30.4. Infiltration Capacity Curves

The variation of infiltration capacity with time is typically shown using an infiltration capacity curve, which can be described using empirical models such as:

Infiltration capacity curves graphically represent how the ability of soil to absorb water changes over time. These curves are important for understanding how water infiltrates into different types of soil under varying conditions. The specific shape and characteristics of these curves can help engineers and hydrologists predict how land will respond to rainfall or irrigation.

Imagine a sponge. At the beginning, when a dry sponge comes into contact with water, it absorbs quickly. As it becomes saturated, its ability to take in more water decreases. Infiltration capacity curves describe a similar process—starting with high absorption that slows down as the soil becomes drier.

30.4.1 Horton’s Equation

f(t)=f₀+(fₗ−f₀)e^(−kt)

Where:

• f(t) = infiltration capacity at time t
• f₀ = initial infiltration capacity
• fₗ = final infiltration capacity
• k = decay constant

Horton’s Equation is a mathematical representation used to model the change in infiltration capacity over time. It shows that the infiltration rate starts high at the beginning of a rainfall event and decreases exponentially as time passes. The equation includes variables for the initial and final infiltration capacities, as well as a decay constant that indicates how quickly the rate drops.

Think of pouring a drink into a glass. Initially, you can pour quickly because there is plenty of space, but as the glass fills up, you have to pour more slowly to prevent overflow. Horton’s equation captures this dynamic, where the initial capacity is high, but as the soil fills, the capacity lessens.

30.4.2 Philip’s Equation

f(t)=S t^{-1/2} + A

Where:

• S = sorptivity
• A = steady infiltration rate

Philip’s Equation provides another way to describe how water moves into the soil. It incorporates terms for sorptivity, which describes how quickly and efficiently soil can absorb water from the surface, and a steady infiltration rate, which is the constant rate of infiltration after the initial absorption phase.

Picture a dry towel spread out on a table. If you pour water onto the towel, it initially absorbs quickly (like sorptivity) but will eventually reach a point where it can only take in water at a constant slow rate (the steady infiltration rate).

30.4.3 Green-Ampt Equation

f(t)=K(1+ψ)(F(t)−Δθ)

Where:

• K = hydraulic conductivity
• ψ = wetting front suction head
• Δθ = change in moisture content
• F(t) = cumulative infiltration

The Green-Ampt Equation models infiltration based on hydraulic conductivity and other soil properties. It accounts for both the capillary movement of water through the soil (wetting front suction) and the cumulative amount of water that has infiltrated over time. This makes it a comprehensive model for varying soil conditions.

Consider a sponge submerged in water that is gradually pulled up. The rate at which the sponge absorbs water changes, depending on how much water is already in it and how quickly water can pass through its structure, mirroring the principles of the Green-Ampt Equation regarding different saturation levels and water movement.

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