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Geotechnical Foundation Engineering, Driven Piles & Hammer Dynamics

Hiley Dynamic Pile-Driving Set & Ultimate Capacity Formula

Calculate Newtonian Cushion Impact Efficiency eta_impact, Net Transferred Blow Energy (kN·m), Hiley Ultimate Driving Resistance R_u (kN), and Safe Working Pile Capacity (kN at FS = 3.0).

Why legacy Engineering-News formulas dangerously overpredict capacity—Hiley penalizes BOTH inelastic ram-pile impact AND elastic bounce!

During impact driving of precast concrete or steel H-piles with a hydraulic or diesel drop hammer of ram weight W_h (kN), stroke H (m), and mechanical efficiency eta_h, much of the hammer blow never performs permanent soil penetration! Under Hiley’s complete energy balance, partially inelastic collision between ram W_h and pile+helmet weight W_p with capblock restitution coefficient e (0.40–0.55) retains only Newtonian Impact Efficiency eta_impact = (W_h + (e^2) * W_p) / (W_h + W_p), while half of temporary elastic compression c = c_cap + c_pile + c_quake (mm) absorbs strain work R_u * (c / 2)! Converting net energy (kN·m * 1,000 mm/m) gives Hiley Ultimate Resistance R_u = (eta_h * W_h * H * eta_impact * 1,000) / (s + c / 2) kN, where s (mm/blow) is permanent set per blow!

Verify on a Precast Driven Pile Refusal Log—Ram_Weight W_h = 50.0 kN (B2), Hammer_Drop_Stroke H = 1.20 m (B3), Hammer_Mech_Efficiency eta_h = 0.85 (B4), Pile_Plus_Helmet_Weight W_p = 35.0 kN (B5), Cushion_Restitution e = 0.50 (B6 -> Impact Efficiency = (50 + 8.75) / 85 = 0.6912 in E2 and Net Transferred Energy = 35.25 kN·m in E3), Permanent_Set_Per_Blow s = 4.0 mm (B7), and Elastic_Compression_Bounce c = 12.0 mm (B8): Ultimate Driving Resistance R_u hits (35.25 * 1,000) / (4.0 + 6.0) = 3,525.00 kN (E4), yielding Safe Working Load (FS = 3.0) = 1,175.00 kN (E5)!

Hiley Pile-Driving KPI (Wh=50 kN, H=1.2 m, Wp=35 kN, e=0.5, s=4 mm, c=12 mm)FormulaVerified Output
Newtonian Impact Efficiency(Wh + (e^2) * Wp) / (Wh + Wp)0.6912
Net Blow Energy Delivered (kN·m)eta_h * Wh * H_m * Impact_Efficiency35.25 kN·m
Hiley Ultimate Resistance Ru (kN)(Net_Energy_kNm * 1000) / (s_mm + c_mm/2)3,525.00 kN (1,762.50 @ s = 14 mm)
Allowable Working Load (FS = 3.0)Ultimate_Resistance_Ru / 31,175.00 kN (587.50 @ s = 14 mm)

Hiley Dynamic Pile Ultimate Driving Resistance Formula

Validate W_h > 0, Stroke H > 0, eta_h in (0.40, 1.0], W_p > 0, Restitution e in [0, 1], Permanent_Set s >= 0, Elastic_Bounce c > 0, and (s + c / 2) > 0!

=LET(wh_k, B2, st_m, B3, eh_m, B4, wp_k, B5, rs_e, B6, st_s, B7, el_c, B8, IF(OR(wh_k <= 0, st_m <= 0, eh_m <= 0.4, eh_m > 1, wp_k <= 0, rs_e < 0, rs_e > 1, st_s < 0, el_c <= 0), "Invalid Pile Blow Input", LET(ei_m, (wh_k + (rs_e ^ 2) * wp_k) / (wh_k + wp_k), en_t, eh_m * wh_k * st_m * ei_m, ROUND((en_t * 1000) / (st_s + el_c / 2), 2))))

Softer Bearing Stratum Easier Set Check (Set Permanent Blow Set s = 14.0 mm/blow)

Simulate a softer sand lens where Permanent_Set B7 widens from 4.0 mm/blow to 14.0 mm/blow (denominator s + c/2 doubles from 10.0 mm to 20.0 mm): Ultimate Driving Resistance E4 halves cleanly to 1,762.50 kN and Safe Working Load E5 drops to 587.50 kN!

=IF(ISTEXT(E4), E4, ROUND(E4 / 3, 2))

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