What this calculator does
A flexible pavement works by spreading the wheel load before it reaches weak ground, so the build-up is judged on the strain left at the top of the subgrade. This tool solves that relation for the thickness you need, then splits it into wearing course, base and sub-base. It deliberately does NOT convert your traffic into an allowable strain for you: that is a code relation, and guessing it would hand you a confident, wrong thickness.
How to use it
- Enter the wheel load and its contact radius. The contact pressure follows from those two, and it is the single most sensitive input here.
- Enter the modulus of the COMBINED pavement section, not of one layer. The whole relation works on the section as a whole.
- Enter the allowable vertical strain from your own fatigue check for the same traffic. This is the number that actually sizes the pavement.
- Check the resulting wearing course against your minimum. The strain relation can be satisfied by a surface course too thin to lay.
Governing formula
ε_z = 1.5 · q_v / E_p · 1 / √(1 + (h/a)²) → h = a · √(k² − 1) Where:
-
q_v= Contact pressure, Q/(π a²) -
E_p= Modulus of the combined pavement section -
a= Wheel contact radius -
h= Total equivalent thickness -
k= Ratio of the bare-subgrade strain to the allowable strain
Derived Equations:
t_wearing = h / f_asphalt t_base = t_wearing / f_base t_subbase = t_base / f_subbase Worked example — 40 kN wheel, 300 MPa section, 0.0025 allowable strain
The figures below were produced by running this page's own engine with the example inputs (Design traffic (ESAL), Design CBR of subgrade (%), Wheel load (kN), Wheel contact radius (m), Section modulus (combined layers) (MPa), Allowable vertical strain (–), Wearing course equivalency factor (–), Base equivalency factor (–), Sub-base equivalency factor (–), Drainage adjustment (–)). If the calculator returns something different for the same numbers, that is a bug, not a rounding difference.
| Required equivalent thickness | 79.5 mm |
|---|---|
| Contact pressure | 0.57 MPa |
| Wearing course | 93.53 mm |
| Granular base | 124.71 mm |
| Granular sub-base | 249.41 mm |
| Combined granular thickness | 374.12 mm |
| Granular per mm of surface | 4 : 1 |
| Strain the thickness actually achieves | 0 – |
| Wearing course buildable | — |
| What this means | A 40 kN wheel over a 150 mm contact radius gives 0.566 MPa, and at 0.0025 allowable strain with a 300 MPa section that needs 79 mm of equivalent thickness. Split at the equivalency factors you entered, that is 94 mm of wearing course, 125 mm of base and 249 mm of sub-base. There is 4.0 mm of granular material for every mm of surface. That ratio is set entirely by the base and sub-base equivalency factors — the asphalt factor cancels out of it — and a ratio of 2 or more is what makes this a flexible pavement rather than a surface over weak ground. The wearing course works out at 94 mm, at or above the 40 mm practical minimum for laying and rolling a bonded surface course. This is sized for 5,000,000 ESALs on a CBR 5.0 % subgrade. The ESAL figure is recorded for the report only — the thickness above comes from the strain relation and the allowable strain YOU entered, which is normally the result of your own fatigue check against that same traffic. |
- The contact pressure is 40 kN over π(0.15)² = 0.0707 m², giving 0.566 MPa.
- The bare subgrade strain would be 1.5 × 0.566 / 300 = 0.00283, which exceeds the 0.0025 allowed, so thickness genuinely has to be solved for.
- k = 0.00283/0.0025 = 1.132, so h = 150 × √(1.132² − 1) ≈ 79 mm of equivalent thickness.
- Split at the equivalency factors: 94 mm wearing course, 125 mm base and 249 mm sub-base.
Assumptions & limitations
Engineering calculation. Vertical strain at the subgrade solved for thickness from the wheel load and section modulus, then split into layers by the equivalency factors you supply.
- Wheel load, contact radius, section modulus, allowable strain, every equivalency factor and the drainage factor are ALL USER inputs. This tool holds no pavement material table, no fatigue relation and no design code, and looks nothing up.
- The ESAL count is RECORDED, NOT USED as a driver. The thickness comes from the strain relation and the allowable strain you entered. This tool does not convert ESALs into an allowable strain, because that is a code relation and inventing one would produce a confident, wrong thickness.
- This is a strain-based check for spreading load. Fatigue cracking and permanent rutting in the asphalt are separate criteria that must be resolved separately, and neither is checked here.
- The section is treated as a single homogeneous modulus. Real layered pavements have different moduli per layer, and the strain at the top of each layer interface is not uniform.
- Drainage is one entered adjustment. Saturation, the loss of granular strength when wet, pumping and water trapped in the build-up are not modelled.
This tool supports professional engineering work; it does not replace a sealed design. Confirm every result against the applicable standard and a licensed engineer before it is built.
References & standards
- FHWA — flexible pavement design, for the strain-based approach and its context.
- Asphalt Institute — MS-2 and MS-4, for the equivalency factors and material moduli.