Civil, Structural & Geotechnical Engineering
AASHTO 1993 Flexible Pavement Structural Number (SN) Formula: Layer & Drainage Design
Calculate composite asphalt highway Structural Number SN = a_1*D_1 + a_2*D_2*m_2 + a_3*D_3*m_3 and minimum required layer thicknesses using the AASHTO (1993) Guide for Design of Pavement Structures.
Convert multi-layer asphalt, crushed base, and subbase thicknesses into one AASHTO Structural Number!
Derived from the AASHO Road Test in Ottawa, Illinois and standardized in the AASHTO (1993) Guide for Design of Pavement Structures, flexible highway design summarizes cumulative 18-kip Equivalent Single Axle Load (ESAL) capacity via an abstract index called the Required Structural Number SN_req! Engineers satisfy SN_req by combining three structural layers — Hot-Mix Asphalt (HMA) surface thickness D_1 (in) with structural layer coefficient a_1 (~= 0.40–0.44 per in), unbound granular base thickness D_2 (in) with coefficient a_2 (~= 0.14) and drainage modifier m_2 (~= 0.80–1.20), and granular subbase thickness D_3 (in) with coefficient a_3 (~= 0.11) and drainage modifier m_3:
Composite Structural Number SN = a_1 * D_1 + a_2 * D_2 * m_2 + a_3 * D_3 * m_3! Under AASHTO’s top-down staged protection rule, HMA thickness D_1 must protect the granular base (a_1 * D_1 >= SN_1), D_1 + D_2 must protect the subbase, AND total provided SN must equal or exceed Subgrade Required SN_req (often rounded up to the nearest 0.5-inch paving lift)!
| Flexible Pavement Layer | Layer Coeff a_i | Thickness D_i (in) | Drainage Coeff m_i | SN Contribution |
|---|---|---|---|---|
| Hot-Mix Asphalt Surface (HMA) | a_1 = 0.44 | D_1 = 5.0 in | 1.00 (Impervious) | 2.200 |
| Crushed Aggregate Base | a_2 = 0.14 | D_2 = 8.0 in | m_2 = 1.00 (Fair-Good) | 1.120 |
| Granular Subbase | a_3 = 0.11 | D_3 = 10.0 in | m_3 = 0.90 (Slow Drain) | 0.990 |
| Total Provided Structural Number SN | Sum of Layers | 23.0 in Total | — | SN = 4.310 |
Composite Provided AASHTO Structural Number SN
Evaluates a_1 * D_1 + a_2 * D_2 * m_2 + a_3 * D_3 * m_3 across HMA (B2, B3), Granular Base (B4, B5, B6), and Subbase (B7, B8, B9).
=IF(OR(B2 <= 0, B3 <= 0, B4 < 0, B5 < 0, B6 <= 0, B7 < 0, B8 < 0, B9 <= 0), "Invalid Layer Coefficients, Thicknesses, or Drainage Modifiers", ROUND(B2 * B3 + B4 * B5 * B6 + B7 * B8 * B9, 3))Minimum Required HMA Surface Thickness D_1 (in) to Meet Target SN_req
Given fixed Base & Subbase contributions and Target Total SN_req (B10), solves MAX(0, (SN_req - (a_2*D_2*m_2 + a_3*D_3*m_3)) / a_1).
=IF(OR(B2 <= 0, B6 <= 0, B9 <= 0, B10 <= 0), "Invalid Pavement Design Inputs", ROUND(MAX(0, (B10 - (B4 * B5 * B6 + B7 * B8 * B9)) / B2), 2))Try the example
Use the original values or change them to test your understanding.