27.5. Empirical Infiltration Models

Proposed by Robert Horton (1933), this model assumes an exponential decay of infiltration rate over time.

f(t)=f₀+(fₐ−f₀)e^{−kt}

Where:

• f(t): Infiltration rate at time t
• f₀: Initial infiltration rate
• fₐ: Final steady infiltration rate
• k: Decay constant (infiltration index)

Horton's Equation helps us understand how the rate at which water infiltrates into the soil changes over time after it starts raining. The equation shows that the infiltration rate starts at an initial high value (f₀) and decreases exponentially until it reaches a final steady state (fₐ). The decay constant (k) indicates how quickly this rate decreases. So, in simple terms, when it starts raining, the ground absorbs water quickly at first, but as the soil becomes more saturated, the rate slows down.

Imagine pouring water on a sponge. At first, the sponge quickly soaks up the water, but as it becomes saturated, it can't absorb much more. This behavior is similar to how soil behaves during rainfall, which is what Horton's equation illustrates.

Based on the theory of capillarity and gravity:

f(t)=S+ A√t

Where:

• S: Sorptivity (capillary effect)
• A: Steady-state infiltration rate

Philip’s Equation looks at how water enters the soil by considering two factors: the sorptivity, which is how well the soil can initially absorb water due to its capillary forces, and the steady-state infiltration rate, which is how fast the soil can absorb water in equilibrium. In essence, this equation helps estimate how much water the soil initially takes in and how quickly it can continue to absorb water over time.

Think of filling a glass with sand and then pouring water over it. The sand can quickly absorb some water because of its tiny pores (sorptivity), but eventually, the rate slows down as the sand becomes wet, which relates to the steady-state infiltration rate.

A physically based model using soil suction head and moisture content:

f=K(1 + (Ψ⋅Δθ)/F)

Where:

• K: Hydraulic conductivity
• Ψ: Wetting front suction head
• Δθ: Change in moisture content
• F: Cumulative infiltration This model is suitable for infiltration under ponded conditions.

The Green-Ampt Model provides a framework for understanding how water moves through saturated soil layers. By taking into account the hydraulic conductivity (how easily water can flow through the soil), the wetting front suction head (how much force is pulling the water into the soil), and changes in moisture content, this model can accurately predict water infiltration particularly when there is standing water on the surface (ponded conditions).

Picture a sponge in a bucket of water. The sponge has certain 'pulling power' to absorb water (suction head) and its ability to soak up water quickly depends on how 'permeable' it is (hydraulic conductivity). When you first place the sponge in the water, it quickly absorbs; similarly, this model helps understand how soil absorbs water in real-world scenarios.

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