Civil, Structural & Geotechnical Engineering
California Bearing Ratio (CBR) & Subgrade Resilient Modulus M_R Formula (ASTM D1883)
Calculate ASTM D1883 California Bearing Ratio CBR (%) at 0.10-in (1,000 psi standard crushed rock) and 0.20-in (1,500 psi) piston penetrations, and convert CBR into AASHTO MEPDG Subgrade Resilient Modulus M_R = 2555 * CBR^0.64.
Benchmark compacted roadbed soil against California standard crushed limestone (1,000 psi at 0.10 in)!
Developed by O. J. Porter for the California Division of Highways in 1929 and standardized worldwide as ASTM D1883 / AASHTO T 193, the California Bearing Ratio (CBR) drives a 3.00-in^2 circular piston into soaked compacted soil at 0.05 in/min! Measured piston unit stress (Force_lb / 3.00 in^2, in psi) is divided by standard crushed California limestone reference stresses — 1,000 psi (6.90 MPa) at 0.10-in (2.54 mm) penetration and 1,500 psi (10.34 MPa) at 0.20-in (5.08 mm) penetration:
CBR_0.10 (%) = 100 * (Stress_0.10_psi / 1000) and CBR_0.20 (%) = 100 * (Stress_0.20_psi / 1500) (reporting CBR_0.10 normally, or re-testing/reporting MAX(CBR_0.10, CBR_0.20) when CBR_0.20 > CBR_0.10)! To convert empirical CBR into elastic Mechanistic-Empirical Pavement Design Guide (AASHTO MEPDG / NCHRP 1-37A) Subgrade Resilient Modulus across fine- and coarse-grained soils, Powell et al. (1984, TRRL) established M_R (psi) = 2,555 * (CBR^0.64) (alongside Heukelom & Klomp’s classic 1,500 * CBR for fine soils CBR <= 10%)!
| Compacted Subgrade / Base Layer | Piston Load at 0.10 in (3.0 in^2 Piston) | Evaluated CBR (%) | AASHTO MEPDG M_R = 2555 * CBR^0.64 |
|---|---|---|---|
| Soft Silty Clay Subgrade | 180 lb (60 psi) | 6.0% CBR | 8,043 psi (55.5 MPa) |
| Compacted Sandy Gravel Subbase | 900 lb (300 psi) | 30.0% CBR | 22,529 psi (155.3 MPa) |
| Crushed Aggregate Road Base | 2,400 lb (800 psi) | 80.0% CBR | 42,197 psi (290.9 MPa) |
ASTM D1883 Governing CBR (%) from 3.00-in^2 Piston Loads (lb)
Divides piston forces B2 (lb at 0.10 in) and B3 (lb at 0.20 in) by piston area 3.00 in^2 and standard stresses 1,000 / 1,500 psi, returning MAX(CBR_0.10, CBR_0.20).
=IF(OR(B2 <= 0, B3 <= 0), "Requires Positive 0.10-in and 0.20-in Piston Forces (lb)", ROUND(MAX(100 * ((B2 / 3) / 1000), 100 * ((B3 / 3) / 1500)), 2))AASHTO MEPDG Subgrade Resilient Modulus M_R (psi) = 2555 * CBR^0.64
Converts governing CBR (%) directly into Resilient Modulus M_R (psi) for flexible and rigid pavement design.
=IF(OR(B2 <= 0, B3 <= 0), "Requires Positive 0.10-in and 0.20-in Piston Forces (lb)", ROUND(2555 * (MAX(100 * ((B2 / 3) / 1000), 100 * ((B3 / 3) / 1500)) ^ 0.64), 0))Try the example
Use the original values or change them to test your understanding.