AASHTO Flexible Pavement Design: 16-Civ-B7 Transportation Planning and Engineering, December 2016, Q3

Question 3: AASHTO Flexible Pavement Design (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Quantity	Symbol	Value
One-way average daily traffic	ADT	10 000 veh/day
Truck proportion	—	6 percent
Annual traffic growth	g	2 percent
Design period	n	20 years
Truck factor	TF	1.8 ESAL per truck
Subgrade resilient modulus	M_R	35 MPa = 5000 psi
Reliability / standard normal deviate	R, Z_R	95 percent, −1.645
Overall standard deviation	S_o	0.49
Serviceability	p_i, p_t	4.5 and 2.6

Find. The design-lane ESAL application, the required structural number, and a layer-by-layer thickness design drawn as a cross section.

Approach. Convert the daily truck stream into 20-year design-lane ESALs with a growth factor and a lane-distribution factor, solve the AASHTO-93 flexible design equation (the equation the supplied nomograph represents) for the structural number over the roadbed, repeat it over the base and subbase moduli to get the layered thickness controls, and then select buildable Canadian layer thicknesses that satisfy every control.

Convert the traffic stream into trucks per day. $$ADTT = 10\,000 \times 0.06 = 600\ \text{trucks/day in one direction}$$
Accumulate 20 years of growth. The cumulative growth factor for a constant annual rate is $$GF = \frac{(1 + g)^{n} - 1}{g} = \frac{(1.02)^{20} - 1}{0.02} = \frac{0.48595}{0.02} = 24.297$$ A sanity check worth doing every time: the cumulative factor can never be less than the design period (24.30 > 20), which is what distinguishes a growth factor from a growth rate when a paper prints an ambiguous number.
Apply the lane-distribution factor and the truck factor. With two lanes in each direction AASHTO gives a design-lane factor D_L between 0.80 and 1.00; take 0.90. Then $$W_{18} = ADTT \times 365 \times GF \times TF \times D_{L}$$ $$W_{18} = 600 \times 365 \times 24.297 \times 1.8 \times 0.90$$ $$\boxed{W_{18} = 8.62 \times 10^{6}\ \text{ESAL on the design lane}}$$
State the design equation the nomograph solves. The chart supplied on pages 4 and 5 is a graphical solution of $$\log_{10} W_{18} = Z_{R}S_{o} + 9.36\log_{10}(SN + 1) - 0.20 + \frac{\log_{10}\!\left(\dfrac{\Delta PSI}{4.2 - 1.5}\right)} {0.40 + \dfrac{1094}{(SN + 1)^{5.19}}} + 2.32\log_{10} M_{R} - 8.07$$ with ΔPSI = p_i − p_t = 4.5 − 2.6 = 1.9. Reading the chart with W₁₈ = 8.62 × 10⁶, R = 95 percent, S_o = 0.49, M_R = 5000 psi and ΔPSI = 1.9 gives SN slightly under 6; solving the equation numerically pins it down.
Solve for the structural number over the roadbed. Bisection on the equation above with M_R = 5000 psi returns $$\boxed{SN_{3} = 5.76}$$ This is the total structural number the completed pavement must provide.
Repeat the solution at the base and subbase moduli. The layered design procedure requires the structural number that protects each successive layer, obtained from the same equation with M_R replaced by the modulus of the material immediately below. Taking the standard values for good-quality unbound materials, E_BS = 30 000 psi for the granular base and E_SB = 15 000 psi for the subbase, $$SN_{1} = 3.13 \ (\text{over the base}), \qquad SN_{2} = 4.02 \ (\text{over the subbase})$$
Fix the asphalt thickness. With a layer coefficient a₁ = 0.44 for a dense-graded asphalt concrete surface, $$D_{1} \ge \frac{SN_{1}}{a_{1}} = \frac{3.13}{0.44} = 7.11\ \text{in} = 181\ \text{mm}$$ Rounding up to a buildable Canadian thickness, D₁ = 190 mm (7.48 in), placed in three lifts. This satisfies the AASHTO Table 5.1 minimum of 4 in for traffic above 7 × 10⁶ ESAL with a large margin, as it must on a 5000 psi subgrade.
Fix the granular base thickness. Adopting D₂ = 200 mm (7.87 in) of granular base with a₂ = 0.14 and a drainage coefficient m₂ = 1.00, the cumulative structural number to the top of the subbase is $$SN_{1}^{*} + SN_{2}^{*} = 0.44(7.48) + 0.14(1.00)(7.87) = 3.291 + 1.102 = 4.393 \ge SN_{2} = 4.02\ \checkmark$$ The 200 mm also clears the 150 mm (6 in) minimum base thickness for this traffic level.
Fix the subbase thickness. The remaining structural number is 5.756 − 4.393 = 1.363, so with a₃ = 0.11 and m₃ = 1.00, $$D_{3} \ge \frac{1.363}{0.11} = 12.39\ \text{in} = 315\ \text{mm} \quad\Longrightarrow\quad \textbf{D}_{3} = 320\ \text{mm}$$
Verify the completed section. $$SN_{\text{provided}} = 0.44(7.48) + 0.14(7.87) + 0.11(12.60)$$ $$\boxed{SN_{\text{provided}} = 3.29 + 1.10 + 1.39 = 5.78 \ge 5.76\ \checkmark}$$ The total structure is 190 + 200 + 320 = 710 mm, a thickness entirely consistent with a heavily trafficked four-lane highway on a soft 35 MPa subgrade.

