Ménard Dynamic Compaction Depth & Specific Energy Formula

Doubling a crawler crane’s drop height does NOT double compaction depth—Rayleigh/compression wave attenuation scales strictly with SQRT(W * H)!

**Deep Dynamic Compaction (`DDC`)** densifies loose hydraulic sand reclamation, rubble fills, and collapsible loess by free-falling a heavy steel Tamper of Mass `W` (`10–35` tonnes) from Crane Boom Height `H` (`15–30` m). Louis Ménard & R. G. Lukas (`FHWA GEC-1`) established that **Maximum Effective Improvement Depth `D_{max} = n * SQRT(W * H)`** (`m`, with `W` in tonnes and `H` in meters!), where Empirical Soil Attenuation Factor `n` equals `0.50–0.60` in clean pervious sands/gravels vs `0.35–0.40` in semi-pervious silty fills (where transient pore-water pressure absorbs impact energy)! Dropping `N_d` blows per crater on Square Print Spacing `S` (m) delivers **Single-Blow Energy `E_1 = (W * 9.80665 * H) / 1,000`** (`MJ`) and **Pass Applied Specific Energy `E_{grid} = (N_d * W * 9.80665 * H) / S^2`** (`kJ/m²`, targeting `800–2,500` kJ/m² across primary + ironing passes)!

Verify on a Port Container-Yard Hydraulic Sand Reclamation Pass—Steel_Tamper_Mass `W` = 18.0 tonnes (B2), Free-Fall_Drop_Height `H` = 22.0 m (B3 -> Nominal Drop Rating `W * H = 396.0` tonne·m in E2 & `3.88` MJ/blow in E4), Clean-Sand_Factor `n` = 0.52 (B4), Drops_Per_Crater `N_d` = 8 (B5), and Primary_Grid_Spacing `S` = 6.0 m (B6): Effective Improvement Depth reaches `10.35` m (E3) and Primary-Pass Specific Energy delivers `863.0` kJ/m² (E5)!

Ménard-Lukas Root-Energy Depth & Crater-Grid Specific Energy Formula

Validate `Tamper_Mass W` in `[2, 50]` t, `Drop_Height H` in `[3, 40]` m, `Soil_Factor n` in `[0.25, 0.70]`, `Drops N_d >= 1`, and `Grid_Spacing S` in `[1.5, 15.0]` m!

=LET(wt_t, B2, hd_m, B3, nf_s, B4, nd_c, B5, sp_m, B6, IF(OR(wt_t < 2, wt_t > 50, hd_m < 3, hd_m > 40, nf_s < 0.25, nf_s > 0.7, nd_c < 1, sp_m < 1.5, sp_m > 15), "Invalid DDC Schedule", ROUND((nd_c * wt_t * 9.80665 * hd_m) / (sp_m ^ 2), 1)))

Fines-Rich Silty Fill (n = 0.36) & Over-Wide 8.5 m Grid Under-Compaction Check

Encounter silty hydraulic fill (`n` B4 = 0.36) while stretching crater spacing to `S` B6 = 8.5 m: Improvement Depth E3 shrinks `-31%` to `7.16` m and Grid Energy E5 halves to `430.0` kJ/m²—leaving loose liquefiable pockets below `7` m unless wick drains and closer `6` m print grids are restored!

=IF(ISTEXT(E5), E5, ROUND(B4 * SQRT(B2 * B3), 2))

Further reading

• Arte Sheets Lesson — Proctor Soil Compaction Dry Density & Zero-Air-Voids Formula
• Arte Sheets Lesson — Hiley Dynamic Pile-Driving Set & Ultimate Capacity Formula