🎓 Lesson 3
D2
Effective Stress Principle and Its Role in Compaction Prediction
Effective stress is the part of soil pressure that actually holds the grains together and controls how the soil behaves when loaded — like the 'real' squeezing force between soil particles after water pressure is subtracted.
🎯 Learning Objectives
- ✓ Calculate effective stress at any depth in layered soil profiles with varying saturation and unit weights
- ✓ Analyze how changes in groundwater level affect compaction potential and tire–soil contact pressure distribution
- ✓ Explain the influence of effective stress on soil bearing capacity and rutting susceptibility under heavy mining equipment
- ✓ Apply Terzaghi’s principle to predict pre-consolidation behavior in compacted haul road subgrades
📖 Why This Matters
In mining operations, haul trucks weighing up to 400+ tonnes exert extreme contact pressures on unsealed roads. If effective stress is misestimated — especially where seasonal water tables rise — compaction becomes non-uniform, leading to premature rutting, reduced tire life, and unsafe operating conditions. Understanding effective stress isn’t just academic: it directly determines whether your modeled tire–soil pressure distribution reflects reality or dangerously overestimates load-bearing capacity.
📘 Core Principles
Terzaghi’s Effective Stress Principle (1923) states that soil behavior depends not on total applied load, but on the portion carried by solid particles — i.e., effective stress. In unsaturated soils, matric suction contributes to effective stress (σ′ = σ − uₐ + uₘ), but for most compacted mining subgrades under saturated or near-saturated conditions (e.g., after rain), the classical form σ′ = σ − u dominates. As pore water pressure increases (e.g., due to poor drainage), effective stress drops — reducing shear strength and increasing compressibility. This is critical when modeling contact pressure distribution: a 20% reduction in effective stress can increase vertical strain by >50%, altering predicted tire sinkage and pressure spread.
📐 Key Calculation
The effective stress equation is foundational for predicting soil response under static and dynamic loading. It must be applied at each stratum in a layered profile to determine vertical effective stress at depth — essential input for bearing capacity and compaction models used in tire–soil interaction simulations.
Terzaghi’s Effective Stress Equation
σ′ = σ − uComputes the stress transmitted through soil particle contacts, controlling deformation and strength.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| σ′ | Effective vertical stress | kPa | Stress carried by soil skeleton; governs compaction and shear resistance. |
| σ | Total vertical stress | kPa | Sum of overburden and applied loads per unit area. |
| u | Pore water pressure | kPa | Fluid pressure in soil voids; zero in dry soil, equals γ_w × depth below water table in saturated zones. |
Typical Ranges:
Compacted gravel subgrade (dry): 20 – 60 kPa
Saturated clay subgrade (monsoon season): 5 – 25 kPa
💡 Worked Example
Problem: A haul road consists of 0.5 m of compacted gravel (γ_dry = 18.5 kN/m³) over 2.0 m of saturated clay (γ_sat = 19.8 kN/m³). Groundwater table is at surface. Calculate effective vertical stress at the clay–gravel interface (z = 0.5 m) and at bottom of clay layer (z = 2.5 m).
1.
Step 1: At z = 0.5 m (interface), total stress σ = γ_dry × 0.5 = 18.5 × 0.5 = 9.25 kPa; pore pressure u = γ_w × 0.5 = 9.81 × 0.5 = 4.91 kPa → σ′ = 9.25 − 4.91 = 4.34 kPa
2.
Step 2: At z = 2.5 m (clay base), total stress σ = (18.5 × 0.5) + (19.8 × 2.0) = 9.25 + 39.6 = 48.85 kPa; u = γ_w × 2.5 = 9.81 × 2.5 = 24.53 kPa → σ′ = 48.85 − 24.53 = 24.32 kPa
3.
Step 3: Verify against typical range: 4–25 kPa is typical for shallow compacted subgrades under light-to-moderate loading; result falls within expected bounds.
Answer:
Effective stress is 4.3 kPa at the interface and 24.3 kPa at 2.5 m depth — both within safe operational ranges for well-drained haul roads.
🏗️ Real-World Application
At Rio Tinto’s Pilbara iron ore operations, haul road failures increased during monsoon season despite design-grade compaction. Investigation revealed rising groundwater elevated pore pressures in the underlying saprolite layer, reducing effective stress by ~35% and decreasing undrained shear strength below 25 kPa — insufficient to resist 1,200 kN axle loads. Remediation included installing wick drains and raising subgrade elevation, restoring effective stress to >40 kPa and extending road life by 4×. This case underscores why tire–soil models ignoring pore pressure dynamics fail in tropical or high-rainfall mining environments.
🔧 Interactive Calculator
🔧 Open Tire–Soil Contact Pressure Distribution Modeling Calculator📋 Case Connection
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