Pavement

5% of exam

Traffic characterization and ESALs, flexible-pavement AASHTO structural number, rigid-pavement slab design parameters, and pavement evaluation and rehabilitation procedures.

6 concepts

Exam areas

D. Traffic characterization, pavement design, and rehabilitation

ESALs & Traffic Characterization

Convert a mixed truck stream into 18-kip equivalent single-axle loads with the fourth-power law, then accumulate design-lane ESALs over the design period with growth and lane factors.

Every pavement-design method on the PE Civil exam — empirical AASHTO-93 or mechanistic-empirical — starts with the same question: how many heavy load repetitions will the design lane carry over its life? The universal currency for that answer is the 18-kip (80 kN) equivalent single-axle load, the ESAL. A loaded truck does not damage a pavement once; it damages it as if it were many passes of a standard 18-kip axle, and the multiplier grows ferociously with axle weight. Get the ESAL accumulation wrong and every downstream number — structural number, slab thickness, overlay — is wrong with it. The handbook gives you the accumulation machinery in §5.1.6 Design Traffic, §5.1.7–5.1.8 (truck volumes and monthly factors) and the ESAL accumulation equation on p. 274; this concept builds the fluency to drive it.

Why the fourth power dominates everything

The load-equivalency factor (LEF, also written

F_E

) is the number of standard 18-kip passes that inflict the same damage as one pass of a given axle. Empirically — from the AASHO Road Test — pavement damage rises roughly with the fourth power of axle load, so a single axle carrying load

W_x

(in kips) has

\text{LEF}\approx (W_x/18)^4

. The consequence is brutal: a legal 20-kip single axle is worth

1.52

ESALs, a 24-kip axle is worth

3.16

, and the family sedan at well under 2 kips contributes essentially nothing. This is why pavement engineers count trucks, not cars, and why overload enforcement matters so much — doubling an axle load multiplies its damage roughly sixteen-fold.

\text{LEF} = F_E \approx \left(\dfrac{W_x}{18}\right)^{4}

Single, tandem, and tridem axles

The clean

(W_x/18)^4

form applies to single axles. Tandem and tridem axle groups spread load over two or three closely spaced axles, so each group does less damage per ton than a single axle would; AASHTO publishes separate LEF tables for single, tandem, and tridem groups (and the factor also depends weakly on the pavement's structural number and terminal serviceability). On the exam you will either be handed LEF values from a table or asked to apply the fourth-power approximation to single axles. The key discipline is to compute one LEF per axle group, not per vehicle, and then sum the groups.

The truck factor: ESALs per truck

It is rarely practical to track every axle, so traffic is summarized by the truck factor

TF

— the average number of ESALs a single truck of a given class applies, equal to the sum of its axle-group LEFs. A typical 5-axle tractor-semitrailer (one steer single plus two tandem groups) carries a truck factor on the order of

1

2.5

ESALs depending on loading. Multiply the truck factor by the number of trucks to get ESALs directly:

\text{ESAL} = (\text{number of trucks})\times TF

. This is the bridge between a traffic count and a damage count.

TF = \sum_{\text{axle groups }i} \text{LEF}_i = \dfrac{\text{total ESALs from a truck class}}{\text{number of trucks in that class}}

Accumulating ESALs over the design period with growth

Traffic grows year over year, so the design ESAL is not the first-year value times the number of years — it is the first-year value times a growth factor that sums a geometric series. For an annual growth rate

r

over a design period of

n

years, the cumulative growth factor is

G_{rn} = \dfrac{(1+r)^n - 1}{r}

(its limit as

r\to 0

is simply

n

). The handbook's accumulation equation (p. 274, end of §5.1) assembles all the pieces — first-year daily traffic, axle counts, the load-equivalency factor, the growth factor, and the design-lane factor — into one product, with the

365

converting daily traffic to annual.

