Question 5 of 7: Flexible pavement design by the AASHTO method

Question 5: Flexible pavement design by the AASHTO method (20 marks — (a) 10, (b) 10)

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 new two-lane two-way highway is to be designed by the AASHTO 1993 flexible method for 15 years at 70 % reliability on a 4000 psi subgrade, carrying 120 trucks per lane per day growing at 5 % per year, with hot-mix asphalt, soil-cement and crushed stone available.

Find. (a) two alternative layer structures and their thicknesses; (b) the criteria for choosing between them.

Approach. Build the cumulative ESALs from the axle-load equivalency factors and the growth factor, solve the AASHTO equation for the required $SN$, then distribute that $SN$ over layers in two different ways using the tabulated structural layer coefficients.

1. Convert one truck into ESALs. From Table 4.2 the 18-kip single axle is the standard axle, $LEF=1.00$ in every $SN$ column; from Table 4.3 the 30-kip tandem at $SN=4$ carries $LEF=0.695$. Hence $$ \text{ESAL per truck}=1.00+0.695=1.695. $$ (The $SN=4$ column is used because the design converges there; the tandem factor only moves from 0.703 to 0.658 across $SN=3$ to $SN=5$, so the choice is not sensitive.)
2. Grow the traffic over the design period. The growth factor from the equation sheet is $$ TGF=\frac{(1+r)^{n}-1}{r}=\frac{1.05^{15}-1}{0.05}=21.5786, $$ so the cumulative design-lane loading is $$ W_{18}=TGF\times(\text{daily ESALs})\times365 =21.5786\times(120\times1.695)\times365=\boxed{1.602\times10^{6}} $$ The 120 trucks are already quoted per lane, so no directional or lane-distribution factor is applied.
3. Solve the AASHTO design equation for the required structural number. With $Z_RS_0=(-0.524)(0.40)=-0.2096$, $\log_{10}(\Delta PSI/2.7)=\log_{10}(0.7407)=-0.1303$ and $2.32\log_{10}(4000)=8.3568$, $$ \log_{10}W_{18}=Z_RS_0+9.36\log_{10}(SN+1)-0.20 +\frac{\log_{10}\!\left(\frac{\Delta PSI}{4.2-1.5}\right)} {0.40+\frac{1094}{(SN+1)^{5.19}}}+2.32\log_{10}M_R-8.07 $$ Iterating on $SN$ (at $SN=3.95$ the right side gives 6.1846, at $SN=4.00$ it gives 6.2215, against the target $\log_{10}W_{18}=6.2047$) yields $$ \boxed{SN_{required}=3.98} $$
4. Set the layer coefficients from the attached table. Of the economically available materials, hot-mix asphaltic concrete gives $a_1=0.44$ as a wearing surface, soil-cement gives $a_2=0.20$ as a base, crushed stone gives $a_2=0.14$ as a base and $a_3=0.11$ as a subbase. No drainage data are given, so $m_2=m_3=1.0$.
5. Proportion Alternative A — the all-granular section. Keeping the asphalt at the practical minimum for this traffic class, $$ SN=a_1D_1+a_2D_2m_2+a_3D_3m_3 =0.44(4)+0.14(8)+0.11(10) $$ $$ =1.76+1.12+1.10=\boxed{3.98\ \ge\ 3.98} $$ so 4 in of hot-mix asphalt over 8 in of crushed-stone base over 10 in of crushed-stone subbase satisfies the requirement exactly.
6. Proportion Alternative B — the stabilised section. Replacing the granular base with soil-cement raises the coefficient from 0.14 to 0.20, which buys back subbase thickness: $$ SN=0.44(4)+0.20(8)+0.11(6)=1.76+1.60+0.66=\boxed{4.02\ \ge\ 3.98} $$ i.e. 4 in of hot-mix asphalt over 8 in of soil-cement base over 6 in of crushed-stone subbase — 4 in thinner overall than Alternative A. Both sections clear the AASHTO minimum thicknesses for the 0.5 to 2 million ESAL band (3.0 in of asphalt concrete and 6 in of base).

Part (b) — choosing between the alternatives

The two sections are structurally equivalent by definition — they carry the same $SN$ — so the choice is an economic and constructability one, not a strength one. The considerations that should decide it are:

• Life-cycle cost, not first cost. Compare present worth of construction, periodic resurfacing and user delay during future works over a common analysis period, discounted at the agency rate. Soil-cement usually wins on materials haul (4 in less total thickness, and the cement can be mixed-in-place from local soil) but is more sensitive to construction quality.
• Availability and haul distance of aggregate. The 18 in of crushed stone in Alternative A is the single largest cost item on a rural project; if the nearest pit is far, Alternative B is cheaper even at a higher unit rate.
• Behaviour of the stabilised layer. Soil-cement shrinks and cracks in a regular block pattern, and those cracks reflect through the asphalt within a few years unless a thicker asphalt layer or an interlayer is provided. Alternative A has no reflective-cracking mechanism.
• Drainage and frost. The open-graded granular subbase in Alternative A drains and acts as a frost cushion; a thin subbase under a cement-stabilised base traps water at the interface. In a Canadian frost environment the depth to which the structure replaces frost-susceptible subgrade often governs the total thickness more than $SN$ does.
• Construction season, plant and workforce. Cement stabilisation needs a mixing train, moisture control and curing time; a granular section can be placed by any contractor with standard equipment and tolerates poorer weather.
• Staged construction and future widening. A granular section is easier to widen or to overlay in stages as traffic grows; soil-cement is difficult to trim and rework.
• Environmental footprint. Cement production is carbon intensive, while aggregate extraction and haul carry their own footprint; several Canadian agencies now score both in the selection.

On the numbers alone, with only 1.6 million ESALs over 15 years and a weak 4000 psi subgrade, most agencies would build Alternative A and reserve the stabilised base for the case where good aggregate is genuinely unavailable.