Structural Number in Pavement Design: SN Formula and Example

The structural number (SN) is the heart of the AASHTO 1993 method for designing asphalt pavements. It is a single figure that rates how much strength a stack of layers provides: asphalt on top, crushed base below, maybe a subbase under that. The design equation tells you what SN the traffic and soil demand, and you choose layers that add up to it. This guide explains the formula, the coefficients that go into it, the inputs that set the required SN and a worked example.

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Quick facts

Formula: SN = a1D1 + a2D2m2 + a3D3m3.
a: layer coefficient, a strength rating per inch of each material.
D: layer thickness in inches.
m: drainage coefficient, applied to unbound base and subbase only.
Method: the AASHTO 1993 Guide for Design of Pavement Structures, still widely used for flexible pavements.

Typical layer coefficients

Layer	Typical coefficient (a)	Note
Dense-graded asphalt surface	0.44	FHWA's geotechnical manual cites 0.40 to 0.44 as typical
Asphalt base course	Varies (Carroll County, MD uses 0.34)	Set by agency
Granular base (crushed stone)	0.14	AASHTO recommended value
Granular subbase	0.11	AASHTO recommended value

Agencies tune these numbers to their own materials, sometimes from the layer's modulus. A stiffer base, measured with tests like resilient modulus or CBR, can earn a higher coefficient.

Drainage coefficients

Water weakens unbound stone layers. The m factor gives more credit to a base that drains quickly and less to one that stays wet. Pavement Interactive explains that the 1993 values run from about 1.4 for quick-draining layers that almost never saturate to about 0.4 for slow-draining layers that often do. Many designers use 1.0 to stay conservative, and Carroll County, Maryland's pavement design guide does exactly that. Asphalt layers do not get an m factor.

What sets the required SN

The AASHTO flexible design equation solves for the SN needed to carry the traffic. Its inputs are:

W18: design traffic in equivalent single axle loads.
Reliability (ZR) and standard deviation (So): how much safety margin to build in. Carroll County uses 80 percent reliability and 0.49 for local roads.
Serviceability loss (ΔPSI): the drop from a new pavement's rating to the end-of-life rating. Carroll County uses 4.2 initial and 2.0 terminal.
Subgrade resilient modulus (MR): how stiff the soil is, in psi.

More traffic, weaker soil or higher reliability all push the required SN up. Designers check not only the total, but also the SN needed above each layer, so that the asphalt protects the base and the base protects the subbase.

Worked example

Suppose the design equation called for an SN of 3.0 (a made-up target for this example). Try this section with the typical coefficients and m = 1.0:

Asphalt: 3 inches × 0.44 = 1.32
Crushed base: 8 inches × 0.14 × 1.0 = 1.12
Granular subbase: 6 inches × 0.11 × 1.0 = 0.66
Total SN = 3.10, which meets the target.

Another way to reach 3.0 would be 4 inches of asphalt (1.76) plus 9 inches of base (1.26), which is 3.02 with no subbase. Several combinations work, so cost, availability and agency minimum thicknesses usually decide the final pick. Our road base guide covers the stone side.

Turning the section into tons

Once you have thicknesses, the material order is simple math. The asphalt tonnage calculator handles the asphalt, the base calculator sizes the stone layers, and the crushed stone calculator works for subbase. For home projects that never get a formal design, compare with the sections in our asphalt driveway thickness guide.

Limits of the method

The AASHTO 1993 equation is empirical, built on road test results, and works best within the conditions it was based on.
Newer mechanistic-empirical methods model stresses and climate directly, and many state DOTs now use them for major roads.
Drainage problems are better fixed with drains and good materials than by adding thickness through the m factor.

Questions people ask

What is the structural number of a pavement?

It is an index of how much load-carrying strength a flexible pavement's layers provide. In the AASHTO 1993 method, the design equation gives a required structural number for the traffic and soil, and the designer then picks layer materials and thicknesses that add up to at least that number.

What is the structural number formula?

SN = a1D1 + a2D2m2 + a3D3m3, where a is each layer's coefficient, D is its thickness in inches and m is a drainage coefficient for the unbound base and subbase. More layers can be added the same way.

What are typical layer coefficients?

Common AASHTO values are about 0.44 for a dense-graded asphalt surface, 0.14 for a granular base and 0.11 for a granular subbase. FHWA's geotechnical manual notes values of 0.40 to 0.44 are typical for dense-graded asphalt. Agencies publish their own values, so use the local ones.

What is a drainage coefficient?

It adjusts the strength credit of an unbound layer for how well it drains and how often it is near saturation. In the 1993 AASHTO Guide it ranges from about 1.40 for excellent drainage down to 0.40 for very poor drainage. Many agencies simply use 1.0.

What structural number does a driveway need?

There is no single number because it depends on soil and traffic. Residential driveways are usually built from experience-based minimum sections rather than a full design. A design matters more when heavy trucks will use the pavement regularly or the soil is weak.

Does a higher structural number always mean a thicker pavement?

Generally yes, but stronger materials can supply the same SN with less thickness. One inch of asphalt with a coefficient of 0.44 earns about as much credit as three inches of granular base at 0.14.

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