Empirical method AASHTO 1993¶
The empirical method is the one proposed by the AASHTO Guide for Design of Pavement Structures (1993), based on the experimental results of the AASHO Road Test. It measures the adequacy of the pavement in terms of the number of 82 kN (8.2 t) standard axles the structure can carry, while maintaining the required serviceability, over the design life.
Verification principle¶
The check compares two quantities:
- N₈.₂,Calc — the standard axles that actually travel on the design lane over the design life (see Design traffic);
- N₈.₂,Lim — the standard axles the pavement is able to carry.
The safety factor is:
FS = N₈.₂,Lim / N₈.₂,Calc
The pavement is verified when FS > 1.
Structural Number (SN)¶
The Structural Number represents the structural capacity of the package. It is the sum of the contributions of the layers:
SN = Σ aᵢ · mᵢ · Dᵢ
where, for each layer i:
- Dᵢ — thickness, in inches;
- aᵢ — structural coefficient (depends on the material);
- mᵢ — drainage coefficient (dimensionless; equal to 1 for bituminous mixes).
Units
In RPD the Structural Number is shown in inches (with the cm equivalent next to it). Layer thicknesses, on the other hand, are entered in cm.
The AASHTO equation¶
The number of allowable axles N₈.₂,Lim is obtained from:
log₁₀(N₈.₂,Lim) = Z_R·S₀ + 9.36·log₁₀(SN+1) − 0.20 + [log₁₀(ΔPSI / 2.7)] / [0.40 + 1094/(SN+1)^5.19] + 2.32·log₁₀(M_R) − 8.07
with:
- Z_R — standard normal deviate related to the reliability R (see table below);
- S₀ — standard deviation (error on traffic and performance): 0.40–0.50;
- ΔPSI = PSI,in − PSI,fin — allowed serviceability loss;
- M_R — resilient modulus of the subgrade, in psi.
Reliability R and the Z_R coefficient¶
The reliability R is the probability that the pavement reaches its intended design life. Each R corresponds to a value of Z_R (negative for R > 50%):
| R (%) | Z_R |
|---|---|
| 50 | 0.000 |
| 90 | −1.282 |
| 95 | −1.645 |
| 99 | −2.327 |
For intermediate values RPD interpolates linearly.
Why is Z_R negative?
It is not an error: Z_R is the deviate of the lower tail of the normal distribution. The higher the reliability, the more negative it becomes, and in the term Z_R·S₀ this makes the design more conservative (higher required SN). With R = 90% → Z_R = −1.282.
Resilient modulus from CBR¶
You can enter M_R directly or derive it from the CBR of the subgrade. In RPD you choose the parameter in Subgrade properties; the CBR → M_R conversion is handled by the software.
Data required in RPD¶
| Section | Data |
|---|---|
| General data | Design life, reliability R, initial and final PSI |
| Design traffic | AADT, growth rate, % commercial, % lane, standard deviation S₀ |
| Subgrade properties | CBR or Resilient modulus |
| Layering | For each layer: thickness, structural coefficient a, drainage coefficient m |
Results¶
In the Results tab you find the safety factor, the Structural Number, the allowable axles (N₈.₂,Lim), the equivalence coefficient, Z_R, ΔPSI and M_R. If the check is not satisfied, the How to pass the check card proposes the thicknesses (or the geogrid TBR) required — see Quick start.
Theoretical background
The full method document can be downloaded from the app (? menu → Resources → "Empirical method"), or consult the AASHTO Guide for Design of Pavement Structures. In Italy the practical reference is the Italian Catalogue of Road Pavements (CNR, BU 168/95).
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