🎓 Lesson 8
D5
Infiltration Physics: Horton, Green-Ampt & Philip Models
Infiltration is how water soaks into the ground from the surface, like rain soaking into dry soil.
🎯 Learning Objectives
- ✓ Calculate infiltration rates over time using Horton’s exponential decay model
- ✓ Apply the Green-Ampt model to estimate time to ponding and cumulative infiltration for unsaturated soils
- ✓ Analyze soil hydraulic properties (Ksat, θi, θs, ψf) and select the most appropriate infiltration model for a given mining site condition
- ✓ Design surface drainage berms and infiltration basins by integrating infiltration capacity with stormwater return periods
📖 Why This Matters
In open-pit mines, uncontrolled infiltration can saturate waste rock dumps, trigger slope failures, or overwhelm dewatering systems—leading to costly shutdowns and safety hazards. Understanding *how fast* and *how much* water enters the ground determines whether a 100-year storm will cause surface ponding on a haul road or percolate deep enough to impact groundwater drawdown targets. This lesson bridges hydrology theory with real-world mine water management decisions.
📘 Core Principles
All three models describe infiltration but assume different physical controls: Horton assumes declining surface conductivity due to pore clogging and crust formation; Green-Ampt treats infiltration as piston-like wetting front advance driven by capillary suction and saturated hydraulic conductivity; Philip’s two-term solution combines short-time diffusion (sorptivity-driven) and long-time conductivity (steady-state) behavior—making it especially robust for heterogeneous mine spoil materials. Each model requires distinct soil property inputs and performs best under specific moisture and textural conditions: Horton for crusted or layered surfaces, Green-Ampt for uniform, initially dry soils, and Philip for transient, low-intensity rainfall on disturbed or rehabilitated landforms.
📐 Green-Ampt Cumulative Infiltration
The Green-Ampt model estimates cumulative infiltration (F) as a function of time by balancing driving force (ponded head + matric suction) against resistance (soil hydraulic conductivity). It’s widely used in mine closure planning because it explicitly incorporates measurable soil parameters and predicts time-to-ponding—a key design threshold for erosion control.
💡 Worked Example
Problem: A waste rock dump has initial volumetric water content θi = 0.08, saturated water content θs = 0.32, average soil suction head ψf = −25 cm, and saturated hydraulic conductivity Ksat = 0.5 cm/hr. Rainfall intensity is 1.2 cm/hr. Calculate time to ponding (tp) and cumulative infiltration at t = 2 hr.
1.
Step 1: Compute effective saturation deficit: Δθ = θs − θi = 0.32 − 0.08 = 0.24
2.
Step 2: Convert ψf to cm (already given): ψf = −25 cm → |ψf| = 25 cm
3.
Step 3: Calculate time to ponding: tp = (|ψf| × Δθ) / (i − Ksat) = (25 × 0.24) / (1.2 − 0.5) = 6.0 / 0.7 ≈ 8.57 hr
4.
Step 4: Since t = 2 hr < tp, no ponding yet → use F(t) = Ksat × t = 0.5 × 2 = 1.0 cm
5.
Step 5: Confirm assumption: i > Ksat required for ponding — true (1.2 > 0.5)
Answer:
Time to ponding is 8.6 hours; cumulative infiltration at 2 hours is 1.0 cm — well below ponding threshold, confirming surface remains unsaturated and runoff-free.
🏗️ Real-World Application
At the Cadia East copper-gold mine (NSW, Australia), geotechnical engineers used the Green-Ampt model to redesign the cover system for a 120-Mt waste dump. Field-saturated hydraulic conductivity (Ksat = 0.3–0.7 cm/hr) and laboratory-determined ψf (−18 to −35 cm) were integrated with 10-yr ARI rainfall hyetographs. Model outputs guided berm spacing and vegetative cover density to ensure <5 mm/hr infiltration exceeded by only 0.3% of annual storms—meeting NSW EPA ‘low risk’ closure criteria (EPA 2021 Guideline No. 1330).
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