🎓 Lesson 7
D4
Janosi–Hanamoto Shear Resistance Model for Lateral Forces
It’s a mathematical model that predicts how much sideways (lateral) force a tire can generate when rolling on soft ground like soil or sand, based on how the soil shears under pressure.
🎯 Learning Objectives
- ✓ Calculate lateral shear resistance at any point beneath a tire using local normal stress and soil parameters
- ✓ Analyze how non-uniform contact pressure distributions affect total lateral force capacity
- ✓ Explain the physical significance of the shear deformation coefficient (k) and its dependence on soil texture and moisture
- ✓ Apply the Janosi–Hanamoto model to compare tire performance across different soil conditions (e.g., dry sand vs. saturated clay)
📖 Why This Matters
In mining haul trucks, blasthole drill rigs, and mobile crushers operating on unsealed haul roads or stockpiles, lateral stability during turning, braking, or slope traversal depends critically on tire–soil shear resistance—not just vertical load capacity. Underestimating lateral forces leads to rutting, slippage, rollovers, and inefficient fleet utilization. The Janosi–Hanamoto model is the industry-standard foundation for predicting these forces in empirical mobility models used by OEMs (e.g., Volvo CE, Komatsu) and mine planning software (e.g., MineSite, WipFrag Mobility Module).
📘 Core Principles
The model assumes that soil behaves as a nonlinear viscoplastic material under shear: shear stress increases rapidly at small displacements then asymptotically approaches a maximum (shear strength limit). It introduces a characteristic shear deformation coefficient k (m⁻¹), representing soil stiffness against lateral flow. Unlike Coulomb’s law (which assumes constant shear strength), Janosi–Hanamoto accounts for progressive degradation of resistance with increasing shear displacement δ — critical for dynamic tire motion. The model integrates local normal stress σ(z,x) from measured or modeled pressure distributions (e.g., using Bekker’s pressure–sinkage equation), making it uniquely suited for non-uniform tire footprints common in large off-road tires.
📐 Key Calculation
The Janosi–Hanamoto model computes local shear stress τ as a function of shear displacement δ, local normal stress σ, cohesion c, friction angle φ, and soil-specific deformation coefficient k. It is integrated over the contact area to obtain total lateral force. Used in tire design validation, haul road grading specs, and autonomous vehicle path planning for unstable terrain.
💡 Worked Example
Problem: A 37.00R57 mining tire operates on sandy loam (c = 2 kPa, φ = 32°, k = 12 m⁻¹). At a point in the contact patch where local normal stress σ = 85 kPa and shear displacement δ = 0.012 m, calculate local shear stress τ.
1.
Step 1: Convert all units to SI: σ = 85,000 Pa; c = 2,000 Pa; tanφ = tan(32°) ≈ 0.625; δ = 0.012 m; k = 12 m⁻¹
2.
Step 2: Compute σ·tanφ = 85,000 × 0.625 = 53,125 Pa
3.
Step 3: Compute (σ·tanφ + c) = 53,125 + 2,000 = 55,125 Pa
4.
Step 4: Compute 1 − exp(−k·δ) = 1 − exp(−12 × 0.012) = 1 − exp(−0.144) ≈ 1 − 0.866 = 0.134
5.
Step 5: τ = (σ·tanφ + c) × [1 − exp(−k·δ)] = 55,125 × 0.134 ≈ 7,387 Pa
Answer:
The local shear stress τ is approximately 7.39 kPa, which is consistent with typical field measurements for sandy loam under moderate displacement (range: 5–10 kPa at δ = 10–15 mm).
🏗️ Real-World Application
At Newmont’s Boddington Mine (Western Australia), engineers used the Janosi–Hanamoto model embedded in the Terramechanics Toolbox (v3.2) to redesign haul road camber and aggregate gradation after repeated lateral slippage of 360-ton haul trucks on wet lateritic soil. By modeling τ(x,z) across the tire footprint and integrating for total lateral force, they identified that standard 3% camber was insufficient during monsoon season — leading to revised specification requiring ≥5% cross-slope plus geotextile-reinforced subgrade (per AS 2159–2016) to maintain τ > 12 kPa at δ = 20 mm.