16-Civ-A6 Highway Design, Construction, and Maintenance · May 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examinations, May 2017 — 16-Civ-A6 Highway Design, Construction and Maintenance. Three-hour closed-book paper (Casio or Sharp approved calculator only). Seven questions, all of equal value at 20 marks; the candidate submits five, and only the first five in the answer book are marked. NOTE 1 invites a written statement of any assumption, and NOTE 2 permits any datum that is required but not given to be assumed. All seven questions are worked below, because the set is a study resource rather than an examination script.
Reference texts.
Canadian context. These are Engineers Canada national examinations, so the Canadian frame governs practice: geometric design in British Columbia follows the TAC Geometric Design Guide and signing follows the MUTCDC. The paper, however, supplies an AASHTO equation sheet and AASHTO tables and names the AASHTO method explicitly in Questions 4 and 5, so every calculation below is carried out with the data the paper gives; where a Canadian practice differs in emphasis it is noted in the concept block rather than substituted for the examiner's method.
Assumptions used throughout (declared under NOTE 1). Gravitational acceleration $g = 9.81\ \text{m/s}^{2}$; perception–reaction time $t_{pr} = 2.5\ \text{s}$ (the AASHTO design value — the paper does not state one); coefficients $f$ and $f_{s}$ read from the paper's own Table 1 at the initial vehicle speed; drainage coefficients $m_{2} = m_{3} = 1.0$ where the question is silent.
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 complete AASHTO 1993 flexible-pavement design brief together with a trial section that must be audited rather than generated.
| Item | Symbol | Value |
|---|---|---|
| Design period | $n$ | $15\ \text{yr}$ |
| Initial / terminal serviceability | $p_{o}$ / $p_{t}$ | $4.5$ / $2.5$ |
| Serviceability loss | $\Delta \text{PSI}$ | $2.0$ |
| Reliability | $R$ | $70\ \%$ → $Z_{R}=-0.524$ |
| Overall standard deviation | $S_{o}$ | $0.40$ |
| Effective roadbed resilient modulus | $M_{R}$ | $4\,000\ \text{psi}$ |
| Truck volume, first year, per lane | — | $120\ \text{/day}$ |
| Traffic growth rate | $r$ | $5.0\ \%$ |
| Axles per truck | — | one 18-kip single + one 30-kip tandem |
| Trial surface / base / subbase | $D_{1}$/$D_{2}$/$D_{3}$ | $4$ / $6$ / $10\ \text{in}$ |
| Layer coefficients (Table 3) | $a_{1}$/$a_{2}$/$a_{3}$ | $0.44$ / $0.20$ / $0.11$ |
Find. Whether the trial section is appropriate — that is, whether the structural number it supplies matches the structural number the traffic demands, with neither a deficit nor a wasteful surplus — and how the AASHTO method accounts for environmental effects.
Approach. Compute the structural number the trial section supplies; convert the truck stream into cumulative 18-kip equivalent single-axle loads over the design period; solve the AASHTO design equation for the structural number that traffic actually requires; and compare the two, expressing the margin both as a reserve in ESALs and as a service life in years.
Conclusion. The design is appropriate. It is not under-designed: the structural number supplied exceeds the requirement, and the section will carry the design traffic for about 16.5 years against a 15-year target. Neither is it over-designed: a 2 % surplus in $SN$ and a 15 % reserve in allowable ESALs is a normal and prudent margin once the layer thicknesses have been rounded to constructible values, and it is far smaller than the spread introduced by the assumptions themselves. The layer thicknesses are also sensible in themselves — a 4-in. hot-mix surface satisfies the usual minimum for a truck route, and the 10-in. crushed-stone subbase does useful work on a weak $4\,000\ \text{psi}$ subgrade. Trimming the section to hit $SN=3.98$ exactly would mean shaving roughly half an inch of asphalt, which is neither constructible nor economic.
