16-Civ-A6 Highway Design, Construction, and Maintenance · December 2018

Question 1 of 5: AASHTO 1993 flexible pavement design for a six-lane urban freeway

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

Notes on this paper

Paper format. National Examinations, December 2018 — 16-Civ-A6 Highway Design, Construction, and Maintenance. Three-hour, closed-book paper with a ten-page appendix. Five questions are printed and four solutions constitute a complete paper; all questions carry equal value (25 % each) and the marks for sub-questions are shown in brackets. Note 1 invites the candidate to state any interpretation assumed, and Note 2 permits any required data that is not given to be assumed. All five questions are worked here, because the set is a study resource rather than an examination attempt.

Reference texts. AASHTO, Guide for Design of Pavement Structures, 1993 — Part II Ch. 2 (flexible pavements) and Ch. 3 (rigid pavements); Figures 2.5–2.7, 3.1, 3.3, 3.6, 3.7 and Tables 2.4–2.6 are reproduced on appendix pages 1–8. Garber, N.J. and Hoel, L.A., Traffic and Highway Engineering, 5th ed. — Ch. 3 (driver characteristics, stopping sight distance), Ch. 15 (geometric design), Ch. 20 (flexible and rigid pavement design). AASHTO, A Policy on Geometric Design of Highways and Streets (Green Book), 7th ed. — Ch. 3. Transportation Association of Canada, Geometric Design Guide for Canadian Roads — Ch. 1.2 (design controls), Ch. 2.1 (sight distance), Ch. 3.2 (horizontal alignment and spirals), Ch. 4 (roadside design and clear zones). AASHTO, Roadside Design Guide, 4th ed. — Ch. 3 (clear zone). Huang, Y.H., Pavement Analysis and Design, 2nd ed. — Ch. 11 and 12.

Check — chart readings and assumed data. Three of the five questions are solved from nomographs and tables reproduced on the appendix pages. Each chart reading used here was taken from the printed appendix chart and is quoted in the step where it is used, so that a reader working from a different print can substitute their own reading. Two items are genuinely not supplied by the paper and are assumed under Note 2: the percentage of time the pavement structure is near saturation in Question 1 (needed for the drainage coefficients $m_2$, $m_3$), and AASHTO Figure 3.4, the rigid-foundation correction needed in Question 3(b), which the ten-page appendix does not include. Both are flagged where they arise and the sensitivity of the answer to each is quantified.

Question 1: AASHTO 1993 flexible pavement design for a six-lane urban freeway (25 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. A three-layer flexible structure — asphalt concrete over granular base over granular subbase — carrying 12 million equivalent single-axle loads over a 30-year life on a 10,000 psi roadbed.

Design inputs read from the question statement
Quantity	Symbol	Value
Design (cumulative) 18-kip applications	$W_{18}$	12,000,000
Effective roadbed resilient modulus	$M_R$	10,000 psi
Subbase resilient modulus (untreated silty sand)	$E_{SB}$	22,000 psi
Base resilient modulus (untreated granular)	$E_B$	30,000 psi
Asphalt concrete elastic modulus at $20^\circ\text{C}$	$E_{AC}$	450,000 psi
Initial and terminal serviceability	$p_0$, $p_t$	4.5 and 2.5
Design life	—	30 years

Find. The thickness of the asphalt concrete, granular base and granular subbase layers that satisfies the AASHTO 1993 flexible design equation, together with a justification for every input the question leaves open.

Figure 1 — the adopted flexible pavement structure, with the layer coefficient and drainage modifier credited to each layer.

Approach. Fix the four "soft" inputs (reliability, overall standard deviation, serviceability loss and drainage coefficients) from the qualitative statements in the question and the appendix tables, read the three structural layer coefficients from Figures 2.5–2.7, then apply the AASHTO layered-analysis procedure — solve the design equation three times, once with each layer's own supporting modulus, and work down from the surface.

