Highway Pavement Design

Transportation · FE Reference Handbook section

Transportation

5 formulas

10 exam-style examples

~55 min

All Transportation lectures

Handbook notes for this section

Definitions and conditions exactly as the handbook states them.

AASHTO Structural Number Equation
Load Equivalency Load Equivalency
Gross Axle Load Gross Axle Load
Single Tandem Single Tandem
Axles Axles Axles Axles

Core formulas for this FE topic

Definitions, applicability, units, assumptions and worked examples for each relation.

Worked exam-style examples

The four ways this section is written on the real exam — thoughts first, then equations, then substitution.

Example 1

Flexible pavement structural number — Highway Pavement Design

A flexible pavement has 6.0 in. of asphalt (a₁ = 0.44), 10 in. of base (a₂ = 0.14) and 12 in. of subbase (a₃ = 0.11) with drainage coefficients of 1.0. Find the structural number.

Given

$D_{1} = 6.0 in., a_{1} = 0.44$
$D_{2} = 10 in., a_{2} = 0.14$
$D_{3} = 12 in., a_{3} = 0.11$
$m = 1.0$

Find

Structural number SN

Start with the thinking

SN sums layer coefficient × thickness × drainage coefficient.
Thicknesses are in inches — never convert to feet here.

Step-by-step solution

AASHTO
$SN = a_{1}D_{1} + a_{2}D_{2}m_{2} + a_{3}D_{3}m_{3}$
Asphalt
$0.44(6.0) = 2.640$
Base
$0.14(10)(1.0) = 1.400$
Subbase
$0.11(12)(1.0) = 1.320$
Total
$SN = 5.36$

Answer:

SN ≈ 5.36

Why the other options are there

28.00 (thicknesses added without coefficients)
4.879 (terms multiplied)

Reference: FE Reference Handbook — Transportation → Highway Pavement Design

Example 2

Flexible pavement structural number — Highway Pavement Design (2)

A flexible pavement has 5.5 in. of asphalt (a₁ = 0.44), 11 in. of base (a₂ = 0.14) and 7 in. of subbase (a₃ = 0.11) with drainage coefficients of 1.0. Find the structural number.

Given

$D_{1} = 5.5 in., a_{1} = 0.44$
$D_{2} = 11 in., a_{2} = 0.14$
$D_{3} = 7 in., a_{3} = 0.11$
$m = 1.0$

Find

Structural number SN

Start with the thinking

SN sums layer coefficient × thickness × drainage coefficient.
Thicknesses are in inches — never convert to feet here.

Step-by-step solution

AASHTO
$SN = a_{1}D_{1} + a_{2}D_{2}m_{2} + a_{3}D_{3}m_{3}$
Asphalt
$0.44(5.5) = 2.420$
Base
$0.14(11)(1.0) = 1.540$
Subbase
$0.11(7)(1.0) = 0.770$
Total
$SN = 4.73$

Answer:

SN ≈ 4.73

Why the other options are there

23.50 (thicknesses added without coefficients)
2.870 (terms multiplied)

Reference: FE Reference Handbook — Transportation → Highway Pavement Design

Example 3

Flexible pavement structural number — Highway Pavement Design (3)

A flexible pavement has 5.0 in. of asphalt (a₁ = 0.44), 10 in. of base (a₂ = 0.14) and 13 in. of subbase (a₃ = 0.11) with drainage coefficients of 1.0. Find the structural number.

Given

$D_{1} = 5.0 in., a_{1} = 0.44$
$D_{2} = 10 in., a_{2} = 0.14$
$D_{3} = 13 in., a_{3} = 0.11$
$m = 1.0$

Find

Structural number SN

Start with the thinking

SN sums layer coefficient × thickness × drainage coefficient.
Thicknesses are in inches — never convert to feet here.

Step-by-step solution

AASHTO
$SN = a_{1}D_{1} + a_{2}D_{2}m_{2} + a_{3}D_{3}m_{3}$
Asphalt
$0.44(5.0) = 2.200$
Base
$0.14(10)(1.0) = 1.400$
Subbase
$0.11(13)(1.0) = 1.430$
Total
$SN = 5.03$

Answer:

SN ≈ 5.03

Why the other options are there

28.00 (thicknesses added without coefficients)
4.404 (terms multiplied)

Reference: FE Reference Handbook — Transportation → Highway Pavement Design

Example 4

Flexible pavement structural number — Highway Pavement Design (4)

A flexible pavement has 6.0 in. of asphalt (a₁ = 0.44), 7 in. of base (a₂ = 0.14) and 11 in. of subbase (a₃ = 0.11) with drainage coefficients of 1.0. Find the structural number.

