Cañas Silva 2010 provides a calibration against and comparison to the AASHTO Pavement ME back-calculation procedure (using BISAR 3.0 and ISLAB2000), which showed errors up to approximately 28%, attributable to differences in load area geometry (circular vs. rectangular), layer boundary conditions (infinite vs. finite slab), and calibration assumptions between the two procedures. The Palmer-Barber approach is simpler and more conservative than Pavement ME, making it well-suited for routine design practice.

Some have suggested that the composite k-value formula used by StreetPave12 and pavementdesigner.org — an equation with roots in AASHTO 1986 and also published in FHWA geotechnical guidance — produces too high of a k-value in many scenarios. In response, many practitioners have continued to use composite k-value tables developed by PCA and ACPA from the 1980s through 2000s. ACPA 2006 is one such example, with tables for unstabilized, asphalt-treated, and cement-treated/econocrete subbases.

The ACPA 2006 tables start with a subgrade k-value, but perception of that value is heavily based in the widely circulated nomograph showing CBR 3 = 100 psi/in., CBR 10 = 200 psi/in., CBR 20 = 250 psi/in., and so on. The Middlebrooks 1942 reference for this conversion makes clear it is an approximation. This dated basis was used here to map the ACPA 2006 subgrade k-values to CBR such that 50 psi/in. = CBR 1, 100 psi/in. = CBR 3, 150 psi/in. = CBR 5.75, and 200 psi/in. = CBR 10.

From that CBR starting point, this calculator converted CBR to resilient modulus per the MEPDG equation and applied the calibrated Palmer-Barber equation to produce the values shown below.

Unstabilized Subbase


A resilient modulus of 25,000 psi is used, per pavementdesigner.org's recommendation for this subbase type. The comparison shows very good correlation (±10%) on almost half the scenarios. The ACPA 2006 table appears to undervalue a stiffer subgrade (higher CBR) and to overvalue a thicker unstabilized layer. While individual differences range from −25% to +30%, the average across all 16 data points is 0%.

ACPA 2006 — Unstabilized Subbase (psi/in.)

CBRResilient
Modulus, psi
k-value,
psi/in.
Unstabilized Subbase Thickness
4"6"9"12"
11,94250657585110
34,118100130140160190
5.756,429150176185215255
109,389200220230270320

This Calculator — Unstabilized, 25,000 psi (psi/in.)

CBRResilient
Modulus, psi
k-value,
psi/in.
Unstabilized Subbase Thickness
4"6"9"12"
12,5556667707582
35,161133134137143151
5.757,827202202205210217
1011,153288287289293299

Difference (this calculator vs. ACPA 2006)

CBR4"6"9"12"
1+3%-7%-12%-25%
3+3%-2%-11%-21%
5.75+15%+11%-2%-15%
10+30%+26%+9%-7%
Average difference: 0%

Difference = (this calculator − ACPA 2006) / ACPA 2006 × 100  · ±10%±11–20%±21–30%>±30%

Asphalt-Treated Base (ATB)


A resilient modulus of 170,000 psi is used, per pavementdesigner.org's recommendation. With an average difference of −21%, the results show that ACPA 2006 generally overestimates k-value with an asphalt-treated base. Only at CBR 10 with 4 inches of ATB does this calculator produce a higher k-value than ACPA 2006. The difference is larger at lower CBRs and greater thicknesses, suggesting that ATB may not provide as much benefit at low CBRs as ACPA 2006 implies and that the returns on a thicker ATB layer may not be as significant as the ACPA table suggests.

ACPA 2006 — Asphalt-Treated Base (psi/in.)

CBRResilient
Modulus, psi
k-value,
psi/in.
ATB Thickness
4"6"9"12"
11,9425085112155200
34,118100152194259325
5.756,429150217271353437
109,389200280345442541

This Calculator — ATB, 170,000 psi (psi/in.)

CBRResilient
Modulus, psi
k-value,
psi/in.
ATB Thickness
4"6"9"12"
12,555667383102123
35,161133142155180210
5.757,827202211226255292
1011,153288296313347388

Difference (this calculator vs. ACPA 2006)

CBR4"6"9"12"
1-14%-26%-34%-38%
3-7%-20%-31%-35%
5.75-3%-17%-28%-33%
10+6%-9%-21%-28%
Average difference: −21%

Difference = (this calculator − ACPA 2006) / ACPA 2006 × 100  · ±10%±11–20%±21–30%>±30%

Cement-Treated Base (CTB)


600,000 psi is the resilient modulus recommended by pavementdesigner.org for a cement-treated base. Using it produces an average difference of −30% versus ACPA 2006. Notably, the maximum dynamic k-value produced is 508 psi/in., for CBR 10 with 12 inches of CTB.

ACPA 2006 — Cement-Treated Base (psi/in.)

CBRResilient
Modulus, psi
k-value,
psi/in.
CTB Thickness
4"6"9"12"
11,94250103148222304
34,118100185257372496
5.756,429150263357506664
109,389200348454634823

This Calculator — CTB, 600,000 psi (psi/in.)

CBRResilient
Modulus, psi
k-value,
psi/in.
CTB Thickness
4"6"9"12"
12,5556684103137173
35,161133156183232287
5.757,827202228260321390
1011,153288316353425508

Difference (this calculator vs. ACPA 2006)

CBR4"6"9"12"
1-18%-30%-38%-43%
3-16%-29%-38%-42%
5.75-13%-27%-37%-41%
10-9%-22%-33%-38%
Average difference: −30%

Difference = (this calculator − ACPA 2006) / ACPA 2006 × 100  · ±10%±11–20%±21–30%>±30%

The ACPA 2006 CTB table is noted as also applying to econocrete subbase. While pavementdesigner.org recommends 1,500,000 psi for lean concrete or econocrete, a value of 2,000,000 psi was tested here and produces k-values much closer to ACPA 2006 at 4 and 6 inches of thickness. The difference grows with increasing thickness but, unlike unstabilized and ATB, it is relatively consistent across CBR values.

This Calculator — Lean Concrete / Econocrete, 2,000,000 psi (psi/in.)

CBRResilient
Modulus, psi
k-value,
psi/in.
CTB Thickness
4"6"9"12"
12,55566103137192250
35,161133183233317406
5.757,827202260322429544
1011,153288354427558700

Difference (2,000,000 psi vs. ACPA 2006 CTB)

CBR4"6"9"12"
10%-7%-14%-18%
3-1%-9%-15%-18%
5.75-1%-10%-15%-18%
10+2%-6%-12%-15%
Average difference: −10%

Difference = (this calculator − ACPA 2006) / ACPA 2006 × 100  · ±10%±11–20%±21–30%>±30%

With such a large difference in resilient modulus between CTB (600,000 psi) and lean concrete or econocrete (1,500,000–2,000,000 psi), a single composite k-value table is not recommended for both material types. The choice of modulus significantly affects the result, particularly at greater subbase thicknesses.