SME
Transportation Engineering
Pavement design
Use this for “A flexible pavement has 4 in of asphalt (a₁ = 0.44), 8 in of base (a₂ = 0.14, m₂ = 1) and 10 in of subbase (a₃ = 0.11, m₃ = 0.9). Find SN, or the subbase depth a required SN needs.”
Diagram
SN = a₁D₁ + a₂D₂m₂ + a₃D₃m₃
SN = 1.76 + 1.12 + 0.99 = 3.87
Layers drawn to scale by thickness; a thicker, stronger layer adds more to SN.
This is an example. Type your own values to start a new problem.
SN
=
a₁
×
D₁ (in)
+
a₂
×
D₂ (in)
×
m₂
+
a₃
×
D₃ (in)
×
m₃
Formulas
SN
=
a₁
×
D₁
+
a₂
×
D₂
×
m₂
+
a₃
×
D₃
×
m₃
3.87 = 0.44 × 4 + 0.14 × 8 × 1 + 0.11 × 10 × 0.9
Assumptions
•
AASHTO 1993 flexible pavement method; thicknesses in inches.
•
The required SN comes from the design chart for the traffic (ESALs) and the subgrade, not from this page.
•
a is each layer’s strength per inch; m reflects how well the base and subbase drain (1 is good drainage).
Step-by-step
WE KNOW
a₁ = 0.44, D₁ = 4 in, a₂ = 0.14, D₂ = 8 in, m₂ = 1, a₃ = 0.11, D₃ = 10 in, m₃ = 0.9
FIND
structural number (SN)
Step 1 · Find structural number (SN)
Use SN = a₁ × D₁ + a₂ × D₂ × m₂ + a₃ × D₃ × m₃
Each layer adds its coefficient × its thickness × its drainage coefficient.
SN = 0.44 × 4 + 0.14 × 8 × 1 + 0.11 × 10 × 0.9
SN = 1.76 + 1.12 + 1.1 × 0.9
SN = 1.76 + 1.12 + 0.99
SN = 3.87
Check
Put the numbers back in. Both sides should match.
3.87 = 0.44 × 4 + 0.14 × 8 × 1 + 0.11 × 10 × 0.9 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.