Given

$D_{1} = 6.0 in., a_{1} = 0.44$
$D_{2} = 7 in., a_{2} = 0.14$
$D_{3} = 11 in., a_{3} = 0.11$
$m = 1.0$

Find

Structural number SN

Start with the thinking

SN sums layer coefficient × thickness × drainage coefficient.
Thicknesses are in inches — never convert to feet here.

Step-by-step solution

AASHTO
$SN = a_{1}D_{1} + a_{2}D_{2}m_{2} + a_{3}D_{3}m_{3}$
Asphalt
$0.44(6.0) = 2.640$
Base
$0.14(7)(1.0) = 0.980$
Subbase
$0.11(11)(1.0) = 1.210$
Total
$SN = 4.83$

Answer:

SN ≈ 4.83

Why the other options are there

24.00 (thicknesses added without coefficients)
3.131 (terms multiplied)

Reference: FE Reference Handbook — Transportation → Highway Pavement Design

Example 5

Flexible pavement structural number — Highway Pavement Design (5)

A flexible pavement has 5.5 in. of asphalt (a₁ = 0.44), 11 in. of base (a₂ = 0.14) and 9 in. of subbase (a₃ = 0.11) with drainage coefficients of 1.0. Find the structural number.

Given

$D_{1} = 5.5 in., a_{1} = 0.44$
$D_{2} = 11 in., a_{2} = 0.14$
$D_{3} = 9 in., a_{3} = 0.11$
$m = 1.0$

Find

Structural number SN

Start with the thinking

SN sums layer coefficient × thickness × drainage coefficient.
Thicknesses are in inches — never convert to feet here.

Step-by-step solution

AASHTO
$SN = a_{1}D_{1} + a_{2}D_{2}m_{2} + a_{3}D_{3}m_{3}$
Asphalt
$0.44(5.5) = 2.420$
Base
$0.14(11)(1.0) = 1.540$
Subbase
$0.11(9)(1.0) = 0.990$
Total
$SN = 4.95$

Answer:

SN ≈ 4.95

Why the other options are there

25.50 (thicknesses added without coefficients)
3.690 (terms multiplied)

Reference: FE Reference Handbook — Transportation → Highway Pavement Design

Example 6

Flexible pavement structural number — Highway Pavement Design (6)

A flexible pavement has 5.0 in. of asphalt (a₁ = 0.44), 8 in. of base (a₂ = 0.14) and 13 in. of subbase (a₃ = 0.11) with drainage coefficients of 1.0. Find the structural number.

Given

$D_{1} = 5.0 in., a_{1} = 0.44$
$D_{2} = 8 in., a_{2} = 0.14$
$D_{3} = 13 in., a_{3} = 0.11$
$m = 1.0$

Find

Structural number SN

Start with the thinking

SN sums layer coefficient × thickness × drainage coefficient.
Thicknesses are in inches — never convert to feet here.

Step-by-step solution

AASHTO
$SN = a_{1}D_{1} + a_{2}D_{2}m_{2} + a_{3}D_{3}m_{3}$
Asphalt
$0.44(5.0) = 2.200$
Base
$0.14(8)(1.0) = 1.120$
Subbase
$0.11(13)(1.0) = 1.430$
Total
$SN = 4.75$

Answer:

SN ≈ 4.75

Why the other options are there

26.00 (thicknesses added without coefficients)
3.524 (terms multiplied)

Reference: FE Reference Handbook — Transportation → Highway Pavement Design

Example 7

Flexible pavement structural number — Highway Pavement Design (7)

A flexible pavement has 4.5 in. of asphalt (a₁ = 0.44), 12 in. of base (a₂ = 0.14) and 11 in. of subbase (a₃ = 0.11) with drainage coefficients of 1.0. Find the structural number.

Given

$D_{1} = 4.5 in., a_{1} = 0.44$
$D_{2} = 12 in., a_{2} = 0.14$
$D_{3} = 11 in., a_{3} = 0.11$
$m = 1.0$

Find

Structural number SN

Start with the thinking

SN sums layer coefficient × thickness × drainage coefficient.
Thicknesses are in inches — never convert to feet here.

