Pile Capacity by Driving (Engineering News)
Estimate a driven pile's allowable load by the Engineering News Record dynamic driving formula, Q_adm = (W_r·h) ÷ (FS·(s + c)), from the hammer weight W_r (kN), the drop height h (m), the set s (permanent penetration per blow, m), a loss constant c (m, ≈ 0.0025 m for drop hammers) and the safety factor FS (≈ 6 in this formula). DYNAMIC driving formulas estimate a pile's capacity from observing how much it PENETRATES per hammer blow during driving — the principle is intuitive: the HARDER to drive (smaller penetration per blow, the 'set'), the GREATER the soil resistance and thus the pile capacity. The blow energy (weight × drop height) is equated to the penetration work (resistance × displacement), with losses. The 'set' (s) is measured in the field during driving (average penetration of the last blows), making these formulas a valuable, cheap EXECUTION CONTROL — driving continues until the set reaches the value matching the desired capacity. The Engineering News formula is the most classic (and conservative, with FS = 6). Modern high-strain dynamic monitoring (PDA, with CAPWAP analysis) replaces these empirical formulas far more accurately, but the set is still used daily on site. Enter the hammer weight, drop height, set, constant and safety factor.
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Driven Pile Capacity (Engineering News Formula)
The allowable load of a driven pile given by the Engineering News Record dynamic formula is Q_all = (W_r·h) ÷ (FS·(s + c)), computed from the hammer weight W_r, the drop height h, the set s (permanent penetration per blow), a loss constant c (≈ 0.0025 m for free-fall drop hammers) and the safety factor FS (≈ 6). Dynamic driving formulas estimate the capacity of a pile by observing how far it penetrates with each blow of the hammer while it is being driven — the principle is intuitive: the harder the pile is to drive (the smaller the penetration per blow, the 'set'), the greater the resistance of the soil and therefore the greater the capacity. The energy of the blow (weight × drop height) is equated to the work of penetration (resistance × displacement), with an allowance for losses. The set (s) is measured on site during driving, as the average penetration over the last blows, which turns these formulas into a valuable and inexpensive construction control — driving continues until the set reaches the value that corresponds to the required capacity. The Engineering News formula is the most classic of them, and the most conservative (FS = 6). Modern practice uses high-strain dynamic testing (PDA, with CAPWAP analysis) in place of these empirical formulas, with far greater accuracy, but set measurement is still part of everyday work on site. Enter the hammer weight, the drop height, the set, the constant and the safety factor.
Related Tools
Pile Bearing Capacity
Calculate a pile's ultimate bearing capacity, Q_ult = Q_p + Q_l, summing the point (tip) resistance Q_p (kN) and the side (skin friction) resistance Q_l (kN). The pile is the DEEP foundation element used when surface soil lacks capacity for the structure's loads — it transfers loads to deeper, stronger subsoil layers. This transfer occurs by TWO mechanisms acting at once: TIP resistance (the pile bears on a firm layer at its base, like a column, mobilizing the soil resistance under the tip) and SIDE resistance (friction and adhesion between the pile's lateral surface and surrounding soil, along its whole length). Their proportion defines the behavior: END-bearing piles (crossing soft soil to bear on rock or firm soil) work mainly by the tip; FLOATING or friction piles (driven in homogeneous soil, no firm layer) work mainly by side friction. The ultimate capacity, divided by a safety factor (typically 2), gives the design allowable load. Determining Q_p and Q_l — by theoretical formulas, SPT-based semi-empirical methods (Aoki-Velloso, Décourt-Quaresma) or load tests — is the central deep-foundation design calculation. Enter the tip resistance and the side resistance.
Pile Structural Stress
Calculate the structural compression stress in a pile shaft, σ = Q ÷ (π·D²/4), from the applied load Q (kN) and the pile diameter D (m); the result is in MPa. Besides the SOIL having capacity to support the pile (geotechnical capacity), the pile itself, as a STRUCTURAL element (concrete, steel or timber), must resist the load without failing or deforming excessively — this is the pile's STRUCTURAL check. The shaft compression stress is simply the load over the cross-sectional area. It must be below the pile material's allowable stress: codes limit cast-in-place pile concrete working stress to conservative values (typically 5-8 MPa, less than the concrete strength, due to subsurface execution uncertainties — blind concreting, possible defects, eccentricities). This check often GOVERNS the minimum pile diameter (the pile may have ample geotechnical capacity, but structural stress limits the load). Pile design is always the SMALLER of geotechnical (soil) and structural (material) capacity — both must be checked. Enter the applied load and the pile diameter.