\text{ESAL}_i = f_d \, G_{rn}\, \text{AADT}_i\, N_i\, F_{Ei}\,(365), \qquad G_{rn} = \dfrac{(1+r)^n - 1}{r}

Directional and lane distribution to the design lane

The accumulation above is two-directional and total — but a pavement is designed for the single most heavily loaded lane. The handbook §5.1.6 reduces total ESALs to the design lane in two steps: a directional distribution factor

D_D

(typically

0.5

for a balanced two-way facility) splits traffic by direction, and a lane distribution factor

D_L

assigns the design-lane share when one direction has multiple lanes. The handbook tabulates

D_L

100\%

for one lane,

80

–

100\%

for two,

60

–

80\%

for three, and

50

–

75\%

for four lanes per direction. Choose the conservative (higher) end unless data say otherwise.

\text{ESAL}_{DL} = D_D \, D_L \, \text{ESAL}_{\text{2-dir, cumulative}}

Exam strategy

Build the design-lane ESAL in a fixed order and you will not drop a factor: (1) find first-year daily ESALs

= \text{AADT}\times(\% \text{trucks})\times TF

; (2) annualize with

\times 365

; (3) grow over the design period with

G_{rn}=\frac{(1+r)^n-1}{r}

; (4) split to the design lane with

D_D

and

D_L

. Watch three traps: the growth factor is a sum, not

n

— using

n

undercounts badly at long design lives; the fourth-power law applies to single axles in kips, so never apply it to a whole truck weight; and the LEF jumps so fast that overload questions hinge on it — a

20\%

axle-weight increase is roughly a

(1.2)^4 = 2.07\times

damage increase. If LEFs are tabulated, use the table; if not, use

(W_x/18)^4

per single axle and say so.

Key equations

Load-equivalency factor (fourth-power law)

F_E = \left(\dfrac{W_x}{18}\right)^{4}

Approximate ESALs per pass of a single axle carrying $W_x$ kips; exact values come from AASHTO single/tandem/tridem tables (functions of $SN$ and $p_t$ ). $W_x$ in kips.

Truck factor

TF = \sum_i F_{Ei}

Average ESALs applied by one truck of a class; the sum of load-equivalency factors over all of that truck's axle groups.

Growth factor (cumulative)

G_{rn} = \dfrac{(1+r)^{n}-1}{r}

Sums the geometric growth series over $n$ years at annual rate $r$ (decimal). Reduces to $n$ when $r=0$ ; never use $n$ alone when $r>0$ .

ESAL accumulation (handbook p. 274)

\text{ESAL}_i = f_d\,G_{rn}\,\text{AADT}_i\,N_i\,F_{Ei}\,(365)

$f_d$ design-lane factor, $\text{AADT}_i$ first-year daily volume in axle category $i$ , $N_i$ axles per vehicle, $F_{Ei}$ load-equivalency factor; $365$ annualizes.

Design-lane ESAL (handbook §5.1.6)

\text{ESAL}_{DL} = D_D\,D_L\,\text{ESAL}

$D_D$ directional distribution (≈0.5), $D_L$ lane distribution ratio; ESAL is the cumulative two-directional 18-kip total over the analysis period.

First-year daily ESALs from truck factor

\text{ESAL}_{\text{day}} = \text{AADT}\times T \times TF

$T$ = decimal fraction of trucks in the stream; multiply by $365$ then $G_{rn}$ to accumulate over the design period.

Cumulative design ESALs (assembled)

W_{18} = \text{AADT}\,T\,TF\,(365)\,G_{rn}\,D_D\,D_L

The full chain from a traffic count to the design-lane $W_{18}$ used in AASHTO-93 / MEPDG.

Worked examples

Load-equivalency factor and a truck factor

Problem. A delivery vehicle has a 12-kip single steer axle and two 20-kip single rear axles. Using the fourth-power law, find the load-equivalency factor of each axle and the vehicle's truck factor.

Solution. Apply

F_E=(W_x/18)^4

to each single axle. Steer:

F_E=(12/18)^4=(0.6667)^4=0.198

ESAL. Each rear axle:

F_E=(20/18)^4=(1.1111)^4=1.524

ESAL. Truck factor:

TF=0.198+2(1.524)=3.25

ESALs per pass. Sanity check: the 20-kip axles are above the 18-kip standard, so each should exceed

1.0

— they do (

1.52

) — and the light steer axle should be well under

1.0

— it is (

0.20

). One vehicle does the damage of about

3.25

standard axle passes.

