Axial geotechnical pile resistance is commonly separated into shaft resistance and base resistance:
$$ Q_{\mathrm{ult}}=Q_s+Q_b $$Topic guide: For background, method selection and related checks, see Pile Capacity.
The equations are simple, but estimating unit shaft and base resistance is method-dependent and uncertain. Pile type, installation, soil behaviour, time effects and verification testing must be considered.
Shaft resistance
For layers along the pile:
$$ Q_s=\sum_{i=1}^{n} f_{s,i}A_{s,i} $$Where:
| Symbol | Meaning |
|---|---|
| \(f_{s,i}\) | Selected unit shaft resistance in layer \(i\) |
| \(A_{s,i}\) | Pile shaft area within layer \(i\) |
| \(Q_s\) | Total shaft resistance |
For a uniform circular pile segment:
$$ A_s=\pi DL $$Unit shaft resistance may be derived by different total-stress, effective-stress, CPT, SPT or other methods. Each should be treated as a distinct method with its own applicability rules, and the method used should always be recorded alongside the result.
Base resistance
$$ Q_b=q_bA_b $$For a circular closed base:
$$ A_b=\frac{\pi D^2}{4} $$The selected unit base resistance \(q_b\), averaging zone and movement required for mobilisation depend on the method and pile system.
Arithmetic example
Assume an illustrative circular pile:
- diameter \(D=0.45\) m
- layer 1 length \(L_1=6\) m with entered \(f_{s,1}=35\) kPa
- layer 2 length \(L_2=4\) m with entered \(f_{s,2}=55\) kPa
- entered unit base resistance \(q_b=2500\) kPa
Layer shaft areas:
$$ A_{s,1}=\pi(0.45)(6)=8.482\ \mathrm{m^2} $$ $$ A_{s,2}=\pi(0.45)(4)=5.655\ \mathrm{m^2} $$Shaft resistance:
$$ Q_s=(35)(8.482)+(55)(5.655)=607.9\ \mathrm{kN} $$Base area and resistance:
$$ A_b=\frac{\pi(0.45)^2}{4}=0.1590\ \mathrm{m^2} $$ $$ Q_b=(2500)(0.1590)=397.6\ \mathrm{kN} $$Total illustrative resistance:
$$ Q_{\mathrm{ult}}=607.9+397.6=1005.5\ \mathrm{kN} $$The entered unit resistances are arithmetic test inputs, not recommended design values.
Design and verification controls
A pile calculation should retain:
- pile type, geometry and installation method
- ground profile and groundwater
- calculation method for every layer
- parameter source
- limiting unit resistance
- shaft and base components
- setup or relaxation assumptions
- negative skin friction and neutral-plane assessment
- group effects
- structural pile resistance
- verification method and test results
- design framework and method version
Pile groups
A pile group may be assessed by more than multiplying single-pile resistance by pile count. Group interaction, block failure, settlement, pile-cap compatibility and construction effects may govern.
Drag load
Negative skin friction is an action on the pile, not a positive resistance. Its treatment depends on the design framework and neutral-plane analysis. It must be stored separately from positive shaft resistance.
Time and installation effects
Driven and bored piles disturb the surrounding ground differently. Resistance may change between installation, initial testing and later service. A static calculation must not be presented as field verification.
Related resources
Authoritative references
Pile design requires a selected method, applicable standards, representative parameters, structural checks and appropriate field verification.