Rational method — Westergaard (rigid pavements)¶
The Westergaard method is based on the solution of Lagrange's equation for thin plates. The pavement is modelled as a multilayer plate on elastic soil: the method computes the maximum deflection of the slab under load. It is particularly suited to rigid pavements.
Verification principle¶
As with Ivanov, the allowable deflection is compared with the computed one:
FS = f_adm / f_d
The pavement is verified when FS ≥ 1. The allowable deflection has the same form as in the Ivanov method: f_adm = 0.17 − 0.026 · log₁₀(N).
How RPD computes it¶
RPD solves the multilayer plate with a double Fourier series, layer by layer, summing the contributions:
- each layer is characterised by an elastic modulus E, a thickness, a Poisson's ratio ν (assigned by position: 0.2 for the 1st layer, 0.3 for the 2nd, 0.4 for the following ones) and a coefficient αK that links the modulus to the modulus of subgrade reaction (
K = E / αK); - the tyre load is distributed over a square area equivalent to the footprint;
- the modulus of subgrade reaction K closes the model at the base.
The verification deflection is the one computed at the surface (first layer).
Data required in RPD¶
| Section | Data |
|---|---|
| Mechanical loads | Tyre footprint diameter, inflation pressure |
| Subgrade properties | Modulus of subgrade reaction K (kg/cm³) |
| Layering | For each layer: thickness, elastic modulus E, coefficient αK |
| Design traffic | Needed for f_adm |
Modulus of subgrade reaction K
The Westergaard method requires the modulus of subgrade reaction K (in Subgrade properties) and the αK coefficients of the individual layers (in Layering).
Results¶
In the Results tab you find the allowable deflection, the computed one, the safety factor and the verification condition.
When to use it
Use Westergaard for rigid pavements (concrete slabs); for flexible ones AASHTO 1993 (empirical) or Ivanov (deflection) are more appropriate.
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