16-Civ-A6 Highway Design, Construction, and Maintenance · May 2017

Question 6 of 7: Service life of an as-built flexible pavement

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

Notes on this paper

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.

Garber, N. J. and Hoel, L. A., Traffic and Highway Engineering, 5th ed., Cengage — the exam's equation sheet, the friction/side-friction table, Table 4.2 and Table 4.4 axle-load equivalency factors, Table 4.5 reliability Z_R values and the structural-layer-coefficient table are all reproduced from this text.
AASHTO, Guide for Design of Pavement Structures, Washington DC, 1993 — the flexible-pavement design equation and nomograph, and the source of the LEF tables.
AASHTO, A Policy on Geometric Design of Highways and Streets (the “Green Book”) — stopping sight distance, horizontal sightline offset and vertical-curve K values.
Transportation Association of Canada, Geometric Design Guide for Canadian Roads (TAC GDG) — the governing Canadian geometric-design reference; its design-domain values parallel the AASHTO relations used here.
Transportation Association of Canada, Manual of Uniform Traffic Control Devices for Canada (MUTCDC) — advance placement of guide signs.

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 6: Service life of an as-built flexible pavement (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. A completed two-layer flexible section whose remaining life must be found under a traffic forecast that grows for five years and then plateaus.

Given data
Item	Symbol	Value
Surface / base thickness	$D_{1}$ / $D_{2}$	$4$ / $12\ \text{in}$
Layer coefficients (Table 3)	$a_{1}$ / $a_{2}$	$0.44$ / $0.20$
Drainage coefficients	$m_{2}$	$1.0$
Initial / terminal serviceability	$p_{o}$ / $p_{t}$	$4.5$ / $2.0$
Serviceability loss	$\Delta \text{PSI}$	$2.5$
Reliability	$R$	$90\ \%$ → $Z_{R}=-1.282$
Overall standard deviation	$S_{o}$	$0.40$
Effective roadbed resilient modulus	$M_{R}$	$5\,000\ \text{psi}$
Truck volume, first year, per lane	—	$300\ \text{/day}$
Axles per truck	—	two 16-kip single axles
Growth	—	$5\ \%$/yr for 5 yr, then constant

Find. The number of years the section will last at 90 % reliability under the two-stage traffic forecast, and three practical measures of pavement quality and performance.

The as-built section. With no subbase the whole structural number comes from the asphalt surface and the soil-cement base.

Approach. Compute the structural number of the as-built section, evaluate the design equation forward to get the allowable cumulative ESALs at 90 % reliability, accumulate the traffic in two stages — five compounding years, then a constant annual rate — and find when the accumulation reaches the allowable total.

Compute the structural number of the as-built section. With no subbase, $$SN=a_{1}D_{1}+a_{2}D_{2}m_{2}=0.44(4)+0.20(12)(1.0)=1.76+2.40=\boxed{4.16}$$
Convert the truck stream to ESALs. From Table 4.2 a 16-kip single axle at $SN\approx4$ carries $\text{LEF}=0.670$, and each truck has two of them: $$\text{ESAL}_{\text{truck}}=2(0.670)=1.340$$ $$\text{ESAL}_{\text{day}}=300(1.340)=402\ \text{ESAL/day}$$ $$\text{ESAL}_{\text{yr 1}}=402(365)=146\,730\ \text{ESALs}$$
Evaluate the design equation forward for the allowable traffic. Rather than solving for $SN$, substitute the known $SN=4.16$ together with $Z_{R}=-1.282$, $S_{o}=0.40$, $\Delta \text{PSI}=2.5$ and $M_{R}=5\,000\ \text{psi}$: $$\log_{10}W_{18}=(-1.282)(0.40)+9.36\log_{10}(5.16)-0.20+\frac{\log_{10}(2.5/2.7)}{0.40+1094/(5.16)^{5.19}}+2.32\log_{10}(5\,000)-8.07$$ Term by term this is $-0.5128+6.6704-0.2000-0.0540+8.5816-8.0700=6.4152$, hence $$W_{18,\text{allow}}=10^{6.4152}=\boxed{2.602\times10^{6}\ \text{ESALs}}$$
Accumulate the first stage of traffic. Over the five growing years the growth factor is $$TGF_{5}=\frac{(1.05)^{5}-1}{0.05}=5.5256$$ $$W_{1-5}=146\,730(5.5256)=810\,776\ \text{ESALs}$$ which is well short of the allowable total, so the pavement clearly survives the growth phase.
Fix the steady annual rate that follows. From year 6 onward the volume stays at its year-5 level: $$W_{\text{yr}}=146\,730\,(1.05)^{4}=146\,730(1.21551)=178\,351\ \text{ESALs/yr}$$ Note the exponent is $4$, not $5$ — year 1 carries no growth, so the fifth year has compounded only four times. This is the single most common slip in two-stage traffic problems.
Find the year the pavement reaches terminal serviceability. The traffic left to be absorbed after year 5 is $$W_{18,\text{allow}}-W_{1-5}=2\,602\,000-810\,776=1\,791\,000\ \text{ESALs}$$ $$\Delta n=\frac{1\,791\,000}{178\,351}=10.04\ \text{years}$$ so the total service life is $$n=5+10.04=\boxed{15.0\ \text{years}}$$ at 90 % reliability — that is, there is a 90 % probability that the pavement is still above $\text{PSI}=2.0$ after 15 years.