Figure 3.1 — Designed flexible pavement cross section, one direction of the four-lane highway. Thicknesses are rounded up to Canadian construction increments; the structural number provided exceeds the structural number required.

Final Results.

Quantity	Value
Truck volume, one direction	600 trucks/day
Growth factor over 20 years at 2 percent	24.297
Design-lane ESALs (D_L = 0.90)	W₁₈ = 8.62 × 10⁶
Serviceability loss	ΔPSI = 1.9
Required structural number (over the roadbed)	SN = 5.76
Structural number over the subbase / base	4.02 / 3.13
Asphalt concrete surface, a₁ = 0.44	190 mm
Granular base, a₂ = 0.14, m₂ = 1.00	200 mm
Granular subbase, a₃ = 0.11, m₃ = 1.00	320 mm
Structural number provided	5.78 (≥ 5.76)
Total pavement thickness	710 mm

Check: under the paper's Note 2 the following data, which the question does not give, are assumed and stated: lane-distribution factor D_L = 0.90 (AASHTO range 0.80–1.00 for two lanes per direction); layer coefficients a₁ = 0.44, a₂ = 0.14, a₃ = 0.11; layer moduli E_BS = 30 000 psi and E_SB = 15 000 psi; drainage coefficients m₂ = m₃ = 1.00. The design is most sensitive to D_L and to the drainage coefficients: taking D_L = 1.00 raises W₁₈ to 9.58 × 10⁶ and SN to 5.85, about 20 mm more subbase, while dropping m to 0.90 on both granular layers would cost about 0.25 of structural number and require roughly 60 mm more granular material. The supplied nomograph is used as the check on the numerical solution rather than as the primary calculation, because a chart cannot be read to the two decimal places the layered procedure needs.

Topic. AASHTO 1993 empirical design of a flexible pavement and the layered thickness procedure.

Key relations. GF = [(1 + g)ⁿ − 1]/g; W₁₈ = ADTT × 365 × GF × TF × D_L; the AASHTO-93 flexible equation for SN; SN = a₁D₁ + a₂m₂D₂ + a₃m₃D₃ with D in inches.

Why this works. The structural number is an abstract index, not a thickness: it is the weighted sum of layer thicknesses in which each material is credited according to how effectively it spreads load. That is why the same SN can be built many ways, and why the layered procedure exists — it prevents a designer from meeting the total SN with a thin asphalt layer over a thick granular one, which would satisfy the arithmetic but overstress the base. Solving the equation once per interface, with the modulus of the material immediately beneath, guarantees that every layer is protected as well as the whole. The equation itself is a regression on the AASHO Road Test, so the reliability term Z_RS_o is a straightforward shift of the traffic axis to allow for the scatter in that experiment, and at 95 percent reliability with S_o = 0.49 the design is effectively carrying 10^0.806 = 6.4 times the mean traffic.

Common pitfall. Three recur. Omitting the lane-distribution factor and designing every lane for the whole directional stream; using the directional ADT when the question gives a two-way ADT (here it explicitly gives one-way, so no halving is applied); and substituting the subgrade modulus in MPa instead of psi, which makes the 2.32 log₁₀M_R term absurd. Reporting the structural number as though it were a depth is a fourth: SN = 5.76 corresponds to 710 mm of construction here.

Source. AASHTO, Guide for Design of Pavement Structures (1993), Part II Chapter 2 and Tables 2.1 and 5.1; Huang, Pavement Analysis and Design, 2nd ed., §7.4.

Question 3 of 7: AASHTO Flexible Pavement Design

Question 3: AASHTO Flexible Pavement Design (20 marks)