Choose the reliability from the functional classification. Table 20.16 gives 85–99.9 % for an urban interstate or other freeway. Two statements in the question push the choice toward the upper part of that band: the road carries six lanes in a busy urban area, and "traffic detours are difficult and expensive", which is precisely the circumstance in which the consequence of premature failure is severe. Adopt $R = 95\ \%$, for which the standard normal deviate is $$Z_R = -1.645$$ A designer who read "detours are difficult and expensive" as decisive could justify $R = 99\ \%$ ($Z_R = -2.327$); Step 8 quantifies what that costs.
Choose the overall standard deviation. The appendix table gives $S_o = 0.40$–$0.50$ for flexible pavements. The question states that the subgrade and the construction materials were tested in the laboratory and that the traffic information is accurate — both of the principal contributors to $S_o$ are therefore better controlled than usual, so the low end of the range applies: $$S_o = 0.40$$
Compute the design serviceability loss. Modern pavers give a high initial ride, so the question supplies $p_0$ directly rather than leaving it at the AASHTO default of 4.2: $$\Delta PSI = p_0 - p_t = 4.5 - 2.5 = 2.0$$
Read the three structural layer coefficients. From Figure 2.5 at $E_{AC} = 450{,}000$ psi the asphalt concrete coefficient is $a_1 = 0.44$ — the value at which the chart's curve is drawn, and the canonical AASHTO surface-course coefficient. From Figure 2.6, entering the "Modulus – 1000 psi" scale at 30 gives $a_2 = 0.14$. Figure 2.7 is entered on its own modulus scale, which stops at 20 (that is, 20,000 psi) opposite $a_3 = 0.14$; the subbase at 22,000 psi therefore reads at the very end of the scale and $$a_1 = 0.44 \qquad a_2 = 0.14 \qquad a_3 = 0.14$$ The two charts are independent correlations and they cross in this range, which is why a 22,000 psi subbase is credited the same coefficient as a 30,000 psi base. Adopting $a_3 = 0.14$ rather than the 0.147 that the underlying correlation $a_3 = 0.227\log_{10}E_{SB} - 0.839$ returns is marginally conservative, and Step 7 shows the choice does not change the answer because a minimum thickness governs the subbase in any case.
Assume the drainage coefficients. The question states that the quality of drainage is good but does not say for what fraction of the year the granular layers are near saturation, so Table 2.4 cannot be entered without an assumption. A new urban freeway built with a designed subdrainage system is taken to be near saturation for 1–5 % of the time, which with "good" drainage gives the band 1.25–1.15: $$m_2 = m_3 = 1.20$$ This is the one genuinely open input in the question. If the Canadian spring-thaw period were judged to put the structure in the 5–25 % column instead, the band becomes 1.15–1.00 and the granular layers would need to be thicker; Step 8 quantifies that case.
Solve the design equation for the structural number required over each supporting layer. The AASHTO 1993 flexible equation printed on appendix page 1 is $$\log_{10}W_{18} = Z_R S_o + 9.36\log_{10}(SN+1) - 0.20 + \frac{\log_{10}\!\left(\dfrac{\Delta PSI}{4.2-1.5}\right)}{0.40 + \dfrac{1094}{(SN+1)^{5.19}}} + 2.32\log_{10}M_R - 8.07$$ It is not invertible in closed form, so it is solved numerically for $SN$ three times, each time entering the resilient modulus of the material that the layer above must protect. With $W_{18} = 12\times10^{6}$, $Z_R = -1.645$, $S_o = 0.40$ and $\Delta PSI = 2.0$: $$SN_1\,(M_R = 30{,}000\ \text{psi}) = 3.10 \qquad SN_2\,(M_R = 22{,}000\ \text{psi}) = 3.47 \qquad SN_3\,(M_R = 10{,}000\ \text{psi}) = 4.55$$ Substituting $SN_3 = 4.55$ back into the equation returns $12.0\times10^{6}$ applications, which confirms the numerical solution.
Work down through the structure. The asphalt concrete must by itself carry the structural number required to protect the base, so $$D_1 \ge \frac{SN_1}{a_1} = \frac{3.10}{0.44} = 7.05\ \text{in.} \;\Rightarrow\; D_1 = 7.5\ \text{in.}\ (190\ \text{mm})$$ which also satisfies the 4.0 in. minimum that the appendix requires above 7,000,000 ESALs. The asphalt then supplies $SN_1^{*} = 0.44\times7.5 = 3.30$. The base must make up the difference to $SN_2$: $$D_2 \ge \frac{SN_2 - SN_1^{*}}{a_2 m_2} = \frac{3.47 - 3.30}{0.14\times1.20} = 0.99\ \text{in.}$$ which is far below the 6 in. minimum aggregate base thickness tabulated for this traffic level, so $D_2 = 6$ in. (150 mm) and the two upper layers together supply $SN_2^{*} = 3.30 + 1.01 = 4.31$. Finally the subbase must make up the difference to $SN_3$: $$D_3 \ge \frac{SN_3 - SN_2^{*}}{a_3 m_3} = \frac{4.55 - 4.31}{0.14\times1.20} = 1.42\ \text{in.}$$ Again a construction minimum rather than the structural requirement governs; a granular subbase is not placed thinner than about 150 mm if it is to be compacted uniformly, so $D_3 = 6$ in. (150 mm). The adopted structure supplies $$SN_{\text{provided}} = 0.44(7.5) + 0.14(1.20)(6) + 0.14(1.20)(6) = \boxed{5.32 \;\gt\; SN_{\text{required}} = 4.55}$$
Test the two open assumptions. Raising the reliability to 99 % lifts $SN_3$ to 4.96 and $SN_1$ to 3.42, so the asphalt requirement becomes $3.42/0.44 = 7.77$ in. and the surface course goes up by one half-inch step to 8.0 in.; both granular layers stay on their 6 in. minimums (the base would need only 1.75 in.) and the structure supplies $SN = 5.54$ against 4.96. The higher reliability therefore costs exactly half an inch of asphalt and nothing else. Moving the drainage assumption to the 5–25 % column ($m = 1.10$) reduces the granular contribution from 2.02 to 1.85, which the 5.32 against 4.55 reserve absorbs completely. The granular layers are therefore robust against both assumed inputs, and the asphalt moves by at most one half-inch step, which is the useful conclusion to report.

