Pile Foundations – Engineering News formula (drop hammer) for safe bearing capacity For driven piles with a drop hammer, the Engineering News formula gives the allowable (safe) load in terms of hammer weight W, height of fall H, observed final penetration per blow S, and an empirical constant C (to account for elastic losses). Which expression is used for the safe bearing capacity (with consistent units)?

Introduction / Context:
Dynamic pile formulas estimate pile capacity from driving resistance. The Engineering News (EN) formula is a traditional method for drop-hammer driving, relating energy per blow to pile set (penetration per blow) and incorporating an empirical constant to represent elastic compression and losses. While modern practice prefers static analyses and load tests, EN remains important for quick checks and exam problems.

Given Data / Assumptions:

• Drop hammer with weight W and fall H.
• Observed final set S per blow at end of driving.
• Empirical constant C (for example, about 2.5 cm in some unit systems).
• Consistent units must be used for W, H, S, and C.

Concept / Approach:

In the EN framework, the allowable load Q_safe is obtained by dividing the estimated ultimate capacity (from energy considerations) by a safety factor. For the commonly cited parameters and safety factor, the simplified result is Q_safe = (W * H) / (S + C), provided W, H, S, and C are expressed in the prescribed units (for example, tons, feet, inches with C = 1 inch, or kN, m, cm with corresponding C). This places more emphasis on measured set than on theoretical wave mechanics.

Step-by-Step Solution:

Verification / Alternative check:

Classic EN/ENR tables show ultimate capacity Q_u = (6 * W * H) / (S + 2.5) with imperial units and then Q_safe = Q_u / 6, yielding Q_safe = (W * H) / (S + 2.5). The generalized compact form matches option (a) with appropriate C.

Why Other Options Are Wrong:

Option (b) and (d) alter coefficients inconsistently with the embedded safety factor; (c) uses S − C which is non-physical; (e) is dimensionally incorrect.

Common Pitfalls:

Mixing units (feet, inches, metres); using temporary high sets affected by soil setup or rebound; relying solely on EN without static checks or load tests.

Final Answer:

Q_safe = (W * H) / (S + C)