.25 cm/h; and the initial infiltration capacity is f_{o} = 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 



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)
(3)
(4)
and then evaluate f_{p}(t_{p}) as follows. The lefthand 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 t_{p} 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 t_{p} obtain: t_{p} = 0.107 h = 6.41 min. Finally, the true infiltration capacity at 20 minutes is obtained using equation 1 as f_{p}(t_{p}) = 6.15 cm/h = f_{op}. 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)
(7)
Table 1
1 
2  Eq. 1 
3  Eq. 2 
4 
5  Eq. 6 
Time (min) 
Infiltration Capacity, f_{p} (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, f_{p} (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 


