16-Civ-B7 Transportation Planning and Engineering · December 2015

Question 6 of 8: AASHTO Flexible Pavement Design for a Rural Interstate

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. 98-Civ-B7 Highway Engineering, National Examinations, December 2015. Three hours, open book, any non-communicating calculator. Eight questions of equal value (20 marks each); five solutions constitute a complete paper and only the first five in the answer book are marked. Note 1 invites the candidate to state any assumption made about an ambiguous input, and Note 2 permits any datum that is required but not given to be assumed. All eight questions are solved here, because the set is a study resource rather than a timed attempt.

Reference texts. Garber & Hoel, Traffic and Highway Engineering, 5th ed. (geometric design, sight distance, pavement design); Transportation Association of Canada, Geometric Design Guide for Canadian Roads (superelevation and spiral tables — the paper's Table 2.1.2.5 is TAC page 2.1.2.12); AASHTO, A Policy on Geometric Design of Highways and Streets (Green Book) for runoff distribution and relative-gradient limits; AASHTO, Guide for Design of Pavement Structures (1993) for the flexible pavement equation and layer/drainage coefficients; Asphalt Institute MS-2, Asphalt Mix Design Methods and Mamlouk & Zaniewski, Materials for Civil and Construction Engineers, for mixture volumetrics and binder grading.

Check: assumptions carried through this paper. Under the paper's own Note 2 the following values are assumed and stated where used: the AASHTO maximum relative gradient (0.50 % at 80 km/h) and the 70 % / 30 % split of superelevation runoff either side of the PC for two lanes rotated (Question 2); a truck factor of 0.52 for all trucks on a rural Interstate and a lane-distribution factor of 0.70 for three lanes in one direction (Question 6); and a downhill 2 % ramp grade in Question 4, since the freeway is elevated above the local street. Each is flagged again at the point of use with the sensitivity of the answer to it.

Question 6: AASHTO Flexible Pavement Design for a Rural Interstate (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.

Traffic, reliability and material data
Item	Value
Facility	six-lane rural Interstate (three lanes each direction)
Truck volume, growth rate, analysis period	578 per day both directions; 4 % per year; 20 years
Reliability, overall standard deviation	$R = 99\ \%$ ($Z_R = -2.327$), $S_o = 0.35$
Serviceability loss	$\Delta PSI = 2.0$
Effective roadbed resilient modulus	5 500 psi
Subbase resilient modulus (sand-gravel)	15 000 psi
Cement-treated base, 7-day unconfined compressive strength	500 psi
HMA resilient modulus	430 000 psi
Drainage	fair (subbase drains in one week); saturated more than 25 % of the time

Find. The thickness of the cement-treated base and of the sand-gravel subbase, with the hot-mix asphalt fixed at the minimum thickness given by the traffic table.

Approach. Convert the truck count to design-lane 18-kip equivalent single-axle loads over 20 years; solve the AASHTO 1993 flexible design equation for the structural number required above each of the two lower layers; read the layer and drainage coefficients; then apply the layered-design procedure from the top down, starting from the tabulated minimum asphalt thickness.