The plateau in the forecast matters a great deal. Had the 5 % growth continued indefinitely, the allowable total would have been reached in about 13.2 years instead of 15.0 — almost two years of life turns on the traffic assumption alone, which is a useful reminder that the forecast, not the design equation, is usually the weakest link in a pavement design.

(b) Three ways to measure pavement quality and performance. The first is ride quality, measured as longitudinal roughness. A vehicle-mounted inertial profilometer or laser profiler records the surface profile at highway speed and reduces it to the International Roughness Index in m/km, which can be converted to the present serviceability index used above. This is the measure that corresponds most directly to $\text{PSI}$ in the AASHTO framework and to what the travelling public actually experiences, and it is the primary network-level trigger for rehabilitation. The second is structural capacity, measured by non-destructive deflection testing. A falling-weight deflectometer drops a known load on the surface and records the deflection basin with a row of geophones; back-calculation of the basin yields the in-situ moduli of each layer and an effective structural number, which can be compared directly with the $SN$ the current traffic requires to decide whether an overlay must be structural or can be a surface treatment. The third is a surface distress survey, in which cracking, rutting, ravelling, potholes and patching are catalogued by type, severity and extent — manually or from automated imaging vehicles — and combined into a pavement condition index. Two further measures are worth naming because they capture what the first three miss: skid resistance, measured as a friction number with a locked-wheel or continuous-friction tester and directly relevant to the wet-weather crash rate, and rut depth, measured transversely with a straight-edge or a laser rut bar, which governs hydroplaning risk. In Canadian asset-management practice these measures are collected on a fixed cycle and fed into a pavement management system, where the trend in each index over time — not its value in any single year — is what drives the treatment decision.

Final results
Quantity	Symbol	Value
Structural number of the as-built section	$SN$	$4.16$
ESALs per truck	—	$1.340$
First-year daily ESALs	—	$402\ \text{/day}$
First-year annual ESALs	—	$146\,730$
Allowable ESALs at $R=90\ \%$	$W_{18,\text{allow}}$	$2.602\times10^{6}$
ESALs accumulated in years 1–5	$W_{1-5}$	$810\,776$
Steady annual ESALs from year 6	$W_{\text{yr}}$	$178\,351$
Additional years after the plateau	$\Delta n$	$10.04\ \text{yr}$
Service life	$n$	$15.0\ \text{years}$

Check: the 16-kip single-axle equivalency factor of $0.670$ at $SN=4$ has been taken from the standard AASHTO Table 4.2, because the copy of that table reproduced in the examination paper is physically cut off at the right margin — only the $SN = 1$, $2$ and $3$ columns are printed in full, and the $SN=4$ column shows just a leading “0.”. The answer is insensitive to this: across $SN = 1$ to $6$ the factor only varies between $0.591$ and $0.670$, and using the printed $SN=3$ value of $0.646$ would give a service life of 15.4 years instead of 15.0.

Topic. Forward use of the AASHTO design equation to predict remaining life, and two-stage traffic accumulation.

Key relations. $SN=a_{1}D_{1}+a_{2}D_{2}m_{2}$; the design equation solved for $W_{18,\text{allow}}$ at known $SN$; $TGF=[(1+r)^{n}-1]/r$ for the growth stage; a constant $W_{\text{yr}}=W_{1}(1+r)^{n_{g}-1}$ thereafter; and $n=n_{g}+(W_{\text{allow}}-W_{1\text{-}n_{g}})/W_{\text{yr}}$.

Why this works. Design and performance prediction are the same equation read in opposite directions. In design, the traffic is known and the equation is solved for the structural number; in a life prediction the structure is known and the equation is evaluated for the traffic it can absorb. Because reliability enters as the additive term $Z_{R}S_{o}$ in log-traffic space, the answer is always tied to a stated confidence level: the same section would “last” considerably longer at 50 % reliability, where $Z_{R}=0$, and the number is meaningless without the qualifier. Accumulating the traffic is then pure bookkeeping, but it is bookkeeping in which the compounding convention has to be right.

Common pitfall. Using $(1+r)^{n_{g}}$ rather than $(1+r)^{n_{g}-1}$ for the plateau rate — an error of one compounding period that shifts the life by several months — and continuing the growth factor past the year the forecast says growth stops, which here would overstate the traffic and understate the life by nearly two years. A third slip is forgetting that $\Delta \text{PSI}$ here is $4.5-2.0=2.5$, not the $2.0$ of the previous question: a lower terminal serviceability buys real extra life.

Source. AASHTO, Guide for Design of Pavement Structures, 1993, Part II Ch. 2; Garber & Hoel, Traffic and Highway Engineering, 5th ed., §20.4 and §21.2 (pavement performance and management).

← Question 5 Next: Question 7 →