TF = (0.6667)^4 + 2(1.1111)^4 = 0.198 + 2(1.524) = 3.25

Cumulative design-lane ESALs over 20 years

Problem. A two-lane-each-direction highway opens with AADT = 12,000, of which 8% are trucks averaging a truck factor of 0.45 ESAL. Traffic grows at 3% per year over a 20-year design life. Use $D_D=0.50$ and $D_L=0.90$ . Find the cumulative design-lane ESALs.

Solution. First-year daily ESALs (both directions):

12{,}000\times0.08\times0.45=432

ESAL/day. Annualize:

432\times365=157{,}680

ESAL/yr. Growth factor:

G_{rn}=\dfrac{(1.03)^{20}-1}{0.03}=\dfrac{1.8061-1}{0.03}=26.87

. Cumulative two-directional:

157{,}680\times26.87=4.24\times10^{6}

ESAL. Design lane:

W_{18}=4.24\times10^{6}\times0.50\times0.90=1.91\times10^{6}

ESAL. Sanity check: had we (wrongly) used

n=20

instead of

G_{rn}=26.87

, we would get

1.42\times10^{6}

— about 26% low. The growth factor must be the series sum.

W_{18} = (12{,}000)(0.08)(0.45)(365)\,\dfrac{(1.03)^{20}-1}{0.03}\,(0.50)(0.90) = 1.91\times10^{6}

Effect of an overloaded axle

Problem. An axle is permitted at 18 kip (single) but is consistently loaded to 22 kip. By what factor does the overload increase the damage from that axle?

Solution. Legal:

F_E=(18/18)^4=1.00

ESAL. Overloaded:

F_E=(22/18)^4=(1.2222)^4=2.23

ESAL. Ratio:

2.23/1.00=2.23

. So a 22% overload more than doubles the pavement damage from that axle. Sanity check: the ratio is just

(22/18)^4=(1.222)^4

; a rough

(1.2)^4\approx2.07

confirms the order of magnitude. This is why a few overloaded trucks can dominate a design-lane ESAL total.

\dfrac{F_{E,22}}{F_{E,18}} = \left(\dfrac{22}{18}\right)^{4} = 2.23

Common pitfalls

•Using the design period $n$ in place of the growth factor $G_{rn}=\frac{(1+r)^n-1}{r}$ . For $r>0$ the factor exceeds $n$ (e.g., 26.9 vs 20 at 3%/20 yr); using $n$ undercounts traffic and underdesigns the pavement.
•Applying the fourth-power law to a whole truck's gross weight. The LEF is per single axle in kips — compute one factor per axle group and sum them for the truck factor.
•Forgetting tandem/tridem axles do less damage per ton than singles. Use AASHTO's separate tandem/tridem tables; the clean $(W/18)^4$ is a single-axle approximation.
•Skipping the directional and lane reduction. Total two-directional ESALs must be multiplied by $D_D$ (≈0.5) and $D_L$ to reach the design lane — pavements are designed for one lane, not the whole roadway.
•Dropping the 365. The handbook accumulation uses first-year DAILY traffic; you must annualize before applying the growth factor.
•Treating cars and light vehicles as contributing ESALs. Their fourth-power factors are negligible — count trucks (and buses), not the full AADT, through the truck factor.

References

NCEES PE Civil Reference Handbook — §5.1.6 Design Traffic
NCEES PE Civil Reference Handbook — §5.1.6–5.1.8 and the ESAL accumulation equation (p. 274)
AASHTO Guide for Design of Pavement Structures (1993) — Appendix D, Load Equivalency Factors — Source of the single/tandem/tridem LEF tables and the fourth-power relationship from the AASHO Road Test.

AASHTO Flexible SN & Rigid Slab Design

Apply the empirical AASHTO-93 flexible structural-number equation and layer build-up, the reliability and serviceability inputs, and the companion rigid-pavement slab-thickness equation.