Answer

 Infiltration Calculation Method

Infiltration is the process through which water from the surface enters into the soil particles through mechanisms such as percolation (Qi et al, 2020). In this paper, three methods will be discussed to present how rates of infiltration can be determined in the soil.

  Horizontal infiltration

The rate of infiltration decreases with increase in time according to this method. Thus, the calculation begins at point f₀ followed by an exponential decrease to constant f_c at the end of the process. This, from the above constants, the equation f_p= f_c + (f₀-f_c) e^kt

Where:

f_p= infiltration capacity measured in millimeters per hour over time t

f₀= the initial infiltration in mm/hour

f_c=the ultimate infiltration capacity at saturation point

t = time measured from the start of rain

k = the exponential constant of decay according to type of soil and vegetation.

During the calculation process, the calculation should be based on capacities that is within or above fp; that is f =fp when i ³ fp, but when i < fp, f < fp and f = i.

Using the same formula, the accumulated infiltration F(t) is obtained by the relationship d(F(t)/dt = f(t) = fp. This process is thus calculated by F(t) = f_c t + ((f₀ – f_c)(1 – e^–kt))/k

The Phillip method

According to Phillip’s argument (Lu et al, 2020), the cumulative infiltration is calculated by:

F (t) = St^0.5 + Kt

 Where:

S= represents suction head of soil.

K= denotes the hydraulic soil conductivity.

t= time from start to the end.

Under this formula the cumulative infiltration is obtained by equation F (t) = dF (t)/dt. Therefore, the infiltration rate is summed by f (t) = 0.5St^-0.5 = K

The Green-Ampt method

Under this method, Decray law is utilized to apply the assumption that water is normally pounded on the surface. A consideration is therefore provided for a vertical soil unit with cross sectional area and volumes rising on surface and depth denoted as L. following diagram expresses this assumption.

Diagram 1.1

Based on the above diagram, the soil initial moisture is presented by q for the whole depth. During the wetting process, moisture level raises from qi to n. thus the rise in water within the control volume of infiltration is presented by L (n- qi) = LDq for all units across the cross-sectional area (Elistratova et al, 2020).

The water volume infiltrated into the soil F is obtained by:

F (t) = L (n –q)

On the other hand, Dacry law provides:

q = -K (¶h/ ¶z)

This case implies that q = -f given the positive values of f in vertical directions. The equation can thus be given as:

F=K((h₁-h₂)(z₁-z₂))

At this point, the top of the soil h1 is expressed as h₀ while that beneath after wetting is provided by h₂ = y-L. The resultant equation is thus:

f = K(h₀ (y-L)L) = K (y +L)/L)

This calculation reveals that h₀ is negligible and thus the pounding water is lost as surface runoff. This brings the replacement of L by F(t)/(Dq) and we thus obtain:

f  = K (yDq  + F/F)

on the other hand, dF/dt = f and therefore the development of Green Ampt equation is obtained by:

F (t) = Kt = yDqin (1+ (Ft/yDq)

However, this donation presents an non-linear equation. To attain a linear form, we apply:

F (t) = Kt + yDqin (1 + Ft/yDq)

In conclusion, the above three methods can be applied to calculate infiltration in different types of soils.