Pile Tip Resistance
Calculate a pile's tip resistance, Q_p = q_p·A_p, from the tip stress (bearing capacity) q_p (kPa) and the tip cross-sectional area A_p (m²). Tip resistance is the share of pile capacity from the BEARING of its base on a strong soil or rock layer — the pile acts as a column compressing the soil under its tip, mobilizing that soil's bearing capacity (like a shallow foundation, but at depth). The tip stress q_p is the soil's unit bearing capacity at the tip elevation, estimated by bearing-capacity theories (Terzaghi, Meyerhof, Vesic for piles), SPT correlations (q_p = K·N, with K depending on soil and pile type) or the CPT (cone) test. Times the tip area, it gives the force the tip supports. Tip resistance dominates in piles reaching a firm layer (end-bearing piles), and then the pile is very stiff (settles little). Large-diameter piles (caissons) have large tip areas and mobilize high tip resistance. This share adds to the side resistance for the total capacity. Enter the tip stress and the tip area.
Unit Skin Friction (Beta Method)
Calculate a pile's unit skin friction in granular soil by the beta method, f_s = β·σ'_v, from the coefficient β (dimensionless) and the vertical effective stress σ'_v at the considered point (kPa). The β method (effective-stress method) is the modern, rational way to estimate pile skin friction in GRANULAR soils (sands) and in clays in effective-stress terms. It starts from the principle that side friction is like any interface friction: the friction stress is the NORMAL stress to the surface (the soil horizontal stress, K_s·σ'_v) times the tangent of the interface friction angle (tan δ). Grouping these two factors into a single coefficient β = K_s·tan δ, the unit friction is simply β·σ'_v. The coefficient β typically ranges 0.2-0.5 for sands (and more for driven piles, which raise K_s by displacing soil). The great advantage of the β method is using EFFECTIVE stress (growing with depth), capturing that friction increases with depth — though there is a limit (the 'critical depth', above which friction stops growing, a still-debated phenomenon). Integrating f_s·perimeter along the length gives the total side resistance. Enter the beta coefficient and the vertical effective stress.
Pile Skin Resistance
Calculate a pile's side (friction) resistance, Q_l = f_s·A_s, from the average unit skin friction f_s (kPa) and the pile lateral surface area A_s (m², = π·D·L for a cylindrical pile). Side resistance is the share of pile capacity from FRICTION and ADHESION between the pile's lateral surface and the surrounding soil, along its whole buried length. As the pile tends to settle under load, the soil 'grips' its sides and resists — as a nail driven in wood resists pulling by face friction. The unit skin friction f_s depends on soil type (in clays, on undrained cohesion via the α method; in sands, on effective stress and friction via the β method), pile type (driven piles mobilize more friction than bored, displacing and compacting the soil) and surface roughness. Side resistance dominates in FLOATING (friction) piles, driven in soils without a firm bearing layer — they hang by friction. It is also the share mobilized FIRST under load (with small settlement), before the tip. This share adds to the tip resistance for the total capacity. Enter the unit skin friction and the side area.
Required Dynamic Capacity (Bearing)
Calculate the dynamic load rating C a bearing needs to reach a desired life, C = P·(L10)^(1/p), from the equivalent dynamic load P (N), the desired nominal life L10 (in millions of revolutions) and the exponent p (3 for balls, 10/3 for rollers). It is the INVERSE of the life calculation, and how bearing SELECTION is done in practice: the designer knows the load the bearing will carry (P) and the life it must reach (L10, derived from required operating hours and rotation), and computes the minimum needed dynamic capacity C. Then a bearing is chosen from the maker's catalog whose tabulated C is EQUAL OR GREATER than the required — and that fits the available dimensions (shaft and housing diameter). The dynamic capacity C is, by definition, the load giving an L10 life of exactly 1 million revolutions, and it is each bearing's 'rating' in the catalog. This calculation is the heart of sizing: it translates the application requirement (load and life) into the component spec (capacity), letting you pick the right bearing — neither undersized (early failure) nor oversized (needless cost and space). Enter the equivalent load, the desired life and the exponent.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.