Growth factor and cumulative truck volume. For a constant annual growth rate the cumulative factor is $$GF = \frac{(1+g)^{n}-1}{g} = \frac{(1.04)^{20}-1}{0.04} = 29.778$$ Note that $GF$ is always at least $n$; a "growth factor" quoted below 20 for a 20-year period would have to be a rate instead.
Design-lane ESALs. The phrase "including two-axle, four-tire panel and pickup trucks" identifies the all trucks category, for which the truck factor on a rural Interstate is $T_F = 0.52$ equivalent axle loads per truck. With a directional split $D_D = 0.50$ and, for three lanes in one direction, a lane distribution factor $D_L = 0.70$, $$ESAL_{total} = 578(365)(0.52)(29.778) = 3.267 \times 10^{6}$$ $$W_{18} = 3.267 \times 10^{6}(0.50)(0.70) = \boxed{1.143 \times 10^{6}\ \text{ESALs}}$$
Minimum asphalt thickness. The table supplied with the question places $1.14 \times 10^{6}$ ESALs in the 500 001 to 2 000 000 band, for which the minimum hot-mix thickness is $$D_1 = 3.0\ \text{in}$$
Structural number required over the roadbed. The AASHTO 1993 flexible equation is $$\log_{10}W_{18} = Z_R S_o + 9.36\log_{10}(SN+1) - 0.20 + \frac{\log_{10}\left(\frac{\Delta PSI}{2.7}\right)} {0.40 + \frac{1094}{(SN+1)^{5.19}}} + 2.32\log_{10}M_R - 8.07$$ Solving it by bisection with $M_R = 5500$ psi, $Z_R = -2.327$, $S_o = 0.35$ and $\Delta PSI = 2.0$ gives $$\boxed{SN_3 = 4.17}$$ and repeating with the subbase modulus $M_R = 15\,000$ psi gives the structural number that must be provided above the subbase, $$\boxed{SN_2 = 2.92}$$
Layer and drainage coefficients. From the AASHTO charts, an asphalt concrete with $E_{AC} = 430\,000$ psi gives $a_1 = 0.43$; a cement-treated base with a 7-day unconfined compressive strength of 500 psi gives $a_2 = 0.15$; and a sand-gravel subbase with $M_R = 15\,000$ psi gives $a_3 = 0.11$. Drainage is described as fair with the pavement near saturation more than 25 % of the time, which is $m = 0.80$ in AASHTO Table 2.4. The description refers explicitly to water draining from the subbase, and the base is cement-stabilised rather than unbound, so $$m_2 = 1.00\ (\text{stabilised base}), \qquad m_3 = 0.80\ (\text{granular subbase})$$
Base thickness. The asphalt contributes $a_1 D_1 = 0.43(3.0) = 1.29$ to the structural number, so the cement-treated base must supply the balance of $SN_2$: $$D_2 = \frac{SN_2 - a_1D_1}{a_2 m_2} = \frac{2.92 - 1.29}{0.15(1.00)} = 10.87\ \text{in} \ \Rightarrow\ \boxed{D_2 = 11.0\ \text{in}\ (280\ \text{mm})}$$
Subbase thickness. The asphalt and base together now provide $1.29 + 0.15(11.0) = 2.94$, so $$D_3 = \frac{SN_3 - (a_1D_1 + a_2m_2D_2)}{a_3 m_3} = \frac{4.17 - 2.94}{0.11(0.80)} = 13.95\ \text{in} \ \Rightarrow\ \boxed{D_3 = 14.0\ \text{in}\ (356\ \text{mm})}$$
Check the section as built. Summing the provided contributions, $$SN_{prov} = 0.43(3.0) + 0.15(1.00)(11.0) + 0.11(0.80)(14.0) = 1.29 + 1.65 + 1.23 = 4.17 \ \ge\ SN_3$$ The section satisfies both the roadbed and the subbase criteria. Its total thickness is 28.0 in, or 711 mm — a heavy but unremarkable section for a 99 % reliability design over a 5500 psi roadbed in a wet climate.

Design-lane cross-section. The hot mix is held at the tabulated minimum, so the base and subbase carry the whole of the remaining structural number.

Question 6 — final results
Quantity	Value
Growth factor, 4 % over 20 years	29.778
Two-directional ESALs	$3.267 \times 10^{6}$
Design-lane ESALs $W_{18}$	$1.143 \times 10^{6}$
$SN$ required over the roadbed (5 500 psi)	4.17
$SN$ required over the subbase (15 000 psi)	2.92
Layer coefficients $a_1 / a_2 / a_3$	0.43 / 0.15 / 0.11
Drainage coefficients $m_2 / m_3$	1.00 / 0.80
Hot-mix asphalt $D_1$	3.0 in (76 mm), tabulated minimum
Cement-treated base $D_2$	11.0 in (280 mm)
Sand-gravel subbase $D_3$	14.0 in (356 mm)
Structural number provided	4.17 (total section 711 mm)

Check: the two judgement calls that move this answer. First, the truck factor. The 0.52 adopted is the tabulated value for all trucks on a rural Interstate, which is the category the question's parenthesis describes; if the traffic were classified and a lower factor used, $W_{18}$ and hence $SN$ would fall. Second, the drainage coefficient on the base. Applying $m_2 = 0.80$ to the cement-treated layer as well — defensible if it is treated as a drainable layer rather than a stabilised one — raises the required base to 13.6 in. AASHTO applies $m$ to unbound layers, and the question ties the "fair" description to the subbase, so $m_2 = 1.00$ has been used and the alternative is stated here.

Topic. AASHTO 1993 flexible pavement thickness design by the layered structural-number procedure.

Key relations. $GF = [(1+g)^n-1]/g$; $W_{18} = (\text{trucks})(365)(T_F)(GF)(D_D)(D_L)$; the AASHTO design equation above; $SN = a_1D_1 + a_2m_2D_2 + a_3m_3D_3$; $D_i \ge (SN_i - \sum \text{above})/(a_im_i)$.

Why this works. The structural number is a single index of a pavement's load-spreading capacity, and the design equation converts it into a number of load repetitions for a given roadbed stiffness, reliability and acceptable loss of ride quality. Because each layer protects the one beneath it, the procedure is applied from the top down: the material immediately under the asphalt must see no more stress than $SN_2$ implies, and the roadbed no more than $SN_3$ implies. The drainage coefficient is a multiplier on the granular layers only, because it models the loss of stiffness of an unbound material that stays saturated — a cemented layer does not soften in the same way.

Common pitfall. Omitting the directional and lane-distribution factors and designing for the full two-way ESAL count, which nearly triples $W_{18}$ here. A second, subtler pitfall is confusing the growth factor with the growth rate; the test is that a cumulative growth factor can never be smaller than the number of years.

Source. AASHTO, Guide for Design of Pavement Structures (1993), Part II §2.3 and Tables 2.2–2.4; Garber & Hoel, Traffic and Highway Engineering, 5th ed., §20.4 and Table 20.9 (truck factors).

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