The result is worth reading as an engineer rather than as an arithmetic exercise. Because the asphalt coefficient is high and the granular materials are stiff, the surface course alone carries almost two-thirds of the required structural number, and the granular layers fall out on their minimum construction thicknesses rather than on strength. That is characteristic of a strong-materials, high-traffic urban design, and it is also why the total structure of 495 mm is comfortably above what the structural number alone demands.

Question 1 — final results
Quantity	Value
Reliability and standard normal deviate	$R = 95\ \%$, $Z_R = -1.645$
Overall standard deviation	$S_o = 0.40$
Design serviceability loss	$\Delta PSI = 2.0$
Layer coefficients	$a_1 = 0.44$, $a_2 = 0.14$, $a_3 = 0.14$
Drainage coefficients (assumed)	$m_2 = m_3 = 1.20$
Structural numbers required	$SN_1 = 3.10$, $SN_2 = 3.47$, $SN_3 = 4.55$
Asphalt concrete surface	7.5 in. (190 mm)
Granular base	6 in. (150 mm), minimum thickness governs
Granular subbase	6 in. (150 mm), minimum thickness governs
Structural number provided	5.32 against 4.55 required
Total pavement thickness	19.5 in. (495 mm)

Topic. AASHTO 1993 layered analysis for flexible pavements.

Key relations. The design equation relating $W_{18}$ to $SN$, $M_R$, $\Delta PSI$, $Z_R$ and $S_o$; the structural number identity $SN = a_1D_1 + a_2D_2m_2 + a_3D_3m_3$; the layer coefficient charts (Figures 2.5–2.7); the drainage modifiers of Table 2.4; and the minimum-thickness table.

Why this works. The design equation is a regression on the AASHO Road Test and it knows nothing about individual layers — it converts traffic, support and an allowable loss of ride into a single number, the structural number, that the pavement as a whole must supply. Layered analysis turns that single number into a set of thicknesses by insisting that each granular layer is itself protected: the material above a layer must supply, on its own, the structural number that the design equation returns when that layer's resilient modulus is entered as the support. Working downward from the surface therefore guarantees that no layer is ever loaded beyond the condition for which its own modulus was measured. The drainage coefficients enter multiplicatively on the granular layers only, because it is the unbound materials whose stiffness collapses when they sit saturated.

Common pitfall. Solving the equation once with the roadbed modulus and then splitting the resulting $SN$ arbitrarily among the three layers — that satisfies the arithmetic but can leave the base loaded far beyond its own capacity. A second common error is applying a drainage coefficient to the asphalt concrete; $m_i$ applies only to untreated base and subbase materials.

Source. AASHTO, Guide for Design of Pavement Structures (1993), Part II §3.1 and Figure 3.2 (layered design); Garber and Hoel, Traffic and Highway Engineering, 5th ed., Ch. 20.

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