(b) Environmental factors in the AASHTO method. Environment enters the 1993 Guide in four distinct places rather than through a single correction. First and most directly, seasonal variation in subgrade support is folded into the effective roadbed soil resilient modulus. The designer estimates $M_{R}$ for each season — a spring-thaw value an order of magnitude below the summer value is normal in Canada — converts each to a relative damage $u_{f} = 1.18\times10^{8}M_{R}^{-2.32}$, averages the damages rather than the moduli, and converts the mean damage back to the single $M_{R}$ that the design equation uses. Averaging the moduli directly would badly overstate support, because damage is a steeply non-linear function of stiffness. The $4\,000\ \text{psi}$ given in this question is already such an effective value. Second, moisture in the unbound layers is handled by the drainage coefficients $m_{2}$ and $m_{3}$ that multiply the base and subbase contributions to $SN$. They are selected from a table indexed on the quality of drainage (how quickly the layer drains) and on the percentage of time the layer is near saturation, and they range from about $1.40$ for excellent drainage that is rarely saturated down to $0.40$ for poor drainage that is saturated much of the year — a factor-of-three swing in the credit a granular layer earns. Third, swelling and frost heave are treated as serviceability losses that consume part of the same $\Delta \text{PSI}$ budget the traffic is competing for. The Guide computes $\Delta \text{PSI}_{SW}$ and $\Delta \text{PSI}_{FH}$ from the rate and maximum extent of heave and the fraction of the project length affected, subtracts them from the total allowable loss, and leaves only the remainder as the traffic-induced $\Delta \text{PSI}$ entering the design equation. Where frost is severe, this can dominate the design. Fourth, temperature acts on the materials themselves: the asphalt-concrete layer coefficient $a_{1}$ is tied to the elastic modulus of the mix measured at $68\,{}^{\circ}\text{F}$, and a designer working in a hotter or colder region adjusts it accordingly, while low-temperature contraction drives the thermal cracking that the structural model does not capture at all. In Canadian practice these mechanisms are what justify spring load restrictions, the use of frost-susceptibility criteria and a frost-penetration depth in setting total pavement thickness, and the emphasis on subsurface drainage; and it is worth stating plainly that the AASHTO environmental treatment is empirical and calibrated on the AASHO Road Test in Illinois, so mechanistic-empirical procedures with local climatic input are increasingly preferred for extreme Canadian conditions.
| Quantity | Symbol | Value |
|---|---|---|
| Structural number supplied | $SN$ | $4.06$ |
| ESALs per truck | — | $1.695$ |
| First-year daily ESALs | — | $203.4\ \text{/day}$ |
| Traffic growth factor, 15 yr at 5 % | $TGF$ | $21.5786$ |
| Design ESALs over 15 years | $W_{18}$ | $1.602\times10^{6}$ |
| Structural number required | $SN_{\text{req}}$ | $3.98$ |
| Allowable ESALs at $SN=4.06$ | $W_{18,\text{allow}}$ | $1.841\times10^{6}$ |
| Reserve capacity | — | $15\ \%$ |
| Service life delivered | $n$ | $16.5\ \text{yr}$ |
| Verdict | — | Appropriate — adequate, not wasteful |
Check: two values had to be supplied. (i) The paper's Table 4.5 tabulates $Z_{R}$ only for $R = 80$–$96\ \%$ and $R = 90$–$96\ \%$; the $70\ \%$ reliability this question specifies is off the table, so the standard normal deviate $Z_{R} = -0.524$ has been used. (ii) Drainage coefficients are not stated and have been taken as $m_{2}=m_{3}=1.0$. Both assumptions are conservative in the sense that a higher reliability or a poorer drainage rating would both increase the required $SN$; at $R = 80\ \%$, for instance, $SN_{\text{req}}$ rises to about $4.06$ and the section becomes exactly critical. Note also that the layered-thickness check (sizing $D_{1}$ on the base modulus and $D_{1}+D_{2}$ on the subbase modulus) cannot be carried out, because the resilient moduli of the base and subbase materials are not given — only the total $SN$ can be audited here.
