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Two-lane rural highway, 20-year flexible pavement: ESALs from a vehicle mix, AASHTO 1993 structural number and layer thicknesses

Tool	Pavement Design
Source	American Association of State Highway and Transportation Officials (1993). AASHTO Guide for Design of Pavement Structures. AASHTO, Washington, DC (equations used as mathematics). The equations are printed in Christopher, B. R., Schwartz, C., and Boudreau, R. (2006), Geotechnical Aspects of Pavements, FHWA NHI-05-037, Appendix C (eq. C.2, C.3) and chapter 5 (eq. 5.13, 5.16, 5.18), whose worked examples the tool reproduces (SN 4.61 and 5.07).
Level	Professional

Problem

A two-lane rural highway carries 4,000 vehicles per day in its first year (both directions), growing 2 % per year. The mix is 84 % cars and pickups, 1 % buses, 6 % two-axle trucks, 3 % three-axle trucks and 6 % five-axle tractor-semitrailers. The roadbed soil has a CBR of 5. Design a flexible pavement (asphalt surface, granular base, granular subbase) for 20 years at 85 % reliability, and cross-check the total thickness with the Corps of Engineers CBR equation.

Inputs to Enter

ADT 4,000, growth 2 %/yr, 20 years, directional distribution 50 %, lane distribution 100 %
Axle-group loads (kip): cars 2 + 2 single; bus 12 + 20 single; two-axle truck 6 + 14 single; three-axle truck 12 single + 30 tandem; five-axle semi 12 single + 34 + 34 tandem; load-equivalency factors iterated to the design structural number (the default; starting value SN 5), p_t 2.5
Reliability 85 %, S_0 0.45, p_0 4.2, p_t 2.5 (ΔPSI 1.7)
Roadbed CBR 5; surface a_1 0.44; base modulus 30,000 psi, m_2 1.0; subbase modulus 15,000 psi, m_3 1.0; minimum base 6 in; rounding up to 0.5 in (surface) and 1 in (unbound)
CBR cross-check: single wheel 9 kip at 80 psi, CBR 5, repetition factor 1.0

Open the Pavement Design tool (loaded with this example)

Answers

Iteration of the factors: SN 5 gives 3,683,717 ESALs and requires SN 4.1107; at 4.1107, 3,796,361 and 4.1300; at 4.1300, 3,793,793 and 4.1296 (agreement within 0.001 after 3 steps)
Truck factors at SN 4.130 (ESALs per vehicle): cars 0.00044, bus 1.686, two-axle truck 0.397, three-axle truck 0.900, five-axle semi 2.431; 855.56 ESALs per day in both directions, 68.2 % from the semis
Growth factor ((1.02)^20 − 1)/0.02 = 24.297; first-year design-lane ESALs 156,140; design W_18 = 3,793,793
Z_R = −1.036; M_R = 1,500 · 5 = 7,500 psi; required structural number SN = 4.130
Above the base (30,000 psi) SN_1 = 2.438: surface 5.54 → 6 in; above the subbase (15,000 psi) SN_2 = 3.184: base 3.95 in, minimum 6 in governs (a_2 = 0.138); subbase 6.08 → 7 in (a_3 = 0.109)
Section 6 in + 6 in + 7 in = 19 in; SN provided 4.230; it carries 4,427,198 ESALs (22.7 years)
CBR equation: t = √(9,000/(8.1 · 5) − 112.5/π) = 13.65 in, against 19 in

Notes

The tool's default inputs are this case; press Submit. The case is illustrative (stated on the page), not a printed example; its vehicle mix, axle loads and layer moduli are assumed values. Checked by test_pavement_design.php (13,487 checks) against the worked examples of FHWA NHI-05-037, the 12,000 required structural numbers of the Florida DOT Flexible Pavement Design Manual (2008) and independent scipy solutions, including the fixed point of the iteration. With the factors evaluated once at the entered SN 5 (the other option of the Factors At select) the case gives 3,683,717 ESALs, SN 4.111 and a 6 + 6 + 6 = 18 in section. Choosing the rigid pavement with the same traffic gives 5,671,401 ESALs (factors iterated to D 9.150 in) and a 9.15 in slab (9.5 in rounded) for S_c′ 650 psi, J 3.2, k 100 pci.