Pile capacity is the maximum load that a pile foundation can safely support without failure.
Pile capacity is a fundamental concept in deep foundation design, used when surface soils are too weak to support structures using shallow foundations.
Piles are used when:
- Surface soils are too weak for shallow foundations
- Settlement must be limited
- Lateral loads are large (bridges, marine structures)
- Uplift forces exist (basements, wind)
- Soil conditions are variable or unpredictable
Pile Types
| Pile Type | Typical Diameter | Maximum Load | Common Use |
|---|---|---|---|
| Driven precast concrete | 250–600 mm | 1,000–5,000 kN | General buildings, bridges |
| Driven steel H-piles | 200–400 mm | 500–3,000 kN | Structures needing high capacity in dense soils |
| Driven steel pipe piles | 300–2,000 mm | 2,000–20,000 kN | Marine, bridges, major infrastructure |
| Bored piles (CFA) | 300–1,200 mm | 1,000–8,000 kN | Urban sites, noise-sensitive areas |
| Bored piles (under-reamed) | 600–3,000 mm | 5,000–30,000 kN | High-capacity single piles |
| Screw piles | 100–600 mm | 100–1,500 kN | Light structures, residential |
| Micropiles | 100–300 mm | 300–2,000 kN | Restricted access, underpinning |
Load Transfer Mechanism
Load (Q)
│
▼
┌──────────────────┐
│ Pile shaft │◄── Skin friction (Qs) — distributed along shaft
│ │
│ │
│ │
│ Pile toe │◄── End bearing (Qb) — concentrated at base
└──────────────────┘
Total capacity: Qu = Qs + Qb = ∑(friction × area) + (bearing × area)
Static Analysis (Ultimate Pile Capacity)
General Equation
$$ Q_u = Q_s + Q_b - W $$Where:
- $Q_s$ = shaft resistance (skin friction)
- $Q_b$ = base resistance (end bearing)
- $W$ = self-weight of pile (often neglected for compression piles)
Shaft Friction in Cohesive Soils ($\alpha$ Method)
$$ Q_s = \sum \alpha \cdot s_u \cdot A_s $$Where:
- $\alpha$ = adhesion factor (0.3–1.0, depending on $s_u$)
- $s_u$ = undrained shear strength
- $A_s = \pi D L$ = shaft surface area
$\alpha$ values (Terzaghi-Peck API method):
| $s_u$ (kPa) | $\alpha$ |
|---|---|
| < 25 | 1.0 |
| 25–50 | 1.0–0.8 |
| 50–100 | 0.8–0.6 |
| 100–150 | 0.6–0.4 |
| 150–200 | 0.4–0.3 |
| > 200 | 0.3–0.25 |
Alternative — $\beta$ Method (effective stress):
$$ Q_s = \sum \beta \cdot \sigma'_{v0} \cdot A_s $$Where $\beta = K \tan \delta$ (typically 0.2–0.6 for clays).
Shaft Friction in Cohesionless Soils ($\beta$ or $K$ Method)
$$ Q_s = \sum K \cdot \sigma'_{v0} \cdot \tan\delta \cdot A_s $$Where:
- $K$ = coefficient of lateral earth pressure on shaft
- $\delta$ = soil-pile interface friction angle ($\delta \approx 0.5\phi'$ to $0.8\phi'$)
- $\sigma'_{v0}$ = effective vertical stress
| Soil Type | $K$ (driven piles) | $K$ (bored piles) |
|---|---|---|
| Loose sand | 1.0–1.5 | 0.5–0.7 |
| Medium dense sand | 1.0–2.0 | 0.7–1.0 |
| Dense sand | 1.5–3.0 | 0.7–1.2 |
Interface friction angle:
| Pile Material | $\delta$ |
|---|---|
| Smooth steel | 20°–25° |
| Rough steel | 25°–30° |
| Concrete | 0.75$\phi'$–1.0$\phi'$ |
| Timber | 0.75$\phi'$–1.0$\phi'$ |
End Bearing
In cohesive soils:
$$ Q_b = N_c \cdot s_u \cdot A_b $$Where $N_c$ = bearing capacity factor (typically 9 for deep foundations).
In cohesionless soils (Terzaghi's method):
$$ Q_b = (\sigma'_{v0} N_q + 0.5\gamma DN_\gamma) \cdot A_b $$For deep foundations, $N_q$ is much larger than for shallow footings. A common approach:
$$ q_b = N_q^* \cdot \sigma'_{v0} $$Where $N_q^*$ is obtained from Meyerhof's deep foundation charts.
| $\phi$' (°) | $N_q^*$ (driven piles) | $N_q^*$ (bored piles) |
|---|---|---|
| 26 | 10 | 5 |
| 30 | 25 | 12 |
| 34 | 60 | 30 |
| 38 | 150 | 80 |
| 40 | 250 | 140 |
| 42 | 400 | 250 |
Limiting end bearing values (Meyerhof):
| Soil Type | $q_{b(limit)}$ (MPa) |
|---|---|
| Loose sand | 5 |
| Medium sand | 10 |
| Dense sand | 15–20 |
| Very dense sand | 20–30 |
Pile Capacity from In-Situ Tests
SPT Method (Meyerhof)
Driven piles — end bearing:
$$ q_b = 40N \frac{D}{B} \leq 400N \quad \text{(kPa)} $$Where $D$ = embedment depth, $B$ = pile width, $N$ = average SPT N-value at toe (typically over 8B above to 4B below).
