Pavements & traffic · Pavement design
Concrete (rigid) pavement thickness calculator
Plain concrete pavement or hardstand under a design axle. The subgrade reaction k comes from the CBR and is lifted by the subbase; the edge stress under half the factored axle load follows Westergaard's edge formula, reduced for a tied shoulder or kerb. The stress ratio to the flexural strength gives the allowable repetitions (PCA fatigue), and the thickness is solved for the design repetitions. Joint spacing and dowel size follow.
Standard: Westergaard edge stress (Ioannides 1985 form) · PCA fatigue criterion · Austroads AGPT02 Ch 9 concepts · subgrade k from CBR
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Inputs in the worked example
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| Input | Value | Unit |
|---|---|---|
| Subgrade CBR | 5 | % |
| Subbase | 150 mm cement-bound (CTSB) | |
| Design axle load (single axle, dual tyres) | 80 | kN |
| Load safety factor | 1.2 | |
| Tyre pressure | 750 | kPa |
| Design repetitions of this axle | 2000000 | |
| Concrete flexural strength f′cf | 4.5 | MPa |
| Concrete modulus E | 32000 | MPa |
| Poisson's ratio | 0.15 | |
| Edge support | Tied shoulder / integral kerb (×0.85) | |
| Trial base thickness | 230 | mm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Subgrade k from CBR (2.55 + 52.5 log CBR) | 39.2 | MPa/m |
| Effective k on the subbase | 70.6 | MPa/m |
| Load per dual-tyre set (factored) | 48.0 | kN |
| Equivalent contact radius | 143 | mm |
| Radius of relative stiffness ℓ | 828 | mm |
| Edge stress (after edge support) | 1.94 | MPa |
| Stress ratio σ/f′cf | 0.431 | |
| Allowable repetitions (PCA fatigue) | unlimited | |
| Fatigue damage at trial thickness | 0.000 | |
| Thickness for damage = 1 | 215 | mm |
| Maximum joint spacing (24h, ≤ 4.5 m) | 4.50 | m |
| Dowel bar diameter | 32 mm × 450 @ 300 |
- ✓ Fatigue damage ≤ 1 at the trial thickness — 0 %
- ✓ Base at least 150 mm
- ✓ Subbase provided under heavy traffic (> 10⁶ axles)
Method, formulas and assumptions
- k (MPa/m) = 2.55 + 52.5·log10(CBR), × 1.25 granular, 1.8 cement-bound, 2.5 lean-mix subbase (effective k on top of the subbase).
- Westergaard edge stress: σe = 3(1 + ν)P/[π(3 + ν)h²]·[ln(Eh³/100ka⁴) + 1.84 − 4ν/3 + (1 − ν)/2 + 1.18(1 + 2ν)a/ℓ].
- PCA fatigue: SR ≥ 0.55: log N = 11.737 − 12.077SR; 0.45 < SR < 0.55: N = (4.2577/(SR − 0.4325))^3.268; SR ≤ 0.45 unlimited.
- Austroads AGPT02 designs with axle-group spectra, fatigue and erosion; this single-axle check is preliminary. Curling stresses and erosion are not included.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.