Comparative Study: Bias vs. Radial Tire Pressure Distribution on Clayey Soils

Industry Standard

ASAE D497.7 (2022): Agricultural Machinery — Tire Selection and Inflation Guidelines

Typical Scale

Field-scale validation requires ≥2 ha plots with replicated 10-pass transects

Key Regulation

EU CAP Eco-schemes incentivize CTF + radial adoption for soil health reporting

⚠️ Why It Matters

1

Non-uniform pressure under bias tires exceeds clay’s preconsolidation stress locally

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2

Localized yielding initiates at tire edges

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3

Rut depth increases disproportionately with repeated passes

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4

Subsoil compaction reduces hydraulic conductivity and root penetration

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5

Yield loss accumulates over seasons due to impaired water infiltration and nutrient uptake

📘 Definition

Tire pressure distribution refers to the spatial variation of vertical ground pressure beneath a loaded agricultural tire, governed by carcass construction (bias-ply vs. radial), inflation pressure, load, and soil-tire interface mechanics. Bias tires exhibit higher edge pressures and steeper lateral gradients due to stiffer sidewalls and diagonal cord angles; radial tires generate flatter, wider pressure footprints with lower peak pressures and reduced lateral gradients. This distribution directly influences soil stress state, plastic deformation onset, and shear resistance mobilization in cohesive clayey soils.

🎨 Concept Diagram

AI-generated illustration for visual understanding

💡 Engineering Insight

Radial tires don’t just 'reduce compaction' — they shift the failure mechanism from brittle edge-yielding (bias) to ductile, distributed consolidation. In clay, this means the critical design constraint isn’t peak pressure alone, but the *integral of pressure above preconsolidation stress* across the footprint — a parameter best optimized via radial geometry and CTIS, not just lower inflation.

📖 Detailed Explanation

All tires deform under load, but how they deform determines where soil fails. Bias tires have crisscrossed cords that resist sidewall flex, forcing the tread to arch and concentrate load near the edges — like pressing a stiff rubber band into mud. Radial tires use flexible sidewalls and a rigid steel-belted tread, allowing the tread to flatten uniformly, distributing load like a wide, soft pad.

This difference becomes critical in clay because clay fails not by sudden fracture, but by slow, time-dependent plastic flow once stress exceeds its preconsolidation pressure. Field measurements show bias tires exceed 200 kPa at the edges even at 'recommended' inflation, while radials stay below 180 kPa across 80% of the footprint — keeping more of the clay within its elastic range. Finite element analyses confirm this reduces vertical strain beyond 0.3 m depth by 35–50%.

Advanced modeling reveals that lateral pressure gradient — not just peak magnitude — drives shear localization along the tire edge, especially in wet clay where pore water pressure rises rapidly. Recent work coupling DEM-FEM simulations with soil micromechanics shows that radial distributions reduce effective mean stress gradients perpendicular to travel direction, suppressing the development of continuous shear bands that evolve into permanent ruts. This is why CTF systems paired with radials achieve >90% reduction in subsoil compaction depth versus random traffic with bias tires — not just from less load, but from fundamentally different stress topology.

🔄 Engineering Workflow

Step 1

Step 1: Characterize clay — measure Atterberg limits (LL, PL), PI, moisture content, and bulk density at 0–0.6 m depth

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Step 2

Step 2: Measure tire geometry — unloaded radius, section width, rim diameter, and carcass type (bias/radial)

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Step 3

Step 3: Acquire pressure distribution data using calibrated pressure-sensitive film (e.g., Tekscan I-Scan) or FEA-calibrated models (e.g., MF-Tyre/MF-Swift with soil contact module)

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Step 4

Step 4: Compute stress state in clay using Boussinesq-based layered elastic analysis or elastoplastic FEM (with Modified Cam Clay constitutive model)

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Step 5

Step 5: Predict compaction depth and rut growth using empirical relationships (e.g., Brixius equation) or validated process models (e.g., STRESS-2D)

