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Geotechnical Earthwork QA/QC, ASTM D698 / D1557 Proctor Compaction & Zero-Air-Voids

Proctor Soil Compaction Dry Density & ZAV Curve Formula

Calculate In-Situ Dry Unit Weight gamma_d = gamma_m/(1+w) (kN/m³), Theoretical 100%-Saturated Zero-Air-Voids Ceiling gamma_ZAV (kN/m³), Relative Proctor Compaction (%), and >= 95% Spec Gate.

Never compare wet field density against lab Proctor MDD—and any nuclear-gage reading plotting ABOVE the Zero-Air-Voids curve is physically impossible!

Highway embankment and building-pad specs (ASTM D698 Standard / D1557 Modified Proctor) never accept Bulk Moist Unit Weight `gamma_m` (`kN/m³`) directly because adding rainwater makes uncompacted mud heavier without packing mineral grains closer! Subtracting pore water via Gravimetric Moisture Content `w` (`%`) isolates **Dry Unit Weight `gamma_d = gamma_m / (1 + w / 100)`** (`kN/m³`), which must achieve **Relative Compaction `RC% = (gamma_d / gamma_d,max) * 100 >= 95.0%`** against Laboratory Maximum Dry Density `gamma_d,max` (`MDD`)! Simultaneously, soil phase relations impose an unbreakable thermodynamic upper ceiling—the **Zero-Air-Voids (`ZAV`, `S = 100%` saturation) curve `gamma_ZAV = (G_s * gamma_w) / (1 + (w / 100) * G_s)`** (with Specific Gravity `G_s ≈ 2.65–2.72` and `gamma_w = 9.80665` kN/m³): any field test where `gamma_d > gamma_ZAV` immediately exposes an uncalibrated nuclear moisture gage or wrong `G_s`!

Verify on a Highway Subbase Nuclear-Gage Lift Inspection—Field_Moist_Unit_Weight `gamma_m` = 21.10 kN/m³ (B2), Field_Moisture_Content `w` = 11.50% (B3), Soil_Grain_Specific_Gravity `G_s` = 2.68 (B4), and Lab_Modified_Proctor_MDD = 19.60 kN/m³ (B5): In-Situ Dry Unit Weight equals `18.92` kN/m³ (E2, safely below the `20.09` kN/m³ Zero-Air-Voids ceiling in E3!), Relative Compaction hits `96.55%` (E4), passing `"PASS (>=95% PROCTOR)"` (E5)!

ASTM D1557 Proctor QA/QC KPI (gamma_m=21.1 kN/m³, w=11.5%, Gs=2.68, MDD=19.6)FormulaVerified Output
In-Situ Dry Unit Weight (kN/m³)Moist_Unit_Weight / (1 + Moisture_Pct / 100)18.92 kN/m³ (17.14 @ wet 15.5% lift)
Zero-Air-Voids Ceiling ZAV (kN/m³)(Gs * 9.80665) / (1 + (Moisture_Pct/100)*Gs)20.09 kN/m³ (18.57 @ w = 15.5%)
Relative Proctor Compaction (%)(Field_Dry_gamma_d / Lab_MDD) * 10096.55% (87.46% < 95% @ wet lift!)
Earthwork Lift Acceptance GateRelative_Compaction_Pct >= 95.0%PASS (>=95% PROCTOR)

Proctor Dry Unit Weight, Zero-Air-Voids Physical Bound & Earthwork Spec Formula

Validate `Moist_Weight > 10` kN/m³, `Moisture w` in `(0%, 60%]`, `Specific_Gravity G_s` in `[2.40, 2.95]`, `Lab_MDD > 10` kN/m³, AND `gamma_d <= gamma_ZAV` right on `E2` (checking `ISTEXT(E2)` on `E3..E4` so text pass/fail strings in `E5` stay clean)—catching impossible above-ZAV gage errors automatically!

=LET(gm_w, B2, wc_p, B3, gs_s, B4, md_d, B5, IF(OR(gm_w <= 10, wc_p <= 0, wc_p > 60, gs_s < 2.4, gs_s > 2.95, md_d <= 10), "Invalid Proctor Input", LET(gd_f, gm_w / (1 + wc_p / 100), gz_v, (gs_s * 9.80665) / (1 + (wc_p / 100) * gs_s), IF(gd_f > gz_v, "Invalid Proctor Input", IF((gd_f / md_d) * 100 >= 95, "PASS (>=95% PROCTOR)", "UNDER-COMPACTED (<95%)")))))

Pumping Wet-of-Optimum Subgrade Lift Reject Check (Set Moist Weight = 19.8 kN/m³ & Moisture = 15.5%)

Test a rain-soaked lift (`B2 = 19.8`, `B3 = 15.5%`): Pore water pushes `gamma_ZAV` E3 down to `18.57` kN/m³, Field Dry Density E2 drops to `17.14` kN/m³, and Relative Compaction E4 falls to `87.46%`—flagging `"UNDER-COMPACTED (<95%)"` in E5 so the contractor discs, aerates, and re-rolls the lift!

=IF(ISTEXT(E2), E2, ROUND(((B2 / (1 + B3 / 100)) / B5) * 100, 2))

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