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.
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Pile bearing capacity
The ultimate bearing capacity of a pile is Q_ult = Q_p + Q_l, adding the end-bearing resistance Q_p and the shaft resistance (skin friction) Q_l. A pile is the deep foundation element used when the near-surface soil lacks the capacity to carry the loads coming from the structure — it transfers those loads down to deeper, stronger layers of the subsoil. That transfer works through two mechanisms at once: end-bearing resistance (the pile sits on a firm layer at its base, like a column, mobilizing the strength of the soil under the tip) and shaft resistance (friction and adhesion between the side surface of the pile and the surrounding soil, along its whole length). The balance between the two governs the behavior: end-bearing piles, which cross soft soil until they reach rock or firm ground, work mainly through the tip; floating or friction piles, driven into homogeneous soil, work mainly through side friction. The ultimate capacity divided by a safety factor (typically 2) gives the allowable load. Determining Q_p and Q_l — from theoretical formulas, from semi-empirical SPT-based methods (Aoki-Velloso and Décourt-Quaresma, the Brazilian standards of practice) or from static load tests — is the central calculation of deep foundation design. Enter the end-bearing resistance and the shaft resistance.
Related Tools
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.
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.
Pile Allowable Load
Calculate a pile's allowable (working) load, Q_adm = Q_ult ÷ FS, from the ultimate bearing capacity Q_ult (kN) and the global safety factor FS. The allowable load is the maximum load that can be applied to the pile in service with adequate safety — obtained by dividing the ultimate capacity (the load that would cause FAILURE of the pile-soil system) by a safety factor covering uncertainties. The pile-foundation safety factor is typically HIGH (FS = 2.0-2.5 for ultimate capacity, higher if based only on theoretical formulas without a load test), reflecting the great uncertainty in determining soil capacity (unseen, heterogeneous and poorly known) and the severity of a foundation failure (which can collapse the whole structure). Codes often require different partial factors for tip and friction (which have different uncertainties), or limit-state methods. The allowable load sets how many piles are needed for the column loads: number of piles = column load ÷ allowable load. Load tests (measuring real field capacity) allow reducing the safety factor and optimizing design. Enter the ultimate capacity and the safety factor.
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 Downdrag (Negative Skin Friction)
Calculate the negative skin friction (downdrag) force on a pile, F_n = f_n·A_s, from the unit negative friction f_n (kPa) and the affected lateral surface area A_s (m²). Negative friction is a DANGEROUS, counterintuitive phenomenon: normally side friction HELPS the pile (resists the load, positive friction, soil holding the pile up); but when the SURROUNDING SOIL SETTLES MORE than the pile — which happens with a soft consolidating layer (from recent overlying fill, water-table lowering, or natural consolidation) — the soil 'goes down' relative to the pile and, instead of holding it, DRAGS the pile DOWN by friction. This negative friction is NOT a resistance: it is an ADDITIONAL LOAD imposed on the pile, adding to the structure load and to be carried by the tip and the positive friction of deeper layers. Ignoring downdrag is a classic cause of excessive settlement or pile failure in soft-soil-and-fill ground. Mitigation includes coating the pile with bitumen (reducing f_n) in the affected zone, or simply sizing the pile for the extra load. Computing F_n is essential in any deep-foundation design on consolidating compressible layers. Enter the unit negative friction and the affected lateral area.
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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