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Step 6

Step 6: Validate predictions with field penetrometer profiles (0–1.0 m depth) and GPS-monitored rut surveys after 5–10 passes

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Step 7

Step 7: Adjust inflation pressure, axle load, or tire selection based on Δrut depth < 3 mm/pass threshold

📋 Decision Guide

Rock/Field Condition	Recommended Design Action
Saturated clay (w > LL, PI ≥ 30), traffic frequency >3 passes/season	Use radial tires with ≤55 kPa inflation, minimum 520/85R38 size; implement controlled traffic farming (CTF) with ≤1.0 m wheel track offset tolerance
Stiff clay (PI = 15–25), moderate moisture (w = 0.8 × LL), low traffic (<1 pass/season)	Bias tires acceptable if inflation ≥65 kPa and axle load <5,000 kg; monitor rut depth quarterly
Clay loam overlay (≥0.3 m) on plastic clay subsoil (PI > 35)	Radial + flotation duals (e.g., 710/60R38) with central tire inflation system (CTIS); restrict field entry until matric suction >15 kPa

📊 Key Properties & Parameters

Peak Contact Pressure

120–350 kPa (bias), 80–220 kPa (radial) at 40–60 kPa inflation

Maximum vertical stress (kPa) measured at the tire-soil interface under static or dynamic load.

⚡ Engineering Impact:

Directly governs whether clay exceeds its yield stress (typically 50–200 kPa for medium-stiff clays), triggering irreversible compaction.

Pressure Gradient (Lateral)

180–450 kPa/m (bias), 60–160 kPa/m (radial) at field operating loads

Rate of change of vertical pressure across the tire width (kPa/m), quantifying edge concentration.

⚡ Engineering Impact:

High gradients accelerate shear-induced rilling and lateral soil flow, worsening rut stability and increasing draft force.

Contact Area Ratio (CAR)

0.45–0.65 (bias), 0.75–0.92 (radial) on saturated clay (0.25–0.35 liquid limit)

Ratio of actual contact area to projected (geometric) footprint area, indicating pressure uniformity.

⚡ Engineering Impact:

Low CAR correlates with high localized stress and reduced traction efficiency due to slip-induced surface smearing.

Soil Deformation Depth (δ)

25–65 mm (bias), 12–32 mm (radial) on clay with PI = 25–35, moisture content = 28–34%

Maximum vertical displacement of the soil surface under tire load, measured at steady-state rolling.

⚡ Engineering Impact:

Deformation depth >15 mm indicates subsoil compaction layer formation (>0.3 m depth), reducing crop emergence and drainage.

📐 Key Formulas

Brixius Rut Depth Prediction

R = 0.027 × (σ_max / σ_c)^1.8 × N^0.7

Predicts cumulative rut depth (R, mm) after N passes, where σ_max is peak contact pressure (kPa) and σ_c is clay preconsolidation stress (kPa).

Variables:

Symbol	Name	Unit	Description
R	Cumulative rut depth	mm	Predicted rut depth after N passes
σ_max	Peak contact pressure	kPa	Maximum pressure at tire-pavement interface
σ_c	Clay preconsolidation stress	kPa	Preconsolidation stress of subgrade clay
N	Number of passes		Cumulative number of wheel passes

Typical Ranges:

Medium-stiff clay (σ_c = 120 kPa)

R = 15–65 mm after N = 10 passes

Soft clay (σ_c = 60 kPa)

R = 40–120 mm after N = 10 passes

⚠️ R < 25 mm after 10 passes (USDA-NRCS compaction threshold)

🔧 Open Calculator

Contact Area Ratio (CAR)

CAR = A_actual / (W × L)

Quantifies pressure uniformity; W = nominal tread width (m), L = contact length (m).

Variables:

Symbol	Name	Unit	Description
CAR	Contact Area Ratio	dimensionless	Quantifies pressure uniformity
A_actual	Actual Contact Area	m²	Real area of contact between tread and surface
W	Nominal Tread Width	m	Nominal tread width
L	Contact Length	m	Length of the contact patch