Driven piles — shaft friction:
$$ q_s = 2N \quad \text{(kPa)} \quad \text{(for displacement piles)} $$ $$ q_s = N \quad \text{(kPa)} \quad \text{(for non-displacement piles)} $$CPT Method
End bearing:
$$ q_b = \frac{q_{c(avg)}}{F} $$Where $F$ = factor (typically 1.5–3.0 for driven piles, 1.5–6.0 for bored piles).
Shaft friction (Nottingham & Schmertmann):
$$ q_s = \alpha_s \cdot f_s $$Where $f_s$ = CPT sleeve friction and $\alpha_s$ = 0.5–1.0 depending on pile type.
De Ruiter & Beringen (OCR-based):
For piles in clay: $q_s = \alpha \times q_c$
| Soil Type | $\alpha$ |
|---|---|
| Normally consolidated clay | 0.03–0.05 |
| Overconsolidated clay | 0.02–0.04 |
Pile Groups
Efficiency
$$ \eta = \frac{Q_{u(group)}}{n \times Q_{u(single)}} $$Where $n$ = number of piles.
Converse-Labarre formula:
$$ \eta = 1 - \frac{\theta}{90°} \cdot \frac{(n' - 1)m + (m - 1)n'}{mn'} $$Where $m$ = number of rows, $n'$ = number of piles per row, $\theta = \tan^{-1}(D/s)$.
Typical group efficiency:
| Spacing | Group Efficiency |
|---|---|
| 2.5D | 0.6–0.7 |
| 3D | 0.7–0.8 |
| 4D | 0.85–0.95 |
| 6D+ | 1.0 |
Group Settlement
For pile groups in clay, the equivalent raft method is commonly used:
- An equivalent footing is placed at depth $2/3L$ from the pile tip
- Settlement of this equivalent raft is calculated using 2:1 load spread
Negative Skin Friction
When fill or soft soil settles around a pile:
- Downdrag force develops on the shaft
- Neutral plane is where soil settlement = pile settlement
- Above neutral plane: negative (downward) friction acts
- Below neutral plane: positive (upward) friction acts
Pile Load Testing
Static Load Test (Maintained Load)
Procedure (AS 2159):
- Load is applied in increments (typically 20–25% of design load)
- Each increment held until settlement stabilises
- Maximum test load = 150% of ultimate design load (or to failure)
- Unload in stages, recording rebound
Cyclic test:
- Load-unload cycles to separate shaft and base resistance
- Typically 3 cycles maximum before loading to failure
Interpretation of Static Load Test
Load (kN)
▲
│ ┌─────── Failure load
│ /
│ / ──── Elastic line
│ /
│ /
│ /
│ / ──── Plastic failure
│ /
│ /
└────────────────────► Settlement (mm)
Failure criteria (Davisson, 1972):
$$ \delta_f = \frac{Q L}{A E} + \frac{D}{120} + 4 \quad \text{(mm)} $$Where $\delta_f$ is the settlement defining failure.
Brinch Hansen 80% criterion:
The load at which the settlement curve reaches a slope corresponding to 0.08 mm/kN (for piles < 600 mm diameter).
Dynamic Load Testing (PDA)
- Instrumented hammer impact measures force and velocity
- Pile Driving Analyzer (PDA) computes:
- Static capacity (using CASE method or CAPWAP analysis)
- Driving stresses (compression, tension)
- Pile integrity
- Hammer efficiency
| Pile Type | Accuracy Compared to Static Test |
|---|---|
| Driven piles | ±15–25% |
| Bored piles | ±20–35% (less reliable) |
Rapid Load Test (Statnamic)
A controlled explosion/burn drives the pile:
- Load duration: 100–200 ms (between static and dynamic)
- Analysis uses unloading point method (UPM)
Advantages over static test:
- Faster: 1–2 days vs 7–14 days
- Higher capacity: can test up to 30 MN
- Safer: no large reaction system
Bi-Directional Load Test (Osterberg Cell / O-Cell)
Hydraulic jacks embedded within the pile shaft push against a steel plate, loading the pile both upwards (shaft friction) and downwards (base resistance):
- Measures shaft and base components separately
- No reaction system needed
- Up to 30 MN or more test capacity
Structural Design of Piles (AS 2159)
Design Approach
AS 2159 uses a limit state design approach:
$$ R_d \geq S^* $$Where $R_d$ = design geotechnical strength, $S^*$ = design load effect.