Step-by-step solution

AASHTO
$SN = a_{1}D_{1} + a_{2}D_{2}m_{2} + a_{3}D_{3}m_{3}$
Asphalt
$0.44(4.5) = 1.980$
Base
$0.14(12)(1.0) = 1.680$
Subbase
$0.11(11)(1.0) = 1.210$
Total
$SN = 4.87$

Answer:

SN ≈ 4.87

Why the other options are there

27.50 (thicknesses added without coefficients)
4.025 (terms multiplied)

Reference: FE Reference Handbook — Transportation → Highway Pavement Design

Example 8

Flexible pavement structural number — Highway Pavement Design (8)

A flexible pavement has 5.5 in. of asphalt (a₁ = 0.44), 6 in. of base (a₂ = 0.14) and 6 in. of subbase (a₃ = 0.11) with drainage coefficients of 1.0. Find the structural number.

Given

$D_{1} = 5.5 in., a_{1} = 0.44$
$D_{2} = 6 in., a_{2} = 0.14$
$D_{3} = 6 in., a_{3} = 0.11$
$m = 1.0$

Find

Structural number SN

Start with the thinking

SN sums layer coefficient × thickness × drainage coefficient.
Thicknesses are in inches — never convert to feet here.

Step-by-step solution

AASHTO
$SN = a_{1}D_{1} + a_{2}D_{2}m_{2} + a_{3}D_{3}m_{3}$
Asphalt
$0.44(5.5) = 2.420$
Base
$0.14(6)(1.0) = 0.840$
Subbase
$0.11(6)(1.0) = 0.660$
Total
$SN = 3.92$

Answer:

SN ≈ 3.92

Why the other options are there

17.50 (thicknesses added without coefficients)
1.342 (terms multiplied)

Reference: FE Reference Handbook — Transportation → Highway Pavement Design

Example 9

Flexible pavement structural number — Highway Pavement Design (9)

A flexible pavement has 6.5 in. of asphalt (a₁ = 0.44), 10 in. of base (a₂ = 0.14) and 7 in. of subbase (a₃ = 0.11) with drainage coefficients of 1.0. Find the structural number.

Given

$D_{1} = 6.5 in., a_{1} = 0.44$
$D_{2} = 10 in., a_{2} = 0.14$
$D_{3} = 7 in., a_{3} = 0.11$
$m = 1.0$

Find

Structural number SN

Start with the thinking

SN sums layer coefficient × thickness × drainage coefficient.
Thicknesses are in inches — never convert to feet here.

Step-by-step solution

AASHTO
$SN = a_{1}D_{1} + a_{2}D_{2}m_{2} + a_{3}D_{3}m_{3}$
Asphalt
$0.44(6.5) = 2.860$
Base
$0.14(10)(1.0) = 1.400$
Subbase
$0.11(7)(1.0) = 0.770$
Total
$SN = 5.03$

Answer:

SN ≈ 5.03

Why the other options are there

23.50 (thicknesses added without coefficients)
3.083 (terms multiplied)

Reference: FE Reference Handbook — Transportation → Highway Pavement Design

Example 10

Flexible pavement structural number — Highway Pavement Design (10)

A flexible pavement has 4.0 in. of asphalt (a₁ = 0.44), 10 in. of base (a₂ = 0.14) and 7 in. of subbase (a₃ = 0.11) with drainage coefficients of 1.0. Find the structural number.

Given

$D_{1} = 4.0 in., a_{1} = 0.44$
$D_{2} = 10 in., a_{2} = 0.14$
$D_{3} = 7 in., a_{3} = 0.11$
$m = 1.0$

Find

Structural number SN

Start with the thinking

SN sums layer coefficient × thickness × drainage coefficient.
Thicknesses are in inches — never convert to feet here.

Step-by-step solution

AASHTO
$SN = a_{1}D_{1} + a_{2}D_{2}m_{2} + a_{3}D_{3}m_{3}$
Asphalt
$0.44(4.0) = 1.760$
Base
$0.14(10)(1.0) = 1.400$
Subbase
$0.11(7)(1.0) = 0.770$
Total
$SN = 3.93$

Answer:

SN ≈ 3.93

Why the other options are there

21.00 (thicknesses added without coefficients)
1.897 (terms multiplied)

Reference: FE Reference Handbook — Transportation → Highway Pavement Design