Rational method — Ivanov (deflection)¶
The maximum deflection method (Ivanov) is a rational method that sets up the elastic problem in soils according to Boussinesq. The verification criterion limits the maximum deflection produced at the surface at the end of the pavement design life.
Verification principle¶
Two deflections are compared:
- f_adm — allowable deflection, a function of traffic;
- f_d — deflection computed under the tyre load.
The safety factor is:
FS = f_adm / f_d
The pavement is verified when FS ≥ 1.
How RPD computes it¶
- Equivalent elastic modulus (E_eq) — the multilayer mass is reduced to a single equivalent modulus, iterating from bottom to top (subbase → base → binder → wearing course). The subgrade starting modulus is estimated from the CBR:
E₀ = 65 · CBR^0.65. Each active layer modifies E_eq as a function of its own elastic modulus E, its thickness and the radius of the tyre footprint. - Allowable deflection —
f_adm = 0.17 − 0.026 · log₁₀(N), where N is the number of standard axles per day in the last year of the design life. - Computed deflection —
f_d = p · Dp / E_eq, with p the tyre inflation pressure and Dp the footprint diameter.
Wearing course
In the rational calculation you can exclude the wearing course (option in Layering): in many approaches the wearing course is not considered load-bearing.
Data required in RPD¶
| Section | Data |
|---|---|
| Mechanical loads | Tyre footprint diameter (Dp), inflation pressure (p) |
| Subgrade properties | CBR (for E₀) |
| Layering | For each layer: thickness and elastic modulus E (kg/cm²) |
| Design traffic | Needed for f_adm (axles/day at end of design life) |
Mechanical loads
The Mechanical loads fields are used only by the rational methods (Ivanov and Westergaard). With the AASHTO method they remain visible but inactive.
Results¶
In the Results tab you see the allowable deflection, the computed one, the equivalent modulus E_eq, the number of axles/day and the safety factor, together with the verification condition.
Theoretical background
The rational method document can be downloaded from the app (? menu → Resources → "Rational method — Ivanov").
Found an error on this page? Let us know or open a Pull Request.