Geotechnical Strength Reduction Factors ($\phi_g$):
| Pile Type | Method of Capacity Determination | $\phi_g$ |
|---|---|---|
| Driven piles | Static analysis, verified by testing | 0.65–0.85 |
| Driven piles | Static analysis only | 0.40–0.65 |
| Bored piles | Static analysis, verified by testing | 0.55–0.75 |
| Bored piles | Static analysis only | 0.35–0.55 |
| Any pile | Static load test to failure | 0.70–0.85 |
| Any pile | Dynamic testing (PDA + CAPWAP) | 0.65–0.80 |
Factor of Safety Equivalence
| $\phi_g$ | Equivalent FS (approx.) |
|---|---|
| 0.85 | 1.2 |
| 0.70 | 1.4 |
| 0.55 | 1.8 |
| 0.40 | 2.5 |
Lateral Load Capacity
Elastic Method (Reese & Matlock)
For piles with lateral load $H$ at ground surface:
$$ y_0 = \frac{H T^3}{EI} A_y + \frac{M_t T^2}{EI} B_y $$ $$ M_{max} = H T A_m + M_t B_m $$Where $T = \sqrt[5]{EI/n_h}$ (characteristic length) and $n_h$ = modulus of subgrade reaction.
Typical $n_h$ values:
| Soil Type | $n_h$ (kN/m³) |
|---|---|
| Dry loose sand | 2,000–5,000 |
| Submerged loose sand | 1,500–4,000 |
| Medium dense sand | 6,000–15,000 |
| Dense sand | 15,000–35,000 |
| Soft clay | 1,000–4,000 |
| Stiff clay | 5,000–15,000 |
p-y Curves (Nonlinear Method)
Defines lateral soil resistance ($p$) as a nonlinear function of pile deflection ($y$):
- p-y curves are defined at depth intervals along the pile
- The pile is analysed as a beam on nonlinear Winkler springs
- More accurate than the elastic method for large deflections
Settlement of Single Piles
Elastic Settlement (Poulos & Davis Method)
$$ S = \frac{Q I}{E_s D} $$Where $I$ = influence factor (depends on slenderness ratio $L/D$, stiffness ratio $K = E_p/E_s$, and soil Poisson's ratio).
Load Transfer Method (t-z Curves)
Defines shaft resistance ($t$) as a function of local displacement ($z$):
- t-z curves are assigned along the shaft
- End bearing q-z curve at the pile base
- The pile is divided into elements and solved iteratively
Allowable Settlement
| Structure Type | Maximum Settlement |
|---|---|
| Single piles — bridge | 25–50 mm |
| Pile groups — building | 50–100 mm |
| Differential (between adjacent piles) | 10–20 mm |
| Machinery foundations | 10–25 mm |
Defects and Integrity Testing
| Test Method | Detects | Cost |
|---|---|---|
| PIT (Pile Integrity Test) | Major defects, changes in cross-section | Low |
| Cross-hole sonic logging | Concrete quality, defects between tubes | Moderate |
| Thermal integrity profiling | Full shaft concrete quality | Moderate |
| Core testing | Concrete strength, actual length | High |
| High-strain dynamic test (PDA) | Capacity + integrity verification | Moderate |
Australian Standards
| Standard | Title | Key Provisions |
|---|---|---|
| AS 2159 | Piling — Design and Installation | Geotechnical strength design, testing requirements |
| AS 2159-2009 | (Amendment 1 2024) | Updated test verification factors |
| AS 3600 | Concrete Structures | Concrete strength, cover, reinforcement |
| AS 4100 | Steel Structures | Steel pile design |
| AS 5100.3 | Bridge Design — Foundations | Bridge pile design |
| TfNSW QA R13 | Piling | NSW Roads specification |
Example
Given: Steel H-pile 350×350 mm (HP 350) driven to 15 m in medium-dense sand ($\gamma = 18$ kN/m³, $\phi' = 34°$). $D_f = 15$ m, water table at 5 m.
Shaft friction:
$K = 1.5$, $\delta = 0.75 \times 34 = 25.5°$Segment 1 (0–5 m, dry): $\sigma'_v$ at 2.5 m = 2.5 × 18 = 45 kPa
$q_{s1} = 1.5 \times 45 \times \tan(25.5°) = 32.2$ kPa $A_{s1} = 1.4 \times 5 = 7.0$ m² (perimeter ≈ 1.4 m) $Q_{s1} = 32.2 \times 7.0 = 225$ kNSegment 2 (5–15 m, submerged): $\sigma'_v$ at 10 m = (5 × 18) + (5 × 9) = 135 kPa
$q_{s2} = 1.5 \times 135 \times \tan(25.5°) = 96.6$ kPa $A_{s2} = 1.4 \times 10 = 14.0$ m² $Q_{s2} = 96.6 \times 14.0 = 1,352$ kNTotal shaft: $Q_s = 225 + 1,352 = 1,577$ kN
End bearing:
$\sigma'_{v(toe)} = (5 \times 18) + (10 \times 9) = 180$ kPa $N_q = 40$ (for $\phi = 34°$, driven pile) $q_b = 180 \times 40 = 7,200$ kPa $A_b = 0.1225$ m² $Q_b = 7,200 \times 0.1225 = 882$ kNUltimate capacity: $Q_u = 1,577 + 882 = 2,459$ kN
Design capacity (with $\phi_g = 0.65$, no testing): $R_d = 0.65 \times 2,459 = 1,598$ kN